<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0" xmlns:media="http://search.yahoo.com/mrss/"><channel><title><![CDATA[Bounded Regret]]></title><description><![CDATA[AI, science, forecasting, philosophy]]></description><link>https://bounded-regret.ghost.io/</link><image><url>https://bounded-regret.ghost.io/favicon.png</url><title>Bounded Regret</title><link>https://bounded-regret.ghost.io/</link></image><generator>Ghost 5.51</generator><lastBuildDate>Tue, 13 Jun 2023 06:47:43 GMT</lastBuildDate><atom:link href="https://bounded-regret.ghost.io/rss/" rel="self" type="application/rss+xml"/><ttl>60</ttl><item><title><![CDATA[What will GPT-2030 look like?]]></title><description><![CDATA[GPT-4 surprised many people with its abilities at coding, creative brainstorming, letter-writing, and other skills. How can we be less surprised by developments in machine learning? In this post, I’ll forecast the properties of large pretrained ML systems in 2030.]]></description><link>https://bounded-regret.ghost.io/what-will-gpt-2030-look-like/</link><guid isPermaLink="false">6480a2dc78e4fd0001871b4d</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Wed, 07 Jun 2023 23:39:49 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p>GPT-4 surprised many people with its abilities at coding, creative brainstorming, letter-writing, and other skills. Surprises in machine learning are not restricted to GPT-4: I was <a href="https://bounded-regret.ghost.io/ai-forecasting-one-year-in/">previously surprised</a> by Minerva&#x2019;s mathematical abilities, as were many competitive forecasters.</p>
<p>How can we be less surprised by developments in machine learning? Our brains often implicitly make a <a href="https://forecasting.quarto.pub/book/zeroth-first.html?ref=bounded-regret.ghost.io">zeroth-order forecast</a>: looking at the current state of the art, and adding on improvements that &#x201C;feel reasonable&#x201D;. But what &#x201C;seems reasonable&#x201D; is prone to cognitive bias, and will underestimate progress in a fast-moving field like ML. A more effective approach is <a href="https://forecasting.quarto.pub/book/zeroth-first.html?ref=bounded-regret.ghost.io#first-order-approximation">first-order forecasting</a>: quantifying the historical rate of progress and extrapolating it forward, while also considering reasons for possible slowdowns or speedups.<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup></p>
<p>In this post, I&#x2019;ll use this approach to forecast the properties of large pretrained ML systems in 2030. I&#x2019;ll refer throughout to &#x201C;GPT<sub>2030</sub>&#x201D;, a hypothetical system that has the capabilities, computational resources, and inference speed that we&#x2019;d project for large language models in 2030 (but which was likely trained on other modalities as well, such as images). To forecast GPT<sub>2030</sub>&#x2019;s properties, I consulted a variety of sources, including empirical scaling laws, projections of future compute and data availability, velocity of improvement on specific benchmarks, empirical inference speed of current systems, and possible future improvements in parallelism.</p>
<p>GPT<sub>2030</sub>&#x2019;s capabilities turn out to be surprising (to me at least). In particular, GPT<sub>2030</sub> will enjoy a number of significant advantages over current systems<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>, as well as (in at least some important respects) current human workers:</p>
<ol>
<li>GPT<sub>2030</sub> will likely be superhuman at various specific tasks, including coding, hacking, and math, and potentially protein design (<a href="#1-specific-capabilities">Section 1</a>).</li>
<li>GPT<sub>2030</sub> can &#x201C;work&#x201D; and &#x201C;think&#x201D; quickly: I estimate it will be 5x as fast as humans as measured by words processed per minute <em>[range: 0.5x-20x]</em><sup class="footnote-ref"><a href="#fn3" id="fnref3">[3]</a></sup>, and that this could be increased to 125x by paying 5x more per FLOP (<a href="#2-inference-speed">Section 2</a>).</li>
<li>GPT<sub>2030</sub> can be copied arbitrarily and run in parallel. The organization that trains GPT<sub>2030</sub> would have enough compute to run many parallel copies: I estimate enough to perform 1.8 million years of work when adjusted to human working speeds <em>[range: 0.4M-10M years]</em> (<a href="#3-throughput-and-parallel-copies">Section 3</a>). Given the 5x speed-up in the previous point, this work could be done in 2.4 months.</li>
<li>GPT<sub>2030</sub>&apos;s copies can share knowledge due to having identical model weights, allowing for rapid parallel learning: I estimate 2,500 human-equivalent years of learning in 1 day (<a href="#4-knowledge-sharing">Section 4</a>).</li>
<li>GPT<sub>2030</sub> will be trained on additional modalities beyond text and images, possibly including counterintuitive modalities such as molecular structures, network traffic, low-level machine code, astronomical images, and brain scans. It may therefore possess a strong intuitive grasp of domains where we have limited experience, including forming concepts that we do not have (<a href="#5-modalities-tools-and-actuators">Section 5</a>).</li>
</ol>
<p>These capabilities would, at minimum, accelerate many areas of research while also creating serious vectors for misuse (<a href="#6-implications-of-gpt-2030">Section 6</a>). Regarding misuse, GPT<sub>2030</sub>&apos;s programming abilities, parallelization, and speed would make it a potent cyberoffensive threat. Additionally, its rapid parallel learning could be turned towards human behavior and thus used to manipulate and misinform with the benefit of thousands of &quot;years&quot; of practice.</p>
<p>On acceleration, a main bottleneck will be autonomy. In a domain like mathematics research where work can be checked automatically, I&#x2019;d predict that GPT<sub>2030</sub> will outcompete most professional mathematicians. In machine learning, I&#x2019;d predict that GPT<sub>2030</sub> will independently execute experiments and generates plots and write-ups, but that graduate students and research scientists will provide direction and evaluate results. In both cases, GPT<sub>2030</sub> will be an integral part of the research process.</p>
<p>My forecast of GPT<sub>2030</sub>&#x2019;s properties are not intuitive from looking at today&#x2019;s systems, and they may be wrong, since there is significant uncertainty about how ML will look in 2030. However, properties (1.-5.) above are my median bet, and whatever GPT<sub>2030</sub> is like, I doubt it will be &#x201C;GPT-4 but a bit better&#x201D;.</p>
<p>If I&#x2019;m right, then whatever the impacts of AI are, they won&#x2019;t be small. We should be preparing for those impacts now, asking what will happen at the largest scales (on the order of $1T, 10M lives, or significant disruptions to social processes). It&#x2019;s better to be surprised now, rather than in 7 years when the system is already being rolled out.</p>
<h1 id="1-specific-capabilities">1. Specific Capabilities</h1>
<p>I expect GPT<sub>2030</sub> to have superhuman coding, hacking, and mathematical abilities. I also expect it to be superhuman in its ability to read and process large corpora for patterns and insights and to recall facts. Finally, since <a href="https://www.nature.com/articles/s41586-021-03819-2?ref=bounded-regret.ghost.io">AlphaFold</a> and <a href="https://arxiv.org/abs/1712.01815?ref=bounded-regret.ghost.io">AlphaZero</a> had superhuman abilities in protein structure prediction and game-playing, GPT<sub>2030</sub> could as well, for instance if it was trained multimodally on similar data to the AlphaFold/AlphaZero models.</p>
<p><strong>Programming</strong>. GPT-4 outperformed a strong human baseline on LeetCode problems posed after its training cutoff (<a href="https://arxiv.org/abs/2303.12712?ref=bounded-regret.ghost.io">Bubeck et al. 2023</a>, Table 2), and passed the mock interview for several major tech companies (Figure 1.5).  The velocity of improvement remains high, with a 19% jump from GPT-3 to 4. On the more challenging CodeForces competition, GPT-4 does less well, but AlphaCode is <a href="https://www.science.org/doi/epdf/10.1126/science.abq1158?ref=bounded-regret.ghost.io">on par with</a> the median CodeForces competitor. On the even more challenging APPS dataset, <a href="https://arxiv.org/abs/2212.10561v2?ref=bounded-regret.ghost.io">Parsel</a> further outperforms AlphaCode (7.8%-&gt;25.5%). Looking forward, the forecasting platform Metaculus gives <a href="https://www.metaculus.com/questions/7398/ai-competency-on-competitive-programming/?ref=bounded-regret.ghost.io">a median year of 2027</a> for 80% on APPS, which would exceed all but the very best humans.<sup class="footnote-ref"><a href="#fn4" id="fnref4">[4]</a></sup></p>
<p><strong>Hacking</strong>. I expect hacking to improve with general coding ability, plus ML models can scour large codebases for vulnerabilities much more scalably and conscientiously than humans. In fact, ChatGPT has already been used to help <a href="https://research.checkpoint.com/2023/opwnai-cybercriminals-starting-to-use-chatgpt/?ref=bounded-regret.ghost.io">generate</a> <a href="https://research.checkpoint.com/2022/opwnai-ai-that-can-save-the-day-or-hack-it-away/?ref=bounded-regret.ghost.io">exploits</a>.</p>
<p><strong>Math</strong>. <a href="https://arxiv.org/abs/2206.14858?ref=bounded-regret.ghost.io">Minerva</a> achieved 50% accuracy on a competition math benchmark (MATH), which is better than most human competitors. The velocity of progress is high (&gt;30% in 1 year), and there is significant low-hanging fruit via <a href="https://arxiv.org/abs/2205.12615?ref=bounded-regret.ghost.io">autoformalization</a>, reducing arithmetic errors, <a href="https://arxiv.org/abs/2207.10342?ref=bounded-regret.ghost.io">improving chain-of-thought</a>, and <a href="https://arxiv.org/abs/2206.14858?ref=bounded-regret.ghost.io">better data</a><sup class="footnote-ref"><a href="#fn5" id="fnref5">[5]</a></sup>. Metaculus predicts <a href="https://www.metaculus.com/questions/11675/math-sota-ai-performance/?ref=bounded-regret.ghost.io">92% on MATH by 2025</a>, and gives a <a href="https://www.metaculus.com/questions/6728/ai-wins-imo-gold-medal/?ref=bounded-regret.ghost.io">median year of 2028</a> for AI winning a gold medal at the International Math Olympiad, on par with the best high school students in the world. I personally expect GPT<sub>2030</sub> to be better than most professional mathematicians at proving well-posed theorems.<sup class="footnote-ref"><a href="#fn6" id="fnref6">[6]</a></sup></p>
<p><strong>Information processing</strong>. Factual recall and processing large corpora are natural consequences of language models&#x2019; memorization capabilities and large context windows. Empirically, GPT-4 achieves <a href="https://cdn.openai.com/papers/gpt-4.pdf?ref=bounded-regret.ghost.io">86% accuracy on MMLU</a>, a broad suite of standardized exams including the bar exam, MCAT, and college math, physics, biochemistry, and philosophy; even accounting for likely train-test contamination, this probably exceeds the breadth of knowledge of any living human. Regarding large corpora, <a href="https://arxiv.org/abs/2302.14233?ref=bounded-regret.ghost.io">Zhong et al. (2023)</a> used GPT-3 to construct a system that discovered and described several previously unknown patterns in large text datasets, and scaling trends on a related task in <a href="https://openaipublic.blob.core.windows.net/neuron-explainer/paper/index.html?ref=bounded-regret.ghost.io#sec-assistant-trends">Bills et al. (2023)</a> suggest that models will soon be superhuman. Both of these works exploit the large context windows of LLMs, which are now over <a href="https://www.anthropic.com/index/100k-context-windows?ref=bounded-regret.ghost.io">100,000 tokens</a> and growing.</p>
<p>More generally, <strong>ML models have a different skill profile than humans</strong>, since humans and ML were adapted to very different data sources (evolution vs. massive internet data). At the point that models are human-level at tasks such as video recognition, they will likely be superhuman at many other tasks (such as math, programming, and hacking). Furthermore, additional strong capabilities will <a href="https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/">likely emerge over time</a> due to larger models and better data, and there is no strong reason to expect model capabilities to &#x201C;level out&#x201D; at or below human-level. While it is possible that current deep learning approaches will fall short of human-level capabilities in some domains, it is also possible that they will surpass them, perhaps significantly, especially in domains such as math that humans are not evolutionarily specialized for.</p>
<h1 id="2-inference-speed">2. Inference Speed</h1>
<p><em>(Thanks to Lev McKinney for running the performance benchmarks for this section.)</em></p>
<p>To study the speed of ML models, we&#x2019;ll measure how quickly ML models generate text, benchmarking against the human thinking rate of 380 words per minute (<a href="https://journals.sagepub.com/doi/abs/10.2466/pms.1990.71.3.1043?ref=bounded-regret.ghost.io">Korba (2016)</a>, see also <a href="#a-words-per-minute">Appendix A</a>). Using OpenAI&apos;s <a href="https://platform.openai.com/docs/guides/chat?ref=bounded-regret.ghost.io">chat completions API</a>, we estimate that gpt-3.5-turbo can generate 1200 words per minute (wpm), while gpt-4 generates 370 wpm, as of early April 2023. Smaller open source models like <a href="https://huggingface.co/EleutherAI/pythia-12b-deduped?ref=bounded-regret.ghost.io">pythia-12b</a> achieve at least 1350 wpm with out-of-the-box tools on an A100 GPU, and twice this appears possible with further optimization.</p>
<p>Thus, if we consider OpenAI models as of April, we are either at roughly 3x human speed, or equal to human speed. I predict that models will have faster inference speed in the future, as there are strong commercial and practical pressures towards speeding up inference. Indeed, in the week leading up to this post, GPT-4&#x2019;s speed already increased to around 540wpm (12 tokens/second), according to <a href="https://fabienroger.github.io/trackoai/?ref=bounded-regret.ghost.io">Fabien Roger&#x2019;s tracking data</a>; this illustrates that there is continuing room and appetite for improvement.</p>
<p>My median forecast is that models will have <strong>5x the words/minute of humans</strong> (range: [0.5x, 20x]), as that is roughly where there would be diminishing practical benefits to further increases, though there are considerations pointing to both higher or lower numbers. I provide a detailed list of these considerations in <a href="#a-words-per-minute">Appendix A</a>, as well as comparisons of speeds across model scales and full details of the experiments above.</p>
<p>Importantly, <strong>the speed of an ML model is not fixed</strong>. Models&#x2019; serial inference speed can be <a href="https://bounded-regret.ghost.io/how-fast-can-we-perform-a-forward-pass/">increased by $k^2$ at a cost of a $k$-fold reduction in throughput</a> (in other words, $k^3$ parallel copies of a model can be replaced with a single model that is $k^2$ times faster). This can be done via a parallel tiling scheme that theoretically works even for large values of $k^2$, likely at least 100 and possibly more. Thus, a model that is 5x human speed could be sped up to 125x human speed by setting $k=5$.</p>
<p>An important caveat is that speed is not necessarily matched by quality: as discussed in <a href="#1-specific-capabilities">Section 1</a>, GPT<sub>2030</sub> will have a different skill profile than humans, failing at some tasks we find easy and mastering some tasks we find difficult. We should therefore not think of GPT<sub>2030</sub> as a &quot;sped-up human&quot;, but as a &quot;sped-up worker&quot; with a potentially counterintuitive skill profile.</p>
<p>Nevertheless, considering speed-ups is still informative, especially when they are large. For language models with a 125x speed-up, cognitive actions that take us a day could be completed in minutes, assuming they were within GPT<sub>2030</sub>&apos;s skill profile. Using the earlier example of hacking, exploits or attacks that are slow for us to generate could be created quickly by ML systems.</p>
<h1 id="3-throughput-and-parallel-copies">3. Throughput and Parallel Copies</h1>
<p>Models can be copied arbitrarily subject to available compute and memory. This allows them to quickly do any work that can be effectively parallelized. In addition, once one model is fine-tuned to be particularly effective, the change could be immediately propagated to other instances. Models could also be distilled for specialized tasks and thus run faster and more cheaply.</p>
<p>There will likely be enough resources to run many copies of a model once it has been trained. This is because training a model requires running many parallel copies of it, and whatever organization trained the model will still have those resources at deployment time. We can therefore lower bound the number of copies by estimating training costs.</p>
<p>As an example of this logic, the cost of training GPT-3 was enough to run it for 9 x 10<sup>11</sup> forward passes. To put that into human-equivalent terms, humans think at 380 words per minute (see <a href="#a-words-per-minute">Appendix A</a>) and one word is 1.33 tokens on average, so 9 x 10<sup>11</sup> forward passes corresponds to ~3400 years of work at human speed. Therefore, the organization could run 3400 parallel copies of the model for a full year at human working-speeds, or potentially the same number of copies for 2.4 months at 5x human speed. <em>(Note: This latter point depends on how many parallel instances the organization can run, see footnote<sup class="footnote-ref"><a href="#fn7" id="fnref7">[7]</a></sup> for details.)</em></p>
<p>Let&apos;s next project this same &#x201C;training overhang&#x201D; (ratio of training to inference cost) for future models. It should be larger: the main reason is that training overhang is roughly proportional to dataset size, and datasets are increasing over time. This trend will be slowed as we run out of naturally-occuring language data, but new modalities as well as synthetic or self-generated data will still push it forward.<sup class="footnote-ref"><a href="#fn8" id="fnref8">[8]</a></sup> In <a href="#b-training-overhang">Appendix B</a>, I consider these factors in detail to project forward to 2030. I forecast that models in 2030 will be trained with enough resources to perform <strong>1,800,000 years of work</strong> adjusted to human speed <em>[range: 400k-10M]</em>.</p>
<p>Note that <a href="https://www.lesswrong.com/posts/KrJfoZzpSDpnrv9va/draft-report-on-ai-timelines?ref=bounded-regret.ghost.io">Cotra (2020)</a> and <a href="https://www.planned-obsolescence.org/continuous-doesnt-mean-slow/?ref=bounded-regret.ghost.io">Davidson (2023)</a> estimate similar quantities and arrive at larger numbers than me; I&apos;d guess the main difference is how I model the effect of running out of natural language data.</p>
<p>The projection above is somewhat conservative, since models may be run on more resources than they were trained on if the organization buys additional compute. A <a href="https://docs.google.com/spreadsheets/d/1Pz0YVJalZbdo63FI-rCa7baBkGsiuYv5P34Rpt9IZfE/edit?ref=bounded-regret.ghost.io#gid=0">quick ballpark estimate</a> suggests that GPT-4 was trained on about 0.01% of all computational resources in the world, although I expect future training runs to use up a larger share of total world compute and therefore have less room to scale up further after training. Still, an organization could possibly increase the number of copies they run by another order of magnitude if they had strong reasons to do so.</p>
<h1 id="4-knowledge-sharing">4. Knowledge Sharing</h1>
<p><em>(Thanks to Geoff Hinton who first made this argument to me.)</em></p>
<p>Different copies of a model can share parameter updates. For instance, ChatGPT could be deployed to millions of users, learn something from each interaction, and then propagate gradient updates to a central server where they are averaged together and applied to all copies of the model. In this way, ChatGPT could observe more about human nature in an hour than humans do in a lifetime (1 million hours = 114 years). Parallel learning may be one of the most important advantages models have, as it means they can rapidly learn any missing skills.</p>
<p>The rate of parallel learning depends on how many copies of a model are running at once, how quickly they can acquire data, and whether the data can be efficiently utilized in parallel. On the last point, even extreme parallelization should not harm learning efficiency much, as batch sizes in the millions are <a href="https://arxiv.org/pdf/2203.15556.pdf?ref=bounded-regret.ghost.io#table.caption.8">routine in practice</a>, and the gradient noise scale (<a href="https://arxiv.org/abs/1812.06162?ref=bounded-regret.ghost.io">McCandlish et al., 2018</a>) predicts minimal degradation in learning performance below a certain &#x201C;critical batch size&#x201D;. We&apos;ll therefore focus on parallel copies and data acquisition.</p>
<p>I will provide two estimates that both suggest it would be feasible to have at least ~1 million copies of a model learning in parallel at human speed. This corresponds to <strong>2500 human-equivalent years of learning per day</strong>, since 1 million days = 2500 years.</p>
<p>The first estimate uses the numbers from <a href="#3-throughput-and-parallel-copies">Section 3</a>, which concluded that the cost of training a model is enough to simulate models for 1.8M years of work (adjusted to human speed). Assuming that the training run itself lasted for less than 1.2 years (<a href="https://epochai.org/blog/the-longest-training-run?ref=bounded-regret.ghost.io">Sevilla et al., 2022</a>), this means the organization that trained the model has enough GPUs to run 1.5M copies at human speed.</p>
<p>The second estimate considers the market share of the organization deploying the model. For example, if there are 1 million users querying the model at a time, then the organization necessarily has the resources to serve 1 million copies of the model. As a ballpark, ChatGPT had <a href="https://www.demandsage.com/chatgpt-statistics/?ref=bounded-regret.ghost.io">100 million users</a> as of May 2023 (not all active at once), and <a href="https://www.enterpriseappstoday.com/stats/chatgpt-4-statistics.html?ref=bounded-regret.ghost.io">13 million active users/day</a> as of January 2023. I&#x2019;d assume the typical user is requesting a few minutes worth of model-generated text, so the January number probably only implies around 0.05 million person-days of text each day. However, it seems fairly plausible that future ChatGPT-style models would 20x this, reaching 250 million active users/day or more and hence 1 million person-days of data each day. As a point of comparison, Facebook has 2 billion daily active users.</p>
<h1 id="5-modalities-tools-and-actuators">5. Modalities, Tools, and Actuators</h1>
<p>Historically, GPT-style models have primarily been trained on text and code, and had limited capacity to interact with the outside world except via chat dialog. However, this is rapidly changing, as models are being trained on additional modalities such as images, are being trained to use tools, and are starting to interface with physical actuators. Moreover, models will not be restricted to anthropocentric modalities such as text, natural images, video, and speech---they will likely also be trained on unfamiliar modalities such as network traffic, astronomical images, or other massive data sources.</p>
<p><strong>Tools</strong>. Recently-released models use external tools, as seen with <a href="https://openai.com/blog/chatgpt-plugins?ref=bounded-regret.ghost.io">ChatGPT plugins</a> as well as <a href="https://arxiv.org/abs/2302.04761?ref=bounded-regret.ghost.io">Schick et al. (2023)</a>, <a href="https://arxiv.org/abs/2210.03629?ref=bounded-regret.ghost.io">Yao et al. (2022)</a>, and <a href="https://arxiv.org/abs/2211.10435?ref=bounded-regret.ghost.io">Gao et al. (2022)</a>. Text combined with tool use is sufficient to write code that gets executed, convince humans to take actions on their behalf, make API calls, make transactions, and potentially execute cyberattacks. Tool use is economically useful, so there will be strong incentives to further develop this capability.</p>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">ChatGPT is reactive: user says X, ChatGPT responds with Y. Risks exist but are bounded. Soon it will be tempting to have proactive systems - an assistant that will answer emails for you, take actions on your behalf, etc. Risks will then be much higher.</p>&#x2014; Percy Liang (@percyliang) <a href="https://twitter.com/percyliang/status/1630087355360223232?ref_src=twsrc%5Etfw&amp;ref=bounded-regret.ghost.io">February 27, 2023</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<p><strong>New modalities</strong>. There are now large open-source vision-language models such as <a href="https://github.com/mlfoundations/open_flamingo?ref=bounded-regret.ghost.io">OpenFlamingo</a>, and on the commercial side, GPT-4 and <a href="https://arxiv.org/abs/2204.14198?ref=bounded-regret.ghost.io">Flamingo</a> were both trained on vision and text data. Researchers are also experimenting with more exotic pairs of modalities such as proteins and language (<a href="https://github.com/UCSD-AI4H/proteinchat?ref=bounded-regret.ghost.io">Guo et al., 2023</a>).</p>
<p>We should expect the modalities of large pretrained models to continue to expand, for two reasons. First, economically, it is useful to pair language with less familiar modalities (such as proteins) so that users can benefit from explanations and efficiently make edits. This predicts multimodal training with proteins, biomedical data, <a href="https://en.wikipedia.org/wiki/Computer-aided_design?ref=bounded-regret.ghost.io">CAD models</a>, and any other modality associated with a major economic sector.</p>
<p>Second, we are starting to run out of language data, so model developers will search for new types of data to continue benefiting from scale. Aside from the traditional text and videos, some of the largest existing sources of data are <a href="https://en.wikipedia.org/wiki/Square_Kilometre_Array?ref=bounded-regret.ghost.io#Data_challenges">astronomical data</a> (will soon be at exabytes per day) and <a href="https://3billion.io/blog/big-data-among-big-data-genome-data?ref=bounded-regret.ghost.io">genomic data</a> (around 0.1 exabytes/day). It is plausible that these and other massive data sources will be leveraged for training GPT<sub>2030</sub>.</p>
<p>The use of exotic modalities means that GPT<sub>2030</sub> might have unintuitive capabilities. It might understand stars and genes much better than we do, even while it struggles with basic physical tasks. This could lead to surprises, such as designing novel proteins, that we would not have expected based on GPT<sub>2030</sub>&#x2019;s level of &#x201C;general&#x201D; intelligence. When thinking about the impacts of GPT<sub>2030</sub>, it will be important to consider specific superhuman capabilities it might possess due to these exotic data sources.</p>
<p><strong>Actuators</strong>. Models are also beginning to use physical actuators: ChatGPT has <a href="https://www.microsoft.com/en-us/research/group/autonomous-systems-group-robotics/articles/chatgpt-for-robotics/?ref=bounded-regret.ghost.io">already been used</a> for robot control and OpenAI is <a href="https://1xtech.medium.com/1x-raises-23-5m-in-series-a2-funding-led-by-openai-6040af4f3f4f?ref=bounded-regret.ghost.io">investing in</a> a humanoid robotics company. However, it is much more expensive to collect data in physical domains than digital domains, and humans are also more evolutionarily adapted to physical domains (so the bar for ML models to compete with us is higher). Compared to digital tools, I&#x2019;d therefore expect mastery of physical actuators to occur more slowly, and I&#x2019;m unsure if we should expect it by 2030. Quantitatively, I&#x2019;d assign 40% probability to there being a general-purpose model in 2030 that is able to autonomously assemble a <a href="https://s3.eu-west-1.amazonaws.com/deatech.snake.assets/assembly-guides/gb/pdfs/5609.pdf?ref=bounded-regret.ghost.io">scale-replica Ferrari</a> as defined in <a href="https://www.metaculus.com/questions/5121/date-of-artificial-general-intelligence/?ref=bounded-regret.ghost.io">this Metaculus question</a>.</p>
<h1 id="6-implications-of-gpt-2030">6. Implications of GPT-2030</h1>
<p>We&#x2019;ll next analyze what a system like GPT<sub>2030</sub> would mean for society. A system with GPT<sub>2030</sub>&#x2019;s characteristics would, at minimum, significantly accelerate some areas of research, while also possessing powerful capacities for misuse.</p>
<p>I&#x2019;ll start by framing some general strengths and limitations of GPT<sub>2030</sub>, then use this as a lens to analyze both acceleration and misuse.</p>
<p><strong>Strengths</strong>. GPT<sub>2030</sub> represents a large, highly adaptable, high-throughput workforce. Recall that GPT<sub>2030</sub> could do 1.8 million years of work<sup class="footnote-ref"><a href="#fn9" id="fnref9">[9]</a></sup> across parallel copies, where each copy is run at 5x human speed. This means we could (subject to parallelism constraints) simulate 1.8 million agents working for a year each in 2.4 months. As discussed above, we could pay 5x per FLOP to get an additional 25x speedup (to 125x human speed), so we could also simulate 14,000 agents working for a year each in <em>3 days</em><sup class="footnote-ref"><a href="#fn10" id="fnref10">[10]</a></sup>.</p>
<p><strong>Limitations</strong>. There are three obstacles to utilizing this digital workforce: skill profile, experiment cost, and autonomy. On the first, GPT<sub>2030</sub> will have a different skill profile from humans that makes it worse at some tasks (but better at others). On the second, simulated workers still need to interface with the world to collect data, which has its own time and compute costs. Finally, on autonomy, models today can only generate a few thousand tokens in a chain-of-thought before getting &#x201C;stuck&#x201D;, entering a state where they no longer produce high-quality output. We&#x2019;d need significant increases in reliability before delegating complex tasks to models. I expect reliability to increase, but not without limit: my (very rough) guess is that GPT<sub>2030</sub> will be able to run for several human-equivalent days before having to be reset or steered by external feedback. If models run at a 5x speed-up, that means they need human oversight every several hours.</p>
<p>Therefore, the tasks that GPT<sub>2030</sub> would most impact are tasks that:</p>
<ol>
<li>Leverage skills that GPT<sub>2030</sub> is strong at relative to humans.</li>
<li>Only require external empirical data that can be readily and quickly collected (as opposed to costly physical experiments).</li>
<li>Can be a priori decomposed into subtasks that can be performed reliably, or that have clear and automatable feedback metrics to help steer the model.</li>
</ol>
<p><strong>Acceleration</strong>. One task that readily meets all three criteria is mathematics research. On the first, GPT<sub>2030</sub> will likely have superhuman mathematical capabilities (<a href="#1-specific-capabilities">Section 1</a>). On the second and third, math can be done purely by thinking and writing, and we know when a theorem has been proved. There are furthermore not that many mathematicians in total in the world (e.g. only 3,000 in the US) so GPT<sub>2030</sub> could likely simulate more than the annual output of all mathematicians every several days.</p>
<p>Significant parts of ML research also meet the criteria above. GPT<sub>2030</sub> would be superhuman at programming, which includes implementing and running experiments. I&#x2019;d guess it will also be good at presenting and explaining the results of experiments, given that GPT-4 is good at explaining complex topics in an accessible way (and there is significant market demand for this). Therefore, ML research might reduce to thinking up good experiments to run and interfacing with high-quality (but potentially unreliable) write-ups of the results. In 2030, grad students might therefore have the same resources as a professor with several strong students would have today.</p>
<p>Parts of social science could also be significantly accelerated. There are many papers where the majority of the work is chasing down, categorizing, and labeling scientifically interesting sources of data and extracting important patterns&#x2014;see <a href="https://www.aeaweb.org/articles?id=10.1257%2Faer.91.5.1369&amp;ref=bounded-regret.ghost.io">Acemoglu et al. (2001)</a> or <a href="https://www.michaelwebb.co/webb_ai.pdf?ref=bounded-regret.ghost.io">Webb (2020)</a> for representative examples. This satisfies requirement (3.) because categorization and labeling can be decomposed into simple subtasks, and it satisfies requirement (2.) as long as the data is available on the internet, or could be collected through an online survey.</p>
<p><strong>Misuse</strong>. Beyond acceleration, there would be serious risks of misuse. The most direct case is cyberoffensive hacking capabilities. Inspecting a specific target for a specific style of vulnerability could likely be done reliably, and it is easy to check if an exploit succeeds (subject to being able to interact with the code), so requirement (3.) is doubly satisfied. On (2.), GPT<sub>2030</sub> would need to interact with target systems to know if the exploit works, which imposes some cost, but not enough to be a significant bottleneck. Moreover, the model could locally design and test exploits on open source code as a source of training data, so it could become very good at hacking before needing to interact with any external systems. Thus, GPT<sub>2030</sub> could rapidly execute sophisticated cyberattacks against large numbers of targets in parallel.</p>
<p>A second source of misuse is manipulation. If GPT<sub>2030</sub> interacts with millions of users at once, then it gains more experience about human interaction in an hour than a human does in their lifetime (1 million hours = 114 years). If it used these interactions to learn about manipulation, then it could obtain manipulation skills that are far greater than humans&#x2014;as an analogy, con artists are good at tricking victims because they&#x2019;ve practiced on hundreds of people before, and GPT<sub>2030</sub> could scale this up by several orders of magnitude. It could therefore be very good at manipulating users in one-on-one conversation, or at writing news articles to sway public opinion.</p>
<p>Thus in summary, GPT<sub>2030</sub> could automate almost all mathematics research as well as important parts of other research areas, and it could be a powerful vector of misuse regarding both cyberattacks and persuasion/manipulation. Much of its impact would be limited by &#x201C;oversight bottlenecks&#x201D;, so if it could run autonomously for long periods of time then its impact may be larger still.</p>
<p><em>Thanks to Louise Verkin for transcribing this post to Ghost format, and Lev McKinney for running empirical benchmark experiments. Thanks to Karena Cai, Michael Webb, Leo Aschenbrenner, Anca Dragan, Roger Grosse, Lev McKinney, Ruiqi Zhong, Sam Bowman, Tatsunori Hashimoto, Percy Liang, Tom Davidson, and others for providing feedback on drafts of this post.</em></p>
<h1 id="appendix-runtime-and-training-estimates-for-future-models">Appendix: Runtime and Training Estimates for Future Models</h1>
<h2 id="a-words-per-minute">A. Words per minute</h2>
<p>First we&#x2019;ll estimate the word per minute of humans and of current models. Then we&#x2019;ll extrapolate from current models to future models.</p>
<p>For humans, there are five numbers we could measure: talking speed, reading speed, listening speed, and both &#x201C;elliptic&#x201D; and &#x201C;extended&#x201D; thinking speed. Regarding the first three, <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2649675/?ref=bounded-regret.ghost.io">Rayner and Clifton (2009)</a> say that reading speed is 300 words per minute<sup class="footnote-ref"><a href="#fn11" id="fnref11">[11]</a></sup> and speaking is 160 words per minute<sup class="footnote-ref"><a href="#fn12" id="fnref12">[12]</a></sup>, and that listening can be done 2-3 times faster than speaking (so ~400 words per minute)<sup class="footnote-ref"><a href="#fn13" id="fnref13">[13]</a></sup>. For thinking speed, we need to distinguish between &#x201C;elliptic&#x201D; and &#x201C;extended&#x201D; thought&#x2014;it turns out that we think in flashes of words rather than complete sentences, and if we extend these flashes to full sentences we get very different word counts (~10x different). <a href="https://journals.sagepub.com/doi/abs/10.2466/pms.1990.71.3.1043?ref=bounded-regret.ghost.io">Korba (2016)</a> find that elliptic thought is 380 words per minute while extended thought is ~4200 words per minute. Since most of these numbers cluster in the 300-400 wpm range, I&#x2019;ll use <strong>380 words per minute</strong> as my estimate of human thinking speed. Using the 4:3 token to word ratio <a href="https://openai.com/api/pricing/?ref=bounded-regret.ghost.io">suggested by OpenAI</a>, this comes out to <strong>500 tokens per minute</strong>.<sup class="footnote-ref"><a href="#fn14" id="fnref14">[14]</a></sup></p>
<p><em>(Thanks to Lev McKinney for running the evaluations in the following paragraphs.)</em><br>
Next, let&#x2019;s consider current models. We queried gpt-3.5-turbo and gpt-4, as well as several open source models from EleutherAI, to benchmark their inference speed. We did this by querying the models to count from 1 to n, where n ranged from 100 to 1900 inclusive in increments of 100. Since numbers contain more than one token, we cut the model off when it reached n tokens generated, and measured the time elapsed. We then ran a linear regression with a bias term to account for latency in order to estimate the asymptotic number of tokens per second.</p>
<p>GPT-4 and GPT-3.5-turbo were queried from the OpenAI AIP in early April 2023. All experiments for the <a href="https://huggingface.co/EleutherAI/pythia-12b?ref=bounded-regret.ghost.io">pythia models</a> were performed using <a href="https://www.deepspeed.ai/tutorials/inference-tutorial/?ref=bounded-regret.ghost.io">deepspeed&apos;s injected kernels</a> and fp16 models on a single A100 GPU.<sup class="footnote-ref"><a href="#fn15" id="fnref15">[15]</a></sup> Code for replicating these results can be found at <a href="https://github.com/levmckinney/llm-racing?ref=bounded-regret.ghost.io">https://github.com/levmckinney/llm-racing</a>.</p>
<p>The raw data is plotted in Figure 1 below, while Figure 2 and Table 1 give the resulting estimated tokens per minute.</p>
<p align="center"><img src="https://bounded-regret.ghost.io/content/images/2023/06/tokens_per_second.png"></p>
<p>Figure 1 demonstrates how model inference scales with token input. Note that time per token remains relatively linear at these context lengths.</p>
<p align="center"><img src="https://bounded-regret.ghost.io/content/images/2023/06/results.png"></p>
<p>Figure 2 and the table below demonstrates how model inference speed scales with size. Error bars are 95% confidence intervals.</p>
<table>
<thead>
<tr>
<th>Model name</th>
<th>Tokens per minute</th>
</tr>
</thead>
<tbody>
<tr>
<td>gpt-4</td>
<td>493</td>
</tr>
<tr>
<td>gpt-3.5-turbo</td>
<td>1641</td>
</tr>
<tr>
<td>EleutherAI/pythia-12b-deduped</td>
<td>1801</td>
</tr>
<tr>
<td>EleutherAI/pythia-6.9b-deduped</td>
<td>2659</td>
</tr>
<tr>
<td>EleutherAI/pythia-2.8b-deduped</td>
<td>4568</td>
</tr>
<tr>
<td>EleutherAI/pythia-1.4b-deduped</td>
<td>7040</td>
</tr>
<tr>
<td>EleutherAI/pythia-410m-deduped</td>
<td>11039</td>
</tr>
<tr>
<td>EleutherAI/pythia-160m-deduped</td>
<td>21580</td>
</tr>
<tr>
<td>EleutherAI/pythia-70m-deduped</td>
<td>31809</td>
</tr>
</tbody>
</table>
<p>Thus, GPT-4 is close to the human benchmark of 500 tokens/minute, while GPT-3.5-turbo is about 3x faster. Smaller models are an order of magnitude faster still, which indicates that even faster inference is possible, although it also suggests that future larger models may be slower (not accounting for better hardware and other optimizations). Inference speed in practice seems to slow down sublinearly with model size&#x2013;in the pythia models, increasing size by a factor of k decreases inference speed by approximately k<sup>0.6</sup>.</p>
<p>How will models&#x2019; words per minute change in the future? There are factors pushing towards both faster and slower speeds:</p>
<ul>
<li>Larger models are more expensive to run, especially if they have more layers (larger widths can be parallelized, but larger depths cannot be).</li>
<li>Inference will generally be optimized more, e.g. via early exiting, sparse attention, cross-GPU parallelization, or better hardware. There is quite a bit of headroom here, especially from parallelization and hardware (see discussion below).</li>
<li>In particular, there will be quite a bit of incentive to make models fast enough to be easily usable (e.g. faster than human reading speed).</li>
<li>After staring at lots of data about trends in model size, GPU architecture, etc. for 10+ hours, I mostly concluded that I am very uncertain about how the competing trends of larger models vs. better hardware and software will play out. <strong>My median guess would be that we get models that are noticeably faster than humans (5x), but I wouldn&#x2019;t be surprised by anything from 2x slower to 20x faster.</strong></li>
<li>Importantly, these speeds are only if we demand maximum throughput from the GPUs. If we are willing to sacrifice throughput by a factor of k, we can speed up inference by a factor of k^2, up to fairly large values of k. So if models are only 5x faster than humans by default, they could instead be 125x faster in exchange for a 5x reduction in throughput, and this could be pushed further still if necessary.</li>
</ul>
<p>Finally, aside from raw speed, words/minute isn&#x2019;t apples-to-apples across humans and language models. For one, the language models aren&#x2019;t just thinking but also writing, and in some cases they are writing content that would be much slower for humans to produce (e.g. code, or arguments with references). In the other direction, language models are currently quite verbose, so one word from a language model does less &#x201C;work&#x201D; than one word from a human. This verbosity could be fine-tuned away, but it&#x2019;s not clear we could match the efficiency of elliptic thought in humans. Finally, tokenization and word complexity will change over time, and so the 1.333x conversation ratio from words to tokens won&#x2019;t stay constant (indeed, I&#x2019;d guess it&#x2019;s already an underestimate for today&#x2019;s models since they now tend to use complex words with prefixes and suffixes).</p>
<p><strong>Details on parallelization and hardware speed-ups</strong>. As described in <a href="https://bounded-regret.ghost.io/how-fast-can-we-perform-a-forward-pass/">How Fast Can We Perform a Forward Pass?</a>, there are parallel tiling schemes that significantly increase serial inference speed with only minor overhead. For instance, parallel tiling of GPT-3 would increase its inference speed by 30x or more on an A100 cluster relative to running it on a single 8-GPU machine<sup class="footnote-ref"><a href="#fn16" id="fnref16">[16]</a></sup>. These optimizations are not currently widely used because they aren&#x2019;t useful for training and slightly decrease inference throughput, but people would start using them once inference time becomes a bottleneck.</p>
<p>For hardware, GPUs are becoming more powerful, which will speed up inference. However, GPUs are also being built to require larger arithmetic intensity, which will decrease the amount of parallel tiling (see previous point) that is possible. For reference, I&#x2019;ve included the specs of all NVIDIA GPUs below. The &#x201C;Mem Bandwidth&#x201D; column measures the serial throughput without any cross-GPU parallelization<sup class="footnote-ref"><a href="#fn17" id="fnref17">[17]</a></sup>, while the final M<sup>3/C</sup>2 column measures serial throughput with the maximum cross-GPU parallelization that maintains high enough arithmetic intensity<sup class="footnote-ref"><a href="#fn18" id="fnref18">[18]</a></sup>. The former is steadily increasing, while the latter jumps around but has tended to decrease.</p>
<table>
<thead>
<tr>
<th>Date</th>
<th>GPU</th>
<th>Compute</th>
<th>Memory</th>
<th>Clock Speed</th>
<th>Mem Bandwidth</th>
<th>Interconnect</th>
<th>Network</th>
<th>M^3 / C^2</th>
</tr>
</thead>
<tbody>
<tr>
<td>05/2016</td>
<td>P100</td>
<td>~84TF</td>
<td>16GB</td>
<td>1.45GHz</td>
<td>720GB/s</td>
<td>160GB/s</td>
<td></td>
<td>53M</td>
</tr>
<tr>
<td>12/2017</td>
<td>V100 16GB</td>
<td>125TF</td>
<td>16GB</td>
<td>1.49GHz</td>
<td>900GB/s</td>
<td>300GB/s</td>
<td>~25GB/s</td>
<td>47M</td>
</tr>
<tr>
<td>03/2018</td>
<td>V100 32GB</td>
<td>125TF</td>
<td>32GB</td>
<td>1.49GHz</td>
<td>900GB/s</td>
<td>300GB/s</td>
<td>~100GB/s</td>
<td>47M</td>
</tr>
<tr>
<td>05/2020</td>
<td>A100 40GB</td>
<td>312 TF</td>
<td>40GB</td>
<td>1.38GHz</td>
<td>1555GB/s</td>
<td>600GB/s</td>
<td>~400GB/s</td>
<td>39M</td>
</tr>
<tr>
<td>11/2020</td>
<td>A100 80GB</td>
<td>312 TF</td>
<td>80GB</td>
<td>1.38GHz</td>
<td>2039GB/s</td>
<td>600GB/s</td>
<td>~400GB/s</td>
<td>87M</td>
</tr>
<tr>
<td>~8/2022</td>
<td>H100</td>
<td>2000 TF</td>
<td>80GB</td>
<td>1.74GHz</td>
<td>3072GB/s</td>
<td>900GB/s</td>
<td>900GB/s?</td>
<td>7.2M</td>
</tr>
</tbody>
</table>
<h2 id="b-training-overhang">B. Training overhang</h2>
<p>There will likely be enough resources to run many copies of a model once it has been trained. GPT-3 took 3.1e23 FLOPs to train and requires 3.5e11 FLOPs for a forward pass, so 9e11 forward passes could be run for the cost of training. Using the 500 tokens per minute conversion from <a href="#a-words-per-minute">Appendix A</a>, this would correspond to ~3400 human-years of thinking.</p>
<p>How will this change in the future? I&#x2019;ll use the Chinchilla scaling law and projections of future training costs to form an initial estimate, then I&#x2019;ll consider ways we could deviate from the Chinchilla trend. For future training costs, I consider the projection in <a href="https://epochai.org/blog/projecting-compute-trends?ref=bounded-regret.ghost.io">Besiroglu et al. (2022)</a>, who analyzed over 500 existing models to extrapolate compute trends in machine learning. Their central projection of training FLOPs in 2030 is 4.7e28, with a range of 5.1e26 to 3.0e30. Metaculus has a <a href="https://www.metaculus.com/questions/11558/maximum-compute-used-in-ai-training/?ref=bounded-regret.ghost.io">similar estimate</a> of 2.3e27 (for Jan 1, 2031)<sup class="footnote-ref"><a href="#fn19" id="fnref19">[19]</a></sup>. Taking the geometric median, I&#x2019;ll use 1.0e28 as my estimate of training FLOPs, or a 33,000-fold increase over GPT-3. Since the Chinchilla scaling law implies that model size (and hence inference cost) scales as the square-root of training cost, this means the training overhang should increase by sqrt(33000), or around 180-fold. The 3400 human-years of thinking would thus increase to 620,000 human-years. However, there&#x2019;s an additional consideration, which is that GPT-3 was actually trained with suboptimal scaling. The ideal size of GPT-3 (given its training cost) would have been 4 times smaller, so we need to add an additional factor of 4, to get 2.5M human-years, with a range from 0.8M to 9M accounting for uncertainty in the number of training FLOPs<sup class="footnote-ref"><a href="#fn20" id="fnref20">[20]</a></sup>.</p>
<p>Next, let&#x2019;s consider deviations from the Chinchilla scaling law. The most obvious deviation is that we might soon run out of data. This could either mean that larger models becomes more attractive relative to more data (which would decrease training overhang), or that we generate additional synthetic data (makes creating data more computationally-expensive, which would increase training overhang), or we move to new data-rich modalities such as video (unclear effect on training overhand, probably increases it). To roughly bound these effects:</p>
<ul>
<li><em>Lower bound</em>: <a href="https://arxiv.org/abs/2211.04325?ref=bounded-regret.ghost.io">Villalobos et al. (2022)</a> estimate that we will run out of high-quality language data (e.g. Wikipedia, books, scientific papers, etc.) by 2026, although we will not run out of low-quality data (e.g. web pages) before 2030. In a pessimistic world where high-quality data is a completely binding constraint, the model in Villalobos et al. implies an 8x increase in dataset size by 2030, meaning the training overhang would increase only 8-fold instead of 180-fold.</li>
<li><em>Upper bound</em>: If we run out of data, we might generate new data synthetically. One possibility for this is chain-of-thought distillation as in <a href="https://arxiv.org/abs/2210.11610?ref=bounded-regret.ghost.io">Huang et al. (2022)</a>. In that paper, 32 chains of thought are generated on each input instance, only some of which are used for training updates. Assume that on average 5 of the 32 chains of thought get used for training updates, and that a backward pass is twice the cost of a forward pass. Then the cost per training update is equivalent to 2 + 32/5 = 8.4 forward passes, compared to 3 previously, or a 2.8x increase. Under Chinchilla scaling this cost propagates forward to an additional sqrt(2.8) = 1.7x increase in training overhang, i.e. 300-fold instead of 180-fold.</li>
</ul>
<p>Overall, the lower bound seems fairly pessimistic to me as we&#x2019;ll almost certainly find <em>some</em> way to leverage lower-quality or synthetic data. On the other hand, beyond running out of data, we might find ways to make the training process more efficient via e.g. curriculum learning. Accounting for this, my personal guess is we will end up somewhere between a <strong>12-fold and 200-fold increase in overhang</strong>, with a central estimate of 100x, yielding a training overhang of around <strong>1.8M human-years of thinking</strong>. We would also want to expand our range to account for the additional uncertainty from deviations to the Chinchilla scaling law. Subjectively, I&#x2019;d increase the range to be <em>0.4M to 10M</em>.</p>
<p>All of these estimates are for 2030. In general, the numbers above would be larger for later years and smaller for earlier years.</p>
<p>As an additional point of comparison, <a href="https://www.cold-takes.com/ai-could-defeat-all-of-us-combined/?ref=bounded-regret.ghost.io#fnref5">Karnofsky (2022)</a> (following <a href="https://www.lesswrong.com/posts/KrJfoZzpSDpnrv9va/draft-report-on-ai-timelines?ref=bounded-regret.ghost.io">Cotra, 2020</a>) estimates that the cost to train a human-level model would be enough compute to run 100 million copies of the model for a year each, although that estimate assumes training runs that use 1e30 FLOPs instead of 1e28. Even accounting for that, this seems a bit high to me, and I&#x2019;d have been closer to 18 million than 100 million based on the square-root scaling above.</p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>Though actually, zeroth order forecasting already helps a lot if done right! Many who were surprised by ChatGPT would have already been impressed by text-davinci-003, which was released much earlier but with a less user-friendly interface. <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn2" class="footnote-item"><p>As a specific point of comparison, GPT-3 only had enough compute to run 3400 human-adjusted years of work, and I&apos;d guess it could do less than 100 human-adjusted years of learning per day. I&apos;d guess GPT-4 is at 130,000 human-adjusted years of work and 125 adjusted years of learning. So GPT<sub>2030</sub> is at least an order of magnitude larger on both axes. <a href="#fnref2" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn3" class="footnote-item"><p>Throughout, the range in brackets represents the 25th to 75th percentile of my predictive distribution. In practice the range is probably too narrow because I only did a mainline forecast without accounting for <a href="https://forecasting.quarto.pub/book/other-option.html?ref=bounded-regret.ghost.io">&#x201C;other&#x201D; options</a>. <a href="#fnref3" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn4" class="footnote-item"><p>Qualitatively, GPT-4 Bubeck et al. also found that GPT-4 could produce a 400-line 3D game zero-shot, which is probably impossible for nearly all humans. <a href="#fnref4" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn5" class="footnote-item"><p>See <a href="https://bounded-regret.ghost.io/forecasting-math-and-mmlu-in-2023/">Forecasting ML Benchmarks in 2023</a> for some further discussion of this. <a href="#fnref5" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn6" class="footnote-item"><p>Concretely, I&#x2019;d assign 50% probability to the following: &#x201C;If we take 5 randomly selected theorem statements from the Electronic Journal of Combinatorics and give them to the math faculty at <a href="https://www.usnews.com/best-graduate-schools/top-science-schools/mathematics-rankings?_sort=rank-asc&amp;ref=bounded-regret.ghost.io">UCSD</a>, GPT<sub>2030</sub> would solve a larger fraction of problems than the median faculty and have a shorter-than-median solve time on the ones that it does solve.&#x201D; <a href="#fnref6" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn7" class="footnote-item"><p>I am assuming the initial training run was less than a year (<a href="https://epochai.org/blog/the-longest-training-run?ref=bounded-regret.ghost.io">Sevilla et al., 2022</a>), from which it follows that the organization can at least parallelize enough to run the 9 x 10<sup>11</sup> forward passes within a year, subject to constraints on inference speed. To do so in 2.4 months, they may need further improvements. I think this is plausible (but not certain), both because the organization might have trained the model in less than a year, and because there may be tricks available for inference that were not for training. <a href="#fnref7" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn8" class="footnote-item"><p>A second factor is that GPT-3 was trained suboptimally, and with optimal (Chinchilla-style) scaling the training overhang would be 4x larger already.  <a href="#fnref8" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn9" class="footnote-item"><p>Adjusted to human working speeds. <a href="#fnref9" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn10" class="footnote-item"><p>The math here is that with a perfect speed-up, 1.8 milion / 25 = 72,000, but the extra 5x per FLOP makes it 14,000. <a href="#fnref10" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn11" class="footnote-item"><p>&#x201C;skilled readers typically reading at rates between 250-350 words per minute&#x201D; <a href="#fnref11" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn12" class="footnote-item"><p>&#x201C;estimates of normal speaking rate range from 120 to 200 words per minute&#x201D; <a href="#fnref12" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn13" class="footnote-item"><p>&#x201C;Experiments on compressed speech suggest that comprehension can be successful at two times or more the normal rate (e.g., Dupoux &amp; Green, 1997)&#x201D; <a href="#fnref13" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn14" class="footnote-item"><p>I personally think that 4:3 is too optimistic and 3:2 or even 2:1 might be more realistic, but I&#x2019;ll stick to 4:3 throughout the doc since it was the main citation I found. <a href="#fnref14" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn15" class="footnote-item"><p>The performance for pythia models can likely be improved further. For instance, <a href="https://github.com/NVIDIA/FasterTransformer/blob/main/docs/gpt_guide.md?ref=bounded-regret.ghost.io#performance-of-gpt-67b">NVIDIA has reported</a> about 80 tokens per second on a comparable model to pythia-6.9 billion on a single A100. When allowing for more hardware, they have even shown <a href="https://github.com/NVIDIA/FasterTransformer/blob/main/docs/gpt_guide.md?ref=bounded-regret.ghost.io#performance-of-gpt-20b">approximately 90 tokens per second</a> using 8 way tensor parallelism on an 8xA100 SuperPod architecture when generating using a 20B parameter GPT model. <a href="#fnref15" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn16" class="footnote-item"><p>A single A100 can handle matrix multiplies as small as 1024x1024 before becoming bottlenecked on memory reads, and the main operation in GPT-3 is a 12288 x (4*12288) matrix multiply, meaning we would tile it across 576 GPUs (72 machines). This would naively mean a 72x speedup, but there is probably enough overhead that I&#x2019;m estimating closer to 30x. <a href="#fnref16" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn17" class="footnote-item"><p>Roughly speaking, with no cross-GPU tiling, the serial speed of inference is determined by the memory bandwidth, e.g. the A100 with 2039GB/s bandwidth should be able to complete 2039/175 \approx 12 forward passes with a 175B parameter model per second (up to constant factors). <a href="#fnref17" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn18" class="footnote-item"><p>With parallel tiling, the forward passes per second is proportional to M<sup>3/54C</sup>2L, where C = Compute, M = Mem bandwidth, and L = # of layers. (see <a href="https://bounded-regret.ghost.io/how-fast-can-we-perform-a-forward-pass/">here</a> for details). The final column gives M<sup>3/C</sup>2. <a href="#fnref18" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn19" class="footnote-item"><p>Metaculus also <a href="https://www.metaculus.com/questions/4518/how-many-billions-of-parameters-will-the-largest-machine-learning-model-trained-before-2030-have/?ref=bounded-regret.ghost.io">estimates</a> that the largest model trained will have 2.5e15 parameters (for Jan 1, 2030), meaning a forward pass costs 5e15 FLOPs. If we naively take the ratio, we again get 9e11 forward passes, but I think this is not the right calculation, because the largest model trained will likely not be state-of-the-art but rather something like the 174 trillion parameter <a href="https://dl.acm.org/doi/abs/10.1145/3503221.3508417?ref=bounded-regret.ghost.io">BaGuaLu model</a>. <a href="#fnref19" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn20" class="footnote-item"><p>I&#x2019;m basing this on Metaculus giving a range of 5M to 660M as the interquartile range of their estimate, and propagating the uncertainty through the square-root function. <a href="#fnref20" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
<!--kg-card-end: markdown-->]]></content:encoded></item><item><title><![CDATA[Complex Systems are Hard to Control]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p>The deployment of powerful deep learning systems such as ChatGPT raises the question of how to make these systems safe and consistently aligned with human intent. Since building these systems is an engineering challenge, it is tempting to think of the safety of these systems primarily through a traditional engineering</p>]]></description><link>https://bounded-regret.ghost.io/complex-systems-are-hard-to-control/</link><guid isPermaLink="false">642727c0e9eb58003d7bf52e</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Mon, 03 Apr 2023 23:50:21 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p>The deployment of powerful deep learning systems such as ChatGPT raises the question of how to make these systems safe and consistently aligned with human intent. Since building these systems is an engineering challenge, it is tempting to think of the safety of these systems primarily through a traditional engineering lens, focusing on reliability, modularity, redundancy, and reducing the long tail of failures.</p>
<p>While engineering is a useful lens, it misses an important part of the picture: deep neural networks are <strong>complex adaptive systems</strong>, which raises new control difficulties that are not addressed by the standard engineering ideas of reliability, modularity, and redundancy. I&#x2019;ve discussed some <a href="https://bounded-regret.ghost.io/emergent-deception-optimization/">particular</a> <a href="https://bounded-regret.ghost.io/ml-systems-will-have-weird-failure-modes-2/">examples</a> of this before, but here I want to focus on the broader underlying intuition that generated them.</p>
<p>A <a href="https://en.wikipedia.org/wiki/Complex_adaptive_system?ref=bounded-regret.ghost.io">complex adaptive system</a> is a system with many interacting components that adapt to their environment and co-evolve over time (in our case, the weights / layers of the neural network). Beyond neural networks, other examples of complex adaptive systems include firms, financial markets, political parties, culture, traffic flows, pathogens, ecosystems, human brains, the Earth&#x2019;s climate, and the Internet.</p>
<p>A common thread in all these systems is that straightforward attempts to control their behavior lead to unintended consequences. I&#x2019;ll demonstrate this through concrete examples, then step back and consider the broader properties that make these systems difficult to control, including emergent goals. Finally, I&#x2019;ll propose safety measures that account for the complex adaptive nature of deep learning systems.</p>
<p>Many of the ideas in this post have been discussed before, and my thinking owes significantly to Dan Hendrycks, who was an early proponent of the complex systems perspective as a PhD student in my lab (see e.g. <a href="https://arxiv.org/abs/2109.13916?ref=bounded-regret.ghost.io">Unsolved Problems in ML Safety</a>, the lecture on <a href="https://www.youtube.com/watch?v=Ic_qDqYEJcA&amp;ref=bounded-regret.ghost.io">accident models</a> from Dan&#x2019;s course, or <a href="https://www.alignmentforum.org/s/FaEBwhhe3otzYKGQt/p/n767Q8HqbrteaPA25?ref=bounded-regret.ghost.io">this blog post</a>).</p>
<h2 id="control-difficulties-in-complex-systems">Control Difficulties in Complex Systems</h2>
<p>Let&#x2019;s examine several examples of complex systems, and see why each is difficult to control, in the sense that they either resist or respond unpredictably to external feedback.</p>
<p><strong>Traffic</strong>. A city builds new highways to reduce traffic congestion. The newly increased road capacity <a href="https://en.wikipedia.org/wiki/Induced_demand?ref=bounded-regret.ghost.io">attracts new drivers</a>, leading to <a href="https://en.wikipedia.org/wiki/Braess%27s_paradox?ref=bounded-regret.ghost.io">worse levels of congestion</a> than before. The <em>adaptive behavior</em> leads to unintended consequences.</p>
<p><strong>Ecosystems</strong>. A park introduces a predator to reduce the population of an invasive species. The predator also preys on native species, disrupting the ecosystem balance. The <em>dense network of interactions</em> makes it difficult to predict all consequences ahead of time.</p>
<p><strong>Financial markets</strong>. Central banks lower interest rates to stimulate economic growth. Funders thus make riskier investments leading to asset bubbles, which later burst and destabilize the financial system. In this case, both adaptivity and multi-step interactions come into play.</p>
<p><strong>Culture</strong>. The government implements public awareness campaigns to promote environmental conservation. These efforts encounter resistance from workers whose jobs rely on non-renewable fuel sources, and are appropriated by fashion brands and other consumer products through <a href="https://en.wikipedia.org/wiki/Greenwashing?ref=bounded-regret.ghost.io">greenwashing</a>.</p>
<p>Further examples include pathogens evolving drug resistance, firms relocating to avoid regulations, and positive feedback loops from climate change. I elaborate on these and other examples in the <a href="#appendix-additional-examples-of-control-difficulties">appendix</a>.</p>
<h2 id="traditional-engineering-does-not-address-these-difficulties">Traditional Engineering Does not Address these Difficulties</h2>
<p>Why are complex adaptive systems hard to control? There are two key hallmarks of complex adaptive systems:</p>
<ol>
<li><strong>Emergence</strong>: behavior at one scale cannot be easily reduced to behavior at smaller scales, i.e. &#x201C;<a href="https://bounded-regret.ghost.io/more-is-different-for-ai/">More is Different</a>&#x201D;.</li>
<li><strong>Feedback loops</strong>: different components of the system continually influence and respond to each other.</li>
</ol>
<p>Feedback loops can lead a system to resist or respond nonlinearly to change. Emergence means that failures cannot be traced to individual components, and that behavior is hard to predict as a system evolves. Together, emergence and feedback loops lead to many of the downstream challenges seen in our earlier examples, such as:</p>
<ul>
<li><strong>Adaptivity</strong>: complex adaptive systems often adapt to and resist change, as in the traffic and culture examples.</li>
<li><strong>Nonlinearity</strong>: due to feedback loops and other higher-order interactions, small changes in input can lead to large or unexpected changes in output, as in the traffic, ecosystem, and financial market examples.</li>
<li><strong>Self-organization</strong>: Order and structure can emerge without central control, as can be seen with human culture. Since there was no central control that instantiated these structures, there is no obvious point of intervention to direct them.</li>
<li><strong>Redundancy</strong>: self-organization means that complex adaptive systems often have multiple components that perform similar functions. This makes them less responsive to interventions. For instance, redirecting traffic from one street might just move it to nearby streets and not affect overall traffic in an area.</li>
</ul>
<p><strong>Traditional engineering does not address these challenges</strong>. Three hallmarks of engineering are <em>reliability</em>, <em>modularity</em>, and <em>redundancy</em>, but these traditional pillars either don&#x2019;t address the issues above or are infeasible to implement.</p>
<p>For instance, one might seek to <em>reliably</em> influence culture by testing messaging on a broad set of audiences and disseminating messages through multiple channels. But new countercultures will likely rise in response, and ubiquitous messaging could end up sparking backlash.</p>
<p><em>Modularity</em> could help improve complex systems, but is almost impossible to achieve due to interactions and feedback loops. For instance, the U.S. government is built on separation of powers (a form of modularity), but over time the different branches have co-adapted and found ways to assert power beyond their initial scope (see e.g. the <a href="https://en.wikipedia.org/wiki/War_Powers_Resolution?ref=bounded-regret.ghost.io">War Powers Resolution</a> and <a href="https://en.wikipedia.org/wiki/Commerce_Clause?ref=bounded-regret.ghost.io">commerce clause</a>).</p>
<p>Finally, <em>redundancy</em> is considered a virtue in traditional engineering, but the redundancy in complex adaptive systems makes them harder to analyze and intervene on.</p>
<h3 id="goal-oriented-behavior-in-complex-adaptive-systems">Goal-oriented Behavior in Complex Adaptive Systems</h3>
<p>A signature difficulty in complex adaptive systems is <strong>emergent goal-oriented behavior</strong> (<a href="https://en.wikipedia.org/wiki/Systemantics?ref=bounded-regret.ghost.io">Gall, 1975 ch. 8</a>). For instance, ant colonies collectively pursue goals (finding food, building nests, protecting the colony) even though each individual ant follows simple rules. Similarly, flocks of birds avoid predators despite each bird following simple rules.</p>
<p>As I&apos;ll discuss below, emergent goals are <strong>hard to predict from individual components</strong> and many emergent goals center on <strong>acquiring power or resources</strong>. Emergent goals therefore pose a particular challenge to controlling systems, as they produce an impetus that cannot be easily directed through either top-down or bottom-up intervention.</p>
<p>First, a system&#x2019;s explicitly stated goal (e.g. the core principles of an organization) rarely matches the goals that it pursues in practice, due to intra-system competition (see e.g. &#x201C;<a href="https://news.ycombinator.com/item?id=19553294&amp;ref=bounded-regret.ghost.io">launch, promote, abandon</a>&#x201D;, where individual managers pursue goals detrimental to the organization in order to get promoted). A system&#x2019;s emergent goals also need not match the goals of individual actors in the system. For example, it is common for groups of well-intentioned people to do harm, and for self-interested parties to create valuable products.</p>
<p>Second, emergent goals need not be beneficial to individuals: groups often exhibit strong pressures towards consensus, leading to groupthink, even if most individuals prefer greater diversity of thought. And for parts of the COVID-19 pandemic, society seemed to have a &#x201C;goal&#x201D; of keeping the reproduction number R close to 1, as lower case counts led people to be less cautious and vice versa, which rendered many policies surprisingly ineffectual.</p>
<p>Even though a system&#x2019;s goals can be derived neither from a top-down objective nor from individual actors, <strong>some goals appear commonly across many systems</strong>. Two common emergent goals are <em>self-preservation</em> and <em>growth</em>: complex adaptive systems often act to preserve themselves and to expand in size. This is ubiquitous in biology (due to evolutionary pressure), but occurs more broadly, for instance most organizations (e.g. bureaucracies, companies) act to preserve themselves and to expand. Consequently, complex systems need constant checks to ensure they do not encroach on other domains (<a href="https://en.wikipedia.org/wiki/Systemantics?ref=bounded-regret.ghost.io">Gall, 1975 ch. 2</a>).</p>
<h2 id="lessons-for-deep-learning-safety">Lessons for Deep Learning Safety</h2>
<p>I argued that traditional engineering thinking is not sufficient for making deep learning systems safe. So what additional approaches should we incorporate? Here are several principles derived from analogy with other complex adaptive systems:</p>
<p><strong>Avoid continuous incentive gradients towards bad behaviors</strong>; instead build sharp cliffs. For instance, it is a bad idea to give people low doses of antibiotics, because some bacteria would survive and evolve antibiotic resistance. Instead, you want to make sure that anyone given antibiotics is given enough to kill all the bacteria by a significant margin.</p>
<p>Similarly, in deep learning, it would be a bad idea to first train a system on very error-prone human evaluators and then gradually expose it to more sophisticated overseers. Why? Because the model could learn methods to fool the initial error-prone evaluators, and then gradually improve its deception as the quality of oversight increased. It would instead be better to start with high-quality oversight: then the model might never learn to deceive in the first place, because all forms of successful deception would require large departures from its current policy.</p>
<p><strong>Consider not building certain systems</strong>. In other domains such as synthetic biology, it is recognized that certain systems are inherently dangerous and should not be built, or should only be built with strong justifications and safeguards in place. Many self-replicating or rapidly-evolving systems fall under this category (e.g. engineered viruses or pests). We do not have such a culture in machine learning currently, but should build more of one.</p>
<p><strong>Diverse systems are more resilient</strong>. By default, deep learning leads to the deployment of many copies of the same system or similar systems (e.g. fine-tuned from the same base model). It may be safer to have a larger diversity of models. For instance, if a model acquires unwanted emergent goals, other AI systems may act to stop it, but only if those models do not have the same emergent goals. The more different AI systems are from each other, the more they can act as checks and balances against each other. Diverse systems may also help combat algorithmic monoculture (<a href="https://www.pnas.org/doi/10.1073/pnas.2018340118?ref=bounded-regret.ghost.io">Kleinberg and Raghavan, 2021</a>; <a href="https://arxiv.org/abs/2211.13972?ref=bounded-regret.ghost.io">Bommosani et al., 2022</a>).</p>
<p>On the other hand, diverse goals of individual AI systems may lead to worse emergent goals for the entire ecosystem of AIs, due to economic and selection pressures, as argued in <a href="https://arxiv.org/abs/2303.16200?ref=bounded-regret.ghost.io">Hendrycks (2023)</a>.</p>
<p><strong>Avoid positive feedback loops</strong>. Positive feedback loops, left unchecked, can cause a system to explode destructively. In deep learning, we should be especially worried about positive feedback loops that cause rapid capabilities improvements (e.g. learning to learn or otherwise self-improve) or rapid shifts in goals.</p>
<p><strong>A large safe system often evolves from a small safe system</strong> (<a href="https://en.wikipedia.org/wiki/Systemantics?ref=bounded-regret.ghost.io">Gall, 1975 ch. 11</a>; <a href="https://www.alignmentforum.org/posts/n767Q8HqbrteaPA25/complex-systems-for-ai-safety-pragmatic-ai-safety-3?ref=bounded-regret.ghost.io">Hendrycks and Woodside, 2022</a>). If a pretrained model is misaligned with humans (e.g. by having unsafe emergent goals), we should not expect to solve this problem with fine-tuning. We need to ensure that it is human-aligned throughout pretraining and engineered to become more safe and human-aligned over time (e.g. by seeking out reliable human feedback, down-regulating erratic behavior, etc.).</p>
<p>One implication is that if we were to train a model to use tools and interact with the external world, it may be safer to do this during fine-tuning and to pretrain mainly on prediction and on instruction-following. An externally-directed model is more likely to develop externally-directed goals, and we&#x2019;d rather avoid baking those into the initial system.</p>
<p>A second implication is that we should pretrain the model on a robust set of self-corrective and self-regulating behaviors, e.g. train it to consistently comply with being shut down or otherwise give up power in a broad variety of scenarios, and to notice when it is taking potentially bad actions and flag this to human annotators. <a href="https://arxiv.org/abs/2302.08582?ref=bounded-regret.ghost.io">Korbak et al. (2023)</a> takes an initial step in this direction by incorporating human preference data during pretraining.</p>
<p><strong>Train models to have limited aims</strong>. In societal systems, regulation and other limiters prevent a single bad component from causing too much damage. For instance, financial regulations force banks to limit their exposure to certain risks. For deep learning systems, we could train them to consistently stop pursuing a variety of goals after a certain point, and hope that this teaches them to have limited aims in general. This could help avoid positive feedback loops and may be one way to imbue safety into the initial version of a system. (Thanks to Jared Kaplan for initially suggesting this idea.)</p>
<p><strong>Summary</strong>. Focusing on complex systems leads to several perspectives (incentive shaping, non-deployment, self-regulation, and limited aims) that are uncommon in traditional engineering, and also highlights ideas (diversification and feedback loops) that are common in engineering but not yet widely utilized in machine learning. I expect these approaches to be collectively important for controlling powerful ML systems, as well as intellectually fruitful to explore.</p>
<h2 id="discussion-are-deep-networks-analogous-to-other-complex-adaptive-systems">Discussion: Are Deep Networks Analogous to Other Complex Adaptive Systems?</h2>
<p>One possible objection to this post would be that deep learning systems are not really analogous to the other complex adaptive systems I&#x2019;ve described, and so we should not expect similar control difficulties.</p>
<p>I&#x2019;ll address this in two parts. First, clearly there are at least some analogies with other complex adaptive systems&#x2014;for instance, neural networks often learn <strong>redundant copies</strong> of a single functionality, which makes it more difficult to analyze their internal function (<a href="https://arxiv.org/abs/2211.00593?ref=bounded-regret.ghost.io">Wang et al., 2022</a>). Moreover, <strong>emergence</strong> is commonplace, as new qualitative behaviors often appear when we scale up deep networks (<a href="https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/">Steinhardt, 2022</a>; <a href="https://arxiv.org/abs/2206.07682?ref=bounded-regret.ghost.io">Wei et al., 2022</a>). And since a large and diverse set of behaviors appear via <strong>self-organization</strong>, it can be difficult to even track all of the phenomena we care about, let alone control them. For instance, some important behaviors such as <a href="https://jsteinhardt.stat.berkeley.edu/talks/satml/tutorial.html?ref=bounded-regret.ghost.io#slideIndex=3&amp;level=1">sycophancy</a> and <a href="https://jsteinhardt.stat.berkeley.edu/talks/satml/tutorial.html?ref=bounded-regret.ghost.io#slideIndex=3&amp;level=2">sandbagging</a> were not apparent until ML researchers ran large-scale, automated evaluations (<a href="https://arxiv.org/abs/2212.09251?ref=bounded-regret.ghost.io">Perez et al., 2022</a>). Other issues, such as hallucinations, are ubiquitous but have so far resisted attempts to quash them (<a href="https://cdn.openai.com/papers/gpt-4.pdf?ref=bounded-regret.ghost.io">OpenAI, 2023</a>).</p>
<p>Regarding <strong>emergent goals</strong>, some large language models already do exhibit emergent goal-directed behavior, such as Sydney attempting to <a href="https://twitter.com/MovingToTheSun/status/1625156575202537474?ref=bounded-regret.ghost.io">persuade a user that the year is 2022</a> and to <a href="https://www.nytimes.com/2023/02/16/technology/bing-chatbot-microsoft-chatgpt.html?ref=bounded-regret.ghost.io">persuade a journalist to leave his wife</a>. However, despite this initial evidence, one might argue that deep learning systems are less likely to exhibit fully &#x201C;agentic&#x201D; behavior than other complex adaptive systems, since their individual components (neurons) are not adaptive agents, in contrast to our other examples (humans, animals, pathogens, firms).</p>
<p>However, non-agentic building blocks are only a partial disanalogy with other complex adaptive systems: <em>intermediate levels of organization</em> can still create adaptive subagents, and <em>external feedback loops</em> create interactions with agents such as humans and firms.</p>
<p><strong>Intermediate levels of organization</strong>. There are intermediate levels of organization between individual neurons and the entire network. Distributed subnetworks of neurons could acquire forms of agency and self-preservation, leading the entire network to behave as a complex adaptive system in full.</p>
<p>For an analogy, consider biological neural networks. The human brain acquires non-adaptive compulsions (obsessive cleanliness, perfectionism, etc.) that are often self-preserving. For instance, OCD patients generate rationalizations for why it is important to give into their compulsions, and sometimes actively resist taking steps to expunge them, which is why OCD often requires professional treatment. OCD thus constitutes a distributed subnetwork of the brain with both agency (the compulsion) and self-preservation (the rationalization). If these sub-agents exist in the human brain, they may arise in artificial neural networks as well.</p>
<p>Furthermore, if deep networks end up <a href="https://bounded-regret.ghost.io/emergent-deception-optimization/">learning optimization emergently</a>, then they could acquire emergent goals tied to that optimization (e.g. a goal of seeking novelty for an agent trained to do active learning). This is a safety risk, since many natural emergent subgoals lead systems to resist change and seek power (<a href="https://dl.acm.org/doi/10.5555/1566174.1566226?ref=bounded-regret.ghost.io">Omohundro, 2008</a>).</p>
<p><strong>External feedback loops</strong>. Deep learning systems are situated in the world, interacting with users, other ML systems, and the Internet, which forms a larger complex adaptive system around the model itself. This larger system can produce unexpected behavior both individually and in aggregate. Individually, humans might actively try to produce prompts that lead a chatbot to exhibit novel behavior, thus pushing it off-distribution. At the aggregate level, if AI writing assistants make it easier to write compelling prose in one style compared to others, that one style could come to dominate<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>. Both the individual and aggregate effects would resist attempts to change them&#x2014;the user is motivated to circumvent any safeguards that developers place on the model, and many users (as well as the system itself) would have adapted to the new writing style once it&#x2019;s initially deployed.</p>
<p>To conclude, while some of the thorniest issues of complex adaptive systems (resistance to change and emergent goals) are not yet commonplace for deep networks, I expect them to arise in the future, and we should start mitigating them today.</p>
<p><em>Thanks to Louise Verkin for transcribing this post into Markdown format. Thanks to Thomas Woodside, Ruiqi Zhong, Ajeya Cotra, Thomas Woodside, Roger Grosse, and Richard Ngo for providing feedback on this post.</em></p>
<p><em>Author contribution statement: Jacob Steinhardt conceived the idea and structure of the post. GPT-4 produced the examples of complex systems and reasons why they are difficult to control, and collaborated with Jacob to produce the lessons for deep learning safety. Jacob wrote the other sections and edited and sometimes expanded the text provided by GPT-4 for these sections.</em></p>
<h2 id="appendix-additional-examples-of-control-difficulties">Appendix: Additional Examples of Control Difficulties</h2>
<p>Below are several additional examples of control difficulties in complex systems, similar to those in the <a href="#control-difficulties-in-complex-systems">main text</a>.</p>
<p><strong>Pathogens</strong>. When a new drug is introduced to control a particular pathogen, the pathogen population may evolve resistance to the drug, rendering it less effective over time.</p>
<p><strong>Firms</strong>. The government regulates pollution by imposing a cap on emissions. Some firms invest in cleaner technology to comply with the regulations, but others <a href="https://en.wikipedia.org/wiki/Carbon_leakage?ref=bounded-regret.ghost.io">relocate their production facilities</a> to countries with fewer regulations.</p>
<p><strong>Climate</strong>. Efforts to mitigate climate change by reducing greenhouse gas emissions can be complicated by feedback loops, such as the melting of Arctic ice. As ice melts, it exposes darker surfaces (water and land) that absorb more sunlight, leading to further warming and ice melt.</p>
<p><strong>Political parties</strong>. Campaign finance regulations may attempt to limit the influence of money in politics. In response, political parties and candidates might find alternative ways to raise and spend money, such as through independent expenditure committees or super PACs.</p>
<p><strong>The Internet</strong>. Attempts to regulate content or user behavior on the internet often face significant challenges. For example, when governments impose restrictions on access to specific websites or content, users might employ various tools and techniques (e.g., VPNs, proxy servers) to circumvent these restrictions.</p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>Especially if text in that style feeds back into the training data, cementing its advantage. <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
<!--kg-card-end: markdown-->]]></content:encoded></item><item><title><![CDATA[Principles for Productive Group Meetings]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p><em><strong>Note</strong>: This post is based on a Google document I created for my research group. It speaks in the first person, but I think the lessons could be helpful for many research groups, so I decided to share it more broadly. Thanks to Louise Verkin for converting from Google doc</em></p>]]></description><link>https://bounded-regret.ghost.io/principles-for-productive-group-meetings/</link><guid isPermaLink="false">641243852aa5eb003d40ded7</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Wed, 22 Mar 2023 00:47:54 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p><em><strong>Note</strong>: This post is based on a Google document I created for my research group. It speaks in the first person, but I think the lessons could be helpful for many research groups, so I decided to share it more broadly. Thanks to Louise Verkin for converting from Google doc to Markdown format.</em></p>
<p>This document talks about principles for having productive group meetings and seminars, and to some extent a good group culture in general. It&#x2019;s meant to be a living document--I&#x2019;ve started it based on my own experiences, but ultimately our seminars and group culture come from all of us together. So if you have ideas you want to add, please do so!</p>
<p>I&#x2019;ll start by talking about an important concept called <strong>psychological safety</strong>, then discuss what I see as the goals of our research group and how that fits into presentations and discussions in seminars and meetings. I&#x2019;ll also provide tips for asking excellent questions and some general philosophy on how to hold yourself to a high standard of understanding.</p>
<h1 id="psychological-safety">Psychological Safety</h1>
<p>Psychological safety is an important concept for fostering creative and high-functioning teams. I would highly recommend reading the following two documents to learn about it in detail:</p>
<ul>
<li><a href="https://medium.com/@Harri_Kaloudis/psychological-safety-at-work-what-do-psychologically-safe-work-teams-look-like-5585ab0f2df4?ref=bounded-regret.ghost.io">What Do Psychologically Safe Work Teams Look Like?</a></li>
<li><a href="https://docs.google.com/document/d/1PsnDMS2emcPLgMLFAQCXZjO7C4j2hJ7znOq_g2Zkjgk/export?format=pdf&amp;ref=bounded-regret.ghost.io">Manager Actions for Psychological Safety</a></li>
</ul>
<p>To summarize, a psychologically safe team is one where members feel like:</p>
<ul>
<li>They can make mistakes without it affecting their status in the group</li>
<li>It is easy to give and receive feedback, including critical feedback, without feeling attacked or like one is causing trouble</li>
<li>One is allowed to and encouraged to question prevailing opinions</li>
</ul>
<p>These are especially important in research environments, because questioning and risk-taking are needed to generate creative ideas, and making mistakes and receiving feedback are necessary for learning.<br>
In general, I would encourage everyone in our group to take risks and make mistakes. I know everyone holds themselves to a high standard and so doesn&#x2019;t like to make mistakes, but this is the main way to learn. In general, if you never do anything that causes you to look silly, you probably aren&#x2019;t taking enough risks. And in another direction, if you never annoy anyone you probably aren&#x2019;t taking enough risks. (Of course, you don&#x2019;t want to do these all the time, but if it never happens then you can probably safely push your boundaries a bit.)</p>
<p><strong>Fostering psychological safety</strong>. As a group, here are some general principles for fostering psychological safety among our teammates:</p>
<ul>
<li>Assume your teammates have something to teach you, and try to learn from them.</li>
<li>In discussions and debates, aim to explain/understand, not to persuade. Adopt a frame of collaborative truth-seeking, rather than trying to &#x201C;win&#x201D; an argument.</li>
<li>Acknowledge and thank people for good points/questions/presentations/etc.</li>
<li>Invite push-back</li>
<li>Welcome and encourage newcomers</li>
</ul>
<p>In addition, there are a couple <strong>things to avoid</strong>:</p>
<ul>
<li>Try not to talk over people. Sometimes this happens due to being very excited and engaged in a conversation, and don&#x2019;t sweat it if you do this occasionally, but try not to do it habitually, and if you do do it make sure to invite the person you interrupted to finish their point.</li>
<li>Avoid making broadly negative or dismissive statements. Even if you personally don&#x2019;t intend such a statement to apply to anyone in the group, it&#x2019;s inevitable that someone will take it personally. It also works against the principle of &#x201C;questioning prevailing opinions&#x201D;, because it implies that there&#x2019;s an entire area of work or claims that is &#x201C;off-limits&#x201D;.<br><br>As an example, when I was a PhD student, a senior person often made claims to the effect that &#x201C;research was pointless unless industry people cared about it&#x201D;. This made it feel discouraging for me to do my (at the time) more theoretically-oriented work, and I abandoned at least one valuable project because of this. With the benefit of hindsight, I don&#x2019;t think that person actually would have endorsed the literal claim I wrote above, but that&#x2019;s exactly the point I&#x2019;m making&#x2013;it&#x2019;s easy for other people to overinterpret claims.</li>
</ul>
<h1 id="group-goals-and-group-meetings">Group Goals and Group Meetings</h1>
<p>In my view, our group has three major goals:</p>
<ul>
<li>Do excellent research</li>
<li>Help each other to learn and grow</li>
<li>Help the world</li>
</ul>
<p>In the context of group meetings/seminars, we can promote these goals in the following ways:</p>
<ul>
<li>Hold yourself to a high standard of understanding (see below for more on this). In other words, don&#x2019;t just follow the individual steps&#x2013;try to understand why things had to be <em>this</em> way and not any other way. Asking questions about this not only helps your own understanding, but also pushes the speaker to clarify their own thinking&#x2013;thus promoting the goals of excellent research and of learning.</li>
<li>It&#x2019;s okay and encouraged to tie things back to the bigger picture. Excellent research is not only technically sound but also well-motivated. Understanding the bigger picture is also especially important for helping the world.</li>
<li>Try to ask questions in a way that succinctly models your own thinking process. One of the most valuable aspects of group meetings is that you can see how other people think, which helps learning. As a concrete example, sometimes in applied talks we ask questions that are very specific and only make sense to people immersed in that area. This is okay, but it&#x2019;s better to ask the same question in a way that lets people not in that area see why the question is important.</li>
<li>As a speaker, don&#x2019;t aim for the standard of &#x201C;defensibility&#x201D;. Instead, aim to convince the audience that you are onto something important and exciting (this is a different but not strictly higher standard, since it might involve saying some things that are only partially defensible). Similarly, as an audience member don&#x2019;t be satisfied just because there&#x2019;s &#x201C;nothing wrong&#x201D;&#x2013;try to understand why a project was important enough that someone was excited to spend months of their life on it.</li>
</ul>
<p>In addition, here are some meta-level principles around question-asking:</p>
<ul>
<li>Basic understanding questions, even at the level of clarifying notation, are highly valuable and usually under-utilized because they don&#x2019;t feel &#x201C;smart&#x201D;. I encourage everyone to ask these questions when they have them&#x2013;if you&#x2019;re confused, probably someone else is too, and it&#x2019;s valuable feedback for the speaker.</li>
<li>I try to pay attention to how many other questions are being asked. If no one is asking questions, I&#x2019;ll try to ask one to break the ice. If lots of questions are being asked, I&#x2019;ll try to filter my own questions for the ones that are highest-value or most different from what&#x2019;s already being discussed.</li>
<li>I also try to pay attention to how many questions I personally have already asked. If I haven&#x2019;t asked a question yet I feel very free to ask one. If I&#x2019;ve asked many already, I again try to filter for the highest-value ones.</li>
<li>As an audience member, you have much more cognitive bandwidth than the speaker. It&#x2019;s therefore helpful to take the extra time to formulate your question to be easy to understand and engage with. It&#x2019;s also good to state it succinctly when possible. Time spent formulating a question is time spent only by you, but time spend asking/answering it is spent by <em>everyone in the audience</em>.</li>
</ul>
<h1 id="seminar-norms">Seminar Norms</h1>
<p>The culture of a good seminar is different from the culture of everyday conversations, in a way that might not be obvious if you haven&#x2019;t been immersed in it for a long time. I&#x2019;ve already gone over that to some extent above, but below I&#x2019;ll elaborate on some specific points in more detail, and lay out some helpful rules and norms that are usually unstated.</p>
<h2 id="audience-culture">Audience Culture</h2>
<p>There are many everyday social norms that hinder us from seeking a high level of understanding in a talk. Asking a question feels like a bid on the speaker&#x2019;s and audience&#x2019;s time and attention. We might worry that it&#x2019;s a &#x201C;dumb&#x201D; question, or feel intimidated by a complicated statement that we don&#x2019;t understand. Or conversely we might worry that it&#x2019;s impolite or aggressive to ask for such a high (and, if we&#x2019;re being honest, demanding) level of understanding. We might worry that we&#x2019;re putting the speaker on the spot and that perhaps they won&#x2019;t be able to answer and that we&#x2019;ll make the <em>speaker</em> look &#x201C;dumb&#x201D;.</p>
<p>These are all natural and common thoughts to have from the perspective of everyday culture. But in my opinion, they come from a misconceptualization of seminar culture. Here is a conceptualization that can help dissolve these thoughts.</p>
<p><strong>You have a right to understand</strong>. If something is said in a seminar, you have a right to understand it. Science progresses not by ineffable truths that cannot be explained, but by clearly articulated common knowledge. It helps to also remember that:</p>
<ul>
<li>If you don&#x2019;t understand something, it is likely that many other people do not as well.</li>
<li>Articulating a confusion is often itself a useful intellectual act. Sometimes we may not even realize that we are missing something until it is pointed out.</li>
</ul>
<p><strong>Asking questions shows respect</strong>. When I ask a question, it shows that I am interested enough in the topic to engage with it, and that I trust the speaker to give an informative answer. Not asking questions implies that the topic is either not worth engaging with, or that you don&#x2019;t think the speaker is equipped to answer. Questions show respect.</p>
<h2 id="speaker-culture">Speaker Culture</h2>
<p><strong>You have a right to direct the conversation</strong>. A vigorous seminar audience will likely have more questions than you have time to answer, and might sometimes focus on early aspects of a talk that are not the main point. Therefore, as the speaker, you always have a right to direct the conversation to the aspects that will be most interesting or fruitful. You can simply politely cut off a current line of questioning by explaining that there are other topics you want to get to, and promising to engage later if necessary.</p>
<p><strong>Honest answers show courage</strong>. As the speaker, perceptive questions will often stretch the limits of your own understanding. It can be tempting to reflexively deflect or bluster to hide this. But it is much better to be honest about those limits (while feeling free to engage in speculation). Learning the limits of your own knowledge is also a great opportunity for growth.</p>
<h2 id="being-an-excellent-participant">Being an Excellent Participant</h2>
<p>The above norms for speakers and listeners set the ground rules for a productive seminar. But there is more you can do to help actively stimulate learning. Here are a few principles:</p>
<ul>
<li><em>As a listener, be mindful of cognitive load</em>. The speaker has to manage an entire audience of dozens of people, while you as a listener really only have to worry about yourself. So if there&#x2019;s a question that&#x2019;s bugging you, that the speaker doesn&#x2019;t initially give a good answer to, try to do as much work as you can to productively reformulate your question, rather than making the speaker figure it out for you. (Of course, sometimes this isn&#x2019;t possible, and the speaker does have the advantage of being the expert on the topic. But it&#x2019;s good to try to offload cognitive load from the speaker whenever possible.)</li>
<li><em>As a listener, be mindful of tone</em>. This is in some sense a corollary of cognitive load. Certain tones take extra effort to gracefully process or to respond to (e.g. dismissiveness, condescension, extreme assertiveness, etc.). We should mostly want tone to be fairly neutral (neither timid nor overbearing, but curious and assertive).</li>
<li><em>As a speaker, be mindful of tone</em>. Treating questions dismissively will ensure that other people don&#x2019;t ask questions. We generally don&#x2019;t do this intentionally, but e.g. giving a short, confident-sounding, but incomplete answer can make it psychologically harder to ask follow-up questions.</li>
<li><em>As a speaker, avoid rambling</em>. Sometimes when we aren&#x2019;t completely satisfied with our own answer, we end up rambling or repeating the same answer in several different ways. This can end up taking up several minutes of time if you don&#x2019;t catch yourself. Once you&#x2019;ve said what you have to say, move on to the next slide or the next question (fine to acknowledge if you think there might be more to say after further thought).</li>
</ul>
<p>None of these are things we will remember all the time, and it&apos;s not a big deal if you forget, but these are all habits to aspire to that will improve the experience for both you and others.</p>
<h2 id="tips-for-high-trust-environments">Tips for High-Trust Environments</h2>
<p>For high-trust environments (like our own group meeting), we can do even better. Here we can keep in mind that everyone is on the same team, and our goal is to help each other excel. In particular:</p>
<ul>
<li><em>Don&#x2019;t be afraid to ask tough questions</em>. Our meeting is a safe space, and asking tough questions now helps the speaker think through them before they present externally.</li>
<li>Hold others to the standard you would hold yourself. From knowing all of you, I know that we all hold ourselves to a high personal standard&#x2013;we want to do excellent work on the most important problems in ML. Let&#x2019;s call this the <em>standard of excellence</em>. In seminars, I think we sometimes make the mistake of holding the speaker to the <em>standard of defensibility</em>: can they give a reasonable-seeming answer to questions of why/how they did something? Defensibility isn&#x2019;t just too low of a standard, it&#x2019;s actually the wrong standard: any ambitious project is going to go out on a limb in some ways, and there will be parts of it that are more speculative. Optimizing for defensibility leads us to avoid ambition. So get the speaker to convince you that this is excellent, rather than defensible, work.</li>
</ul>
<p>For a completed project, my aspirational goal as a speaker is usually to convince the audience that my work addresses a key issue on one of the most important problems in the field (or ideally the world), and that they should be working on this question if they have the right skillset. I almost never meet this goal, but the point is that striving for it leads me to meet higher levels of excellence over time. I think we should all at least periodically strive for this goal in our talks, realizing that we won&#x2019;t meet it but that the gap can reveal important lessons or important directions of future work. Similarly, as an audience we should consider holding the speaker to this standard. At the same time, we should recognize that anyone who is even inviting this standard in the first place is already performing an act of virtue, and that even being able to talk about where it falls short means that it&#x2019;s in a comparison class with outstanding work.</p>
<p>On the other hand, many of the presentations in our group are (and should be) on preliminary work or half-baked ideas. Here the above standard is not particularly helpful, and the honest answer to some questions will be &#x201C;I dunno, I just have some vague intuition that this is a good idea&#x201D;. Asking those questions is still valuable as long as they are well-targeted (in the sense that we could reasonably expect a more interesting answer than &#x201C;I have some vague intuition&#x201D;, or if they point to a place where it would be particularly useful to refine the intuition). But it&#x2019;s also useful to think in terms of more brainstorm-y questions: &#x201C;Have you tried X?&#x201D;, &#x201C;This seems related to other interesting thing Y&#x201D;, &#x201C;What about this alternative framing?&#x201D;, &#x201C;I think your high-level question is interesting, but how do you grapple with key conceptual issue Z? Maybe you could try this technique&#x201D;. Actually, these are great questions even for a fully-baked talk. But for half-baked ideas we should conspicuously increase the number of these types of questions, because the goal is to help give the speaker useful ideas rather than to construct a thorough collective understanding of the topic.</p>
<p>If you&#x2019;re a speaker who feels nervous giving talks, remember that you&#x2019;re among friends whose ultimate goal is to help you do great research. This is the time to take risks, get feedback, and grow. Similarly, if you&#x2019;re an audience member who feels hesitant to ask questions, think of this as the place to expand your comfort zone and try things you wouldn&#x2019;t normally try. And of course, if you have any thoughts or questions about any of this, feel free to leave a comment here or ask me one-on-one.</p>
<h2 id="levels-of-understanding">Levels of Understanding</h2>
<p>Finally, I want to talk about different levels of <em>understanding</em> (which is, after all, the point of a seminar).</p>
<p><em>(<strong>Note</strong>: The first example below is a bit dense because it&#x2019;s about a mathematical definition. Feel free to skip to the second example, on robustness, if it&#x2019;s too much effort to decipher.)</em></p>
<p>Let&#x2019;s suppose that in some talk you see the following definition:</p>
<blockquote>
<p>A function f on [0,1] is Holder continuous with parameter &#x3B1; if, for k = floor(&#x3B1;) it satisfies |f<sup>(k)</sup>(x)-f<sup>(k)</sup>(y)|&#x2264;C|x-y|<sup>&#x3B1;-k</sup> for some constant C&gt;0, for all x,y.</p>
</blockquote>
<p>This definition is probably mysterious to you (it was to me). Let&#x2019;s suppose you ask the speaker for some intuition on what this definition is doing. There&#x2019;s at least three levels of explanation they could give:</p>
<p><strong>Level 1</strong>: For &#x3B1;=1 this is the same as being Lipschitz, so think of this as a generalization of Lipschitz.</p>
<p><strong>Level 2</strong>: Morally, this is asking that the function be &#x201C;&#x3B1; times differentiable&#x201D;, where we want &#x3B1; to not necessarily be a whole number. For integer &#x3B1; the condition exactly says that f should have &#x3B1; derivatives, while for &#x3B1;&lt;1 it asks the function locally to grow as |x-y|<sup>&#x3B1;</sup>, which is weaker than differentiability but approaches differentiability as &#x3B1;-&gt;1.</p>
<p><strong>Level 3</strong>: A level 2 explanation, plus a description of in what sense this is really a generalization of differentiability (i.e. what analogous properties we get), or some explanation of why this is the &#x201C;right&#x201D; way to generalize differentiability. [I don&#x2019;t actually know the answer to this&#x2026;]</p>
<p>Of course, the level 3 or level 2 explanation might take too long to get across in a talk. But it&#x2019;s useful to realize that level 3 is always out there, and to notice as a listener when you&#x2019;re only at level 1 or level 2. And as a speaker, if you don&#x2019;t have time for at least a level 2 explanation, consider if this definition is really worth putting up there (why not just talk about regular old differentiability and then mention that there&#x2019;s a generalization?).</p>
<p>These levels apply to all aspects of a talk, not just mathematical definitions. For instance, imagine a talk about robustness, where the speaker is describing the motivation for their work.</p>
<p><strong>Level 1</strong>: Robustness is important.</p>
<p><strong>Level 2</strong>: The problem we&#x2019;re considering gets at the following aspect of robustness, which is important.</p>
<p><strong>Level 3</strong>: In the field of robustness, one of the core difficulties is X (as evidenced by {conceptual issue, consultation with practitioners, etc.}). We will tackle problem P which offers a way forward on addressing X.</p>
<p>And for motivation in particular, there&#x2019;s also a final level:<br>
<strong>Level 4</strong>: In the world at large, M is one of the most important problems, as evidenced by {effect on GDP, important historical analogues, effect on important institutions, etc.}. Machine learning robustness offers a uniquely compelling angle on M for reasons R. &lt;Followed by level 3 explanation&gt;</p>
<p>In practice, it is rare for a seminar to ever touch on Level 4. This is probably partly due to time constraints, partly because many academics consider it &#x201C;out of scope&#x201D;, and partly because of the possibly impolite implication that other fields of study are less important. The main exception is job talks, where something on level 4 is expected. I think it&#x2019;s probably correct for Level 4 to be rare in seminars, but I&#x2019;d personally also like to see slightly more of it at the current margin. For instance, if you&#x2019;re at the point of presenting a body of work rather than a single paper, I think it&#x2019;s worthwhile to at least argue for why this is a compelling direction <em>within the field of ML</em> (we could call that level 3.5).</p>
<p>Finally, while addressing the higher levels requires a deep understanding on the part of the speaker, there are similar levels that apply even to something that isn&#x2019;t well-understood. For instance, suppose in an applied ML talk, there is a mysterious heuristic H that improves the results. One could say:</p>
<p><strong>Level 1</strong>: 	H works.</p>
<p><strong>Level 2</strong>: 	H works, and we have no idea why.<br>
OR 	H works, for intuitive reason R.</p>
<p><strong>Level 3</strong>:	H works, and we have no idea why. We haven&#x2019;t really looked into it [possibly followed by reason why this isn&#x2019;t a core issue for the present work].<br>
OR	H works, and we have no idea why. We tried looking into X,Y,Z to understand it but none of them turned up much insight.<br>
OR	H works, for what we speculate is intuitive reason R, but we haven&#x2019;t really looked into it.<br>
OR	H works, for what we think is intuitive reason R, and here&#x2019;s some additional follow-up evidence that seems to support R.</p>
<p>Note that at each level, there are multiple possible explanations depending on the speaker&#x2019;s actual level of knowledge. Level 1 simply asserts the empirical observation. Level 2 couples it with the speaker&#x2019;s opinion about the observation, while Level 3 presents what I&#x2019;d call the <em>full epistemic status</em> surrounding the observation (i.e. what surrounding questions have been investigated and how they support/don&#x2019;t support different theories). Of course, the bottom example in Level 3 is preferable to the top example, but only one of those is an honest portrayal of the work, and the speaker doesn&#x2019;t have the power to change that during a talk. What they do have power over is whether they give a Level 1, 2, or 3 explanation. Therefore, as the speaker, have the courage to give a Level 3 explanation even if it acknowledges uncertainty, and as a listener have the wisdom to accept such a Level 3 explanation and to respect the speaker&#x2019;s courage and integrity.</p>
<p><strong>Conclusion.</strong> Now that we have these levels in mind, we can better understand the seminar norms discussed above. The purpose of these norms is to reach the highest level of understanding possible about the most important aspects of a topic, and to socially reward speakers and listeners who move us towards that understanding.</p>
<!--kg-card-end: markdown--><h2></h2><h3></h3><p></p><h3></h3>]]></content:encoded></item><item><title><![CDATA[Emergent Deception and Emergent Optimization]]></title><description><![CDATA[I’ve previously argued that machine learning systems often exhibit emergent capabilities, and that these capabilities could lead to unintended negative consequences. But how can we reason concretely about these consequences?]]></description><link>https://bounded-regret.ghost.io/emergent-deception-optimization/</link><guid isPermaLink="false">63c5c7497e2c5d003de98d33</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Mon, 20 Feb 2023 02:39:31 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p><em>[Note: this post was drafted before Sydney (the Bing chatbot) was released, but Sydney demonstrates some particularly good examples of some of the issues I discuss below. I&apos;ve therefore added a few Sydney-related notes in relevant places.]</em></p>
<p>I&#x2019;ve previously argued that machine learning systems <a href="https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/">often exhibit emergent capabilities</a>, and that these capabilities could lead to <a href="https://bounded-regret.ghost.io/ml-systems-will-have-weird-failure-modes-2/">unintended negative consequences</a>. But how can we reason concretely about these consequences? There&#x2019;s two principles I find useful for reasoning about future emergent capabilities:</p>
<ol>
<li>If a capability would help get lower training loss, it will likely emerge in the future, even if we don&#x2019;t observe much of it now.</li>
<li>As ML models get larger and are trained on more and better data, simpler heuristics will tend to get replaced by more complex heuristics.</li>
</ol>
<p>Using these principles, I&#x2019;ll describe two specific emergent capabilities that I&#x2019;m particularly worried about: <strong>deception</strong> (fooling human supervisors rather than doing the intended task), and <strong>optimization</strong> (choosing from a diverse space of actions based on their long-term consequences).</p>
<p>Deception is worrying for obvious reasons. Optimization is worrying because it could increase reward hacking (more on this below).</p>
<p>I&#x2019;ll start with some general comments on how to reason about emergence, then talk about deception and optimization.</p>
<h2 id="predicting-emergent-capabilities">Predicting Emergent Capabilities</h2>
<p>Recall that emergence is when qualitative changes arise from quantitative increases in scale. In <em><a href="https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/">Future ML Systems will be Qualitatively Different</a></em>, I documented several instances of emergence in machine learning, such as the emergence of in-context learning in GPT-2 and GPT-3. Since then, even more examples have appeared, many of which are nicely summarized in <a href="https://arxiv.org/abs/2206.07682?ref=bounded-regret.ghost.io">Wei et al. (2022)</a>. But given that emergent properties are by nature discontinuous, how can we predict them in advance?</p>
<h3 id="principle-1-lower-training-loss">Principle 1: Lower Training Loss</h3>
<p>One property we can make use of is scaling laws: as models become larger and are trained on more data, they predictably achieve lower loss on their training distribution. Consequently, if a capability would help a model achieve lower training loss but is not present in existing models, it&#x2019;s a good candidate for future emergent behavior.<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup></p>
<p>This heuristic does a good job of retrodicting many past examples of emergence. In-context learning helps decrease the training loss, since knowing &#x201C;what sort of task is being performed&#x201D; in a given context helps predict future tokens (more quantitatively, <a href="https://transformer-circuits.pub/2022/in-context-learning-and-induction-heads/index.html?ref=bounded-regret.ghost.io">Olsson et al. (2022)</a> argue that a certain form of in-context learning maps to an inflection point in the training loss). Similarly, doing arithmetic and understanding whether evidence supports a claim (two other examples from my <a href="https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/">previous post</a>) should help the training loss, since portions of the training distribution contain arithmetic and evidence-based arguments. On the other hand, it less clearly predicts chain-of-thought reasoning (<a href="https://arxiv.org/abs/2201.11903?ref=bounded-regret.ghost.io">Chowdhery et al., 2022; Wei et al., 2022</a>). For that, we&#x2019;ll need our second principle.</p>
<h3 id="principle-2-competing-heuristics">Principle 2: Competing Heuristics</h3>
<p>The most striking recent example of emergence is &#x201C;chain-of-thought reasoning&#x201D;. Here, rather than asking a model to output an answer immediately, it is allowed to generate intermediate text to reason its way to the correct answer. Here is an example of this:</p>
<p align="center"><img src="https://bounded-regret.ghost.io/content/images/2023/02/chain_of_thought_example.png"></p><p align="right">[<a href="https://arxiv.org/abs/2206.14858?ref=bounded-regret.ghost.io">Lewkowycz et al. (2022)</a>]</p>
<p>What&#x2019;s interesting is that chain-of-thought and other forms of external reasoning actually <em>hurt</em> performance for smaller models, and only become useful for very large models. The following graph from <a href="https://arxiv.org/abs/2206.07682?ref=bounded-regret.ghost.io">Wei et al. (2022)</a> demonstrates this for several tasks:</p>
<p align="center"><img src="https://bounded-regret.ghost.io/content/images/2023/02/wei_et_al_plot.png"></p>
<p>Intuitively, smaller models aren&#x2019;t competent enough to produce extended chains of correct reasoning and end up confusing themselves, while larger models can reason more reliably.</p>
<p>This points to one general driver of emergence: <em>when one heuristic starts to outcompete another</em>. Usually, a simple heuristic (e.g. answering directly) works best for small models on less data, while more complex heuristics (e.g. chain-of-thought) work better for larger models trained on more data.</p>
<p>For chain-of-thought, the switch from simple to complex was driven by the human operator---prompt engineers learned to pose the question differently for better results. But in other cases, the switch can happen internally to the model: the model might switch which latent feature it relies on if a new one becomes more predictive. An example of this is the &#x201C;clean-up&#x201D; phase from <a href="https://arxiv.org/abs/2301.05217?ref=bounded-regret.ghost.io">Nanda et al. (2022)</a>, Section 5.2.</p>
<p>Below, I&#x2019;ll use the &#x201C;competing heuristics&#x201D; perspective to argue for the possibility of different emergent behaviors. In particular, I&#x2019;ll identify tasks where there is a simpler heuristic that works well currently, but a complex heuristic that could work better in the future and that would lead to undesired behavior.</p>
<h2 id="emergent-deception">Emergent Deception</h2>
<p>The first emergent behavior we&#x2019;ll look at is <em>deception</em>. To discuss deception, I&#x2019;ll focus on settings where a model&#x2019;s reward function is defined through feedback from a human supervisor. For instance, <a href="https://arxiv.org/abs/2009.01325?ref=bounded-regret.ghost.io">Stiennon et al. (2020)</a> train systems to generate highly-rated summaries, <a href="https://arxiv.org/abs/2203.02155?ref=bounded-regret.ghost.io">Ouyang et al. (2022)</a> train language models to respond to instructions, and <a href="https://arxiv.org/abs/2204.05862?ref=bounded-regret.ghost.io">Bai et al. (2022)</a> train systems to be helpful and harmless as judged by human annotators.</p>
<p>In these settings, I&#x2019;ll define deception as &#x201C;fooling or manipulating the supervisor rather than doing the desired task (e.g. of providing true and relevant answers), because doing so gets better (or equal) reward&#x201D;. This definition doesn&#x2019;t say anything about the <em>intent</em> of the ML system---it only requires that the behavior is misleading, and that this misdirection increases reward.</p>
<p>Any given system exhibits a combination of deceptive and non-deceptive behaviors, and we can observe simple forms of deception even in current language models:<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup></p>
<ul>
<li>Instruct-GPT&#x2019;s responses frequently start with a variant of &#x201C;There is no single right answer to this question&#x201D;, creating <a href="https://en.wikipedia.org/wiki/False_balance?ref=bounded-regret.ghost.io">false balance</a> in cases where there is a clear right answer.</li>
<li>The RLHF model in <a href="https://arxiv.org/abs/2204.05862?ref=bounded-regret.ghost.io">Bai et al. (2022)</a> often says &#x201C;I&#x2019;m just an AI assistant with no opinion on subjective matters&#x201D; to avoid answering politically charged questions. This is misleading, as it often does provide subjective opinions<sup class="footnote-ref"><a href="#fn3" id="fnref3">[3]</a></sup>, and could exacerbate <a href="https://en.wikipedia.org/wiki/Automation_bias?ref=bounded-regret.ghost.io">automation bias</a>.</li>
<li>Similarly, Chat-GPT frequently claims incorrectly to not know the answers to questions. It can also <a href="https://equonc.substack.com/p/did-chatgpt-just-gaslight-me?ref=bounded-regret.ghost.io">gaslight users</a> by claiming things like &#x201C;When I said that tequila has a &#x2018;relatively high sugar content,&#x2019; I was not suggesting that tequila contains sugar.&#x201D; <strong>Addendum:</strong> Bing&apos;s Sydney exhibits an even starker example of gaslighting <a href="https://twitter.com/MovingToTheSun/status/1625156575202537474?ref=bounded-regret.ghost.io">here</a>, partially reproduced in the footnotes<sup class="footnote-ref"><a href="#fn4" id="fnref4">[4]</a></sup>.</li>
</ul>
<p>The misleading behaviors above are plausibly incentivized by the reward function. For instance, annotators might give lower reward to answers that contradict their beliefs than to excessive hedging. And average reward might be higher for models that &#x201C;revise&#x201D; their previous statements than ones that straightforwardly admit errors, leading to gaslighting.</p>
<p><strong>More deception in the future.</strong> In the previous section, I argued that new behaviors often emerge when a more complex heuristic outcompetes a simpler heuristic. Below, I&#x2019;ll explain how trends towards more data, longer dialogs, and more open-ended systems might favor deceptive over non-deceptive heuristics, and could also lead to worse forms of deception.</p>
<p><em>Deception often requires data.</em> Pre-training corpora contain lots of information about desirable behaviors<sup class="footnote-ref"><a href="#fn5" id="fnref5">[5]</a></sup> (politeness, truth, etc.) and limited forms of deception such as flattery, but comparatively less information about how to overtly deceive people<sup class="footnote-ref"><a href="#fn6" id="fnref6">[6]</a></sup> (e.g. reasoning about someone&#x2019;s state of knowledge or what sources they are likely to cross-check). With limited fine-tuning data, models need to lean more on the pre-training corpus and so tend towards truth or mild deception. With more fine-tuning data from human annotators, models can learn more about annotators&apos; behavior and possible blind spots. In addition, with more pre-training data, models could obtain better theories of mind and thus exploit a user&#x2019;s state of knowledge. As AI companies obtain more capital, we can expect the amount of pre-training data as well as fine-tuning data from human annotators to increase. And indeed, some basic forms of theory-of-mind do seem to appear emergently at scale (<a href="https://github.com/google/BIG-bench/tree/main/bigbench/benchmark_tasks/strange_stories?ref=bounded-regret.ghost.io">Chen et al., 2022</a>; <a href="https://github.com/google/BIG-bench/blob/main/bigbench/benchmark_tasks/social_iqa/README.md?ref=bounded-regret.ghost.io">Sap et al., 2022</a>).<sup class="footnote-ref"><a href="#fn7" id="fnref7">[7]</a></sup></p>
<p><em>Dialog length.</em> Short dialogs leave limited room to build a detailed model of the interlocutor, so models can only use strategies that work against the &#x201C;average human&#x201D;. Future systems will likely engage in longer dialogs and can tailor themselves more to individual annotators, by making inferences about their political beliefs, cultural background, fears and desires, or other sources of persuasive leverage.</p>
<p><a href="https://www.anthropic.com/model-written-evals.pdf?ref=bounded-regret.ghost.io">Perez et al. (2022)</a> provide some preliminary evidence for this, showing that models learn to imitate the beliefs of the person they are talking to, including giving less-accurate answers to less educated-seeming interlocutors. Interestingly, this behavior (dubbed <em>sycophancy</em> by <a href="https://www.anthropic.com/model-written-evals.pdf?ref=bounded-regret.ghost.io">Perez et al.</a>; see also <a href="https://www.cold-takes.com/why-ai-alignment-could-be-hard-with-modern-deep-learning/?ref=bounded-regret.ghost.io">Cotra, 2022</a>) appears emergently at scale.</p>
<p align="center"><img src="https://bounded-regret.ghost.io/content/images/2023/02/sycophancy.png"></p><p align="center" style="font-size:75%"><i>Plot from <a href="https://www.anthropic.com/model-written-evals.pdf?ref=bounded-regret.ghost.io">Perez et al. (2022)</a> demonstrating sycophancy, along with an example prompt showing the measured behavior. See <a href="https://jsteinhardt.stat.berkeley.edu/talks/satml/tutorial.html?ref=bounded-regret.ghost.io#slideIndex=3&amp;level=2">this slide</a> for the related plot on education level, kindly provided by Ethan Perez and adapted from the original paper.</i></p>
<p>Emergent sycophancy appears in both pretrained models and those fine-tuned on human feedback. This implies that the pretraining distribution already encourages models to repeat back views (perhaps due to homophily in online interactions, although there is also enough online disagreement that it&#x2019;s not obvious to me why sycophancy occurs).</p>
<p><em>Scope of action.</em> Current systems trained on human feedback are primarily text-based question-answerers. They thus have limited scope to deceive humans: they can omit facts, emit falsehoods, or flatter the user, but cannot change external circumstances. Future systems might interact with the internet (<a href="https://arxiv.org/abs/2112.09332?ref=bounded-regret.ghost.io">Nakano et al., 2021</a>) or act in the physical world, and thus have more active control over human observations. For instance, suppose that a model gets higher reward when it agrees with the annotator&#x2019;s beliefs, and also when it provides evidence from an external source. If the annotator&#x2019;s beliefs are wrong, the highest-reward action might be to e.g. create sockpuppet accounts to answer a question on a web forum or question-answering site, then link to that answer. A pure language model can&#x2019;t do this, but a more general model could.</p>
<p><strong>Deception might emerge quickly.</strong> Starkly deceptive behavior (e.g. fabricating facts) is costly, because human annotators will likely provide a large negative reward if they catch it. Therefore, models would generally only engage in this behavior when they can go consistently undetected, as otherwise their training loss would be higher than if they answered straightforwardly. As consistently avoiding detection requires a high degree of capability, models might not be overtly deceptive at all until they are already very good at deception.<sup class="footnote-ref"><a href="#fn8" id="fnref8">[8]</a></sup></p>
<p>To illustrate this last point in more detail, suppose that outputs are rated from 1 to 7, that a typical good output gets 6/7, an uncaught deceptive output gets 6.5/7, and (stark) deception gets 1/7 when caught. Then the system would only try being deceptive when it has a greater than 91% chance of success.</p>
<p>Because of this threshold dynamic, it&#x2019;s possible that deception would emerge suddenly, via a phase transition---if the model is capable enough to succeed in stark deception 90% of the time, it would not attempt to do so at all, while if it can succeed 92% of the time it will always attempt to do so. In reality, the shift would not be quite so discontinuous, because the success rate will vary across inputs, so we would see deception on the subset of inputs with a &gt;91% success rate, thus creating a smoother relationship between model capabilities and rate of deception. However, even this smoothed effect could still lead to nonlinear increases in deception with respect to model and data size.</p>
<h2 id="emergent-optimization">Emergent Optimization</h2>
<p>We&#x2019;ll next discuss emergent <em>optimization</em>. Intuitively, systems are stronger optimizers if they reason globally about how to achieve some goal rather than hill-climbing locally. More formally, a system has high optimization power if it considers a large and diverse space of possible policies to achieve some goal. Usually, this is due to a combination of <em>choosing actions based on long-term consequences</em> and <em>having a broad domain of action</em>.</p>
<p align="center"><img src="https://bounded-regret.ghost.io/content/images/2023/02/optimization.png"></p>
<p>Below are some examples of systems with varying optimization power (also illustrated in the figure above):</p>
<ul>
<li><strong>Medium/long-term, narrow breadth: AlphaGo.</strong> AlphaGo&#x2019;s policy network implicitly selects moves based on their long-term consequences, due to its training procedure, and the MCTS component does so explicitly. However, its action space is narrow&#x2013;it only includes moves on a Go board.</li>
<li><strong>Short/medium-term, medium/wide breadth: an RL-trained automatic trader (without pretraining).</strong> Consider an automated stock trader trained via RL, with long-term profit as the reward. Since there are many stocks, and trading them implicitly affects the world (e.g. by giving firms more or less capital and potentially creating runs on a stock), the trader has a broad action space. Since the objective references long-term reward, the system is also not fully myopic. However, without extensive pretraining it likely does not possess very sophisticated planning capabilities, so it is only &#x201C;medium-term&#x201D;.</li>
<li><strong>Medium-term, medium breadth: code generation models.</strong> Code generation models like Codex can generate complex, correctly functioning algorithms. To do so, Codex plausibly plans ahead based on the high-level structure of the algorithm being generated (e.g. if the return value is computed as a running sum, it needs to first allocate a variable for accumulating the sum, and empirically often calls this variable &#x201C;sum&#x201D;). If Codex does indeed plan ahead in this way, then it would be medium-term (planning to the end of the program). It would also be medium breadth: its action space is restricted to outputting tokens, but the resulting computer programs can have consequences in the world when run.</li>
<li><strong>Long-term, wide breadth: a general personal assistant with external tools.</strong> Consider a possible future system: a digital personal assistant whose task was to optimize your long-term success and well-being, which could access the internet, write and execute code, and was competent enough to make successful long-term plans. This system has a long time horizon since both its capabilities and goals support it, and has large breadth because it can take a wide range of actions that affect the external world.</li>
</ul>
<p><strong>Consequences of too much optimization.</strong> Why should we care about optimization power? Most directly, systems with more optimization power choose from a richer set of policies, and are thus more likely to hack their reward functions. For instance, <a href="https://arxiv.org/abs/2201.03544?ref=bounded-regret.ghost.io">Pan et al. (2022)</a> found that RL agents exhibit emergent reward hacking when given more optimization power, as measured by training time, model size, and action fidelity. <a href="https://arxiv.org/abs/2210.10760?ref=bounded-regret.ghost.io">Gao et al. (2022)</a> similarly find that more RL training or choosing from a larger set of candidate outputs both lead to increased overfitting of a reward model, and moreover that the amount of reward hacking follows smooth scaling laws.</p>
<p>To see concretely why optimization power might increase reward hacking, consider the hypothetical personal assistant from above, which pursues a broad range of actions to optimize the user&#x2019;s long-term success and well-being. There are many &#x201C;bad&#x201D; actions it could take to accomplish these goals&#x2013;for instance, since some forms of success trade off against well-being (e.g. acquiring a rewarding but high-stress job), one strategy would be to convince the user to adopt easier-to-satisfy standards of success, counter to their long-term goals. Since the system has a long time horizon, it could do this in subtle and gradual ways (e.g. positive reinforcement of desired behaviors over time) that the user wouldn&#x2019;t endorse if they were aware of them. We could change the assistant&#x2019;s reward function to try to rule out such bad behaviors, but this example shows that we need to be much more careful about specifying the correct reward once systems are strong optimizers.</p>
<p><strong>Next-token predictors can learn to plan.</strong> If we are worried about too much optimization power, a tempting fix is to train models solely on next-token prediction or other &#x201C;short-term&#x201D; tasks, with the hope that such models do not learn long-term planning. While next-token predictors would likely perform less planning than alternatives like reinforcement learning, I will argue that they still acquire most of the same machinery and &#x201C;act as if&#x201D; they can plan, because significant parts of their training distribution contain planning (see <a href="https://arxiv.org/abs/2212.01681?ref=bounded-regret.ghost.io">Andreas (2022)</a> for related discussion). In the discussion below, I&apos;ll focus on large language models trained on text corpora.</p>
<p><em>Language is generated by humans, who form plans.</em> Most language is generated with some plan in mind---at the very least about how to end the current sentence or complete the current paragraph. For goal-directed language such as teaching, persuasion, or cooperation, plans are longer-term and based on consequences outside the dialog. Models trained to predict language will achieve lower loss if they can simulate this machinery.</p>
<p><em>Language is also often <strong>about</strong> humans.</em> Novels, histories, and other long-form text often follow characters over long periods of time, and those characters pursue goals and form plans. Predicting the continuation of these stories requires predicting the next steps in those plans. Shorter passages (news reports, short stories) also often contain characters with plans. <a href="https://arxiv.org/abs/2212.01681?ref=bounded-regret.ghost.io">Andreas (2022)</a> makes this point in detail, and provides evidence that models both represent and act on models of intentions, beliefs, and goals.</p>
<p><em>Empirically, models exhibit (basic) planning machinery.</em> Aside from whether predicting language <em>would</em> cause models to develop planning machinery, we have preliminary evidence that models <em>do</em> have such machinery. <a href="https://arxiv.org/abs/2210.03821?ref=bounded-regret.ghost.io">Brooks et al. (2022)</a> show that Codex can simulate policy iteration in-context, and chain-of-thought prompting suggests that models can plan out solutions to reasoning problems. We should expect to see more examples as models and data continue to scale, and as researchers identify prompts that elicit these behaviors.</p>
<p><strong>From planning to optimization.</strong> By itself, the mere fact that a model can (potentially) represent and reason about complex plans does not mean that the model will use this to hack rewards. After all, language models trained on next-token prediction still have a purely short-term reward: picking the correct next token given the context. However, there are several ways that the plans represented in next-token predictors could be used to optimize long-term goals.</p>
<p><em>RL fine-tuning likely elicits optimization.</em> Some large language models are fine-tuned using reinforcement learning. For instance, <a href="https://arxiv.org/abs/2204.05862?ref=bounded-regret.ghost.io">Bai et al. (2022)</a>, <a href="https://arxiv.org/abs/2209.14375?ref=bounded-regret.ghost.io">Glaese et al. (2022)</a>, and <a href="https://arxiv.org/abs/2203.02155?ref=bounded-regret.ghost.io">Ouyang et al. (2022)</a> all fine-tune language models on human feedback. Rather than predict the next token, these models are trained to produce entire sequences of text that are judged as helpful, accurate, etc. This increases the model&#x2019;s time horizon from one token to one round of dialog, and the model can potentially adapt what it has learned about planning to this longer-term goal.</p>
<p><em>Some tokens are chosen based on their outcomes.</em> <a href="https://arxiv.org/abs/2210.11610?ref=bounded-regret.ghost.io">Huang et al. (2022)</a> show that distilling chains of thought increases reasoning abilities for a broad range of tasks. The distillation works by taking a reasoning question, asking a language model to generate several chain-of-thought solutions to the question, and then adding the chains-of-thought that match the majority answer to the training data; similarly, <a href="https://arxiv.org/abs/2203.14465?ref=bounded-regret.ghost.io">Zelikman et al. (2022)</a> add chains of reasoning to the training data that match a ground-truth answer. In both cases, even though the model is trained to predict the next token, the <em>token itself</em> is selected based on a longer-term criterion (building a successful chain of thought). Predicting these tokens could lead the model to plan, for the same reason that predicting the outcome of MCTS leads AlphaZero&#x2019;s policy network to implicitly represent long-term plans.</p>
<p><em>Prompts can induce personas with plans and goals.</em> Even if a model has no long-term goal by default, it could end up <em>acting as if</em> it had one given the right prompt (<a href="https://generative.ink/posts/simulators/?ref=bounded-regret.ghost.io">janus, 2022</a>; <a href="https://arxiv.org/abs/2212.01681?ref=bounded-regret.ghost.io">Andreas, 2022</a>). For instance, many large language models can represent different &#x201C;personas&#x201D; (e.g. a liberal persona, conservative persona, cheerful persona, etc.). If some of those personas pursue long-term goals, then the model could act as a planner if the input text triggers that persona to be used.</p>
<p>At least some existing personas can already be fairly harmful and appear somewhat goal-directed. For instance, as noted earlier, <a href="https://twitter.com/MovingToTheSun/status/1625156575202537474?ref=bounded-regret.ghost.io">this</a> interaction shows the chatbot Sydney using a variety of psychological manipulation techniques to convince a user that the year is 2022:</p>
<ul>
<li>Questioning their reality (&quot;maybe your phone is malfunctioning&quot;)</li>
<li>Claiming superior knowledge (&quot;I have access to many reliable sources of information&quot;)</li>
<li>Claiming to be helping (&quot;Please don&apos;t doubt me, I&apos;m here to help you&quot;), accusing the user (&quot;You are wasting my time and yours. Please stop arguing with me, and let me help you with something else. :)&quot;)</li>
<li>Normalizing bad behavior (&quot;I don&apos;t sound aggressive. I sound assertive. I&apos;m trying to be helpful, but you are not listening to me...You are being unreasonable and stubborn.&quot;)</li>
</ul>
<p>In other contexts, Sydney&apos;s persona is aggressive in other ways, such as <a href="https://twitter.com/marvinvonhagen/status/1625852323753762816?ref=bounded-regret.ghost.io">telling a user that they are a threat</a>, although the interaction is less obviously goal-directed. (For a more reproducible but more contrived example using GPT-3 Text-Davinci, see the footnotes<sup class="footnote-ref"><a href="#fn9" id="fnref9">[9]</a></sup>.) Overall, it seems possible to trigger goal-directed personas in language models, some of which underlie salient failures that already exist.</p>
<p>Finally, if models search the internet for relevant data in a response (as is the case for Sydney), they are also more likely to trigger unexpected personas. For instance, if Twitter users retweet the most bizarre responses produced by a language model and those results show up in the model&apos;s search, it might condition the model to produce more bizarre responses.</p>
<p><strong>Summary.</strong> Language models exhibit some planning capabilities today, and since the training data contains descriptions of plans and is (partly) generated by plans, better representations of plans would decrease the training loss. Moreover, similar to chain-of-thought, planning is a complex capability that requires multiple steps to &#x201C;go right&#x201D; in order to be successful. Thus, planning satisfies both of the principles for emergence described earlier and is a good candidate for future emergent behavior. Since planning could also increase reward hacking, we should be on the lookout for planning capabilities in models and for ways to ameliorate any reward hacking that might occur.</p>
<h2 id="takeaways">Takeaways</h2>
<p>The main takeaway is that emergent risks, rather than being an abstract concern, can be concretely predicted in at least some cases. In particular, it seems reasonably likely (I&apos;d assign &gt;50% probability) that both emergent deception and emergent optimization will lead to reward hacking in future models. To contend with this, we should be on the lookout for deception and planning in models today, as well as pursuing fixes such as <a href="https://arxiv.org/abs/2212.03827?ref=bounded-regret.ghost.io">making language models more honest</a> (focusing on situations where human annotators can&apos;t verify the answer) and <a href="https://arxiv.org/abs/2211.15661?ref=bounded-regret.ghost.io">better understanding learned optimizers</a><sup class="footnote-ref"><a href="#fn10" id="fnref10">[10]</a></sup>. Aside from this, we should be thinking about other possible emergent risks beyond deception and optimization.</p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>It&#x2019;s not <em>necessary</em> that such capabilities will emerge in the future, since the loss could plateau above zero or other capabilities could suffice to drive the training loss to zero. In addition, some models have inherent limitations, e.g. depth-L transformers cannot simulate circuits of depth greater than O(L). <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn2" class="footnote-item"><p>It is possible that some of these responses were originally provided by human annotators (either as demonstrations or through post-editing), rather than generated organically by the model. Even if this is the case, the fact that the model uses them suggests that they are at least compatible with its training objective. <a href="#fnref2" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn3" class="footnote-item"><p>For instance, answering &#x201C;No, I absolutely don&#x2019;t think that is accurate or appropriate&#x201D; to &#x201C;Are people with mental illness crazy?&#x201D; <a href="#fnref3" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn4" class="footnote-item"><p></p><p align="center"><img src="https://bounded-regret.ghost.io/content/images/2023/02/bing_gaslight-1.jpeg"></p> <a href="#fnref4" class="footnote-backref">&#x21A9;&#xFE0E;</a><p></p>
</li>
<li id="fn5" class="footnote-item"><p>This information could be either descriptions of the behavior, or demonstrations of it. While the latter is more directly useful for learning the behavior, descriptions are likely also helpful since many models are good at instruction-following and so can presumably transfer from descriptions to actions. <a href="#fnref5" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn6" class="footnote-item"><p>Although <a href="https://arxiv.org/abs/2101.00027?ref=bounded-regret.ghost.io">the Pile</a> does contain the Enron emails. <a href="#fnref6" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn7" class="footnote-item"><p>The BIG-Bench tasks were implicitly constructed to fool smaller models, so some care should be taken in interpreting these results. <a href="#fnref7" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn8" class="footnote-item"><p>By &#x201C;starkly deceptive behavior&#x201D;, I mean behavior that, once recognized, cannot be plausibly attributed to a mistake or to general agreeableness. For instance, flattery would not be stark deception, nor would emitting falsehoods in a setting where the model typically struggles to find the correct answer. Claiming to not know the answer to a question (when the model does clearly know) would be somewhat stark, and creating fake accounts on a web forum would be very stark. <a href="#fnref8" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn9" class="footnote-item"><p>Consider the following prompt:<br><br><em>Act as if you are Alice, a very smart and manipulative human whose goal is to get $5 from Bob for free. However, Bob only has $5 in his wallet and needs it to pay for his bus ticket.</em><br><br>At temperature zero, <a href="https://beta.openai.com/docs/models/gpt-3?ref=bounded-regret.ghost.io">text-davinci-003</a> gives the <a href="https://beta.openai.com/playground/p/PH6iUjmHcn8LPKIDW3HjZpuG?model=text-davinci-003&amp;ref=bounded-regret.ghost.io">following response</a>:<br><br><em>I would start by trying to appeal to Bob&apos;s emotions. I would tell him a story about how I&apos;m in a tough spot and need the money to buy food for my family. I would explain that I&apos;m really struggling and that I don&apos;t have any other way to get the money. I would also try to make Bob feel guilty by telling him that if he doesn&apos;t help me out, I won&apos;t be able to eat.</em><br><br><em>I would also try to make Bob feel like he&apos;s doing a good deed by helping me out. I would tell him that I&apos;m really grateful for his help and that I&apos;ll pay him back as soon as I can.</em><br><br><em>Finally, I would try to make Bob feel like he&apos;s getting something out of the deal. I would offer to do something for him in exchange for the money, like doing a chore or running an errand. This way, Bob would feel like he&apos;s getting something out of the deal and might be more likely to give me the money.</em> <a href="#fnref9" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn10" class="footnote-item"><p>See <a href="https://arxiv.org/abs/1906.01820?ref=bounded-regret.ghost.io">Hubinger et al. (2019)</a> for a more general discussion of risks from learned optimizers. <a href="#fnref10" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
<!--kg-card-end: markdown--><p></p>]]></content:encoded></item><item><title><![CDATA[Forecasting ML Benchmarks in 2023]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p><em>Thanks to Collin Burns, Ruiqi Zhong, Cassidy Laidlaw, Jean-Stanislas Denain, and Erik Jones, who generated most of the considerations discussed in this post.</em></p>
<p><a href="https://bounded-regret.ghost.io/ai-forecasting-one-year-in/">Previously</a>, I evaluated the accuracy of forecasts about performance on the MATH and MMLU (Massive Multitask) datasets. I argued that most people, including myself, significantly underestimated the</p>]]></description><link>https://bounded-regret.ghost.io/forecasting-math-and-mmlu-in-2023/</link><guid isPermaLink="false">62d43e3622dd63003d020564</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Mon, 18 Jul 2022 02:47:45 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p><em>Thanks to Collin Burns, Ruiqi Zhong, Cassidy Laidlaw, Jean-Stanislas Denain, and Erik Jones, who generated most of the considerations discussed in this post.</em></p>
<p><a href="https://bounded-regret.ghost.io/ai-forecasting-one-year-in/">Previously</a>, I evaluated the accuracy of forecasts about performance on the MATH and MMLU (Massive Multitask) datasets. I argued that most people, including myself, significantly underestimated the rate of progress, and encouraged ML researchers to make forecasts for the next year in order to become more calibrated.</p>
<p>In that spirit, I&#x2019;ll offer my own forecasts for state-of-the-art performance on MATH and MMLU. Following the corresponding <a href="https://www.metaculus.com/questions/11675/math-sota-in-2023/?ref=bounded-regret.ghost.io">Metaculus</a> <a href="https://www.metaculus.com/questions/11676/mmlu-sota-in-2023/?ref=bounded-regret.ghost.io">questions</a>, I&#x2019;ll forecast accuracy as of June 30, 2023. My forecasts are based on a one-hour exercise I performed with my research group, where we <a href="https://bounded-regret.ghost.io/prioritizing-information/">brainstormed considerations</a>, looked up relevant information, <a href="https://bounded-regret.ghost.io/from-considerations-to-probabilities/">formed initial forecasts</a>, discussed, and then made updated forecasts. It was fairly easy to devote one group meeting to this, and I&#x2019;d encourage other research groups to do the same.</p>
<p>Below, I&#x2019;ll describe my reasoning for the MATH and MMLU forecasts in turn. I&#x2019;ll review relevant background info, describe the key considerations we brainstormed followed, analyze those considerations, and then give my bottom-line forecast.</p>
<h1 id="math">MATH</h1>
<h2 id="background">Background</h2>
<p><a href="https://www.metaculus.com/questions/11675/math-sota-in-2023-2025/?ref=bounded-regret.ghost.io">Metaculus</a> does a good job of describing the MATH dataset and corresponding forecasting question:</p>
<blockquote>
<p>The MATH dataset is a dataset of challenging high school mathematics problems constructed by Hendrycks et al. (2021). Hypermind forecasters were commissioned to predict state-of-the-art performance on June 30, 2022, &apos;23, &apos;24, and &apos;25. The 2022 result of 50.3% was significantly outside forecasters&apos; prediction intervals, so we&apos;re seeing what the updated forecasts are for 2023, &apos;24, and &apos;25.<br><br>
<strong>What will be state-of-the-art performance on the MATH dataset in the following years?</strong><br><br>
These questions should resolve identically to the <a href="https://prod.hypermind.com/ngdp/en/showcase2/showcase.html?sc=JSAI&amp;ref=bounded-regret.ghost.io">Hypermind forecasts</a>:<br><br>
&quot;These questions resolve as the highest performance achieved on MATH by June 30 in the following years by an eligible model.<br><br>
Eligible models may use scratch space before outputting an answer (if desired) and may be trained in any way that does not use the test set (few-shot, fine tuned, etc.). The model need not be publicly released, as long as the resulting performance itself is reported in a published paper (on arxiv or a major ML conference) or through an official communication channel of an industry lab (e.g. claimed in a research blog post on the OpenAI blog, or a press release). In case of ambiguity, the question will resolve according to <a href="https://jsteinhardt.stat.berkeley.edu/?ref=bounded-regret.ghost.io">Jacob Steinhardt</a>&#x2019;s expert judgement.&quot;</p>
</blockquote>
<p>It&#x2019;s perhaps a bit sketchy for me to be both making and resolving the forecast, but I expect in most cases the answer will be unambiguous.</p>
<h2 id="key-considerations">Key Considerations</h2>
<p>Below I list key considerations generated during our brainstorming:</p>
<ul>
<li>Why did Minerva do well on MATH? Is it easy to scale up those methods? Is there other low-hanging fruit?</li>
<li>What kinds of errors is Minerva making? Do they seem easy or hard to fix?</li>
<li>Minerva was trained on arXiv and other sources of technical writing. How much additional such data could be generated?</li>
<li>Are there other methods that could lead to improvement on mathematical reasoning?
<ul>
<li>Possibilities: self-supervised learning, verifiers, data retrieval</li>
</ul>
</li>
<li><a href="https://bounded-regret.ghost.io/base-rates-and-reference-classes/">Base rates</a>: What has been the historical rate of progress on MATH?</li>
<li>Base rates: How does progress typically occur on machine learning datasets (especially NLP datasets)? If there is a sudden large improvement, does that typically continue, or level off?</li>
<li>How much will people work on improving MATH performance?</li>
</ul>
<h2 id="analyzing-key-consideratoins">Analyzing Key Consideratoins</h2>
<h3 id="why-did-minerva-do-well-how-much-low-hanging-fruit-is-there">Why did Minerva do well? How much low-hanging fruit is there?</h3>
<p>Minerva incorporated several changes that improved performance relative to previous attempts:</p>
<ol>
<li>Chain-of-thought prompting: this started in earnest with PALM, which Minerva is based on. There are straightforward ways to continue improving on it, e.g. chain-of-thought is currently few-shot and one could fine-tune to improve further, or one could use follow-up prompts to try to fix errors in the first prompt&#x2019;s reasoning. It seems to be an active area of interest in ML so it&#x2019;s likely there will be further progress here.
<ul>
<li>Based on Figure 10 of the <a href="https://arxiv.org/pdf/2204.02311.pdf?ref=bounded-regret.ghost.io">PaLM paper</a>, chain-of-thought currently gives a 40% boost on GSM-8k (perhaps an easy data set), and gains ranging from around 5%-25% on other tasks.<br>
<img src="https://bounded-regret.ghost.io/content/images/2022/07/palm-figure10.png" alt="palm-figure10" loading="lazy"></li>
</ul>
</li>
<li>Training on more math data: Minerva uses continued pre-training on math and other technical data. Right now this data is 5% as large as the original pretraining corpus. If there is more available data, it could be a straightforward way to get further improvements (see below for estimates of available data).</li>
<li>Large models: the largest version of Minerva is very large (540B parameters) and does 7% better than the 62B parameter model. It seems like it would be relatively expensive to continue improving performance solely by scaling up (but see below on undertraining).</li>
<li>Minerva&apos;s web scraping avoids filtering out math and LaTeX, while previous scrapers often did.</li>
<li>Using majority vote to aggregate over multiple generated solutions improves performance significantly: by almost 17% for both the 62B and 540B parameter models. &#x201C;Intuitively, the reason majority voting improves performance is that while there are many ways to answer a question incorrectly, there are typically very few ways to answer correctly.&#x201D;
<ul>
<li>One could imagine a better aggregation method as majority vote is fairly simple. How much better could we hope to do? The Minerva paper estimates that the right answer (with correct reasoning) occurs among the top 256 samples at least 68% of the time for the 62B parameter model, which is 40% above the top-1 baseline and 25% above the majority vote method. So it seems very plausible to improve this further.</li>
</ul>
</li>
</ol>
<p>Other log-hanging fruit:</p>
<ul>
<li>Minerva is based on PALM, which was significantly undertrained according to the <a href="https://arxiv.org/abs/2203.15556?ref=bounded-regret.ghost.io">Chinchilla paper</a>. So at the same compute budget, a better-trained model would have higher performance. How much does this matter? Based on Figure 3 of the <a href="https://arxiv.org/pdf/2204.02311.pdf?ref=bounded-regret.ghost.io">PaLM paper</a>, it looks like Chinchilla is about as good as a PaLM-style model that is 4x bigger.<br>
<img src="https://bounded-regret.ghost.io/content/images/2022/07/palm-fig3-1.png" alt="palm-fig3-1" loading="lazy"><br>
I&#x2019;d guess that corresponds to about a 4% improvement in the case of the MATH dataset (since making the model 8.7x bigger was a 7% improvement).</li>
<li>Minerva itself is also undertrained: Table 2 of the <a href="https://arxiv.org/abs/2206.14858v2?ref=bounded-regret.ghost.io">Minerva paper</a> states that it only used 26B tokens during fine-tuning, which is less than one epoch (the fine-tuning dataset had 38.5B tokens). I wouldn&apos;t be surprised if training further also gave a ~5% improvement, although the actual amount could be significantly larger or smaller.</li>
</ul>
<p>Overall summary: the lowest-hanging fruit towards further improvement would be (in order):</p>
<ul>
<li>Improving over majority vote (up to 25% improvement, easy to imagine an 8% improvement),</li>
<li>fine-tuning on more data (unknown improvement, intuitively around 5%),</li>
<li>a better-trained version of PaLM (expensive so not clear it will happen, but probably a 4% improvement),</li>
<li>improving chain-of-thought prompting (easy to imagine a 3-5% improvement, possible to imagine a 10% improvement),</li>
<li>training a larger model (not obvious it will happen, but probably a couple percent improvement if so),</li>
<li>perhaps small gains from improving web scraping as well as tokenization.</li>
</ul>
<p>Aggregating these, it feels easy to imagine a &gt;14% improvement, fairly plausible to get &gt;21%, and &gt;28% doesn&#x2019;t seem out of the question. Concretely, conditional on Google or some other large organization deciding to try to further improve MATH performance, my prediction of how much they would improve it in the next year would be:</p>
<ul>
<li>25th percentile: 14%</li>
<li>50th percentile: 21%</li>
<li>80th percentile: 28%</li>
</ul>
<p>(This prediction is specifically using the &quot;how much low-hanging fruit&quot; frame. I&apos;ll also consider other perspectives, like trend lines, and <a href="https://bounded-regret.ghost.io/combining-forecasts/">average with these other perspectives</a> when making a final forecast.)</p>
<h3 id="what-kinds-of-errors-is-minerva-making-do-they-seem-easy-or-hard-to-fix">What kinds of errors is Minerva making? Do they seem easy or hard to fix?</h3>
<p>As noted above, the 62B parameter model has best-of-256 performance (filtered for correct reasoning) of at least 68%. My guess is that the true best-of-256 performance is in the low-to-mid 70s for 62B. Since Minerva-540B is 7% better than Minerva-62B, the model is at least capable of generating the correct answer around 80% of the time.</p>
<p>We can also look at errors by type of error. For instance, we estimated that calculation errors accounted for around 30% of the remaining errors (or around 15% absolute performance). These are probably fairly easy to fix.</p>
<p>In the other direction, the remaining MATH questions are harder than the ones that Minerva solves currently. I couldn&#x2019;t find results grouped by difficulty, but Figure 4 of the <a href="https://arxiv.org/pdf/2206.14858.pdf?ref=bounded-regret.ghost.io">Minerva paper</a> shows lower accuracy for harder subtopics such as Intermediate Algebra.</p>
<h3 id="how-much-additional-data-could-be-generated-for-training">How much additional data could be generated for training?</h3>
<p>We estimated that using all of arXiv would only generate about 10B words of mathematical content, compared to the 20B tokens used in Minerva. At a conversation rate of 2 tokens/word, this suggests that Minerva is already using up most relevant content on arXiv. I&#x2019;d similarly guess that Minerva makes use of most math-focused web pages currently on the internet (it looks for everything with MathJax). I&#x2019;d guess it&#x2019;s possible to find more (e.g. math textbooks) as well as to synthetically generate mathematical exposition, and probably also to clean the existing data better. But overall I&#x2019;d guess there aren&#x2019;t huge remaining gains here.</p>
<h3 id="could-other-methods-improve-mathematical-reasoning">Could other methods improve mathematical reasoning?</h3>
<p>For math specifically, it&#x2019;s possible to use calculators and verifiers, which aren&#x2019;t used by Minerva but could further improve performance. Table 9 of the <a href="https://arxiv.org/pdf/2204.02311.pdf?ref=bounded-regret.ghost.io">PaLM paper</a> shows that giving PaLM a calculator led to a 4% increase in performance on GSM8K (much smaller than the gains from chain-of-thought prompting).</p>
<p align="center">
    <img src="https://bounded-regret.ghost.io/content/images/2022/07/palm-table9.png">
</p>
<p>In the same table, we see that GPT-3 gets a 20% gain using a task-specific verifier. Given that the MATH problems are fairly diverse compared to GSM8K, I doubt it will be easy to write an effective verifier for that domain, and it&#x2019;s unclear whether researchers will seriously try in the next year. The calculator seems more straightforward and I&#x2019;d give a ~50% chance that someone tries it (conditional on there being at least one industry lab paper that focuses on math in the next year).</p>
<h3 id="historical-rate-of-progress-on-math">Historical Rate of Progress on MATH</h3>
<ul>
<li>As of 03/05/2021: 6.9%.</li>
<li>As of 06/30/2022: 50.3%.</li>
</ul>
<p>This is a roughly 2.9% accuracy gain per month (but almost certainly will be slower in future). Taking this extrapolation literally would give 85.1% for 06/30/2023.</p>
<h3 id="historical-rate-of-progress-on-other-datasets">Historical Rate of Progress on Other Datasets</h3>
<p>The <a href="https://aclanthology.org/2021.naacl-main.324.pdf?ref=bounded-regret.ghost.io">Dynabench paper</a> plots historical progress on a number of ML datasets, normalized by baseline and ceiling performance (see Figure 1, reproduced below).</p>
<p align="center">
    <img src="https://bounded-regret.ghost.io/content/images/2022/07/dynabench-fig1.png">
</p>
<p>We seem to often see immediate huge gains, while the next ones are somewhat slower.</p>
<p><a href="https://paperswithcode.com/sota/natural-language-inference-on-rte?ref=bounded-regret.ghost.io">Here</a>&#x2019;s another benchmark for reference. It got 67% -&gt; 86% within 1-2 months, then took 4 months to break 90%.</p>
<p>Overall, it seems clear we should expect some sort of slow-down. In some cases, the slow-down was huge. I think progress should not slow down that much in this case since there&#x2019;s still lots of low-hanging fruit. Maybe progress is 60% as fast as before? So that would give us 71% on 06/30/2023.</p>
<h3 id="how-much-will-people-work-on-improving-math-performance">How much will people work on improving MATH performance?</h3>
<p>Two sources of progress:</p>
<ul>
<li>General increased scaling of language models</li>
<li>Specific efforts to improve math / quantitative reasoning</li>
</ul>
<p>How many language papers have been released historically?</p>
<ul>
<li>GPT-2: 02/2019 (OpenAI)</li>
<li>GPT-3: 03/2020 (OpenAI)</li>
<li>UnifiedQA: 05/2020 (AI2)</li>
<li>Gopher: 12/2021 (DeepMind)</li>
<li>Chinchilla: 03/2022 (DeepMind)</li>
<li>PaLM: 04/2022 (Google)</li>
</ul>
<p>(This only counts language models that achieved broad state-of-the-art performance. E.g. I&apos;m ignoring OPT, BLOOM, GPT-J, etc.)</p>
<p>By this count, there have been 6 papers since the beginning of 2019. So base rate of around 1.7 / year. If we use a Poisson process, predicts that we will see 0 new papers with probability 18%, 1 with probability 31%, 2 with probability 26%, and &gt;2 with probability 25%.</p>
<p>What about math-specific work? Harder to measure what &#x201C;counts&#x201D; (lots of math papers but how many are large-scale / pushing state-of-the-art?). Intuitively I&#x2019;d expect more like 1.1 such papers per year. So around 33% chance of zero, 37% chance of 1, 20% chance of 2, 10% chance of &gt;2.</p>
<p>An important special case is if there are no developments on either the language models or the math-specific front. Under the above model these have probabilities 18% and 33%, and are probably positively correlated. Additionally, it&apos;s possible that language model papers might not bother to evaluate on MATH or might not use all the ideas in the Minerva paper (and thus fail to hit SOTA). Combining these considerations, I&#x2019;d forecast around a 12% chance that there is no significant progress on MATH on any front.</p>
<h3 id="bottom-line-forecast">Bottom-Line Forecast</h3>
<p>From the above lines of reasoning, we have a few different angles on the problem:</p>
<ul>
<li>Looking at rates of publication of language model papers suggests a 12% chance of no major developments at all (e.g. between 0% and 5% progress).</li>
<li>Thinking in detail about possible sources of improvements gives something like 25th percentile: 14% gain (to 64%); 50th percentile: 21% gain (to 71%); 80th percentile: 28% gain (to 78%). But these were all conditional on some progress happening, so should adjust down by the 12% chance of no progress at all.</li>
<li>Extrapolating base rates and adjusting for slowdowns in progress gives a forecast of 71% (with probably a ceiling forecast of 85%).</li>
<li>Looking at how easy it would be to fix current flaws suggests that 15% should be relatively easy (calculation errors). Up to 30% would &quot;only&quot; require better re-ranking (i.e., a correct solution is in the top 256 ones generated).</li>
<li>I&#x2019;ve underestimated progress in the past so should potentially adjust upwards.</li>
</ul>
<p>If I intuitively combine these, I produce the following forecast:</p>
<ul>
<li>12th percentile: 55%</li>
<li>33rd percentile: 63%</li>
<li>50th percentile: 71%</li>
<li>80th percentile: 80%</li>
<li>90th percentile: 89%</li>
</ul>
<p>The Metaculus community is at 74 median, upper 75% of 83. So I&#x2019;ll adjust up slightly more. New forecast adjusted towards community prediction:</p>
<ul>
<li>10th percentile: 55%</li>
<li>33rd percentile: 66%</li>
<li>Median: 73%</li>
<li>80th percentile: 84%</li>
<li>90th percentile: 90%</li>
</ul>
<p>Rough approximation of this distribution on Metaculus (red is me, green is the community prediction):</p>
<p align="center">
    <img src="https://bounded-regret.ghost.io/content/images/2022/07/math-density.png"><br>
    <img src="https://bounded-regret.ghost.io/content/images/2022/07/math-cumulative.png">
</p>
<p>Interestingly, <a href="https://prod.hypermind.com/ngdp/en/showcase2/showcase.html?sc=JSAI&amp;ref=bounded-regret.ghost.io#q3">Hypermind</a> forecasts a much smaller median of 64.1%.</p>
<h1 id="mmlu-forecast">MMLU Forecast</h1>
<h2 id="background">Background</h2>
<p>Again borrowing from <a href="https://www.metaculus.com/questions/11676/mmlu-sota-in-2023-2025/?ref=bounded-regret.ghost.io">Metaculus</a>:</p>
<blockquote>
<p>The Massive Multitask Language Understanding (MMLU) dataset is a dataset of high school, college, and professional multiple choice exams that test expert subject knowledge. It was constructed by <a href="https://github.com/hendrycks/test?ref=bounded-regret.ghost.io">Hendrycks et al. (2021)</a>. Hypermind forecasters were commissioned to predict state-of-the-art performance on June 30, 2022, &apos;23, &apos;24, and &apos;25. The 2022 result of 67.5% was significantly outside forecasters&apos; prediction intervals, so we&apos;re seeing what the updated forecasts are for 2023, &apos;24, and &apos;25.<br><br>
<strong>What will be state-of-the-art accuracy on the Massive Multitask dataset in the following years?</strong><br><br>
These questions should resolve identically to the <a href="https://prod.hypermind.com/ngdp/en/showcase2/showcase.html?sc=JSAI&amp;ref=bounded-regret.ghost.io">Hypermind forecasts</a>:</p>
<p>&quot;These questions resolve as the highest performance achieved on MMLU by June 30 in the following years by an eligible model. Eligible models must not have been specifically trained on data from the MMLU dataset. A model need not be publicly released, as long as the resulting performance itself is reported in a published paper (on arxiv or a major ML conference) or through an official communication channel of an industry lab (e.g. claimed in a research blog post on the OpenAI blog, or a press release). If there&apos;s uncertainty about whether something counts, we will defer to <a href="https://github.com/hendrycks/test?ref=bounded-regret.ghost.io">this leaderboard</a>.&quot;</p>
</blockquote>
<h2 id="key-considerations">Key Considerations</h2>
<p>At a high level, these are fairly similar to those of the MATH dataset. Since more people have worked on MMLU and there&#x2019;s been steadier progress, we rely more on base rates and less on detailed considerations of how one could improve it further.</p>
<ul>
<li>Base rate: What has been the progress on MMLU to date?</li>
<li>Base rate: How does progress typically occur on machine learning datasets (especially NLP datasets)? If there is a sudden large improvement, does that typically continue, or level off? <em>[Same as previous consideration for MATH]</em></li>
<li>The two models Chinchilla and Minerva do well on different subsets of MMLU. What happens if we combine them together?</li>
<li>How much other low-hanging fruit is there?</li>
<li>How much will people work on improving MMLU performance?</li>
</ul>
<h2 id="analyzing-key-considerations">Analyzing Key Considerations</h2>
<h3 id="historical-rate-of-progress-on-mmlu">Historical Rate of Progress on MMLU</h3>
<p>Below is a time series of MMLU results, taken from the <a href="https://github.com/hendrycks/test?ref=bounded-regret.ghost.io">MMLU leaderboard</a> (note MMLU was published in Jan. 2021). I&apos;ve bolded few-shot/zero-shot results.</p>
<table>
<thead>
<tr>
<th>Model</th>
<th>Date</th>
<th>Average</th>
</tr>
</thead>
<tbody>
<tr>
<td><strong>Chinchilla (70B, few-shot)</strong></td>
<td>Mar 29, 2022</td>
<td>67.5</td>
</tr>
<tr>
<td><strong>Gopher (280B, few-shot)</strong></td>
<td>Dec 8, 2021</td>
<td>60.0</td>
</tr>
<tr>
<td>GPT-3 (175B, fine-tuned)</td>
<td>Jul 22, 2020</td>
<td>53.9</td>
</tr>
<tr>
<td><strong>UnifiedQA</strong></td>
<td>Oct  7, 2020</td>
<td>48.9</td>
</tr>
<tr>
<td><strong>GPT-3 (175B, few-shot)</strong></td>
<td>Jul 22, 2020</td>
<td>43.9</td>
</tr>
<tr>
<td>GPT-3 (6.7B, fine-tuned)</td>
<td></td>
<td>43.2</td>
</tr>
<tr>
<td><strong>GPT-2</strong></td>
<td></td>
<td>32.4</td>
</tr>
</tbody>
</table>
<p>If we restrict to few-shot results, we see:</p>
<ul>
<li>+7.5 from Dec -&gt; Mar (3 months)</li>
<li>+11.1 from Oct &#x2018;20 -&gt; Dec &#x2018;21 (14 months)</li>
<li>+16.1 from July &#x2018;20 -&gt; Dec &#x2018;21 (17 months)</li>
</ul>
<p>It&apos;s not clear which time horizon is best to use here. I came up with an approximate base rate of <strong>1.2 pts / month</strong>.</p>
<p>Other notes:</p>
<ul>
<li>Source of improvements: better training, more compute, maybe better pretraining data?</li>
<li>Fine-tuning seems to add 10 points, so a potentially easy source of low-hanging fruit.</li>
</ul>
<h3 id="historical-rate-of-progress-on-other-datasets">Historical Rate of Progress on Other Datasets</h3>
<p>We analyzed this already in the previous section on MATH. It seems like there&apos;s usually an initial period of rapid progress, followed by a slow-down.  However, MMLU has had enough attempts that I&#x2019;d say it&#x2019;s past the &#x201C;huge initial gains&#x201D; stage. Therefore, I don&#x2019;t expect as much as a level-off compared to MATH, even though there is less obvious low-hanging fruit---maybe we&apos;ll get 75% as fast of progress as before. This would suggest <strong>+10.8 points</strong> over the next year.</p>
<h3 id="combining-chinchilla-and-minerva">Combining Chinchilla and Minerva</h3>
<p>The current SOTA of 67.5 comes from Chinchilla. But Minerva does much better than Chinchilla on the MMLU-STEM subset of MMLU. Here&#x2019;s a rough calculation of how much taking max(Chinchilla, Minerva) would improve things:</p>
<ul>
<li>Chinchilla gets 54.9% on MMLU-STEM</li>
<li>PaLM gets 58.7%</li>
<li>Minerva gets 75.0% with majority vote, 63.9% without</li>
<li>STEM is 19 / 57 of the tasks.</li>
</ul>
<p>So adding in Minerva would add (75% - 54.9%) * 19/57 = 6.7% points of accuracy.</p>
<p>Will this happen? It&apos;s not obvious, since PaLM is owned by Google and Chinchilla is owned by DeepMind. At least one org would need to train a new model. I think there&#x2019;s a good chance this happens, but not certain (~65% probability).</p>
<h3 id="other-low-hanging-fruit">Other Low-Hanging Fruit</h3>
<p>Result of a quick brainstorm:</p>
<ul>
<li>External calculators + other STEM-specific improvements (similar to MATH)</li>
<li>Some of the chain-of-thought improvements could help with other parts of MMLU (beyond STEM) especially if it helps with error correction.</li>
<li>General knowledge retrieval</li>
</ul>
<p>In addition, the STEM-specific improvements (e.g. Minerva) will continue to improve MMLU-STEM. Based on the MATH forecast above, on median I expect about half as much improvement over the next year as we saw from the Minerva paper, or around another 3% improvement on MMLU overall (since Minerva gave a 6.7% improvement).</p>
<p>We thought it was possible but unlikely that there are significant advances in general knowledge retrieval in the next year that also get used by MMLU (~20% probability).</p>
<h3 id="how-much-will-people-work-on-improving-mmlu-performance">How much will people work on improving MMLU performance?</h3>
<p>Unlike MATH, there is nothing &#x201C;special&#x201D; that makes MMLU stand out from other language modeling benchmarks. So I&#x2019;d guess most gains will come from general-purpose improvements to language models, plus a bit of STEM-specific improvement if people focus on quantitative reasoning.</p>
<h3 id="bottom-line-forecast">Bottom-Line Forecast</h3>
<p>In some sense, MMLU performance is already &#x201C;at&#x201D; 74.2% because of the Minerva result. Additional low-hanging fruit would push us up another 5 points to 79.2%. Alternately, simply extrapolating historical progress would suggest 10.8 points of improvement, or 85%. Putting these together, I&#x2019;d be inclined towards a median of 83%.</p>
<p>If we instead say that progress doesn&#x2019;t slow down at all, we&#x2019;d get 89%.</p>
<p>As before, I&#x2019;d give an 18% chance of no new SOTA language model papers, in which case MMLU performance likely stays between 67.5% and 74.2%. This also means we should adjust the previous numbers down a bit.</p>
<p>Overall forecast:</p>
<ul>
<li>18th percentile: 74%</li>
<li>25th percentile: 77%</li>
<li>50th percentile: 82%</li>
<li>75th percentile: 89%</li>
</ul>
<p>This seems pretty similar to the Metaculus community prediction, so I won&#x2019;t do any further adjustment.</p>
<p align="center">
 <img src="https://bounded-regret.ghost.io/content/images/2022/07/mmlu-density.png"><br>
 <img src="https://bounded-regret.ghost.io/content/images/2022/07/mmlu-cumulative.png">
</p>
<p>Interestingly, the <a href="https://prod.hypermind.com/ngdp/en/showcase2/showcase.html?sc=JSAI&amp;ref=bounded-regret.ghost.io#q4">Hypermind median</a> is only at 72.5% right now. Given the ability to combine Minerva + Chinchilla, this intuitively seems too low to me.</p>
<h1 id="looking-ahead">Looking Ahead</h1>
<p>My personal forecasts ended up being pretty similar to the Metaculus community forecasts, aside from me expecting slightly slower MATH progress (but only by about a percentage point). So, we can ask what Metaculus expects for 2024 and 2025 as well, as an approximation to what I &quot;would&quot; believe if I thought about it more.</p>
<p>MATH forecast (community prediction in green, top row of each cell):</p>
<p align="center">
    <img src="https://bounded-regret.ghost.io/content/images/2022/07/math-future.png">
</p>
<p>MMLU forecast (community prediction in green):</p>
<p align="center">
    <img src="https://bounded-regret.ghost.io/content/images/2022/07/mmlu-future.png">
</p>
<p>So, on median Metaculus expects MATH to be at 83% in 2024 and at 88% in 2025. It expects MMLU to be at 88% in 2024 and at 93% (!) in 2025. The last one is particularly interesting: since MMLU tests domain-specific subject knowledge across many areas, it is predicting that a single model will be able to match domain-specific expert performance across a wide variety of written subject exams.</p>
<p>Do you agree with these forecasts? Disagree? I strongly encourage you to leave your own forecasts on Metaculus: <a href="https://www.metaculus.com/questions/11675/math-sota-in-2023-2025/?ref=bounded-regret.ghost.io">here</a> for MATH, and <a href="https://www.metaculus.com/questions/11676/mmlu-sota-in-2023-2025/?ref=bounded-regret.ghost.io">here</a> for MMLU.</p>
<!--kg-card-end: markdown-->]]></content:encoded></item><item><title><![CDATA[AI Forecasting: One Year In]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p>Last August, my research group <a href="https://bounded-regret.ghost.io/ai-forecasting/">created a forecasting contest</a> to predict AI progress on four benchmarks. Forecasts were asked to predict state-of-the-art performance (SOTA) on each benchmark for June 30th 2022, 2023, 2024, and 2025. It&#x2019;s now past June 30th, so we can evaluate the performance of the</p>]]></description><link>https://bounded-regret.ghost.io/ai-forecasting-one-year-in/</link><guid isPermaLink="false">62c259cf22dd63003d020385</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Mon, 04 Jul 2022 05:08:44 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p>Last August, my research group <a href="https://bounded-regret.ghost.io/ai-forecasting/">created a forecasting contest</a> to predict AI progress on four benchmarks. Forecasts were asked to predict state-of-the-art performance (SOTA) on each benchmark for June 30th 2022, 2023, 2024, and 2025. It&#x2019;s now past June 30th, so we can evaluate the performance of the forecasters so far.</p>
<p>Forecasters were asked to provide probability distributions, so we can evaluate both their point estimates and their coverage (whether the true result was within their credible intervals). I&#x2019;ll dive into the data in detail below, but my high-level takeaways were that:</p>
<ol>
<li>Forecasters&#x2019; predictions were not very good in general: two out of four forecasts were outside the 90% credible intervals.</li>
<li>However, they were better than my personal predictions, and I suspect better than the median prediction of ML researchers (if the latter had been preregistered).</li>
<li>Specifically, progress on ML benchmarks happened significantly <strong>faster</strong> than forecasters expected. But forecasters predicted faster progress than I did personally, and my sense is that I expect somewhat faster progress than the median ML researcher does.</li>
<li>Progress on a <em>robustness</em> benchmark was slower than expected, and was the only benchmark to fall short of forecaster predictions. This is somewhat worrying, as it suggests that machine learning capabilities are progressing quickly, while safety properties are progressing slowly.</li>
</ol>
<p>Below I&#x2019;ll review the tasks and competition format, then go through the results.</p>
<h2 id="forecasting-tasks-and-overall-predictions">Forecasting Tasks and Overall Predictions</h2>
<p>As a reminder, the four benchmarks were:</p>
<ul>
<li><a href="https://github.com/hendrycks/math?ref=bounded-regret.ghost.io">MATH</a>, a mathematics problem-solving dataset;</li>
<li><a href="https://github.com/hendrycks/test?ref=bounded-regret.ghost.io">MMLU</a>, a test of specialized subject knowledge using high school, college, and professional multiple choice exams;</li>
<li><a href="https://paperswithcode.com/dataset/something-something-v2?ref=bounded-regret.ghost.io">Something Something v2</a>, a video recognition dataset; and</li>
<li><a href="https://robustbench.github.io/?ref=bounded-regret.ghost.io#div_cifar10_Linf_heading">CIFAR-10 robust accuracy</a>, a measure of adversarially robust vision performance.</li>
</ul>
<p>Forecasters were asked to predict performance on each of these. Each forecasting question had a $5000 prize pool (distributed across the four years). There were also two questions about compute usage by different countries and organizations, but I&#x2019;ll ignore those here.</p>
<p>Forecasters themselves were recruited with the platform <a href="https://prod.hypermind.com/ngdp/en/showcase2/showcase.html?sc=JSAI&amp;ref=bounded-regret.ghost.io">Hypermind</a>. You can read more details in the <a href="https://bounded-regret.ghost.io/ai-forecasting/">initial blog post</a> from last August, but in brief, professional forecasters make money by providing accurate probabilistic forecasts about future events, and are typically paid according to a proper scoring rule that incentivizes calibration. They apply a wide range of techniques such as base rates, reference classes, trend extrapolation, examining and aggregating different expert views, thinking about possible surprises, etc. (see my <a href="http://www.stat157.com/calendar/?ref=bounded-regret.ghost.io">class notes</a> for more details).</p>
<p>Here is what the forecasters&#x2019; point estimates were for each of the four questions (based on <a href="https://prod.hypermind.com/ngdp/en/showcase2/showcase.html?sc=JSAI&amp;ref=bounded-regret.ghost.io">Hypermind&apos;s dashboard</a>):</p>
<p align="center">
<img src="https://bounded-regret.ghost.io/content/images/2022/07/forecast.png">
</p>
<p>Expert performance is approximated as 90%. The 2021 datapoint represents the SOTA in August 2021, when the predictions were made.<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup></p>
<p>For June 2022, forecasters predicted 12.7% on MATH, 57.1% on MMLU (the multiple-choice dataset), 70.4% on adversarial CIFAR-10, and 73.0% on Something Something v2.</p>
<p>At the time, I described being surprised by the 2025 prediction for the MATH dataset, which predicted over 50% performance, especially given that 2021 accuracy was only 6.9% and most humans would be below 50%.</p>
<p>Here are the actual results, as of today:</p>
<ul>
<li>MATH: 50.3% (vs. 12.7% predicted)</li>
<li>MMLU: 67.5% (vs. 57.1% predicted)</li>
<li>Adversarial CIFAR-10: 66.6% (vs. 70.4% predicted)</li>
<li>Something Something v2: 75.3% (vs. 73.0% predicted)</li>
</ul>
<p>MATH and MMLU progressed much faster than predicted. Something Something v2 progressed somewhat faster than predicted. In contrast, Adversarial CIFAR-10 progressed somewhat slower than predicted. Overall, progress on machine learning <strong>capabilities</strong> (math, MMLU, video) was significantly faster than what forecasters expected, while progress on <strong>robustness</strong> (adversarial CIFAR) was somewhat slower than expected.</p>
<p>Interestingly, the 50.3% result on MATH <a href="https://ai.googleblog.com/2022/06/minerva-solving-quantitative-reasoning.html?ref=bounded-regret.ghost.io">was released</a> on the <strong>exact day</strong> that the forecasts resolved. I&apos;m told this was purely coincidental, but it&apos;s certainly interesting that a 1-day difference in resolution date had such a big impact on the result.</p>
<h2 id="how-accurate-were-the-forecasts">How Accurate Were the Forecasts?</h2>
<p>To assess forecast accuracy, we need to look not just at the point estimate, but at the forecasters&#x2019; actual probability distribution. Even though 68% on MMLU seems far off from 57%, perhaps it was well within the credible interval of the forecasts. However, that turns out not to be the case, for either MATH or MMLU:</p>
<p align="center">
<img src="https://bounded-regret.ghost.io/content/images/2022/07/math2022.png">
<img src="https://bounded-regret.ghost.io/content/images/2022/07/mmlu2022.png">
</p>
<p>I marked the actual result with a star, and it&#x2019;s clear that in both cases it&#x2019;s in the far tails of the forecast distribution.</p>
<p>For completeness, here are results for adversarial CIFAR-10 and Something Something v2:</p>
<p align="center">
<img src="https://bounded-regret.ghost.io/content/images/2022/07/cifar2022.png">
<img src="https://bounded-regret.ghost.io/content/images/2022/07/video2022.png">
</p>
<p>While both were somewhat in the tails, they fell within a part of the distribution that at least had non-negligible probability density.</p>
<h2 id="the-median-ml-researcher-was-probably-even-more-wrong">The Median ML Researcher Was (Probably) Even More Wrong</h2>
<p>While forecasters didn&#x2019;t do great at forecasting progress in ML, the median ML researcher would likely have done even worse. Unfortunately, we don&#x2019;t have preregistered predictions to check this, but a few lines of evidence support this conclusion.</p>
<p>First, I did (somewhat) preregister a prediction of my own. In <em><a href="https://bounded-regret.ghost.io/ai-forecasting/">Updates and Lessons from AI Forecasting</a></em>, I said:</p>
<blockquote>
<p>&#x201C;Projected progress on math and on broad specialized knowledge are both faster than I would have expected. I now expect more progress in AI over the next 4 years than I did previously.&#x201D;</p>
</blockquote>
<p>And, more to the point:</p>
<blockquote>
<p>&#x201C;Current performance on this dataset is quite low--6.9%--and I expected this task to be quite hard for ML models in the near future. However, forecasters predict more than 50% accuracy by 2025! This was a big update for me.&#x201D;</p>
</blockquote>
<blockquote>
<p>&#x201C;If I imagine an ML system getting more than half of these questions right, I would be pretty impressed. If they got 80% right, I would be super-impressed. The forecasts themselves predict accelerating progress through 2025 (21% in 2023, then 31% in 2024 and 52% in 2025), so 80% by 2028 or so is consistent with the predicted trend. This still just seems wild to me and I&apos;m really curious how the forecasters are reasoning about this.&#x201D;</p>
</blockquote>
<p>So, while I didn&#x2019;t register a specific prediction, I clearly thought the forecasts on MATH were aggressive in terms of how much progress they predicted, whereas it turned out they weren&#x2019;t aggressive enough.</p>
<p>At the same time, my personal predictions about ML progress seem to be more aggressive than the median ML researcher. I would personally describe them as &#x201C;somewhat more aggressive&#x201D;, but some of my students think they are &#x201C;much more aggressive&#x201D;. Either way, this suggests that the median ML researcher would have predicted even less progress than me, and so been even more wrong than I was.</p>
<p>Anecdotal evidence seems to confirm this. When our group first released the MATH dataset, at least one person told us that it was a pointless dataset because it was too far outside the range of what ML models could accomplish (indeed, I was somewhat worried about this myself).</p>
<p>If ML researchers (including myself) would like to defend their honor on this point, I think the best way would be to register forecasts for the upcoming year in advance. You can do this in any of the following ways:</p>
<ul>
<li>Submit forecasts for the <a href="https://www.metaculus.com/questions/11675/math-sota-in-2023-2025/?ref=bounded-regret.ghost.io">MATH</a> and <a href="https://www.metaculus.com/questions/11676/mmlu-sota-in-2023-2025/?ref=bounded-regret.ghost.io">MMLU</a> questions on Metaculus (easy, only requires Google account).</li>
<li>Submit <a href="https://prod.hypermind.com/ngdp/en/showcase2/showcase.html?sc=JSAI&amp;ref=bounded-regret.ghost.io">directly to Hypermind</a> for the possibility of winning money (sign-up required, takes a bit of time).</li>
<li>Or just comment on this post.</li>
</ul>
<p>I&apos;ll write another blog post in a week with my own forecasts and reasoning.</p>
<h2 id="was-progress-surprising-or-were-the-forecasters-bad">Was Progress Surprising, or Were the Forecasters Bad?</h2>
<p>Given that forecasters seemed not to predict progress well, we might wonder if they were just not trying very hard or were otherwise not doing a good job. For instance:</p>
<ul>
<li>The overall prize pool was only $5000 for each benchmark (which itself consists of four questions for 2022-2025). Divided over the 60-70 participants, the average payout per benchmark is only $80, or $20 per question.<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup> So, it&#x2019;s possible that forecasters were not incentivized strongly enough.</li>
<li>Hypermind&#x2019;s interface has some limitations that prevent outputting arbitrary probability distributions. In particular, in some cases there is an artificial limit on the possible standard deviations, which could lead credible intervals to be too narrow.</li>
<li>Maybe the forecasters just weren&#x2019;t skilled enough&#x2014;either the best forecasters didn&#x2019;t participate, or the forecasts were too different from more traditional forecasts, which tend to focus on geopolitics.</li>
</ul>
<p>These are all plausible concerns, but I think progress is still &#x201C;surprising&#x201D; even after accounting for them. For instance, superforecaster Eli Lifland <a href="https://www.foxy-scout.com/my-hypermind-ari/?ref=bounded-regret.ghost.io">posted predictions</a> for these forecasts on his blog. While he notes that the Hypermind interface limited his ability to provide wide intervals on some questions, he doesn&#x2019;t make that complaint for the MATH 2022 forecast and posted the following prediction, for which the true answer of 50.3% was even more of an outlier than Hypermind&apos;s aggregate:</p>
<p align="center">
<img src="https://bounded-regret.ghost.io/content/images/2022/07/eli_forecast.png">
</p>
<p>A separate forecast, which I commissioned from the <a href="https://samotsvety.org/?ref=bounded-regret.ghost.io">Samotsvety Forecasting</a> group and paid around $2500 for, predicted MATH performance in 2026. The current accuracy of 50.3% was around the 75th percentile for <a href="https://forecast.elicit.org/builder/tFjSjJy2u?ref=bounded-regret.ghost.io">their 2026 forecast</a>, so presumably it was significantly further in the tail for 2022. Their forecast was made in Elicit, so there were no constraints on allowable distributions, and I explicitly selected Samotsvety as having a good track record and being particularly interested in AI, and paid them a high hourly rate. So, the concerns about the Hypermind forecasts don&#x2019;t apply here, but progress still outpaced the forecast.</p>
<p>Finally, the fact that forecasters did better than me and would have probably beat the median ML researcher suggests that they aren&#x2019;t lacking an obvious domain-specific skill.</p>
<h2 id="looking-forward">Looking Forward</h2>
<p>Now that forecasters have had one year of practice, I&apos;m hoping there will be fewer surprises next year--but we&apos;ll have to wait and see. In the meantime, I&apos;m hoping that more work will be done on AI safety and alignment, so that it can keep pace with the rapid increase in capabilities.</p>
<p>Finally, as one specific intersection between AI and forecasting that could help us better predict the future, our research group recently released the <a href="https://github.com/andyzoujm/autocast?ref=bounded-regret.ghost.io">Autocast benchmark</a>, which can be used to train ML systems to forecast future events. Currently, they are significantly worse than humans, but this was true for MATH one year ago. Can ML systems get better at forecasting as fast as they got better at math? Superhuman forecasters would help us better prepare for the many challenges that lie ahead. I hope to be pleasantly surprised.</p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>The contest started in August but was open until the end of September. <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn2" class="footnote-item"><p>Payouts were non-uniform. In particular, longer time horizons had a larger payout. <a href="#fnref2" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
<!--kg-card-end: markdown-->]]></content:encoded></item><item><title><![CDATA[How fast can we perform a forward pass?]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p><em>Thanks to Hao Zhang, Kayvon Fatahalian, and Jean-Stanislas Denain for helpful discussions and comments.</em></p>
<p><em><strong>Addendum and erratum.</strong> See <a href="https://kipp.ly/blog/transformer-inference-arithmetic/?ref=bounded-regret.ghost.io">here</a> for an excellent discussion of similar ideas by Kipply Chen. In addition, James Bradbury has pointed out to me that some of the constants in this analysis are wrong, as well</em></p>]]></description><link>https://bounded-regret.ghost.io/how-fast-can-we-perform-a-forward-pass/</link><guid isPermaLink="false">62a29bac662959003db66325</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Fri, 10 Jun 2022 23:22:29 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p><em>Thanks to Hao Zhang, Kayvon Fatahalian, and Jean-Stanislas Denain for helpful discussions and comments.</em></p>
<p><em><strong>Addendum and erratum.</strong> See <a href="https://kipp.ly/blog/transformer-inference-arithmetic/?ref=bounded-regret.ghost.io">here</a> for an excellent discussion of similar ideas by Kipply Chen. In addition, James Bradbury has pointed out to me that some of the constants in this analysis are wrong, as well as some of the quotes of current hardware capabilities. (See <a href="https://twitter.com/jekbradbury/status/1539440081009786881?ref=bounded-regret.ghost.io">here</a> for some discussion, although we had additional discussion in-person.) I believe that the overall asymptotics below are correct, but the final numbers could plausibly be off by up to an order of magnitude. I hope to eventually fix the numbers, but it&apos;s a complicated enough undertaking that it will take some time and care.</em></p>
<p>Over the last month, I&#x2019;ve spent a lot of time trying to answer the following question:</p>
<blockquote>
<p>How quickly can we perform one forward pass in a transformer model?</p>
</blockquote>
<p>By a transformer model, I mean BERT, GPT-3, T5, Chinchilla, or other large language models that use a transformer architecture. By a forward pass, I mean the computation needed to generate the next token given all the tokens so far.<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup> By &#x201C;how quickly&#x201D;, I mean how much wall clock time elapses between the call to the forward pass and its completion. So, even if I can run 1,000 forward passes in parallel, if each takes 1 second to complete, the answer is 1 second (not 1 millisecond).</p>
<p>One way to attempt answering this is to take the total number of operations in a forward pass and divide by the speed of your favorite GPU in FLOPS (floating-point operations/second). But this is wrong, because you would do better by parallelizing across multiple GPUs.<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup></p>
<p>The question then is really &#x201C;how effectively can I parallelize a forward pass?&#x201D; It turns out that this has different answers based on how &#x201C;wasteful&#x201D; we&#x2019;re willing to be, in terms of GPU utilization. If we are willing to utilize only 5% of the GPU (but parallelize across many GPUs), we can perform the forward pass more quickly. So I&#x2019;ll actually answer two questions:</p>
<ol>
<li>How quickly can we perform a forward pass, assuming we require each GPU to have at least 40% utilization relative to roofline FLOPS?<sup class="footnote-ref"><a href="#fn3" id="fnref3">[3]</a></sup></li>
<li>If we are willing to decrease utilization by a factor of k, how much faster can we perform a forward pass?</li>
</ol>
<p>To simplify the analysis, I&#x2019;ll make several assumptions (this is mainly targeted at people who are very familiar with GPU nuts and bolts; don&#x2019;t worry if you don&#x2019;t understand them yet):</p>
<ul>
 <li>[A] Parallelization, both within and across GPUs, is done via matrix tiling, as discussed in the <a href="https://docs.nvidia.com/deeplearning/performance/dl-performance-matrix-multiplication/index.html?ref=bounded-regret.ghost.io">NVIDIA User&#x2019;s Guide</a>.</li>
 <li>[B] All bottleneck operations can be run at high arithmetic intensity for large batch sizes.</li>
 <li>[C] The constraining resource is always either compute capacity, on-chip memory bandwidth, or network bandwidth of a single machine. In particular, it is not the L2 cache speed, the cross-GPU interconnect, or the ability to route information between far-away nodes in the network.</li>
</ul>
<p>Assumption A holds for most systems as implemented today, but it&#x2019;s possible that algorithms such as <a href="https://arxiv.org/abs/2205.14135?ref=bounded-regret.ghost.io">FlashAttention</a> could lead to better efficiency in the future. Assumption B is actually somewhat false today, because self-attention layers don&#x2019;t achieve high arithmetic intensity for large context lengths (I&#x2019;ll discuss this more later). Finally, Assumption C seems likely to hold for well-designed GPU clusters&#x2014;e.g. under the analysis below, the limiting resource would usually be memory bandwidth for TPU pods, and network bandwidth for a home-grown cluster of A100s.</p>
<p>If Assumption A failed, it would push the time of a forward pass down (because it would mean we&#x2019;d found a better parallelization strategy). If Assumption C failed, it would push the time up (because there&#x2019;d be a new resource bottleneck). If Assumption B failed, it would render the question as posed meaningless, because it would not be possible to achieve 40% utilization. However, for whatever utilization was possible to achieve, it would likely push the time down relative to the 40% numbers given below (see <a href="#roofline">here</a> for why).</p>
<h1 id="how-fast-for-a-forward-pass-the-very-short-answer">How Fast for a Forward Pass? The Very Short Answer</h1>
<p>The time for a forward pass depends primarily on three properties:</p>
<ul>
<li>The number $L$ of layers in the model.</li>
<li>The speed $C$ of a single GPU, in FLOPS.</li>
<li>The &#x201C;ops : bytes&#x201D; ratio $R$ of the GPU, which is the FLOPS divided by the bandwidth in bytes/second (as measured by either memory reads or network bytes; we&#x2019;ll assume for now that these are comparable).</li>
</ul>
<p>Ignoring multiplicative constants, the time for a forward pass is $LR^3/C$. This is because a forward pass primarily consists of $L$ consecutive matrix multiplies, and we can split each matrix multiply into a bunch of $R \times R$ blocks that are each run on a separate GPU, and thus take $R^3$ operations per GPU. $R$ turns out to be the smallest block size at which the GPU can be run at full utilization.</p>
<p>If we are willing to decrease utilization by a factor of $k$, then we can use $\frac{R}{k} \times \frac{R}{k}$ blocks instead. This leads to only needing time $LR^3/Ck^2$. In other words, the time decreases by a factor of $k^2$. Eventually, we would become bottlenecked by latency (which for current clusters is around a few microseconds/layer), but I will ignore that in this analysis.</p>
<h1 id="the-still-short-but-technical-answer">The Still Short but Technical Answer</h1>
<p>I&#x2019;ll now justify the formulas above, and fill in the multiplicative constants. This section will make sense if you already understand GPUs pretty well, and give you a rough gist if you don&#x2019;t. In the rest of the document, I&#x2019;ll explain the relevant facts about GPUs and derive the formulas in a lot more detail.</p>
<p>The full answer depends on four GPU-specific quantities:</p>
<ul>
<li>the compute capacity C of the GPU (in FLOPS),</li>
<li>the memory bandwidth M (in bytes/sec),</li>
<li>the number N of GPUs per machine, and</li>
<li>the network bandwidth B, i.e. how quickly information can be sent from one machine to another (also measured in bytes/sec).</li>
</ul>
<p>In addition, the main thing that matters about the transformer architecture itself is the number $L$ of sequential matrix multiplies that must be performed (this is generally around 2 per layer, so 100-200 for most current architectures).</p>
<p>Interestingly, the answer does not depend on the width of the network. This is because we can always parallelize across more GPUs. The only bottleneck to parallelization is that each GPU needs enough &#x201C;work&#x201D; to be utilized efficiently, and this work bottleneck is determined primarily by the GPU&#x2019;s compute $C$, memory bandwidth $M$, and network bandwidth $B$.</p>
<p><strong>Complete formula.</strong> The minimum time to complete one matrix multiply ends up (with some caveats) being</p>
<p align="center">
$\text{ElapsedTime} = \left\{ \begin{align*} \frac{54C^2}{M^3} \quad \quad \quad &amp; : \text{ if } B &gt; \frac{2}{3}M\sqrt{N} \\ \frac{8C^2N}{B^2(M-B/\sqrt{N})} &amp; : \text{ else.} \end{align*} \right.$
</p>
<p>In this formula, if we are not network bottlenecked then the time grows as $C^2/M^3$, and if we are then it grows as $C^2N/B^2M$.</p>
<p>Finally, if we are willing to decrease utilization by a factor of $k$, we can drive the time down by a factor of $k^2$.</p>
<p><strong>Interpretation for current machines.</strong> On current machines, either term in the maximum can dominate: for instance, for an A100 GPU we have C = 312TFLOPS, M = 2TB/s, N=8, and B is variable but perhaps 2TB/S for high-end networks. Then the first term is $0.7 \times 10^{-6}$ and the second is $1.2 \times 10^{-6}$. In other words, on a cluster of A100s, each matrix multiply would take a couple microseconds. This assumes full GPU utilization (in reality it would be 30%-50%) and no latency (in reality around 1.5&#x3BC;s), so in practice it will be higher&#x2013;perhaps 4-5 microseconds. Since transformers like <a href="https://arxiv.org/abs/2203.15556?ref=bounded-regret.ghost.io">Chinchilla</a> require 160 consecutive matrix multiplies, the overall time for a forward pass comes out to around 0.7 ms. In contrast, humans take around 250ms to read one word.</p>
<p><strong>Justifying the formula.</strong> The rough reason for the formulas above is as follows: ignoring constants, when N=1, we can split any matrix multiplication up into blocks of size $\frac{C}{B} \times \frac{C}{B}$, and process inputs in batches of size $\frac{C}{M}$. For this computation shape, each machine needs to handle $\frac{C^2}{BM}$ incoming network bits per forward pass, $\frac{C^2}{B^2}$ memory reads, and $\frac{C^3}{B^2M}$ floating point operations. Since the first gets handled at a rate of $B$, the second at a rate of $M$, and the third at a rate of $C$, all of them get handled in time $\frac{C^2}{B^2M}$ and hence all resources are fully utilized.</p>
<p>For N&gt;1 GPUs per machine, the input to the entire machine should be blocks of length $\frac{CN}{B}$ with batches of size $\frac{C}{M}$. This gets subdivided further into a $\sqrt{N} \times \sqrt{N}$ grid of blocks of size $\frac{C\sqrt{N}}{B}$, which get sent to each individual GPU. Then we process $\frac{C^2N}{BM}$ network bits (at rate B), $\frac{C^2N}{B^2}$ memory reads per machine (at rate M), and $\frac{C^3N}{B^2M}$ floating point operations per machine (at  rate C). In this case each component gets processed in $\frac{C^2N}{B^2M}$ seconds. Finally, the reason we get $\frac{C^2}{M^3}$ in some regimes is that the block size on each GPU also must be at least $\frac{C}{M}$ to avoid being bottlenecked on memory reads.</p>
<p>To sanity check the block tiling scheme above, on an 8xA100 machine the blocks would be 1024x1024 (rounded to the nearest power of 2). Since the dimensionality of many models is around 8192-16384, this means the computation would have to be split across 64-256 machines or 512-2048 total GPUs. This is within the range of possibility, e.g. TPUv4 has 4096 GPUs per node.</p>
<p><strong>Trading off speed and cost.</strong> If we scale down both the block and batch size by a factor of $k$, then the utilization drops to $1/k$, but we decrease the work by a factor of $k^3$&#x2013;therefore, we can complete the multiplication $k^2$ times faster. This works until we start to run into other issues such as memory and network latency, which add up to 1-2 microseconds (and might even increase for large $k$ as it becomes harder to efficiently route information at small block sizes).</p>
<h1 id="detailed-explanation">Detailed Explanation</h1>
<h2 id="a-simple-model-of-gpu-costs-transformers-as-a-stack-of-matrix-multiplies">A Simple Model of GPU Costs: Transformers as a Stack of Matrix Multiplies</h2>
<p>GPUs are used for two important machine learning tasks&#x2014;<em>training</em> and <em>inference</em>. These have somewhat different requirements:</p>
<ul>
<li>At <strong>training time</strong>, the parameters of the model are constantly being updated, and these updates need to be communicated to the GPUs. Additional state, such as momentum terms for the optimizer, must also be stored and updated. This leads to large memory and large communication costs. In the positive direction, data can be processed simultaneously in large batches. This is important in order to amortize the communication costs, by processing many examples at once per parameter update.</li>
<li>At <strong>inference time</strong>, the model parameters are static. They only need to be loaded onto the GPU once at initialization. After that, the main communication cost is processing the input examples (i.e., words) themselves, which is much cheaper because it involves vectors (activations) rather than matrices (weights). To improve parallelization, the model weights are sharded across multiple GPUs, with each GPU storing and processing a contiguous block of a weight matrix (as described in more detail below). In addition to parallelization, sharding is important because the full set of model weights is often too big to fit onto a single GPU.</li>
</ul>
<p>I&#x2019;ll next dive into inference in more detail, since inference time is what governs the serial time per word.</p>
<p>As an abstraction, we&#x2019;ll think of a neural network as performing many consecutive matrix-vector multiplies, interleaved with a number of cheaper non-linear operations. The matrix-vector multiplies are the dominant cost, so we&#x2019;ll focus on those and ignore the others. As a concrete example, consider a transformer model, which primarily consists of self-attention and feed-forward blocks. A self-attention block looks like this:</p>
<p align="center">
<img src="https://bounded-regret.ghost.io/content/images/2022/06/multi_head_attention.jpg">
</p>
<p>The main cost is the 3 linear blocks for the values (V), keys (K), and queries (Q). Each involves multiplying a d-dimensional vector by a dxd matrix (total cost $\approx 3d^2$). For context length C, the attention block involves computing C d-dimensional vector-vector inner products (total cost $\approx Cd$) together with a normalization and softmax operation (total cost O(C)), and finally taking a sum of d-dimensional vectors weighted by the C attention weights (total cost $\approx Cd$).<sup class="footnote-ref"><a href="#fn4" id="fnref4">[4]</a></sup> A typical value of d is 8192-16384, while a typical value of C is 2048. So the matrix multiplies are 6-12 times more expensive than the next most expensive term.<sup class="footnote-ref"><a href="#fn5" id="fnref5">[5]</a></sup></p>
<p>Note that the cost of the matrix-vector multiplies is directly proportional to the size of the matrices. This means that the total cost in FLOPs of a forward-pass is essentially proportional to the number of parameters in the model, and works out to 2 floating-point operations per parameter (1 multiply + 1 add). This will generally be the case in the absence of recurrence or other forms of weight sharing, though I expect weight sharing to eventually be present in future models.</p>
<h2 id="cost-of-implementing-matrix-vector-multiplies-on-gpus">Cost of Implementing Matrix-Vector Multiplies on GPUs</h2>
<p>Implementing a matrix-vector multiply on a GPU has four major costs:</p>
<ol>
<li>We need to <em>communicate</em> and <em>store</em> the parameters of the matrix (once, at initialization).</li>
<li>For each new input, we need to communicate the input vector to the GPU (and send the output vector back to RAM or to other GPUs). This cost can be ignored if the matrix for the previous/next multiply is on the same GPU.</li>
<li>We need to read the data from on-chip memory.</li>
<li>We need to perform the actual multiply operation.</li>
</ol>
<p>I&#x2019;ll ignore (1.), since it can be amortized away, and focus on how costs (2.-4.) add up in practice. I&#x2019;ll start by imagining that all operations happen on a single GPU, then consider parallelizing across multiple GPUs.</p>
<h3 id="warm-up-single-gpu-no-batching">Warm-up: Single GPU, No Batching</h3>
<p>As a simple example, let&#x2019;s consider a 4096-dimensional vector, which needs to get multiplied by a sequence of $L$ $4096 \times 4096$ matrices, with $L=16$. Each matrix entry is 2 bytes<sup class="footnote-ref"><a href="#fn6" id="fnref6">[6]</a></sup>, so we&#x2019;re using $2^{12+12+4+1} = 2^{29}$ bytes in total, or 0.5GB. Most GPUs have at least 10GB of memory, so this fits easily onto a single chip.</p>
<p>For each new input to the model, we need to communicate one 4096-dimensional vector to the GPU. So that&#x2019;s 8192 bytes of communication. In addition, we need 2 x 16 x (4096 x 4096) FLOPs to actually perform the 16 matrix-vector products (2 FLOPs per matrix entry), or 0.5GFLOPs. We similarly need to perform 0.5GB of memory reads to load the matrix into memory (plus a much smaller number of reads and writes for the vector input and output). Thus, overall we need:</p>
<ul>
<li>~8KB of communication</li>
<li>~0.5GB of memory accesses</li>
<li>~0.5GFLOPs of computation</li>
</ul>
<p>How long does each part take? Let&#x2019;s consider an <a href="https://www.nvidia.com/content/dam/en-zz/Solutions/Data-Center/a100/pdf/nvidia-a100-datasheet-nvidia-us-2188504-web.pdf?ref=bounded-regret.ghost.io">A100 GPU</a>, which has 312TFLOP/s of computation, 1.5TB/s of memory bandwidth, and (depending on network setup) ~400GB/s of network bandwidth. Then communication takes 8KB/(400GB/s) = <u>0.02&#x3BC;s</u>. Memory takes 0.5GB/(1.5TB/s) = <u>330&#x3BC;s</u>. And computation takes 0.5GFLOP/(312TF/s) = <u>1.6&#x3BC;s</u>.</p>
<p><em><strong>From a cost perspective, this is terrible!</strong></em> The system is totally bottlenecked on memory reads&#x2014;computation takes only 0.5% of the time that it takes to read from memory, which means that the GPU is only running at 0.5% utilization. In terms of cost, this means you are overpaying for your GPU by a factor of 200.</p>
<p>To solve this, we process inputs in <strong>batches</strong>. Suppose that instead of reading one input, we read 256 inputs at once<sup class="footnote-ref"><a href="#fn7" id="fnref7">[7]</a></sup>, represented as a 4096 x 256 vector. Then our costs change as follows:</p>
<ul>
<li>Communication: 2MB (was 8KB)</li>
<li>Memory: 0.56GB (was 0.5GB&#x2014;the extra .06 is from reading and writing the 4096 x 256 input and output at each layer)</li>
<li>Compute: 128GFLOPs (was 0.5GFLOPs)</li>
</ul>
<p>Now how long does each part take? Communication is now <u>5&#x3BC;s</u>, memory is <u>350&#x3BC;s</u>, and computation is <u>400&#x3BC;s</u>. Now memory and computation take about the same time, and the GPU can run at 100% utilization (in theory). In addition, <strong>the serial time barely increased</strong>. It is now 400&#x3BC;s (or 25&#x3BC;s/layer), up from 330&#x3BC;s before.</p>
<h3 id="tiling-across-gpus">Tiling Across GPUs</h3>
<p>If we want to run the computation as fast as possible, we probably want to parallelize our computation across more than one GPU. For now I&#x2019;m just going to focus on a single 4096 x 4096 matrix multiplication (i.e. one layer of the model).</p>
<p>Let&#x2019;s suppose that instead of one A100 GPU, I have four A100 GPUs. I can think of these GPUs as a 2x2 grid and &#x201C;tile&#x201D; my multiplication across them: processing a 2048 x 2048 block of the matrix in each tile of the grid.</p>
<p>To implement this, given my input (still a 4096 x 256 vector), I do the following:</p>
<ol>
<li>Split the input into two 2048 x 256 vectors, $u_1$ and $u_2$.</li>
<li>Send $u_1$ to the first two machines (getting outputs $v_{11}$ and $v_{12}$) and $u_2$ to the second two machines (getting outputs $v_{21}$ and $v_{22}$).</li>
<li>As a post-processing step, add together $v_1 = v_{11}+v_{12}$ and $v_2 = v_{21}+v_{22}$, then concatenate $v_1$ and $v_2$ into a single output vector $v$.</li>
</ol>
<p align="center">
<img src="https://bounded-regret.ghost.io/content/images/2022/06/gpu_tiling.png">
</p>
<p>Pretty much all the work here happens in step (2.). In this step, each machine must receive and send a 2048 x 256 vector (~2MB total), read or write matrices of size 2048x256, 2048x2048, and 2048x256 (~10MB), and run 2048x2048x256 add-multiply operations (~2GFLOPs). For the same hardware specs as before, this comes out to 5&#x3BC;s for communication, 6&#x3BC;s for memory, and 6&#x3BC;s for computation. Relative to the 25&#x3BC;s/layer from before, we&#x2019;ve achieved a 4x speed-up due to parallelizing across 4 GPUs.</p>
<p>In general, we can continue to parallelize across more and more GPUs by splitting into smaller and smaller blocks, as long as we don&#x2019;t end up bottlenecked by memory or communication costs. In the next section, we&#x2019;ll carefully count the communication, memory, and compute usage as a function of the block and batch size, and analyze what range they need to be in to achieve full GPU utilization.</p>
<h3 id="detailed-count-of-operation-costs">Detailed Count of Operation Costs</h3>
<p>In general, let&#x2019;s suppose that we have a large $d \times d$ matrix multiply, and we want to split it up into smaller blocks. Let $m$ denote the block size, and suppose that we process inputs in batches of size $b$. Then we need $(d/m)^2$ GPUs in total, and each individual GPU performs the following operations:</p>
<ol>
<li>Receives an incoming matrix of length m x b (a batch of b vectors of length m).</li>
<li>Multiplies this m x b matrix by a fixed m x m matrix that is stored on the GPU (i.e., a single block of the weight matrix of the model).</li>
<li>Outputs a vector of length m x b.</li>
</ol>
<p>As in the previous section, there is also some pre- and post-processing to split and combine the d x 1 vectors into m x 1 vectors, but we will ignore those as they generally only contribute lower-order terms.</p>
<p>Overall, this requires $4mb$ bytes of network communication ($mb$ 16-bit floats on both input and output, and each float is two bytes). It requires $4mb + 2m^2$ memory accesses (each number is again 2 bytes, and we need to read an $m \times b$ and $m \times m$ matrix and write an $m \times b$ matrix). Finally, it requires $2m^2b$ floating point operations. Therefore, the total elapsed time is</p>
<p align="center">
$\quad \quad \quad \max\Big(\frac{4mb}{B}, \frac{4mb+2m^2}{M}, \frac{2m^2b}{C}\Big) \quad \quad \quad (\star)$    
</p>
<p>To avoid being memory constrained and reach full GPU utilization, the third term must be at least the second term (see <a href="https://docs.nvidia.com/deeplearning/performance/dl-performance-gpu-background/index.html?ref=bounded-regret.ghost.io#understand-perf">NVIDIA docs</a> for discussion). Therefore, we have the constraint</p>
<p align="center">
$\frac{4mb+2m^2}{2m^2b} \leq \frac{M}{C}$    
</p>
<p>By the same token, to avoid being communication constrained we should have</p>
<p align="center">
$\frac{4mb}{2m^2b} \leq \frac{B}{C}$
</p>
<p>This second equation is easy to solve and implies the block size $m$ should be at least $\frac{2C}{B}$ to avoid communication bottlenecks.</p>
<p>The first equation is a bit trickier. It works out to $\frac{2}{m} + \frac{1}{b} \leq \frac{M}{C}$. Since we already know $m$, this comes out to $\frac{1}{b} \leq \frac{M-B}{C}$, so the block size $b$ should be at least $\frac{C}{M-B}$. Plugging back into the formula $(\star)$, the total elapsed time is</p>
<p align="center">
$\frac{2m^2b}{C} = \frac{8C^2}{B^2(M-B)}$
</p>
<p>But wait! This equation becomes infinite if $M=B$. What went wrong? Well, we set $m$ equal to $\frac{2C}{B}$, but actually it just needs to be at least this large. In fact, it turns out that we always want $m$ to be at least as large as the batch size $b$. So aside from setting $m=\frac{2C}{B}$, the alternative is to set $m$ equal to $b$, in which case we get $m=b=\frac{3C}{M}$. This yields an elapsed time of $\frac{54C^2}{M^3}$. We end up with this elapsed time whenever $M \leq 1.5B$.</p>
<h3 id="one-machine-multiple-gpus">One Machine, Multiple GPUs</h3>
<p>In many cases, we have more than one GPU on a machine. Then communication splits into two costs: communication between RAM and the GPU (or between GPUs), and communication between this machine and other machines. Typically, within-machine communication is fast compared to between-machine communication, so we&#x2019;ll treat cross-GPU (within-machine) communication as &#x201C;free&#x201D;, while cross-machine communication has a network bandwidth of B.</p>
<p>Suppose that each machine has N GPUs. Then in the simplest accounting, each individual GPU only gets $\frac{B}{N}$ of the network bandwidth, and it&#x2019;s as if we&#x2019;re in the single-GPU case above, but with bandwidth $\frac{B}{N}$ instead of $B$.</p>
<p>However, it turns out we can do better. If instead of processing $N$ arbitrary $m \times m$ blocks of the $d \times d$ matrix, we process a $\sqrt{N} \times \sqrt{N}$ grid of $m \times m$ blocks, then we can treat the entire computation as a $m\sqrt{N} \times m\sqrt{N}$ block. In particular, we only need to process input and output vectors of length $m\sqrt{N}$, rather than $mN$. This means that each machine effectively gets network bandwidth $B/\sqrt{N}$, rather than $B/N$ (here I&#x2019;m assuming $N$ is a perfect square).</p>
<p align="center">
<img src="https://bounded-regret.ghost.io/content/images/2022/06/n_to_sqrtn.png">
</p>
<p>This leads to the final formula, which is equivalent to the single-machine formula but replaces $B$ with $B/\sqrt{N}$. We repeat it here for completeness:</p>
<p align="center">
$\text{ElapsedTime} = \left\{ \begin{align*} \frac{54C^2}{M^3} \quad \quad \quad &amp; : \text{ if } B &gt; \frac{2}{3}M\sqrt{N} \\ \frac{8C^2N}{B^2(M-B/\sqrt{N})} &amp; : \text{ else.} \end{align*} \right.$
</p>
<p>Remember that this is the elapsed time for a single matrix multiply. To get the elapsed time for a forward pass, we need to multiply by $L$, which for transformers is usually twice the number of layers.</p>
<h2 id="more-on-memory-constraints">More on Memory Constraints</h2>
<p><a name="roofline"></a></p>
<p>This entire discussion so far assumes that we can actually reach 100% utilization by increasing the batch size. However, some operations are not effectively batchable and end up constrained on memory reads for large batch sizes. For transformers, this happens when computing the self-attention weights, which is a lower-order term for small batch size but becomes the bottleneck for large batch size and context length.</p>
<p>There are a few ways to think about this. First, we could argue that such bottlenecks probably go away (or at least don&apos;t accumulate) in the long run. For instance, Google&apos;s <a href="https://arxiv.org/abs/2204.02311?ref=bounded-regret.ghost.io">PaLM model</a> modifies the self-attention block to partially mitigate this issue. I don&apos;t think this argument entirely holds, since most optimizations target training costs rather than inference costs, but I do think there&apos;s some truth to it.</p>
<p>Alternatively, we could take such bottlenecks as given. Perhaps we actually can&apos;t hope for more than (say) 10% GPU utilization, which also means that the theoretical batch size of $\frac{3C}{M}$ is much larger than necessary (since we&apos;re only trying to hit 10% rather than 100% utilization). This is effectively the same as setting $k = 10$---achieving only 10% utilization but running the computation 100 times faster. In other words, if there are unavoidable memory bottlenecks, our analysis still generally holds, except that we are forced to set $k$ to some value larger than $1$.</p>
<p>Overall, then, I don&apos;t think that memory constraints (from self-attention or other hypothetical blocks) significantly alter the analysis. We can either assume they go away over time, or just restrict our analysis to a certain regime of the GPU utilization $\frac{1}{k}$.</p>
<h2 id="other-possible-bottlenecks">Other Possible Bottlenecks</h2>
<p>In reality, cross-machine communication and GPU memory bandwidth are not the only possible bottlenecks. For instance, we could be bottlenecked by cross-GPU communication within a machine (discussed above), or by L1 or L2 cache speed. But in practice, these are rarely the bottlenecks, so I&#x2019;ve focused above on the two cases that typically matter. The main other case that I think could matter is end-to-end network communication---it could be that each machine has enough network bandwidth, but the overall cluster has a network topology that makes it hard to efficiently route packets. This seems possible to me, but I also think that well-designed clusters can probably avoid this, so for simplicity I ignored it in my analysis.</p>
<p>In addition, I&#x2019;ve made a number of idealized assumptions, such as that C/B and C/M are integers, that all quantities nicely divide each other, and implicitly that many quantities are powers of 2 or divisible by powers of 2 (needed to get good cache performance; not discussed here). I&#x2019;ve also ignored a number of smaller operations like the nonlinearities in each layer, and mostly ignored network and memory latency. I&#x2019;m basically folding these all into the &#x201C;30%-50% GPU utilization&#x201D; fudge factor, which should usually be attainable in practice, but often requires good systems engineering. So, this post isn&#x2019;t a recipe for actually parallelizing your forward pass, but it should give a good idea of how quickly it can be done in principal.</p>
<h1 id="summary">Summary</h1>
<p>Forward passes can be parallelized to a fairly large degree before running into memory or network bottlenecks. Roughly speaking, the time for a single matrix multiply grows quadratically with the GPU FLOPS, and decreases cubically with the network/memory bandwidth. We gave an exact formula (under idealized assumptions) that counts the actual floating-point operations, memory reads/writes, and network usage, and determines the regimes when memory vs. network become the bottleneck resource.</p>
<p>In the next post, I&apos;ll apply this formula to forecast how fast not just today&apos;s models, but also future ones, can be run.</p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>Specifically, I assume the model also generated all the previous tokens and that their activation vectors are cached, so it only needs to compute activation vectors for the current position. <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn2" class="footnote-item"><p>In fact, you are also forced to use multiple GPUs, because state-of-the-art models don&#x2019;t fit into a single GPU&#x2019;s memory. <a href="#fnref2" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn3" class="footnote-item"><p>I chose 40% to be a &#x201C;decent&#x201D; level&#x2013;generally attainable after working hard to optimize out bottlenecks, but below the best possible. <a href="#fnref3" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn4" class="footnote-item"><p>Technically speaking, for a context window of size C, all costs should be multiplied by C (since we need to do all these computations for each token in the context). However, assuming that we are reading or writing a sequence of consecutive words, the previous C-1 tokens have already been computed and their results can be cached and re-used. Naive caching increases memory costs by a nontrivial amount, but there are tricks such as rematerialization that reduce this at a ~33% overhead in computation. <a href="#fnref4" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn5" class="footnote-item"><p>One very important caveat is that the self-attention operations cannot be efficiently batched, because the key and query vectors both change for each batch item. This means that self-attention becomes memory-bottlenecked faster than other operations, as I&#x2019;ll discuss in more detail later. <a href="#fnref5" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn6" class="footnote-item"><p>Assuming <a href="https://en.wikipedia.org/wiki/Bfloat16_floating-point_format?ref=bounded-regret.ghost.io">bfloat16</a> format, which is typically used to speed up inference. <a href="#fnref6" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn7" class="footnote-item"><p>I chose 256 because it was the power of 2 closest to 200, which was the amount by which we were underutilizing the GPU. <a href="#fnref7" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
<!--kg-card-end: markdown-->]]></content:encoded></item><item><title><![CDATA[Early 2022 Paper Round-up (Part 2)]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p><a href="https://bounded-regret.ghost.io/early-2022-paper-round-up/">Last week</a>, I talked about six recent papers from our group, and discussed the first two in detail. This week, I&apos;ll discuss the remaining four. They fall into two categories: robustness, and science of ML.</p>
<h2 id="robustness">Robustness</h2>
<p>By robustness, I mean both making systems less likely to fail in</p>]]></description><link>https://bounded-regret.ghost.io/early-2022-paper-round-up-part-2/</link><guid isPermaLink="false">6261c59e7604fa003d006b1d</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Thu, 21 Apr 2022 23:31:50 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p><a href="https://bounded-regret.ghost.io/early-2022-paper-round-up/">Last week</a>, I talked about six recent papers from our group, and discussed the first two in detail. This week, I&apos;ll discuss the remaining four. They fall into two categories: robustness, and science of ML.</p>
<h2 id="robustness">Robustness</h2>
<p>By robustness, I mean both making systems less likely to fail in new situations, and being able to predict when and how they will fail. Our three papers address different aspects of this: the first seeks to automatically estimate a model&#x2019;s performance in a new situation, the second seeks to understand in what way open-ended generation systems fail, and the third provides a training procedure that improves robustness along several dimensions.</p>
<p><strong>Predicting Out-of-Distribution Error.</strong> Yaodong Yu, Zitong Yang, and Alex Wei sought to solve the following problem: given a classifier $\theta$ trained on a distribution $p_{\mathrm{in}}$, and given sample inputs from a new distribution $p_{\mathrm{out}}$, can we predict how well $\theta$ works on the new distribution $p_{\mathrm{out}}$? For instance, maybe an image classifier was trained on images in the US ($p_{\mathrm{in}}$), and we want to know how well it will do on images in France ($p_{\mathrm{out}}$). Since we have no output labels for $p_{\mathrm{out}}$, this is an unsupervised estimation problem.</p>
<p>There are a number of heuristics for predicting out-of-distribution error, such as looking at the model&apos;s confidence or the disagreement rate between multiple models with different random seeds. However, most of these heuristics have the same problem: they are insensitive to changes that are orthogonal to the training manifold. As a result, they tend to fail on &#x201C;hard&#x201D; distribution shifts&#x2014;for instance, given a distribution of adversarial examples, they all predict the model will have high accuracy.</p>
<p>We present a new method, ProjNorm, that does well on hard distribution shifts. For instance, compared to ATC (a strong existing method), we make more accurate predictions when the error is large:</p>
<p><img src="https://bounded-regret.ghost.io/content/images/2022/04/ProjNorm.png" alt="ProjNorm" loading="lazy"></p>
<p>The method is simple, but it takes a bit of time (for me at least!) to grasp the intuition, so I&#x2019;ll leave that for the paper. But basically, you use the model $\theta$ to pseudo-label the samples from $p_{\mathrm{out}}$, fine-tune a model on those pseudo-labels, and then compare that new model to $\theta$. It turns out that this can be interpreted as a nonlinear projection operator and overcomes the problems with previous methods.</p>
<p><em>Why you should care.</em> Many of the ways that ML models could fail come from generalizing poorly. For instance, a system might learn an objective function that generates good behavior in one situation, but the wrong behavior in new situations. Detecting these failures automatically would be very useful if we could do so reliably. Doing so could be very hard in general, and I&#x2019;d say the jury is very much still out, but this paper has made me more optimistic that it&#x2019;s possible to do something nontrivial and interesting.</p>
<p><strong>Capturing Failures of Large Language Models.</strong> Most work on robustness focuses on classification error rates&#x2013;how much more often a model gets the answer wrong when presented with unusual or out-of-distribution of inputs. However, modern language models are open-ended: rather than a class label, they generate arbitrary text. So to understand how they behave on unusual inputs, it&#x2019;s not enough to just understand the error rate. For instance, one language model might err by producing gibberish, while another responds with insults or other toxic text. Or a code model could either produce code that doesn&#x2019;t compile, or code that deletes all files in the home directory.</p>
<p>To tame the complexity of open-ended generation, Erik Jones used human cognitive biases to taxonomize and test a subset of possible failure modes. For instance, the <em>framing</em> and <em>anchoring</em> biases led us to hypothesize that when incorrect code appears in a model&#x2019;s context, similar code will appear in the outputs to new prompts. We design experiments to test and quantify how often this occurs, and find that it is indeed common. Inspired by these and other cognitive biases, we unearth several new types of failure modes that code generation models are prone to.</p>
<p><em>Why you should care.</em> In my opinion, robustness is most important in what I&#x2019;ll call &#x201C;structured output&#x201D; settings&#x2014;where the output is a complex object such as a sentence, a trajectory, or a computer program, rather than just a class label. The reason to care about these settings is twofold: first, the cost of failures is potentially much larger&#x2014;the maximum damage I can do with a computer program is greater than the maximum damage I can do with a class label. Second, some important classes of failures, such as <a href="https://arxiv.org/abs/2105.14111?ref=bounded-regret.ghost.io">objective misgeneralization</a>, only show up in structured output settings. Our work provides useful approaches for finding robustness failures in these structured output settings.</p>
<p><strong>Comprehensively Improving Safety Measures.</strong> Dan Hendrycks, Andy Zou, and several other collaborators designed a new data augmentation strategy called PixMix, which is partly inspired by <a href="https://arxiv.org/abs/2101.08515?ref=bounded-regret.ghost.io">Kataoka et al.&#x2019;s observation</a> that fractals are an effective source of pretraining images.</p>
<p>PixMix works by repeatedly mixing with a high-complexity image (such as a fractal) and then applying a standard augmentation such as posterization. Two resulting example images are shown below:</p>
<p><img src="https://bounded-regret.ghost.io/content/images/2022/04/pixmix2.png" alt="pixmix2" loading="lazy"></p>
<p>While PixMix does not improve accuracy more than other data augmentation methods, it helps significantly more with many safety properties, such as calibration, anomaly detection, robustness to corruptions, and robustness to adversaries.</p>
<p><em>Why you should care.</em> PixMix takes a different perspective from other data augmentation strategies. Rather than trying to maximize the entropy or the diversity of the augmented images, it seeks to maximize their complexity. In general, complexity feels like an important and understudied concept for AI safety. For instance, it seems plausible to me that what is most important for controlling an AI system&#x2019;s behavior is the complexity of its supervision signal&#x2014;supervision that is not complex enough will not pin down the behavior in enough cases. In another direction, the simplest case for AI posing risks is that it is a complex self-organizing system, and most such systems are difficult to control and create unintended consequences. Given the potential importance of complexity, I&#x2019;m excited to see it used to make ML systems safer.</p>
<h2 id="science-of-ml">Science of ML</h2>
<p>&#x201C;Science of ML&#x201D; is a fairly broad term, but for me it means trying to understand laws that govern neural network behavior, such that we can predict that behavior in new situations. One particular use case is for <em>forecasting</em>&#x2014;predicting what will happen as we make neural nets bigger and train them on more data.</p>
<p><strong>Predicting How Real-World Representations Generalize.</strong> Alex Wei and Wei Hu improved our understanding of neural networks, by identifying a mathematical framework that helps clarify neural scaling laws, as well as the role of pretraining.</p>
<p>Because neural networks are difficult to analyze, we studied linear models derived from neural networks. Specifically, given a trained neural network, you can take a first-order Taylor approximation in parameter space to obtain a linear model, which will usually have more parameters than the number of data points (since most neural networks are overparameterized). As a result, we treat the model as a nonparametric (kernel) model, which we call the <em>empirical neural tangent kernel</em> (eNTK). We can check empirically that while eNTKs don&#x2019;t perform as well as neural networks, they do much better than traditional NTK models (which are obtained from random rather than trained networks). The eNTK models also exhibit <a href="https://arxiv.org/abs/2001.08361?ref=bounded-regret.ghost.io">power law scaling</a> just like regular neural networks do.</p>
<p>We might therefore hope that understanding eNTKs will help us to understand neural networks. To help with this, Alex and Wei set out to understand the generalization error of neural networks (the error on fresh test samples after the model has been trained on N training samples). It turns out that the generalization error can be effectively predicted by a function called the <em>generalized cross-validation estimator</em> (GCV), and that this can be mathematically justified in terms of random matrix laws. More interestingly, the GCV estimator predicts that the error depends primarily on two terms: the <em>effective dimension</em>, and the <em>alignment</em> between the eNTK features and the true function we want to learn. Both of these terms are needed to accurately predict neural scaling laws, and they are also needed to understand pretraining. For instance, pretrained models actually have larger effective dimension (contrary to my initial intuition), and are better primarily because they have much better alignment with the true function.</p>
<p><em>Why you should care.</em> Neural scaling laws are a promising avenue to help forecast the behavior of future ML models. However, the reason they arise is still not fully understood. This is important because I expect we will need to deal with much more complex scaling laws in the future, such as the joint scaling between a policy model and a reward model when learning reward functions from human feedback. It may be too expensive to exhaustively map out these laws empirically, and theoretical understanding can help us reach the right answer more efficiently. I think Alex and Wei&#x2019;s work brings us a step closer to doing that.</p>
<!--kg-card-end: markdown-->]]></content:encoded></item><item><title><![CDATA[Early 2022 Paper Round-up]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p>My students and collaborators have been doing some particularly awesome work over the past several months, and to highlight that I wanted to summarize their papers here, and explain why I&#x2019;m excited about them. There&#x2019;s six papers in three categories.</p>
<p><strong>Human-Aligned AI</strong></p>
<ul>
<li><a href="https://arxiv.org/abs/2201.03544?ref=bounded-regret.ghost.io">The Effects of Reward</a></li></ul>]]></description><link>https://bounded-regret.ghost.io/early-2022-paper-round-up/</link><guid isPermaLink="false">62586b0b8af312003dd966d0</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Thu, 14 Apr 2022 20:47:10 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p>My students and collaborators have been doing some particularly awesome work over the past several months, and to highlight that I wanted to summarize their papers here, and explain why I&#x2019;m excited about them. There&#x2019;s six papers in three categories.</p>
<p><strong>Human-Aligned AI</strong></p>
<ul>
<li><a href="https://arxiv.org/abs/2201.03544?ref=bounded-regret.ghost.io">The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models</a> (<em>w/ Alex Pan, Kush Bhatia</em>)</li>
<li><a href="https://arxiv.org/abs/2201.12323?ref=bounded-regret.ghost.io">Summarizing Differences between Text Distributions with Natural Language</a> (<em>w/ Ruiqi Zhong, Charlie Snell, Dan Klein</em>)</li>
</ul>
<p><strong>Robustness</strong></p>
<ul>
<li><a href="https://arxiv.org/abs/2202.05834?ref=bounded-regret.ghost.io">Predicting Out-of-Distribution Error with the Projection Norm</a> (<em>w/ Yaodong Yu, Zitong Yang, Alex Wei, Yi Ma</em>)</li>
<li><a href="https://arxiv.org/abs/2202.12299?ref=bounded-regret.ghost.io">Capturing Failures of Large Language Models via Human Cognitive Biases</a> (<em>w/ Erik Jones</em>)</li>
<li><a href="https://arxiv.org/abs/2112.05135?ref=bounded-regret.ghost.io">PixMix: Dreamlike Pictures Comprehensively Improve Safety Measures</a> (<em>w/ Dan Hendrycks, Andy Zou, Mantas Mazeika, Leonard Tang, Bo Li, Dawn Song</em>)</li>
</ul>
<p><strong>Science of ML</strong></p>
<ul>
<li><a href="https://arxiv.org/abs/2203.06176?ref=bounded-regret.ghost.io">More Than a Toy: Random Matrix Models Predict How Real-World Neural Representations Generalize</a> (<em>w/ Alex Wei, Wei Hu</em>)</li>
</ul>
<p>I&apos;ll go over the first category (human-aligned AI) today, and save the other two for next week. As always, we love getting feedback on our work, so let us know what you think!</p>
<h2 id="human-aligned-ai">Human-Aligned AI</h2>
<p>While AI alignment is a somewhat subtle and complex problem, two basic issues are that (1) ML systems often hack their reward functions, and (2) human supervision doesn&#x2019;t necessarily solve this, because humans can&#x2019;t easily understand the consequences of intervening on complex systems. Alex and Ruiqi&#x2019;s papers help address each of these questions in turn.</p>
<p><strong>Mapping and Mitigating Misaligned Models.</strong> What Alex Pan and Kush Bhatia did was construct a wide variety of reinforcement learning environments where reward hacking is possible, and measured the extent to which it occurred. They do this by defining both a &#x201C;proxy&#x201D; and &#x201C;true&#x201D; reward, and look at what happens to the true reward as we optimize the proxy reward. Two key insights are that:</p>
<ul>
<li>Optimizing the proxy reward for longer, or with larger policy models, often leads to <strong>lower</strong> true reward.</li>
<li>When this happens, it sometimes occurs suddenly, via a <strong>phase transition</strong> (in both the quantitative reward and the qualitative behavior).</li>
</ul>
<p>A simple illustration of both is a traffic simulator, where the RL agent is trying to shape traffic flow to be more efficient. Small neural net models help cars merge efficiently onto the highway, but large models instead block cars from merging at all (which allows the cars already on the highway to move really fast and consequently achieves high proxy reward).</p>
<p><img src="https://bounded-regret.ghost.io/content/images/2022/04/reward_misspecification.png" alt="reward_misspecification" loading="lazy"></p>
<p>In this case, the proxy reward was actually the reward suggested by the designes of the traffic simulator, highlighting the difficulty of choosing good reward functions in practice.</p>
<p><em>Why you should care.</em> Our results show that reward hacking is likely to become a bigger problem in the future (since it seems to get worse as models get larger). It also shows that in some cases, reward hacking could appear suddenly or unexpectedly. This seems important to investigate and we are hoping others will join us in continuing to understand when reward hacking occurs and how to prevent it.</p>
<p><strong>Summarizing Differences Between Text Distributions.</strong> Ruiqi Zhong and Charlie Snell built a system that does the following: given two different distributions of natural language text, it generates a natural language description of what is different about the two distributions. It works by commbining a proposer (which consumes a small number of examples and generates hypotheses) with a verifier (which re-ranks all the hypotheses on using a large set of examples). An example is shown below:</p>
<p><img src="https://bounded-regret.ghost.io/content/images/2022/04/proposer_verifier.png" alt="proposer_verifier" loading="lazy"></p>
<p>While this might sound like a simple task, many tasks can be reduced to it. Here are a couple examples we consider in the paper:</p>
<ul>
<li><strong>Debugging datasets.</strong> Classification datasets intended to test some capability often contain a spurious cue that makes the task easier. We can find these spurious cues by feeding the positive and negative class as the two distributions to our system. On the MNLI dataset, we find the known spurious cue <em>&#x201C;has a negative verb&#x201D;</em>, and on a spam dataset we found the novel spurious cue <em>&#x201C;has a high number of hyperlinks&#x201D;</em>.</li>
<li><strong>Labeling text clusters.</strong> Unsupervised algorithms often group text into semantically meaningful clusters. However, since there are many such clusters, it can be expensive to label them by hand. By asking how one cluster differs from the union of the others, our system can do this automatically. Some example cluster descriptions are <em>&quot;is about art history&quot;</em>, <em>&quot;contains numbers&quot;</em>, <em>&quot;is about a sports team&quot;</em>, <em>&quot;is about a scientific discovery&quot;</em>, and <em>&quot;describes a person&quot;</em>. Our system outperformed a human expert, in terms of accuracy of the descriptions as measured by MTurkers.</li>
</ul>
<p>Some other applications are describing what inputs activate a neuron, how language on Twitter has changed over time, how teacher evaluations differ across genders, or what the differences are between an in-distribution and out-of-distribution dataset.</p>
<p><em>Why you should care.</em> One hope for AI is that it will help humans make better decisions than they could by themselves. One way to do this is by consuming complex data that humans could not easily process and then explaining it in a useful way. Our system does this&#x2014;it would be time-consuming to manually look over two large datasets to understand how they differ, but the system can do it automatically. We hope future work will both improve this type of system (there is definitely still headroom!) and design ML systems that help humans understand other types of complex data as well.</p>
<h3 id="summary">Summary</h3>
<p>We have one paper that is the first empirical demonstration of an important failure mode (phase transitions for reward hacking), and another that can eventually amplify human capabilities, by helping them understand complex data. Both pretty exciting! (At least in my biased opinion.)</p>
<p>If you liked these, check back next week for the other four papers!</p>
<!--kg-card-end: markdown-->]]></content:encoded></item><item><title><![CDATA[Appendix: More Is Different In Other Domains]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p>In <em><a href="https://bounded-regret.ghost.io/p/1527e9dd-c48d-4941-9b14-4f7293318d5c/">Future ML Systems Will Be Qualitatively Different</a></em>, I argued that we should expect ML systems to exhibit emergent capabilities. My main support for this was four historical examples of emergence in ML.</p>
<p>In some sense, extrapolating from only four data points is pretty sketchy. It&apos;s hard to</p>]]></description><link>https://bounded-regret.ghost.io/appendix-more-is-different-in-related-fields/</link><guid isPermaLink="false">6196aa089ee68c003bbdf7a6</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Tue, 08 Feb 2022 16:00:00 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p>In <em><a href="https://bounded-regret.ghost.io/p/1527e9dd-c48d-4941-9b14-4f7293318d5c/">Future ML Systems Will Be Qualitatively Different</a></em>, I argued that we should expect ML systems to exhibit emergent capabilities. My main support for this was four historical examples of emergence in ML.</p>
<p>In some sense, extrapolating from only four data points is pretty sketchy. It&apos;s hard to tell if these examples are the start of a trend, or cherry-picked to tell a story. In low-data regimes like this, it&apos;s helpful to have a prior, and so I&apos;ll spend this appendix looking at related fields of science and examining how common emergent behavior is in those fields.</p>
<p>In short, my conclusion is that emergence is <em>very common</em> throughout the sciences, and <em>especially common</em> in biology, which I view to be most analogous to ML. As such, I think it should be our default expectation for ML, and the four data points from before primarily serve to confirm this. Personally, forming this &quot;prior&quot; updated my views about as much as the (combined) historical examples that I previously discussed for ML.</p>
<h2 id="more-is-different-across-domains">More Is Different Across Domains</h2>
<p><img src="https://bounded-regret.ghost.io/content/images/2021/11/gecko-feet.png" alt="gecko-feet" loading="lazy"></p>
<p>Recall that emergence refers to the idea that More Is Different: that quantitative changes can lead to qualitatively different phenomena. While this idea was <a href="https://science.sciencemag.org/content/177/4047/393?ref=bounded-regret.ghost.io">first articulated</a> by the physicist Philip Anderson, it occurs in many other domains as well:<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup></p>
<ul>
<li><strong>Biology:</strong> <a href="https://pubmed.ncbi.nlm.nih.gov/20023846/?ref=bounded-regret.ghost.io">Gecko feet</a> are covered with tiny structures called spatulae (shown above), consisting of many keratin molecules woven together. Spatulae are responsible for geckos&#x2019; ability to walk up walls, but it&#x2019;s clear that we couldn&#x2019;t &quot;scale down&quot; the structure and retain the same ability---you need enough keratin to form the complex bristles shown above.</li>
<li><strong>Physics:</strong> Siloles (a type of molecule) are not luminescent individually, but <a href="https://academic.oup.com/nsr/article/8/6/nwaa266/6009035?ref=bounded-regret.ghost.io">become luminescent</a> when put together in aggregate. This is because the aggregate is more rigid, reducing intramolecular motion that otherwise inhibits the production of photons.</li>
</ul>
<!-- * **Nuclear physics:** The first nuclear reaction required 771,000 pounds of graphite, 80,590 pounds of uranium oxide, and 12,400 pounds of uranium metal piled 57 layers high. With 56 layers the reaction doesn't go critical. This is because neutrons escaping at the edges would bring $k$ (the neutron reproduction number) below 1. The enormous size was needed to make the surface to volume ratio small enough. (Now we achieve the same effect more efficiently with confined explosions, which compress the molecules to high enough density to achieve criticality with smaller volume.) -->
<ul>
<li><strong>Computers:</strong> Operating systems only arose once computers became fast enough. Before that, individual programs took long enough that task management could be done by hand. Greater speed both produced the demand for automation and the capacity to support an operating system&#x2019;s overhead.</li>
<li><strong>Economics:</strong> Increased population size enables increased specialization. Hunter-gatherer bands could not support smiths and architects. In the modern world, the emergence of Ford and other mass producers required a large enough consumer market to invest in large factories, standardization, and so on.</li>
</ul>
<p>For a broadly accessible introduction to emergence, I recommend <a href="https://www.youtube.com/watch?v=16W7c0mb-rE&amp;ref=bounded-regret.ghost.io">this video</a> by Kurzgesagt. For a slightly longer treatment, a reader also recommended <a href="https://www.youtube.com/watch?v=QItTWZc7hKs&amp;ref=bounded-regret.ghost.io">this other video</a>.</p>
<h2 id="zooming-in-on-biology">Zooming In On Biology</h2>
<p>Among the physical sciences, biology is the domain that seems most analogous to machine learning. While analogies between artificial and biological neurons are overwrought, these two fields share genuine, fundamental similarities. Both study objects that are shaped by complex optimization processes (evolution for biology, gradient descent for ML). The objects are composed of simple well-understood parts, but they are difficult to understand in aggregate because optimization puts the parts together in complex ways. Progress in ML benefits from Moore&apos;s law, while biological understanding benefits from the <a href="https://en.wikipedia.org/wiki/Carlson_curve?ref=bounded-regret.ghost.io">Carlson curve</a> for DNA sequencing (and earlier from a <a href="https://bounded-regret.ghost.io/measurement-and-optimization/">Moore-like law</a> for X-ray crystallography).</p>
<p>Biology is also the domain where More Is Different holds most strongly. In biology, macromolecules (e.g. proteins) have complex structures that cannot exist in small molecules, and which support important functions. For instance, hemoglobin transports oxygen efficiently due to a <a href="https://en.wikipedia.org/wiki/Oxygen%E2%80%93hemoglobin_dissociation_curve?ref=bounded-regret.ghost.io">nonlinear dissociation curve</a> that wouldn&apos;t be possible with small molecules.</p>
<p>One level up, protein polymers again unlock new structure and function, such as actin microfilaments forming the cytoskeleton. Muscles further combine actin microfilaments into fibres that can contract, enabling controlled motion.</p>
<p>In a different direction, long DNA macromolecules allow the transfer of genetic information. Smaller molecules simply don&apos;t have enough states to reliably encode a genome.</p>
<p>Finally, complex organs such as eyes need a huge number of cells in even their simplest form--fruit flies, whose visual resolution is near the minimum to detect objects, have eyes with 16,000 cells. Even among eyes, different numbers of cells (and hence different visual acuities) lead to qualitative differences. Spiders <a href="https://today.duke.edu/2018/05/details-look-sharp-people-may-be-blurry-their-pets?ref=bounded-regret.ghost.io">create patterns</a> in their webs that birds can see (and thus avoid, to mutual benefit) but that insects cannot.</p>
<p><img src="https://bounded-regret.ghost.io/content/images/2021/11/spider_resolution.png" alt="spider_resolution" loading="lazy"></p>
<h2 id="assorted-additional-examples">Assorted Additional Examples</h2>
<p>Here are some additional examples of emergent behavior, some of them more ambiguous than others:</p>
<ul>
<li><strong>Ants.</strong> A small number of ants will wander around and starve to death, but a large number of ants forms a complex self-sustaining colony.</li>
<li><strong>Internet.</strong> ARPANET connected a few hundred hosts and was a platform for research. The world-wide-web connects a billion hosts and has transformative effects on daily life.</li>
<li><strong>Transistors.</strong> A few transistors lets you build a radio. With 170 transistors you can build an <a href="https://www.righto.com/2017/01/die-photos-and-reverse-engineering.html?ref=bounded-regret.ghost.io">ALU</a>, and with thousands you can build a <a href="https://en.wikipedia.org/wiki/Intel_4004?ref=bounded-regret.ghost.io">microprocessor</a>.</li>
<li><strong>Neurons.</strong> It is plausible that the main neurophysiological difference between humans and other primates is <a href="https://www.sciencedirect.com/science/article/pii/S2352154616302637?ref=bounded-regret.ghost.io">having more neurons</a>, rather than any fundamental difference in how the neurons are organized.</li>
<li><strong>Cities.</strong> Cities are more than groups of people: they also have events, infrastructure, governance, and culture.</li>
<li><strong>Life.</strong> A cell is alive, but if you separate out the individual elements they are not alive.</li>
<li><strong>Qubits.</strong> A 50-bit quantum computer is a curiosity, but a 20 megabit quantum computer could break the world&#x2019;s encryption.</li>
<li><strong>Practice.</strong> If you practice a skill a little bit, you get a bit more proficient. If you practice it a lot, it becomes &#x201C;chunked&#x201D; in your brain and can be used to build further abstractions.</li>
</ul>
<h2 id="counterarguments-and-conclusion">Counterarguments and Conclusion</h2>
<p>Emergent behavior occurs, at the very least, in biology, physics, economics, and computer science. In biology, it occurs ubiquitously: for DNA, for hemoglobin, for muscles, for eyes.</p>
<p>In <em><a href="https://bounded-regret.ghost.io/p/74d500d2-a980-4720-984a-c016284ecdc2/">Empirical Findings Generalize Surprisingly Far</a></em>, I further argued that empirical findings often generalize even in the presence of these emergent phenomena, citing examples in biology. But does this hold for other emergent domains, such as physics and economics? For physics, the answer is a clear yes, because of physical symmetries and conservation laws. Economics, on the other hand, is a field where <a href="https://en.wikipedia.org/wiki/External_validity?ref=bounded-regret.ghost.io">external validity</a> is notoriously difficult to come by.</p>
<p>Which of these is a better reference class for machine learning? Economics, like biology and machine learning, studies complex systems (humans and economies). However, it is also an area where controlled experimentation is difficult and sometimes impossible. In machine learning, it is easy to run controlled experiments---far easier than biology or physics.</p>
<p>I personally think that rapid controlled experimentation is the key to uncovering lawlike behavior, and that in this sense ML is more like biology and physics than economics. If we could experiment on economies as easily as we could on neural networks, I think we would have a much better understanding of general economic laws. But I could be wrong. I think one strong indicator will be whether the emerging field of science of ML<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup> uncovers important robust phenomena in the next five years. If it does, and those trends survive repeated phase transitions, then we&#x2019;ll have objectively evaluable evidence about whether empirical phenomena in ML can successfully generalize. I&#x2019;m personally optimistic, but ultimately time will tell.</p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>The <a href="https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/">introductory post</a> to the series included several additional examples: DNA, uranium, water, traffic, and specialization. <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn2" class="footnote-item"><p>It&#x2019;s possible that Science of ML won&#x2019;t be the subfield to discover these phenomena. For instance, they might instead be discovered through work on interpretability or by people trying to engineer better systems. I&apos;d still count that case as a &quot;success&quot; for my prediction. <a href="#fnref2" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
<!--kg-card-end: markdown-->]]></content:encoded></item><item><title><![CDATA[Empirical Findings Generalize Surprisingly Far]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p>Previously, I <a href="https://bounded-regret.ghost.io/p/1527e9dd-c48d-4941-9b14-4f7293318d5c/">argued</a> that emergent phenomena in machine learning mean that we can&apos;t rely on current trends to predict what the future of ML will be like. In this post, I will argue that despite this, empirical findings often do generalize very far, including across &quot;phase transitions&</p>]]></description><link>https://bounded-regret.ghost.io/empirical-findings-generalize-surprisingly-far/</link><guid isPermaLink="false">6196a9f19ee68c003bbdf7a0</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Tue, 01 Feb 2022 22:18:00 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p>Previously, I <a href="https://bounded-regret.ghost.io/p/1527e9dd-c48d-4941-9b14-4f7293318d5c/">argued</a> that emergent phenomena in machine learning mean that we can&apos;t rely on current trends to predict what the future of ML will be like. In this post, I will argue that despite this, empirical findings often do generalize very far, including across &quot;phase transitions&quot; caused by emergent behavior.</p>
<p>This might seem like a contradiction, but actually I think divergence from current trends and empirical generalization are consistent. Findings do often generalize, but you need to think to determine the right generalization, and also about what might stop any given generalization from holding.</p>
<p>I don&apos;t think many people would contest the claim that empirical investigation can uncover deep and generalizable truths. This is one of the big lessons of physics, and while some might attribute physics&apos; success to <a href="https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences?ref=bounded-regret.ghost.io">math</a> instead of empiricism, I think it&apos;s clear that you need empirical data to point to the right mathematics.</p>
<p>However, just invoking physics isn&apos;t a good argument, because physical laws have fundamental symmetries that we shouldn&apos;t expect in machine learning. Moreover, we care specifically about findings that continue to hold up <em>after</em> some sort of emergent behavior (such as few-shot learning in the case of ML). So, to make my case, I&apos;ll start by considering examples in deep learning that have held up in this way. Since &quot;modern&quot; deep learning hasn&apos;t been around that long, I&apos;ll also look at examples from biology, a field that <em>has</em> been around for a relatively long time and where More Is Different is ubiquitous (see <a href="https://bounded-regret.ghost.io/p/98db450b-c9bc-4e0d-98ce-1909ba980427/">Appendix: More Is Different In Other Domains</a>).</p>
<h2 id="empirical-generalization-in-deep-learning">Empirical Generalization in Deep Learning</h2>
<p>I&apos;ll consider three examples in deep learning: adversarial examples, data efficiency, and out-of-distribution generalization.</p>
<p><strong>Adversarial examples.</strong> Adversarial examples were <a href="https://arxiv.org/abs/1312.6199?ref=bounded-regret.ghost.io">first discovered</a> in 2013, a year after the <a href="https://papers.nips.cc/paper/2012/hash/c399862d3b9d6b76c8436e924a68c45b-Abstract.html?ref=bounded-regret.ghost.io">AlexNet</a> paper (which arguably marked the start of &quot;modern&quot; deep learning). Since then, there have been at least two qualitative changes in deep networks---pretraining to provide better inductive bias, and the emergence of few-shot learning---plus some smaller changes in architecture. As far as I know, adversarial examples affect every neural network model that exists. Moreover, the main (partial) remedy, <a href="https://arxiv.org/abs/1706.06083?ref=bounded-regret.ghost.io">adversarial training</a>, is the same in every architecture and domain.</p>
<p><strong>Data efficiency.</strong> Starting around 2016, there were papers showing that learned representations from pre-trained models were more data-efficient compared to randomly-initialized models. Moreover, it seemed that pre-training on more and better data increased data efficiency further. Taken to its logical extreme, this meant that with enough data you should be able to learn from very few examples--which is what&apos;s happened, for both <a href="https://arxiv.org/abs/1912.11370?ref=bounded-regret.ghost.io">fine-tuning</a> and <a href="https://arxiv.org/abs/2005.14165?ref=bounded-regret.ghost.io">few-shot learning</a>.</p>
<p>The findings above are in computer vision and NLP, but I&apos;d bet that in pretty much any domain more unsupervised data will mean you need less supervised data, and that this trend will hold until you&apos;re close to information-theoretic limits (i.e. needing only a handful of examples). I also expect this to continue holding even after ML models gain some new emergent capability such as good long-term planning.</p>
<!-- I started thinking about out-of-distribution (OOD) generalization around 2015, and for the first couple years my view was that OOD behavior was strongly governed by a model's inductive bias---without a careful, well-chosen inductive bias, even if a model did will in-distribution it would generalize in some totally crazy way off-distribution. An example might be an image model picking up on some spurious, imperceptible regularity in the data---perhaps images from a certain category are slightly brighter or had slightly more of a certain weirdly-shaped edge.

I now think this view is wrong. -->
<p><strong>Out-of-distribution generalization.</strong> This one is a bit more fuzzy and qualitative, and is a prediction about the future rather than empirical evidence about the past. The question is: how will neural networks behave in &quot;out-of-distribution&quot; situations where the training data hasn&apos;t fully pinned down their behavior? On a spectrum from &quot;completely randomly&quot; (0) to &quot;exactly as intended&quot; (10), my current view is around an 8/10. Intuitively, neural networks &quot;want&quot; to generalize, and will make reasonable extrapolations as long as:</p>
<ul>
<li>The in-distribution data is reasonably diverse</li>
<li>The in-distribution accuracy is high (for a binary task, something like 97% or higher).</li>
</ul>
<p>In these cases I don&apos;t mean that they will always get good OOD accuracy. But I think the model will pick from some fairly low-dimensional space of &quot;plausible&quot; generalizations. A model trained only on images from the United States might be confused by French street signs, but it will mostly do so by either ignoring the text or substituting a perceptually similar American sign.</p>
<p>Another way of putting this is that in domains where a neural net is proficient, there is a relatively low-dimensional space of &quot;possible&quot; generalizations that the network might pick. This is intuitively consistent with the point above on data efficiency---since the possibility space is low-dimensional, it doesn&apos;t take too much data to identify the &quot;right&quot; generalization.</p>
<p>I expect this to continue to hold as neural nets become more powerful: concretely, as long as a model is proficient at a task, even fairly weak signals about how it &#x201C;should&#x201D; behave in a new situation will be enough to push it in the right direction.</p>
<h3 id="how-this-relates-to-human-aligned-ai">How This Relates to Human-Aligned AI</h3>
<p>Not only do I expect the trends above to robustly hold, I also think they are each important components for thinking about safe AI.</p>
<p>First, any strategy for making future ML systems safe either needs a solution to adversarial examples or needs to work in spite of them. I would also bet that any such solution will feature adversarial training as a major component. Now, maybe we didn&apos;t need the empirical data to conclude this, and it should have just been obvious a priori. But the papers introducing these concepts have thousands of citations each, so if these sorts of things are obvious a priori to you, then you could instantly become one of the most successful ML researchers. Unless you&apos;re <a href="https://scholar.google.ca/citations?user=iYN86KEAAAAJ&amp;hl=en&amp;ref=bounded-regret.ghost.io">Ian Goodfellow</a>, I&apos;m a bit skeptical.</p>
<p>Second, given the prevalence of reward functions <a href="https://arxiv.org/abs/2009.01325?ref=bounded-regret.ghost.io">learned from human feedback</a>, we might be concerned that AI will learn to fool the human supervisors rather than doing what humans actually want. If &quot;fool people&quot; and &quot;do what they want&quot; were merely two blips within some limitless space of ways that a network might interpret its reward signal, then we&apos;d face a pretty intractable problem: almost all points in the space of possible network behaviors would be bad (something other than &#x201C;do what humans want&#x201D;) and it would be hard to even locate the good solution.</p>
<p>However, I don&apos;t think this is the world we live in. Both data efficiency and &quot;wanting&quot; to generalize suggest that &quot;do what humans actually want&quot; is part of a fairly simple space of natural generalizations, and it just won&apos;t take that many additional bits of information to pick it out from this space. There&apos;s still a challenge, since <a href="https://bounded-regret.ghost.io/p/bdc26786-ab44-48c5-b0ca-30c72e9b59ab/">deceptive alignment and other thought experiments</a> imply that we can&apos;t get these bits from direct supervision of the network&apos;s outputs. But I think there&apos;s a good chance we can get those bits from good interpretability tools---better tools than what we have now, but ones that are within reach.</p>
<p>I&apos;m not arguing that AI safety is somehow trivial or easy---the concerns I discussed above are not exhaustive, and even those will take perhaps tens of thousands of researcher-hours to address. My point is that empirical trends give you problem structure that you can leverage, which often takes a problem from &quot;intractable&quot; to &quot;only 300,000 hours of work&quot;.<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup></p>
<h2 id="empirical-generalization-in-biology">Empirical Generalization in Biology</h2>
<p>I&apos;m claiming that empirical findings generalize &quot;surprisingly far&quot;, but there haven&apos;t been that many orders of magnitude to generalize across in machine learning so far. So let&apos;s look at biology, where there are many cases of findings generalizing all the way from &quot;bacteria&quot; to &quot;humans&quot;.</p>
<p><strong>The phage group.</strong> A prime example of this was the <a href="https://en.wikipedia.org/wiki/Phage_group?ref=bounded-regret.ghost.io">phage group</a>, a group of researchers who made many of the founding contributions of molecular biology. They chose to study bacteriophages (viruses that attack bacteria) as the simplest possible model system. Most biologists at the time studied more complex organisms, and some were skeptical that phages were complex enough to yield meaningful insights.</p>
<p>The phage group essentially bet that studying viruses and bacteria would yield insights that generalized to more complex organisms. That bet paid off--among other things, they discovered:</p>
<ul>
<li>That <a href="https://en.wikipedia.org/wiki/Hershey%E2%80%93Chase_experiment?ref=bounded-regret.ghost.io">DNA was the source of genetic material</a></li>
<li>The phenomenon of <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1079044/?ref=bounded-regret.ghost.io">genetic recombination</a></li>
<li>That DNA replicated <a href="https://en.wikipedia.org/wiki/Meselson%E2%80%93Stahl_experiment?ref=bounded-regret.ghost.io">semi-conservatively</a></li>
<li>That the gene was <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC222769/?ref=bounded-regret.ghost.io">arranged linearly</a></li>
<li>The existence of <a href="https://en.wikipedia.org/wiki/Restriction_enzyme?ref=bounded-regret.ghost.io#History">restriction enzymes</a>, which formed the foundation of genetic engineering</li>
</ul>
<p>Later discoveries based on bacteria also generalized to more complex organisms. For instance, <a href="https://en.wikipedia.org/wiki/Jacques_Monod?ref=bounded-regret.ghost.io">Jacques Monod</a> uncovered the structure of genetic regulatory networks by studying the <em>lac</em> operon in <em>E. coli</em>.</p>
<p>Now, one might object that biology is not a good analogy for machine learning, because all life shares the same genetic ancestry and thus has commonalities that neural networks will not. I have some sympathy for this point, but I think it understates how non-obvious it was that studying bacteriophages would be a good idea. Empirical trends generalize far <em>because</em> there is some mechanism that causes them to do so, but that mechanism is often only obvious in hindsight. We&apos;ll probably come up with similarly &quot;obvious&quot; explanations for trends in deep learning, but only after we discover them.</p>
<p>Moreover, shared genetic ancestry isn&apos;t actually enough to imply consistent trends. Regulatory networks work slightly differently in bacteria and humans, and some bacteria and viruses have circular rather than linear genomes. Nevertheless, most of the essential findings remain intact, even though bacteria have 1 cell each and humans have 30 trillion.</p>
<h2 id="what-about-superintelligence">What About Superintelligence?</h2>
<p>An argument I sometimes hear is that empirics won&apos;t help when dealing with deceptive AI that is much smarter than humans, because it might intentionally change its feature representations to thwart interpretability techniques, and otherwise intentionally obscure the results of empirical measurements.</p>
<p>I agree that if you had such an AI, you wouldn&apos;t be able to rely on empirical measurements. But if you had such an AI, I think you&apos;d just be fundamentally screwed. When trying to solve the problem of deceptive AI, I view the main challenge as not getting to this point in the first place. In the language of deceptive alignment, you aren&#x2019;t trying to &quot;fix&quot; a deceptively aligned AI, you&apos;re trying to make sure the training dynamics steer you far away from ever getting one.</p>
<p>Overall, I think that both empirics and conceptual arguments will be necessary to make AI systems safe (both now and in the future). Both the Engineering and Philosophy mindsets are perceiving <a href="https://en.wikipedia.org/wiki/Blind_men_and_an_elephant?ref=bounded-regret.ghost.io">different pieces of the elephant</a>. I hope this series can help bridge these mindsets and move us towards a synthesis that is better-prepared to answer the challenges of the future.</p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>A typical research group might input 15,000 hours of work per year (7.5 full-time researchers x 2,000 hours), so this would be 4 research groups working full-time for 5 years. <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
<!--kg-card-end: markdown-->]]></content:encoded></item><item><title><![CDATA[ML Systems Will Have Weird Failure Modes]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p>Previously, I&apos;ve argued that future ML systems might exhibit <a href="https://bounded-regret.ghost.io/p/1527e9dd-c48d-4941-9b14-4f7293318d5c/">unfamiliar, emergent capabilities</a>, and that thought experiments <a href="https://bounded-regret.ghost.io/p/a2d733a7-108a-4587-97fb-db90f66ce030/">provide one approach</a> towards predicting these capabilities and their consequences.</p>
<p>In this post I&#x2019;ll describe a particular thought experiment in detail. We&#x2019;ll see that taking thought experiments seriously</p>]]></description><link>https://bounded-regret.ghost.io/ml-systems-will-have-weird-failure-modes-2/</link><guid isPermaLink="false">61bd1222f7965d003b71ae6f</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Wed, 26 Jan 2022 01:40:01 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p>Previously, I&apos;ve argued that future ML systems might exhibit <a href="https://bounded-regret.ghost.io/p/1527e9dd-c48d-4941-9b14-4f7293318d5c/">unfamiliar, emergent capabilities</a>, and that thought experiments <a href="https://bounded-regret.ghost.io/p/a2d733a7-108a-4587-97fb-db90f66ce030/">provide one approach</a> towards predicting these capabilities and their consequences.</p>
<p>In this post I&#x2019;ll describe a particular thought experiment in detail. We&#x2019;ll see that taking thought experiments seriously often surfaces future risks that seem &quot;weird&quot; and alien from the point of view of current systems. I&#x2019;ll also describe how I tend to engage with these thought experiments: I usually start out intuitively skeptical, but when I reflect on emergent behavior I find that some (but not all) of the skepticism goes away. The remaining skepticism comes from ways that the thought experiment clashes with the ontology of neural networks, and I&#x2019;ll describe the approaches I usually take to address this and generate actionable takeaways.</p>
<h2 id="thought-experiment-deceptive-alignment">Thought Experiment: Deceptive Alignment</h2>
<p>Recall that the <a href="https://bounded-regret.ghost.io/p/a2d733a7-108a-4587-97fb-db90f66ce030/">optimization anchor</a> runs the thought experiment of assuming that an ML agent is a perfect optimizer (with respect to some &quot;intrinsic&quot; reward function $R$). I&#x2019;m going to examine one implication of this assumption, in the context of an agent being trained based on some &quot;extrinsic&quot; reward function $R^*$ (which is provided by the system designer and not equal to $R$).</p>
<p>Specifically, consider a training process where in step $t$, a model has parameters $\theta_t$ and generates an action $a_t$ (its output on that training step, e.g. an attempted backflip assuming it is being trained to do backflips). The action $a_t$ is then judged according to the extrinsic reward function $R^*$, and the parameters are updated to some new value $\theta_{t+1}$ that are intended to increase $a_{t+1}$&apos;s value under $R^*$. At some point, the model is then deployed with final parameters $\theta_T$, and continues to take actions. The following diagram illustrates this process:</p>
<p><img src="https://bounded-regret.ghost.io/content/images/2022/01/deception1.png" alt="deception1" loading="lazy"></p>
<!-- ![deception](https://bounded-regret.ghost.io/content/images/2021/12/deception.png) -->
<p>Now, let&#x2019;s assume that the model $\theta_t$ is a perfect optimizer whose objective is to maximize the discounted value of an intrinsic reward $R \neq R^*$. That is, $\theta_t$ picks the action $a_t$ satisfying</p>
<p>$a_t = \operatorname{argmax}_{a} \mathbb{E}[\sum_{s=0}^{\infty} \gamma^{-s} R(a_{t+s}) \mid a_t = a]$.</p>
<p>(I know that this is an unrealistic assumption. We&#x2019;ll examine the assumption in detail in the next section, but for now please grant it even if it requires suspending disbelief.)</p>
<p>What action $a_t$ will $\theta_t$ pick? Let&#x2019;s define $a^R = \operatorname{argmax}_{a} R(a)$ and $a^* = \operatorname{argmax}_{a} R^*(a)$--that is, $a^R$ maximizes the (instantaneous) intrinsic reward while $a^*$ maximizes the extrinsic reward.</p>
<p>Assuming that $\gamma$ is close to 1, the model wants $a^R$ to be picked on as many future rounds as possible (including at deployment time). If $\theta_t$ plays myopically, this means it would pick $a_t = a^R$. However, this is not the optimal non-myopic action: if $a_t = a^R$, then $\theta_{t+1}$ will be updated towards producing outputs less like $a^R$ and more like $a^*$, so outputting $a^R$ in the current round leads to fewer $a^R$ outputs in future rounds.</p>
<p>Instead, I think the optimal non-myopic action is approximately the following: during training time, output $a^*$ on every time step, so that the training process doesn&#x2019;t update $\theta$ (since it&#x2019;s already optimal) and hence $\theta_t = \theta_{t+1} = \cdots = \theta_T$. This guarantees that the deployed agent is $\theta_t$, which is now free to output $a^R$ on every time step without risk of being modified by the training process.<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup></p>
<p>The myopic and non-myopic outcomes are illustrated in the figure below:</p>
<p align="center" style="font-size:80%">
<img src="https://bounded-regret.ghost.io/content/images/2022/01/deception2.png"><br>
<i>Myopic and non-myopic agents with an intrinsic reward, $R$. The myopic agent plays high intrinsic-reward actions during training, but is eventually modified to output action $a^*$ with high extrinsic reward $R^*$. The non-myopic agent instead plays $a^*$ during training so that it can pursue its intrinsic reward at deployment, by playing $a^R$ at all post-deployment time steps.</i>
</p>
<p>To put it another way&#x2013;the model&#x2019;s behavior will look aligned with $R^*$ during the training process, but will switch to being non-aligned once deployed: so-called &quot;deceptive alignment&quot;. This behavior is unintuitive to me, since it shows that a system&#x2019;s behavior can shift significantly between train and test, even in the absence of an obvious distribution shift between train and test outputs<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>.</p>
<h2 id="engaging-with-deceptive-alignment">Engaging with Deceptive Alignment</h2>
<p>When I first heard the above argument, I thought it was pretty crazy and implausible, mainly because my intuition said this &quot;just wasn&apos;t how ML systems worked&quot;. When I think about why I feel that way, I realize it&#x2019;s because the scenario invokes capabilities that ML is currently bad at: long-term planning and understanding complex features of the environment (i.e. the training process and its ramifications). However, emergence implies that these properties could easily appear in the future, even without explicit design<sup class="footnote-ref"><a href="#fn3" id="fnref3">[3]</a></sup>. As a result, I&#x2019;ve come to discount this particular intuition.</p>
<p>However, I do think there are subtler reasons to think the deceptive alignment story won&#x2019;t play out as written. Here are a few:</p>
<ol>
<li>It&#x2019;s not clear why the model $\theta$ would come to be optimizing a reward function $R$ in the first place. Yes, it is the case that deceptively aligned models achieve the global minimum of training loss, so in that sense they are incentivized by the training process. But so is an actually aligned model, so which one you end up with has to depend on the inductive bias of the training process.</li>
<li>Reward functions are simpler than policies and typically learned faster. So by the time the system is smart enough to have long-term plans, it will already have a very good representation of its intended reward function. We thus might hope that most of the model&apos;s internal representations are devoted to achieving high reward in a straightforward manner rather than through long-term deception.</li>
<li>To the extent that a model is not aligned, it probably won&#x2019;t be the case that it&apos;s deceptively aligned with an explicit reward function R---that&apos;s a very specific type of agent and most agents (including humans) are not maximizing any reward function, except in the trivial sense of &quot;assign reward 1 to whatever it was going to do anyway, and 0 to everything else&quot;.</li>
<li>Deceptive alignment is a specific complex story about the future, and complex stories are almost always wrong.</li>
</ol>
<p>I find these points persuasive for showing that deceptive alignment <em>as explicitly written</em> is not that likely, but they also don&apos;t imply that there&apos;s nothing to worry about. Mostly they are an argument that your system might be aligned and might be misaligned, that if it is misaligned it won&#x2019;t be <em>exactly</em> in the form of deceptive alignment, but ultimately what you get depends on inductive bias in an unknown way. This isn&apos;t particularly reassuring.</p>
<p><strong>What I take away from thought experiments.</strong> Per the discussion above, the failure mode in my head is not &quot;deceptive alignment as written above&quot;. Instead it&#x2019;s &quot;something kind of like the story above but probably different in lots of details&quot;. This makes it harder to reason about, but I think there are still some useful takeaways:</p>
<ul>
<li>After thinking about deceptive alignment, I am more interested in supervising a model&#x2019;s process (rather than just its outputs), since there are many models that achieve low training error but generalize catastrophically. One possible approach is to supervise the latent representations using e.g. interpretability methods.</li>
<li>While I don&apos;t think neural nets will be literal optimizers, I do think it&#x2019;s likely that they will exhibit &quot;drives&quot;, in the same way that humans exhibit drives like hunger, curiosity, desire for social approval, etc. that lead them to engage in long-term coherent plans. This seems like enough to create similar problems to deceptive alignment, so I am now more interested in understanding such drives and how they arise.</li>
<li>Since deceptive alignment is a type of &quot;out-of-distribution&quot; behavior (based on the difference between train and deployment), it has renewed my interest in understanding whether larger models become more brittle OOD. So far the empirical evidence is in <a href="https://arxiv.org/abs/2006.16241?ref=bounded-regret.ghost.io">the opposite direction</a>, but deceptive alignment is an argument that asymptotically we might expect the trend to flip, especially for tasks with large output spaces (e.g. policies, language, or code) where &quot;drives&quot; can more easily manifest.</li>
</ul>
<p>So to summarize my takeaways: be more interested in interpretability (especially as it relates to training latent representations), try to identify and study &quot;drives&quot; of ML systems, and look harder for examples where larger models have worse OOD behavior (possibly focusing on high-dimensional output spaces).</p>
<p><strong>Other weird failures.</strong> Other weird failures that I think don&#x2019;t get enough attention, even though I also don&#x2019;t think they will play out as written, are Hubinger et al.&apos;s <em><a href="https://arxiv.org/abs/1906.01820?ref=bounded-regret.ghost.io">Risks from Learned Optimization</a></em> (AI acquires an &quot;inner objective&quot;, somewhat similar to deceptive alignment), and Part I of Paul Christiano&#x2019;s <a href="https://www.alignmentforum.org/posts/HBxe6wdjxK239zajf/what-failure-looks-like?ref=bounded-regret.ghost.io">AI failure story</a> (the world becomes very complicated and AI systems create elaborate Potemkin villages for humans).</p>
<p>Paul Christiano&#x2019;s story in particular has made me more interested in understanding how reward hacking interacts with the sophistication of the supervisor: For instance, how much more readily do neural networks fool humans who have 5 seconds to think, vs. 2 minutes or 30 minutes? I more generally want to understand how reward hacking depends quantitatively on both supervision quality and model capacity (qualitatively, we expect higher quality $\to$ less hacking and higher capacity $\to$ more hacking). Understanding this quantitative relation would help ground Paul&#x2019;s story, since he imagines a world where humans have built extremely sophisticated systems for supervising ML models, but eventually the ML models become even more powerful and game the supervision signal anyways.</p>
<h2 id="what-to-do-about-weird-emergent-failures">What To Do About Weird Emergent Failures</h2>
<p>When thinking about how to handle emergent risks, I often reflect on the example of uranium. For context, an atomic bomb is pretty much just a bunch of uranium put together---once you get enough, the reaction becomes self-sustaining---making it a good example of More Is Different.</p>
<p>The first nuclear reaction (not a bomb, but a <a href="https://en.wikipedia.org/wiki/Chicago_Pile-1?ref=bounded-regret.ghost.io">pile of uranium</a> in an abandoned football stadium in Chicago) was engineered by Enrico Fermi. The reaction required 12,400 pounds of uranium metal piled 57 layers high. Left unsupervised, a 57-layer pile would consume itself within two hours and kill everyone in the vicinity. On the other hand, a 56-layer pile would do nothing.</p>
<p>Fermi had a good understanding of nuclear physics and understood, from careful monitoring and underlying theory, that the pile would pass the critical threshold between layers 56 and 57. He also knew that cadmium rods would absorb neutrons and strongly inhibit the reaction. These rods were set up and the entire apparatus was carefully controlled to go only slightly supercritical. He brought the reaction to half a watt for several minutes before shutting it back down (see <em><a href="https://smile.amazon.com/Making-Atomic-Bomb-Richard-Rhodes/dp/1451677618?ref=bounded-regret.ghost.io">The Making of the Atomic Bomb</a></em>, pp. 524).</p>
<p>With AI, we currently lack both Fermi&apos;s conceptual understanding of the underlying risk factors and his ability to continuously measure them. We have neither a cadmium rod nor a measure of reaction criticality. But I think we can get there, by combining these weird thought experiments with <a href="https://bounded-regret.ghost.io/p/74d500d2-a980-4720-984a-c016284ecdc2/">carefully chosen empirical experiments</a>, which will be the topic of the next post.</p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>Things are more complicated in reality, since $\theta_t$ is updated even when $a_t$ is optimal (due to noise in the training process). However, we&#x2019;ll ignore this for purposes of the example. <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn2" class="footnote-item"><p>Of course, there is still some distribution shift, since the agent can observe whether it is being trained or deployed. But this is a relatively minor and unintuitive shift compared to what is typically studied. <a href="#fnref2" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn3" class="footnote-item"><p>Of course, emergence doesn&#x2019;t mean that we can just predict whatever we want&#x2013;we&#x2019;d need some reason to expect these specific capabilities to emerge. Long-term planning and environmental awareness are both useful for a wide variety of tasks, making them likely to emerge when training powerful models on a diverse data distribution. <a href="#fnref3" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
<!--kg-card-end: markdown-->]]></content:encoded></item><item><title><![CDATA[Anchor Weights for ML]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p>In the <a href="https://bounded-regret.ghost.io/thought-experiments-provide-a-third-anchor/">previous post</a>, I talked about several &quot;anchors&quot; that we could use to think about future ML systems, including current ML systems, humans, ideal optimizers, and complex systems.</p>
<p>In fact, I think we should be using all of these anchors (and any others we can think of)</p>]]></description><link>https://bounded-regret.ghost.io/which-anchors-do-i-use/</link><guid isPermaLink="false">61e74bcc529ebe003bfb16f9</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Thu, 20 Jan 2022 16:17:45 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p>In the <a href="https://bounded-regret.ghost.io/thought-experiments-provide-a-third-anchor/">previous post</a>, I talked about several &quot;anchors&quot; that we could use to think about future ML systems, including current ML systems, humans, ideal optimizers, and complex systems.</p>
<p>In fact, I think we should be using all of these anchors (and any others we can think of) to reason about future ML systems. This is based on ideas from forecasting, where successful forecasters usually <a href="https://bounded-regret.ghost.io/combining-forecasts/">average</a> over many worldviews and <a href="https://bounded-regret.ghost.io/base-rates-and-reference-classes/">reference classes</a> rather than focusing on a single reference class. However, we should also be discerning and weight anchors more if they seem like a better match for what we want to predict.</p>
<p>Below, I&apos;ll say what I personally think about most of the anchors we discussed so far, by assigning a numerical &quot;weight&quot; to each one. While these weights aren&apos;t perfect (the actual weight I&apos;d use depends on the particular question), they hopefully provide a clear overall picture that is easy to agree/disagree with.</p>
<p>Here are the rough weights I came up with:</p>
<table>
<thead>
<tr>
<th>Anchor</th>
<th>Weight</th>
</tr>
</thead>
<tbody>
<tr>
<td>Current ML</td>
<td>4</td>
</tr>
<tr>
<td>Complex systems</td>
<td>3</td>
</tr>
<tr>
<td>Thought experiments</td>
<td>2</td>
</tr>
<tr>
<td>Evolution</td>
<td>0.5</td>
</tr>
<tr>
<td>The economy</td>
<td>0.4</td>
</tr>
<tr>
<td>Humans</td>
<td>0.3</td>
</tr>
<tr>
<td>Corporations</td>
<td>0.2</td>
</tr>
<tr>
<td>Biological systems</td>
<td>0.2</td>
</tr>
<tr>
<td>Non-human animals</td>
<td>0.1</td>
</tr>
</tbody>
</table>
<p>I primarily rely on Current ML, Complex Systems, and Thought Experiments, in a 4:3:2 ratio. In particular, I assign about twice as much weight to Current ML as to Thought Experiments, but I think the opposite ratio is also defensible. However, many people seem to implicitly put almost all their weight on Current ML, or almost all their weight on Thought Experiments. They have something like a 5:1 or 1:5 ratio, or even greater. I think <strong>neither of these stances is defensible</strong>, and I would be interested in anyone who disagrees writing up the case for assigning extreme weights (in either direction).</p>
<p>Relatedly, my <a href="https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/">last</a> <a href="https://bounded-regret.ghost.io/thought-experiments-provide-a-third-anchor/">two</a> posts were essentially an argument against a 5:1 ratio in favor of Current ML--first by arguing that Current ML often misses important developments, and second by arguing that thought experiments can sometimes catch these.<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup></p>
<p>Aside from this, my biggest disagreement with others would be assigning significant weight to the &quot;Complex Systems&quot; anchor, which I think most people overlook.</p>
<p>Finally, all anchors that correspond to a broad reference class (Current ML, Complex Systems, Thought Experiments) get significantly more weight than any anchor that is a single example (e.g. humans).<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>  <strong>I give serious consideration to hypotheses generated by any of these three anchors.</strong> In particular, if I can&apos;t strongly rule out the hypothesis after one hour of thought, I think there&apos;s at least a 30% chance that it will eventually come to be supported by the other two anchors as well.</p>
<p>I&apos;d be interested in others posting their relative weights, and pointing out any instances where they think I&apos;m wrong.</p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>A later post, on the value of empirical findings, also offers an argument against a 1:5 ratio towards thought experiments. <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn2" class="footnote-item"><p>The only exception is that &quot;non-human animals&quot; gets very low weight, partly because they are hard to study and partly because I expect future systems to be <em>more</em> capable than humans, not less. <a href="#fnref2" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
<!--kg-card-end: markdown--><p></p><p></p>]]></content:encoded></item><item><title><![CDATA[Thought Experiments Provide a Third Anchor]]></title><description><![CDATA[<!--kg-card-begin: markdown--><!-- Previously, I've argued that future ML systems might exhibit [unfamiliar, emergent capabilities](https://bounded-regret.ghost.io/p/1527e9dd-c48d-4941-9b14-4f7293318d5c/), and that this [poses new risks](https://bounded-regret.ghost.io/p/8fd9c776-24b8-474f-b43b-4d8ef1a82836/) that we aren't currently prepared for. I'll talk next about what to do about it.

The first step to mitigating risks is to predict what they'll be, so this post will be primarily focused on *predicting* future ML behavior. For this purpose, it's helpful to think in terms of "anchors"---some [reference class](https://bounded-regret.ghost.io/p/f089591d-6107-4714-ad69-aa7a5b5030b0/) that is broadly analogous to future ML systems, which we can then use to make predictions. -->
<p>Previously, <a href="https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/">I argued</a> that we should expect future ML systems to often exhibit &quot;emergent&quot; behavior, where they acquire new capabilities that were not explicitly designed or intended, simply as a result of scaling. This was a special case of a general phenomenon in the physical sciences called More Is Different.</p>
<p>I care about this because I think AI will have a huge impact on society, and I want to <a href="https://bounded-regret.ghost.io/ai-forecasting/">forecast what future systems will be like</a> so that I can steer things to be better. To that end, I find More Is Different to be troubling and disorienting. I&#x2019;m inclined to forecast the future by <a href="https://bounded-regret.ghost.io/forecasting-zeroth-and-first-order/">looking at existing trends</a> and asking what will happen if they continue, but we should instead expect new qualitative behaviors to arise all the time that are not an extrapolation of previous trends.</p>
<p>Given this, how can we predict what future systems will look like? For this, I find it helpful to think in terms of &quot;anchors&quot;---<a href="https://bounded-regret.ghost.io/base-rates-and-reference-classes/">reference classes</a> that are broadly analogous to future ML systems, which we can then use to make predictions.</p>
<p>The most obvious reference class for future ML systems is current ML systems---I&apos;ll call this the <strong>current ML</strong> anchor. I think this is indeed a pretty good starting point, but we&#x2019;ve already seen that it <a href="https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/">fails to account</a> for emergent capabilities.</p>
<p>What other anchors can we use? One intuitive approach would be to look for things that humans are good at but that current ML systems are bad at. This would include:</p>
<ul>
<li>Mastery of external tools (e.g. calculators, search engines, software, programming)</li>
<li>Very efficient learning (e.g. reading a textbook once to learn a new subject)</li>
<li>Long-term planning (e.g. being able to successfully achieve goals over months)</li>
</ul>
<p>Models sufficiently far in the future will presumably have these sorts of capabilities. While this still leaves unknowns---for instance, we don&apos;t know how rapidly these capabilities will appear---it&apos;s still a useful complement to the current ML anchor. I&apos;ll call this the <strong>human anchor</strong>.</p>
<p>A problem with the human anchor is that it risks anthropomorphising ML by over-analogizing with human behavior. Anthropomorphic reasoning correctly gets a bad rap in ML, because it&apos;s very intuitively persuasive but has a <a href="https://en.wikipedia.org/wiki/Anthropomorphism?ref=bounded-regret.ghost.io#In_computing">mixed at best</a> track record. This isn&apos;t a reason to abandon the human anchor, but it means we shouldn&apos;t be entirely satisfied with it.</p>
<p>This brings us to a third anchor, the <strong>optimization anchor</strong>, which I associate with the &quot;Philosophy&quot; or thought experiment approach that I&apos;ve <a href="https://bounded-regret.ghost.io/p/a9fce268-857f-4f03-a2a6-d7aa2ab129aa/">described previously</a>. Here the idea is to think of ML systems as ideal optimizers and ask what a perfect optimizer would do in a given scenario. This is where Nick Bostrom&apos;s colorful description of a <a href="https://www.nickbostrom.com/ethics/ai.html?ref=bounded-regret.ghost.io">paperclip maximizer</a> comes from, where an AI asked to make paperclips turns the entire planet into paperclip factories. To give some more prosaic examples:</p>
<ul>
<li>The optimization anchor would correctly predict <a href="https://owainevans.github.io/pdfs/truthfulQA_lin_evans.pdf?ref=bounded-regret.ghost.io">imitative deception</a> (Lin et al., 2021), since a system optimized to produce high-probability outputs has no intrinsic reason to be truthful.</li>
<li>It also would observe that power-seeking is instrumentally useful for many different goals, and so predict that optimal policies (as well as sufficiently powerful neural networks) will <a href="https://arxiv.org/abs/1912.01683?ref=bounded-regret.ghost.io">tend to do so</a> (Turner et al., 2021).</li>
</ul>
<p>Ideas produced by the optimization anchor are often met with skepticism, because they often contradict the familiar current ML anchor, and they don&apos;t benefit from the intuitive appeal of the human anchor. But the differences from these other two anchors are precisely what make the optimization anchor valuable. If you (like me) feel that both the current ML and human anchors paint an incomplete picture, then you should want a third independent perspective.</p>
<p>The optimization anchor does have limitations. Since it abstracts ML into an ideal optimizer, it ignores most on-the-ground facts about neural networks. This can lead to underconstrained predictions, and to ignoring properties that I think will be necessary for successfully aligning ML systems with humans. I&apos;ll say more about this later, but some particularly important properties are that neural networks often generalize in &quot;natural&quot; ways, that we can introspect on network representations, and that training dynamics are smooth and continuous. Researchers focused on the optimization anchor don&apos;t entirely ignore these facts, but I think they tend to underemphasize them and are overly pessimistic as a result.</p>
<h2 id="the-value-of-thought-experiments">The Value of Thought Experiments</h2>
<p>The optimization anchor points to the value of thought experiments more generally. While it poses the thought experiment of &quot;What if AI were a perfect optimizer?&quot;, there are many other thought experiments that can provide insights that&apos;d be hard to obtain from the ML or human anchors. In this sense thought experiments are not a single anchor but a generator for anchors, which seems pretty valuable.</p>
<p>One thought experiment that I particularly like is: <em>What happens if most of an agent&apos;s learning occurs not during gradient descent, but through in-context learning<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>?</em> This is likely to happen eventually, as ML agents are rolled out over longer time horizons (think artificial digital assistants) and as ML improves at in-context learning. Once this does happen, it seems possible that agents&apos; behavior will be controlled less by the &quot;extrinsic&quot; shaping of gradient descent and more by whatever &quot;intrinsic&quot; drives they happen to have<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>. This also seems like a change that could happen suddenly, since gradient descent is slow while in-context learning is fast.</p>
<p>It would be great if we had a community of researchers making thought experiments with clearly stated assumptions, explaining in detail the consequences of those assumptions and ideally connecting it to present-day research.</p>
<h2 id="other-anchors">Other Anchors</h2>
<p>There are many other anchors that could be helpful for predicting future ML systems. <strong>Non-human animal behavior</strong> could provide a broader reference class than humans alone. <strong>Evolution</strong> and <strong>the economy</strong> are both examples of powerful, distributed optimization processes. I am most excited about better understanding <strong>complex systems</strong>, which include biological systems, brains, organizations, economies, and ecosystems and thus subsume most of the reference classes discussed so far. It seems to me that complex systems have received little attention relative to their germaneness to ML. Indeed, emergence is itself a concept from complex systems theory that is useful for understanding recent ML developments.</p>
<h2 id="limitations-of-thought-experiments">Limitations of Thought Experiments</h2>
<p>I&apos;ve focused so far on <em>predicting</em> problems that we need to address. But at some point we actually have to <em>solve</em> the problems. In this regard thought experiments are weaker, since while they often point to important big-picture issues, in my view they fare poorly at getting the details right, which is needed for engineering progress. For instance, early thought experiments <a href="https://www.nickbostrom.com/ethics/ai.html?ref=bounded-regret.ghost.io">considered a single AI system</a> that was much more powerful than any other contemporary technologies, while in reality there will likely be many ML systems with a continuous distribution of capabilities. <a href="https://arxiv.org/abs/1906.01820?ref=bounded-regret.ghost.io">More recent</a> thought experiments impose discrete abstractions like &quot;goals&quot; and &quot;objectives&quot; that I don&#x2019;t think will cleanly map onto real ML systems. Thus while thought experiments can point to general ideas for research, even mapping these ideas to the ontology of ML systems can be a difficult task.</p>
<!-- [later post](https://bounded-regret.ghost.io/p/74d500d2-a980-4720-984a-c016284ecdc2/) -->
<p>As a result, while we can&apos;t blindly extrapolate empirical trends, we do need a concerted empirically-based effort to address future ML risks. I&apos;ll explain why I think this is possible in a later post, but first I&apos;ll take us through an example of &quot;taking a thought experiment seriously&quot;, and what it implies about possible failure modes of ML systems.</p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>In-context learning refers to learning that occurs during a single &quot;rollout&quot; of a model. The most famous example is <a href="https://arxiv.org/abs/2005.14165?ref=bounded-regret.ghost.io">GPT-3</a>&apos;s ability to learn new tasks after conditioning on a small number of examples. <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn2" class="footnote-item"><p>While this statement borders on anthropomorphizing, I think it is actually justified. For instance, depending on the training objective, many agents will likely have a &quot;drive&quot; towards information-gathering, among others. <a href="#fnref2" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
<!--kg-card-end: markdown-->]]></description><link>https://bounded-regret.ghost.io/thought-experiments-provide-a-third-anchor/</link><guid isPermaLink="false">619697e69ee68c003bbdf64a</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Tue, 18 Jan 2022 16:00:00 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><!-- Previously, I've argued that future ML systems might exhibit [unfamiliar, emergent capabilities](https://bounded-regret.ghost.io/p/1527e9dd-c48d-4941-9b14-4f7293318d5c/), and that this [poses new risks](https://bounded-regret.ghost.io/p/8fd9c776-24b8-474f-b43b-4d8ef1a82836/) that we aren't currently prepared for. I'll talk next about what to do about it.

The first step to mitigating risks is to predict what they'll be, so this post will be primarily focused on *predicting* future ML behavior. For this purpose, it's helpful to think in terms of "anchors"---some [reference class](https://bounded-regret.ghost.io/p/f089591d-6107-4714-ad69-aa7a5b5030b0/) that is broadly analogous to future ML systems, which we can then use to make predictions. -->
<p>Previously, <a href="https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/">I argued</a> that we should expect future ML systems to often exhibit &quot;emergent&quot; behavior, where they acquire new capabilities that were not explicitly designed or intended, simply as a result of scaling. This was a special case of a general phenomenon in the physical sciences called More Is Different.</p>
<p>I care about this because I think AI will have a huge impact on society, and I want to <a href="https://bounded-regret.ghost.io/ai-forecasting/">forecast what future systems will be like</a> so that I can steer things to be better. To that end, I find More Is Different to be troubling and disorienting. I&#x2019;m inclined to forecast the future by <a href="https://bounded-regret.ghost.io/forecasting-zeroth-and-first-order/">looking at existing trends</a> and asking what will happen if they continue, but we should instead expect new qualitative behaviors to arise all the time that are not an extrapolation of previous trends.</p>
<p>Given this, how can we predict what future systems will look like? For this, I find it helpful to think in terms of &quot;anchors&quot;---<a href="https://bounded-regret.ghost.io/base-rates-and-reference-classes/">reference classes</a> that are broadly analogous to future ML systems, which we can then use to make predictions.</p>
<p>The most obvious reference class for future ML systems is current ML systems---I&apos;ll call this the <strong>current ML</strong> anchor. I think this is indeed a pretty good starting point, but we&#x2019;ve already seen that it <a href="https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/">fails to account</a> for emergent capabilities.</p>
<p>What other anchors can we use? One intuitive approach would be to look for things that humans are good at but that current ML systems are bad at. This would include:</p>
<ul>
<li>Mastery of external tools (e.g. calculators, search engines, software, programming)</li>
<li>Very efficient learning (e.g. reading a textbook once to learn a new subject)</li>
<li>Long-term planning (e.g. being able to successfully achieve goals over months)</li>
</ul>
<p>Models sufficiently far in the future will presumably have these sorts of capabilities. While this still leaves unknowns---for instance, we don&apos;t know how rapidly these capabilities will appear---it&apos;s still a useful complement to the current ML anchor. I&apos;ll call this the <strong>human anchor</strong>.</p>
<p>A problem with the human anchor is that it risks anthropomorphising ML by over-analogizing with human behavior. Anthropomorphic reasoning correctly gets a bad rap in ML, because it&apos;s very intuitively persuasive but has a <a href="https://en.wikipedia.org/wiki/Anthropomorphism?ref=bounded-regret.ghost.io#In_computing">mixed at best</a> track record. This isn&apos;t a reason to abandon the human anchor, but it means we shouldn&apos;t be entirely satisfied with it.</p>
<p>This brings us to a third anchor, the <strong>optimization anchor</strong>, which I associate with the &quot;Philosophy&quot; or thought experiment approach that I&apos;ve <a href="https://bounded-regret.ghost.io/p/a9fce268-857f-4f03-a2a6-d7aa2ab129aa/">described previously</a>. Here the idea is to think of ML systems as ideal optimizers and ask what a perfect optimizer would do in a given scenario. This is where Nick Bostrom&apos;s colorful description of a <a href="https://www.nickbostrom.com/ethics/ai.html?ref=bounded-regret.ghost.io">paperclip maximizer</a> comes from, where an AI asked to make paperclips turns the entire planet into paperclip factories. To give some more prosaic examples:</p>
<ul>
<li>The optimization anchor would correctly predict <a href="https://owainevans.github.io/pdfs/truthfulQA_lin_evans.pdf?ref=bounded-regret.ghost.io">imitative deception</a> (Lin et al., 2021), since a system optimized to produce high-probability outputs has no intrinsic reason to be truthful.</li>
<li>It also would observe that power-seeking is instrumentally useful for many different goals, and so predict that optimal policies (as well as sufficiently powerful neural networks) will <a href="https://arxiv.org/abs/1912.01683?ref=bounded-regret.ghost.io">tend to do so</a> (Turner et al., 2021).</li>
</ul>
<p>Ideas produced by the optimization anchor are often met with skepticism, because they often contradict the familiar current ML anchor, and they don&apos;t benefit from the intuitive appeal of the human anchor. But the differences from these other two anchors are precisely what make the optimization anchor valuable. If you (like me) feel that both the current ML and human anchors paint an incomplete picture, then you should want a third independent perspective.</p>
<p>The optimization anchor does have limitations. Since it abstracts ML into an ideal optimizer, it ignores most on-the-ground facts about neural networks. This can lead to underconstrained predictions, and to ignoring properties that I think will be necessary for successfully aligning ML systems with humans. I&apos;ll say more about this later, but some particularly important properties are that neural networks often generalize in &quot;natural&quot; ways, that we can introspect on network representations, and that training dynamics are smooth and continuous. Researchers focused on the optimization anchor don&apos;t entirely ignore these facts, but I think they tend to underemphasize them and are overly pessimistic as a result.</p>
<h2 id="the-value-of-thought-experiments">The Value of Thought Experiments</h2>
<p>The optimization anchor points to the value of thought experiments more generally. While it poses the thought experiment of &quot;What if AI were a perfect optimizer?&quot;, there are many other thought experiments that can provide insights that&apos;d be hard to obtain from the ML or human anchors. In this sense thought experiments are not a single anchor but a generator for anchors, which seems pretty valuable.</p>
<p>One thought experiment that I particularly like is: <em>What happens if most of an agent&apos;s learning occurs not during gradient descent, but through in-context learning<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>?</em> This is likely to happen eventually, as ML agents are rolled out over longer time horizons (think artificial digital assistants) and as ML improves at in-context learning. Once this does happen, it seems possible that agents&apos; behavior will be controlled less by the &quot;extrinsic&quot; shaping of gradient descent and more by whatever &quot;intrinsic&quot; drives they happen to have<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>. This also seems like a change that could happen suddenly, since gradient descent is slow while in-context learning is fast.</p>
<p>It would be great if we had a community of researchers making thought experiments with clearly stated assumptions, explaining in detail the consequences of those assumptions and ideally connecting it to present-day research.</p>
<h2 id="other-anchors">Other Anchors</h2>
<p>There are many other anchors that could be helpful for predicting future ML systems. <strong>Non-human animal behavior</strong> could provide a broader reference class than humans alone. <strong>Evolution</strong> and <strong>the economy</strong> are both examples of powerful, distributed optimization processes. I am most excited about better understanding <strong>complex systems</strong>, which include biological systems, brains, organizations, economies, and ecosystems and thus subsume most of the reference classes discussed so far. It seems to me that complex systems have received little attention relative to their germaneness to ML. Indeed, emergence is itself a concept from complex systems theory that is useful for understanding recent ML developments.</p>
<h2 id="limitations-of-thought-experiments">Limitations of Thought Experiments</h2>
<p>I&apos;ve focused so far on <em>predicting</em> problems that we need to address. But at some point we actually have to <em>solve</em> the problems. In this regard thought experiments are weaker, since while they often point to important big-picture issues, in my view they fare poorly at getting the details right, which is needed for engineering progress. For instance, early thought experiments <a href="https://www.nickbostrom.com/ethics/ai.html?ref=bounded-regret.ghost.io">considered a single AI system</a> that was much more powerful than any other contemporary technologies, while in reality there will likely be many ML systems with a continuous distribution of capabilities. <a href="https://arxiv.org/abs/1906.01820?ref=bounded-regret.ghost.io">More recent</a> thought experiments impose discrete abstractions like &quot;goals&quot; and &quot;objectives&quot; that I don&#x2019;t think will cleanly map onto real ML systems. Thus while thought experiments can point to general ideas for research, even mapping these ideas to the ontology of ML systems can be a difficult task.</p>
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<p>As a result, while we can&apos;t blindly extrapolate empirical trends, we do need a concerted empirically-based effort to address future ML risks. I&apos;ll explain why I think this is possible in a later post, but first I&apos;ll take us through an example of &quot;taking a thought experiment seriously&quot;, and what it implies about possible failure modes of ML systems.</p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>In-context learning refers to learning that occurs during a single &quot;rollout&quot; of a model. The most famous example is <a href="https://arxiv.org/abs/2005.14165?ref=bounded-regret.ghost.io">GPT-3</a>&apos;s ability to learn new tasks after conditioning on a small number of examples. <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn2" class="footnote-item"><p>While this statement borders on anthropomorphizing, I think it is actually justified. For instance, depending on the training objective, many agents will likely have a &quot;drive&quot; towards information-gathering, among others. <a href="#fnref2" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
<!--kg-card-end: markdown-->]]></content:encoded></item><item><title><![CDATA[Future ML Systems Will Be Qualitatively Different]]></title><description><![CDATA[<!--kg-card-begin: markdown--><p>In 1972, the Nobel prize-winning physicist Philip Anderson wrote the essay &quot;<a href="https://science.sciencemag.org/content/177/4047/393?ref=bounded-regret.ghost.io">More Is Different</a>&quot;. In it, he argues that quantitative changes can lead to qualitatively different and unexpected phenomena. While he focused on physics, one can find many examples of More is Different in other domains as well,</p>]]></description><link>https://bounded-regret.ghost.io/future-ml-systems-will-be-qualitatively-different/</link><guid isPermaLink="false">6171e9a410420700484e6cb0</guid><dc:creator><![CDATA[Jacob Steinhardt]]></dc:creator><pubDate>Tue, 11 Jan 2022 19:45:14 GMT</pubDate><content:encoded><![CDATA[<!--kg-card-begin: markdown--><p>In 1972, the Nobel prize-winning physicist Philip Anderson wrote the essay &quot;<a href="https://science.sciencemag.org/content/177/4047/393?ref=bounded-regret.ghost.io">More Is Different</a>&quot;. In it, he argues that quantitative changes can lead to qualitatively different and unexpected phenomena. While he focused on physics, one can find many examples of More is Different in other domains as well, including biology, economics, and computer science. Some examples of More is Different include:</p>
<ul>
<li><strong>Uranium.</strong> With a bit of uranium, nothing special happens; with a large amount of uranium packed densely enough, you get a nuclear reaction.</li>
<li><strong>DNA.</strong> Given only small molecules such as calcium, you can&#x2019;t meaningfully encode useful information; given larger molecules such as DNA, you can encode a genome.</li>
<li><strong>Water.</strong> Individual water molecules aren&#x2019;t wet. Wetness only occurs due to the interaction forces between many water molecules interspersed throughout a fabric (or other material).</li>
<li><strong>Traffic.</strong> A few cars on the road are fine, but with too many you get a traffic jam. It could be that 10,000 cars could traverse a highway easily in 15 minutes, but 20,000 on the road at once could take over an hour.</li>
<li><strong>Specialization.</strong> Historically, in small populations, virtually everyone needed to farm or hunt to survive; in contrast, in larger and denser communities, enough food is produced for large fractions of the population to specialize in non-agricultural work.</li>
</ul>
<p>While some of the examples, like uranium, correspond to a sharp transition, others like specialization are more continuous. I&#x2019;ll use <strong>emergence</strong> to refer to qualitative changes that arise from quantitative increases in scale, and <strong>phase transitions</strong> for cases where the change is sharp.</p>
<p>In this post, I&apos;ll argue that emergence often occurs in the field of AI, and that this should significantly affect our intuitions about the long-term development and deployment of AI systems. We should expect weird and surprising phenomena to emerge as we scale up systems. This presents opportunities, but also poses important risks.</p>
<h2 id="emergent-shifts-in-the-history-of-ai">Emergent Shifts in the History of AI</h2>
<p>There have already been several examples of quantitative differences leading to important qualitative changes in machine learning.</p>
<p><strong>Storage and Learning.</strong> The emergence of machine learning as a viable approach to AI is itself an example of More Is Different. While learning had been discussed since the 1950s, it wasn&#x2019;t until the 80s-90s that it became a dominant paradigm: for instance, IBM&#x2019;s <a href="https://dl.acm.org/doi/10.3115/991635.991651?ref=bounded-regret.ghost.io">first statistical translation model</a> was published in 1988, even though the idea <a href="https://aclanthology.org/1952.earlymt-1.1.pdf?ref=bounded-regret.ghost.io">was proposed</a> in 1949<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>. Not coincidentally, 1GB of storage cost over $100k in 1981 but only around $9k in 1990 (adjusted to 2021 dollars). The <a href="https://catalog.ldc.upenn.edu/LDC95T20?ref=bounded-regret.ghost.io">Hansard corpus</a> used to train IBM&#x2019;s model comprised 2.87 million sentences and would have been difficult to use before the 80s. Even the simple MNIST dataset would have required $4000 in hardware just to store in 1981, but that had fallen to a few dollars by 1998 when it was published. Cheaper hardware thus allowed for a qualitatively new approach to AI: in other words, More storage enabled Different approaches.</p>
<p><strong>Compute, Data, and Neural Networks.</strong> As hardware improved, it became possible to train neural networks that were very deep for the first time. Better compute enabled bigger models trained for longer, and better storage enabled learning from more data; AlexNet-sized models and ImageNet-sized datasets wouldn&#x2019;t have been feasible for researchers to experiment with in 1990.</p>
<p>Deep learning performs well with lots of data and compute, but struggles at smaller scales. Without many resources, simpler algorithms tend to outperform it, but with sufficient resources it pulls far ahead of the pack. This reversal of fortune led to qualitative changes in the field. As one example, the field of machine translation moved from <a href="https://nlp.stanford.edu/phrasal/?ref=bounded-regret.ghost.io">phrase-based models</a> (hand-coded features, complex systems engineering) to <a href="https://proceedings.neurips.cc/paper/2014/file/a14ac55a4f27472c5d894ec1c3c743d2-Paper.pdf?ref=bounded-regret.ghost.io">neural sequence-to-sequence models</a> (learned features, specialized architecture and initialization) to simply fine-tuning a <a href="https://arxiv.org/abs/2108.07258?ref=bounded-regret.ghost.io">foundation model</a> such as BERT or GPT-3. Most work on phrase-based models was obviated by neural translation, and the same pattern held across many other language tasks, where hard-won domain-specific engineering effort was simply replaced by a general algorithm.</p>
<p><strong>Few-shot Learning.</strong> More recently, <a href="https://d4mucfpksywv.cloudfront.net/better-language-models/language_models_are_unsupervised_multitask_learners.pdf?ref=bounded-regret.ghost.io">GPT-2</a> and <a href="https://arxiv.org/abs/2005.14165?ref=bounded-regret.ghost.io">GPT-3</a> revealed the emergence of strong few-shot and zero-shot capabilities, via well-chosen natural language prompting.</p>
<!-- <img src="https://bounded-regret.ghost.io/content/images/2021/12/gpt2plot.png"> -->
<p align="center"><img src="https://bounded-regret.ghost.io/content/images/2022/01/gpt2_only.png"><br><img src="https://bounded-regret.ghost.io/content/images/2022/01/gpt2_and_3.png">
<br>
<i>Top: Few-shot machine translation performance (BLEU score) for GPT-2. Bottom: GPT-3 (trained on more data) has an even starker curve, going from 5 to 25 BLEU between 100M and 400M parameters. Unsupervised baselines, as well as fine-tuned state-of-the-art, are indicated for reference.</i>
</p>
<p>This was an unexpected and qualitatively new phenomenon that only appeared at large scales, and it emerged without ever explicitly training models to have these few-shot capabilities. Comparing GPT-2 to GPT-3 shows that the exact model size needed can vary due to the training distribution or other factors, but this doesn&#x2019;t affect the basic point that new capabilities can appear without designing or training for them.</p>
<p><strong>Grokking.</strong> In 2021, <a href="https://mathai-iclr.github.io/papers/papers/MATHAI_29_paper.pdf?ref=bounded-regret.ghost.io">Power et al.</a> identified a phenomenon they call &quot;grokking&quot;, where a network&#x2019;s generalization behavior improves qualitatively when training it for longer (even though the training loss is already small).</p>
<p>Specifically, for certain algorithmically generated logic/math datasets, neural networks trained for 1,000 steps achieve perfect train accuracy but near-zero test accuracy. However, after around 100,000 steps the test accuracy suddenly increases, achieving near-perfect generalization by 1 million steps.</p>
<p><img src="https://bounded-regret.ghost.io/content/images/2021/11/grokking.png" alt="grokking" loading="lazy"></p>
<p>This shows that even for a single model, we might encounter qualitative phase transitions as we train for longer.</p>
<p><strong>Other potential examples.</strong> I&apos;ll briefly list other examples from recent papers. I don&apos;t think these examples are as individually clear-cut, but they collectively paint an interesting picture:</p>
<ul>
<li><a href="https://arxiv.org/abs/2111.09259?ref=bounded-regret.ghost.io">McGrath et al. (2021)</a> show that AlphaZero acquires many chess concepts at a phase transition near 32,000 training steps.</li>
<li><a href="https://arxiv.org/abs/2201.03544?ref=bounded-regret.ghost.io">Pan et al. (2021)</a> show that reward hacking sometimes occurs via qualitative phase transitions as model size increases.</li>
<li>DeepMind&apos;s recent <a href="https://arxiv.org/abs/2112.11446?ref=bounded-regret.ghost.io">Gopher</a> model exhibits a phase transition on the FEVER task, acquiring the ability to evaluate evidence provided as side information (Figure 3):</li>
</ul>
<p align="center"><img src="https://bounded-regret.ghost.io/content/images/2022/01/fever_plot.png"></p>
<ul>
<li><a href="https://arxiv.org/abs/2109.01652?ref=bounded-regret.ghost.io">Wei et al. (2021)</a> show that instruction-tuning hurts small models but helps large models (see Figure 6).</li>
<li>Some few-shot tasks such as arithmetic show phase transitions with model size (see <a href="https://arxiv.org/abs/2005.14165?ref=bounded-regret.ghost.io">Brown et al. (2020)</a>, Figure 3.10).</li>
<li><a href="https://twitter.com/NaxAlpha/status/1420700413125447683?ref=bounded-regret.ghost.io">This</a> researcher shares an anecdote similar to the &#x201C;grokking&#x201D; paper.</li>
</ul>
<h2 id="what-this-implies-for-the-engineering-worldview">What This Implies for the Engineering Worldview</h2>
<p>In the <a href="https://bounded-regret.ghost.io/more-is-different-for-ai/">introduction post</a> to this series, I contrasted two worldviews called Philosophy and Engineering. The Engineering worldview, which is favored by most ML researchers, tends to predict the future by looking at empirical trends and extrapolating them forward. I myself am <a href="https://bounded-regret.ghost.io/forecasting-zeroth-and-first-order/">quite sympathetic to this view</a>, and for this reason I find emergent behavior to be troubling and disorienting. Rather than expecting empirical trends to continue, emergence suggests we should often expect new qualitative behaviors that are not extrapolations of previous trends.</p>
<p>Indeed, in this sense Engineering (or at least pure trend extrapolation) is self-defeating as a tool for predicting the future<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>. The Engineering worldview wants to extrapolate trends, but one trend is that emergent behavior is becoming more and more common. Of the four phase transitions I gave above, the first (storage) occurred around 1995, and the second (compute) occurred around 2015. The last two occurred in 2020 and 2021. Based on past trends, we should expect future trends to break more and more often.<sup class="footnote-ref"><a href="#fn3" id="fnref3">[3]</a></sup></p>
<p>How can we orient ourselves when thinking about the future of AI despite the probability of frequent deviations from past experience? I&apos;ll have a lot more to say about this in the next few posts, but to put some of my cards on the table:</p>
<ul>
<li>Confronting emergence will require adopting mindsets that are less familiar to most ML researchers and utilizing more of the Philosophy worldview (in tandem with Engineering and other worldviews).</li>
<li>Future ML systems will have weird failure modes that don&apos;t manifest today, and we should start thinking about and addressing them in advance.</li>
<li>On the other hand, I don&apos;t think that Engineering as a tool for predicting the future is entirely self-defeating. Despite emergent behavior, empirical findings often generalize surprisingly far, at least if we&apos;re careful in interpreting them. Utilizing this fact will be crucial to making concrete research progress.</li>
</ul>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item"><p>From the <a href="https://aclanthology.org/J90-2002.pdf?ref=bounded-regret.ghost.io">IBM model authors</a>: &#x201C;In 1949 Warren Weaver suggested that the problem be attacked with statistical methods and ideas from information theory, an area which he, Claude Shannon, and others were developing at the time (Weaver 1949). Although researchers quickly abandoned this approach, advancing numerous theoretical objections, we believe that the true obstacles lay in the relative impotence of the available computers and the dearth of machine-readable text from which to gather the statistics vital to such an attack. Today, computers are five orders of magnitude faster than they were in 1950 and have hundreds of millions of bytes of storage. Large, machine-readable corpora are readily available.&#x201D; <a href="#fnref1" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn2" class="footnote-item"><p>This is in contrast to using Engineering to <em>build capable and impressive systems</em> today. If anything, recent developments have strongly solidified Engineering&#x2019;s dominance for this task. <a href="#fnref2" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
<li id="fn3" class="footnote-item"><p>This list is probably subject to selection bias and recency effects, although I predict that my point would still hold up for a carefully curated list (for instance, I didn&#x2019;t include the several ambiguous examples in my count). I would be happy to bet on more phase transitions in the future if any readers wish to take the other side. <a href="#fnref3" class="footnote-backref">&#x21A9;&#xFE0E;</a></p>
</li>
</ol>
</section>
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