Tengyu Ma

Ekin Akyürek, Dale Schuurmans, Jacob Andreas et al. · microsoft-research, mit

Neural sequence models, especially transformers, exhibit a remarkable capacity for in-context learning. They can construct new predictors from sequences of labeled examples $(x, f(x))$ presented in the input without further parameter updates. We investigate the hypothesis that transformer-based in-context learners implement standard learning algorithms implicitly, by encoding smaller models in their activations, and updating these implicit models as new examples appear in the context. Using linear regression as a prototypical problem, we offer three sources of evidence for this hypothesis. First, we prove by construction that transformers can implement learning algorithms for linear models based on gradient descent and closed-form ridge regression. Second, we show that trained in-context learners closely match the predictors computed by gradient descent, ridge regression, and exact least-squares regression, transitioning between different predictors as transformer depth and dataset noise vary, and converging to Bayesian estimators for large widths and depths. Third, we present preliminary evidence that in-context learners share algorithmic features with these predictors: learners' late layers non-linearly encode weight vectors and moment matrices. These results suggest that in-context learning is understandable in algorithmic terms, and that (at least in the linear case) learners may rediscover standard estimation algorithms. Code and reference implementations are released at https://github.com/ekinakyurek/google-research/blob/master/incontext.

Sang Michael Xie, Shibani Santurkar, Tengyu Ma et al.

Selecting a suitable pretraining dataset is crucial for both general-domain (e.g., GPT-3) and domain-specific (e.g., Codex) language models (LMs). We formalize this problem as selecting a subset of a large raw unlabeled dataset to match a desired target distribution given unlabeled target samples. Due to the scale and dimensionality of the raw text data, existing methods use simple heuristics or require human experts to manually curate data. Instead, we extend the classic importance resampling approach used in low-dimensions for LM data selection. We propose Data Selection with Importance Resampling (DSIR), an efficient and scalable framework that estimates importance weights in a reduced feature space for tractability and selects data with importance resampling according to these weights. We instantiate the DSIR framework with hashed n-gram features for efficiency, enabling the selection of 100M documents from the full Pile dataset in 4.5 hours. To measure whether hashed n-gram features preserve the aspects of the data that are relevant to the target, we define KL reduction, a data metric that measures the proximity between the selected pretraining data and the target on some feature space. Across 8 data selection methods (including expert selection), KL reduction on hashed n-gram features highly correlates with average downstream accuracy (r=0.82). When selecting data for continued pretraining on a specific domain, DSIR performs comparably to expert curation across 8 target distributions. When pretraining general-domain models (target is Wikipedia and books), DSIR improves over random selection and heuristic filtering baselines by 2-2.5% on the GLUE benchmark. Code is available at https://github.com/p-lambda/dsir.

Nicolas Carion, Laura Gustafson, Yuan-Ting Hu et al.

We present Segment Anything Model (SAM) 3, a unified model that detects, segments, and tracks objects in images and videos based on concept prompts, which we define as either short noun phrases (e.g., "yellow school bus"), image exemplars, or a combination of both. Promptable Concept Segmentation (PCS) takes such prompts and returns segmentation masks and unique identities for all matching object instances. To advance PCS, we build a scalable data engine that produces a high-quality dataset with 4M unique concept labels, including hard negatives, across images and videos. Our model consists of an image-level detector and a memory-based video tracker that share a single backbone. Recognition and localization are decoupled with a presence head, which boosts detection accuracy. SAM 3 doubles the accuracy of existing systems in both image and video PCS, and improves previous SAM capabilities on visual segmentation tasks. We open source SAM 3 along with our new Segment Anything with Concepts (SA-Co) benchmark for promptable concept segmentation.

Jerry Wei, Jason Wei, Yi Tay et al. · deepmind

We study how in-context learning (ICL) in language models is affected by semantic priors versus input-label mappings. We investigate two setups-ICL with flipped labels and ICL with semantically-unrelated labels-across various model families (GPT-3, InstructGPT, Codex, PaLM, and Flan-PaLM). First, experiments on ICL with flipped labels show that overriding semantic priors is an emergent ability of model scale. While small language models ignore flipped labels presented in-context and thus rely primarily on semantic priors from pretraining, large models can override semantic priors when presented with in-context exemplars that contradict priors, despite the stronger semantic priors that larger models may hold. We next study semantically-unrelated label ICL (SUL-ICL), in which labels are semantically unrelated to their inputs (e.g., foo/bar instead of negative/positive), thereby forcing language models to learn the input-label mappings shown in in-context exemplars in order to perform the task. The ability to do SUL-ICL also emerges primarily with scale, and large-enough language models can even perform linear classification in a SUL-ICL setting. Finally, we evaluate instruction-tuned models and find that instruction tuning strengthens both the use of semantic priors and the capacity to learn input-label mappings, but more of the former.

Kendrick Shen, Robbie Jones, Ananya Kumar et al. · stanford

We consider unsupervised domain adaptation (UDA), where labeled data from a source domain (e.g., photographs) and unlabeled data from a target domain (e.g., sketches) are used to learn a classifier for the target domain. Conventional UDA methods (e.g., domain adversarial training) learn domain-invariant features to improve generalization to the target domain. In this paper, we show that contrastive pre-training, which learns features on unlabeled source and target data and then fine-tunes on labeled source data, is competitive with strong UDA methods. However, we find that contrastive pre-training does not learn domain-invariant features, diverging from conventional UDA intuitions. We show theoretically that contrastive pre-training can learn features that vary subtantially across domains but still generalize to the target domain, by disentangling domain and class information. Our results suggest that domain invariance is not necessary for UDA. We empirically validate our theory on benchmark vision datasets.

Kaiyue Wen, Zhiyuan Li, Tengyu Ma · stanford

Despite extensive studies, the underlying reason as to why overparameterized neural networks can generalize remains elusive. Existing theory shows that common stochastic optimizers prefer flatter minimizers of the training loss, and thus a natural potential explanation is that flatness implies generalization. This work critically examines this explanation. Through theoretical and empirical investigation, we identify the following three scenarios for two-layer ReLU networks: (1) flatness provably implies generalization; (2) there exist non-generalizing flattest models and sharpness minimization algorithms fail to generalize, and (3) perhaps most surprisingly, there exist non-generalizing flattest models, but sharpness minimization algorithms still generalize. Our results suggest that the relationship between sharpness and generalization subtly depends on the data distributions and the model architectures and sharpness minimization algorithms do not only minimize sharpness to achieve better generalization. This calls for the search for other explanations for the generalization of over-parameterized neural networks.

Kefan Dong, Tengyu Ma · stanford

Real-world machine learning applications often involve deploying neural networks to domains that are not seen in the training time. Hence, we need to understand the extrapolation of nonlinear models -- under what conditions on the distributions and function class, models can be guaranteed to extrapolate to new test distributions. The question is very challenging because even two-layer neural networks cannot be guaranteed to extrapolate outside the support of the training distribution without further assumptions on the domain shift. This paper makes some initial steps toward analyzing the extrapolation of nonlinear models for structured domain shift. We primarily consider settings where the marginal distribution of each coordinate of the data (or subset of coordinates) does not shift significantly across the training and test distributions, but the joint distribution may have a much bigger shift. We prove that the family of nonlinear models of the form $f(x)=\sum f_i(x_i)$, where $f_i$ is an arbitrary function on the subset of features $x_i$, can extrapolate to unseen distributions, if the covariance of the features is well-conditioned. To the best of our knowledge, this is the first result that goes beyond linear models and the bounded density ratio assumption, even though the assumptions on the distribution shift and function class are stylized.

Arvind Mahankali, Jeff Z. Haochen, Kefan Dong et al. · stanford

Despite recent theoretical progress on the non-convex optimization of two-layer neural networks, it is still an open question whether gradient descent on neural networks without unnatural modifications can achieve better sample complexity than kernel methods. This paper provides a clean mean-field analysis of projected gradient flow on polynomial-width two-layer neural networks. Different from prior works, our analysis does not require unnatural modifications of the optimization algorithm. We prove that with sample size $n = O(d^{3.1})$ where $d$ is the dimension of the inputs, the network trained with projected gradient flow converges in $\text{poly}(d)$ time to a non-trivial error that is not achievable by kernel methods using $n \ll d^4$ samples, hence demonstrating a clear separation between unmodified gradient descent and NTK. As a corollary, we show that projected gradient descent with a positive learning rate and a polynomial number of iterations converges to low error with the same sample complexity.

Kefan Dong, Tengyu Ma · stanford

Past research on interactive decision making problems (bandits, reinforcement learning, etc.) mostly focuses on the minimax regret that measures the algorithm's performance on the hardest instance. However, an ideal algorithm should adapt to the complexity of a particular problem instance and incur smaller regrets on easy instances than worst-case instances. In this paper, we design the first asymptotic instance-optimal algorithm for general interactive decision making problems with finite number of decisions under mild conditions. On every instance $f$, our algorithm outperforms all consistent algorithms (those achieving non-trivial regrets on all instances), and has asymptotic regret $\mathcal{C}(f) \ln n$, where $\mathcal{C}(f)$ is an exact characterization of the complexity of $f$. The key step of the algorithm involves hypothesis testing with active data collection. It computes the most economical decisions with which the algorithm collects observations to test whether an estimated instance is indeed correct; thus, the complexity $\mathcal{C}(f)$ is the minimum cost to test the instance $f$ against other instances. Our results, instantiated on concrete problems, recover the classical gap-dependent bounds for multi-armed bandits [Lai and Robbins, 1985] and prior works on linear bandits [Lattimore and Szepesvari, 2017], and improve upon the previous best instance-dependent upper bound [Xu et al., 2021] for reinforcement learning.

Hong Liu, Sang Michael Xie, Zhiyuan Li et al. · stanford

Language modeling on large-scale datasets leads to impressive performance gains on various downstream language tasks. The validation pre-training loss (or perplexity in autoregressive language modeling) is often used as the evaluation metric when developing language models since the pre-training loss tends to be well-correlated with downstream performance (which is itself difficult to evaluate comprehensively). Contrary to this conventional wisdom, this paper shows that 1) pre-training loss cannot fully explain downstream performance and 2) flatness of the model is well-correlated with downstream performance where pre-training loss is not. On simplified datasets, we identify three ways to produce models with the same (statistically optimal) pre-training loss but different downstream performance: continue pre-training after convergence, increasing the model size, and changing the training algorithm. These experiments demonstrate the existence of implicit bias of pre-training algorithms/optimizers -- among models with the same minimal pre-training loss, they implicitly prefer more transferable ones. Toward understanding this implicit bias, we prove that SGD with standard mini-batch noise implicitly prefers flatter minima in language models, and empirically observe a strong correlation between flatness and downstream performance among models with the same minimal pre-training loss. We also prove in a synthetic language setting that among the models with the minimal pre-training loss, the flattest model transfers to downstream tasks.

Margalit Glasgow, Colin Wei, Mary Wootters et al. · stanford

A major challenge in modern machine learning is theoretically understanding the generalization properties of overparameterized models. Many existing tools rely on uniform convergence (UC), a property that, when it holds, guarantees that the test loss will be close to the training loss, uniformly over a class of candidate models. Nagarajan and Kolter (2019) show that in certain simple linear and neural-network settings, any uniform convergence bound will be vacuous, leaving open the question of how to prove generalization in settings where UC fails. Our main contribution is proving novel generalization bounds in two such settings, one linear, and one non-linear. We study the linear classification setting of Nagarajan and Kolter, and a quadratic ground truth function learned via a two-layer neural network in the non-linear regime. We prove a new type of margin bound showing that above a certain signal-to-noise threshold, any near-max-margin classifier will achieve almost no test loss in these two settings. Our results show that near-max-margin is important: while any model that achieves at least a $(1 - ε)$-fraction of the max-margin generalizes well, a classifier achieving half of the max-margin may fail terribly. Building on the impossibility results of Nagarajan and Kolter, under slightly stronger assumptions, we show that one-sided UC bounds and classical margin bounds will fail on near-max-margin classifiers. Our analysis provides insight on why memorization can coexist with generalization: we show that in this challenging regime where generalization occurs but UC fails, near-max-margin classifiers simultaneously contain some generalizable components and some overfitting components that memorize the data. The presence of the overfitting components is enough to preclude UC, but the near-extremal margin guarantees that sufficient generalizable components are present.

Jeff Z. HaoChen, Colin Wei, Ananya Kumar et al. · stanford

Contrastive learning is a highly effective method for learning representations from unlabeled data. Recent works show that contrastive representations can transfer across domains, leading to simple state-of-the-art algorithms for unsupervised domain adaptation. In particular, a linear classifier trained to separate the representations on the source domain can also predict classes on the target domain accurately, even though the representations of the two domains are far from each other. We refer to this phenomenon as linear transferability. This paper analyzes when and why contrastive representations exhibit linear transferability in a general unsupervised domain adaptation setting. We prove that linear transferability can occur when data from the same class in different domains (e.g., photo dogs and cartoon dogs) are more related with each other than data from different classes in different domains (e.g., photo dogs and cartoon cats) are. Our analyses are in a realistic regime where the source and target domains can have unbounded density ratios and be weakly related, and they have distant representations across domains.

Jeff Z. HaoChen, Tengyu Ma · stanford

Understanding self-supervised learning is important but challenging. Previous theoretical works study the role of pretraining losses, and view neural networks as general black boxes. However, the recent work of Saunshi et al. argues that the model architecture -- a component largely ignored by previous works -- also has significant influences on the downstream performance of self-supervised learning. In this work, we provide the first theoretical analysis of self-supervised learning that incorporates the effect of inductive biases originating from the model class. In particular, we focus on contrastive learning -- a popular self-supervised learning method that is widely used in the vision domain. We show that when the model has limited capacity, contrastive representations would recover certain special clustering structures that are compatible with the model architecture, but ignore many other clustering structures in the data distribution. As a result, our theory can capture the more realistic setting where contrastive representations have much lower dimensionality than the number of clusters in the data distribution. We instantiate our theory on several synthetic data distributions, and provide empirical evidence to support the theory.

Haoyuan Cai, Tengyu Ma, Simon Du · stanford

We revisit the incremental autonomous exploration problem proposed by Lim & Auer (2012). In this setting, the agent aims to learn a set of near-optimal goal-conditioned policies to reach the $L$-controllable states: states that are incrementally reachable from an initial state $s_0$ within $L$ steps in expectation. We introduce a new algorithm with stronger sample complexity bounds than existing ones. Furthermore, we also prove the first lower bound for the autonomous exploration problem. In particular, the lower bound implies that our proposed algorithm, Value-Aware Autonomous Exploration, is nearly minimax-optimal when the number of $L$-controllable states grows polynomially with respect to $L$. Key in our algorithm design is a connection between autonomous exploration and multi-goal stochastic shortest path, a new problem that naturally generalizes the classical stochastic shortest path problem. This new problem and its connection to autonomous exploration can be of independent interest.

Nikhila Ravi, Valentin Gabeur, Yuan-Ting Hu et al.

We present Segment Anything Model 2 (SAM 2), a foundation model towards solving promptable visual segmentation in images and videos. We build a data engine, which improves model and data via user interaction, to collect the largest video segmentation dataset to date. Our model is a simple transformer architecture with streaming memory for real-time video processing. SAM 2 trained on our data provides strong performance across a wide range of tasks. In video segmentation, we observe better accuracy, using 3x fewer interactions than prior approaches. In image segmentation, our model is more accurate and 6x faster than the Segment Anything Model (SAM). We believe that our data, model, and insights will serve as a significant milestone for video segmentation and related perception tasks. We are releasing our main model, dataset, as well as code for model training and our demo.

Ananya Kumar, Tengyu Ma, Percy Liang et al.

We often see undesirable tradeoffs in robust machine learning where out-of-distribution (OOD) accuracy is at odds with in-distribution (ID) accuracy: a robust classifier obtained via specialized techniques such as removing spurious features often has better OOD but worse ID accuracy compared to a standard classifier trained via ERM. In this paper, we find that ID-calibrated ensembles -- where we simply ensemble the standard and robust models after calibrating on only ID data -- outperforms prior state-of-the-art (based on self-training) on both ID and OOD accuracy. On eleven natural distribution shift datasets, ID-calibrated ensembles obtain the best of both worlds: strong ID accuracy and OOD accuracy. We analyze this method in stylized settings, and identify two important conditions for ensembles to perform well both ID and OOD: (1) we need to calibrate the standard and robust models (on ID data, because OOD data is unavailable), (2) OOD has no anticorrelated spurious features.

Arvind Mahankali, Tatsunori B. Hashimoto, Tengyu Ma

Recent works have empirically analyzed in-context learning and shown that transformers trained on synthetic linear regression tasks can learn to implement ridge regression, which is the Bayes-optimal predictor, given sufficient capacity [Akyürek et al., 2023], while one-layer transformers with linear self-attention and no MLP layer will learn to implement one step of gradient descent (GD) on a least-squares linear regression objective [von Oswald et al., 2022]. However, the theory behind these observations remains poorly understood. We theoretically study transformers with a single layer of linear self-attention, trained on synthetic noisy linear regression data. First, we mathematically show that when the covariates are drawn from a standard Gaussian distribution, the one-layer transformer which minimizes the pre-training loss will implement a single step of GD on the least-squares linear regression objective. Then, we find that changing the distribution of the covariates and weight vector to a non-isotropic Gaussian distribution has a strong impact on the learned algorithm: the global minimizer of the pre-training loss now implements a single step of $\textit{pre-conditioned}$ GD. However, if only the distribution of the responses is changed, then this does not have a large effect on the learned algorithm: even when the response comes from a more general family of $\textit{nonlinear}$ functions, the global minimizer of the pre-training loss still implements a single step of GD on a least-squares linear regression objective.

Xiaohan Cui, Long Ma, Tengyu Ma et al.

Object detection in low-light scenarios has attracted much attention in the past few years. A mainstream and representative scheme introduces enhancers as the pre-processing for regular detectors. However, because of the disparity in task objectives between the enhancer and detector, this paradigm cannot shine at its best ability. In this work, we try to arouse the potential of enhancer + detector. Different from existing works, we extend the illumination-based enhancers (our newly designed or existing) as a scene decomposition module, whose removed illumination is exploited as the auxiliary in the detector for extracting detection-friendly features. A semantic aggregation module is further established for integrating multi-scale scene-related semantic information in the context space. Actually, our built scheme successfully transforms the "trash" (i.e., the ignored illumination in the detector) into the "treasure" for the detector. Plenty of experiments are conducted to reveal our superiority against other state-of-the-art methods. The code will be public if it is accepted.

Kaiyue Wen, Tengyu Ma, Zhiyuan Li

Sharpness-Aware Minimization (SAM) is a highly effective regularization technique for improving the generalization of deep neural networks for various settings. However, the underlying working of SAM remains elusive because of various intriguing approximations in the theoretical characterizations. SAM intends to penalize a notion of sharpness of the model but implements a computationally efficient variant; moreover, a third notion of sharpness was used for proving generalization guarantees. The subtle differences in these notions of sharpness can indeed lead to significantly different empirical results. This paper rigorously nails down the exact sharpness notion that SAM regularizes and clarifies the underlying mechanism. We also show that the two steps of approximations in the original motivation of SAM individually lead to inaccurate local conclusions, but their combination accidentally reveals the correct effect, when full-batch gradients are applied. Furthermore, we also prove that the stochastic version of SAM in fact regularizes the third notion of sharpness mentioned above, which is most likely to be the preferred notion for practical performance. The key mechanism behind this intriguing phenomenon is the alignment between the gradient and the top eigenvector of Hessian when SAM is applied.

Khashayar Gatmiry, Zhiyuan Li, Ching-Yao Chuang et al.

Recent works on over-parameterized neural networks have shown that the stochasticity in optimizers has the implicit regularization effect of minimizing the sharpness of the loss function (in particular, the trace of its Hessian) over the family zero-loss solutions. More explicit forms of flatness regularization also empirically improve the generalization performance. However, it remains unclear why and when flatness regularization leads to better generalization. This work takes the first step toward understanding the inductive bias of the minimum trace of the Hessian solutions in an important setting: learning deep linear networks from linear measurements, also known as \emph{deep matrix factorization}. We show that for all depth greater than one, with the standard Restricted Isometry Property (RIP) on the measurements, minimizing the trace of Hessian is approximately equivalent to minimizing the Schatten 1-norm of the corresponding end-to-end matrix parameters (i.e., the product of all layer matrices), which in turn leads to better generalization. We empirically verify our theoretical findings on synthetic datasets.

Arvind Mahankali, Kaiyue Wen, Tengyu Ma

Long chain-of-thought reasoning (Long CoT) is now fundamental to state-of-the-art LLMs, especially in mathematical reasoning. However, LLM generation is highly sequential, and long CoTs lead to a high latency. We propose to train Divide-and-Conquer CoT (DC-CoT) to reduce the latency. With DC-CoT, the model can act as a director that identifies distinct subtasks that can be performed in parallel in its reasoning process, and then spawns workers to execute the subtasks. Our goal is to achieve high accuracy, with a low longest path length, which is a theoretical measure of the latency needed for the response. We start with a long CoT base model (DeepScaleR-1.5B-Preview), and first use SFT with a small curated demonstration set to initialize its ability to spawn workers in a certain format. Because SFT degrades the accuracy significantly, we design a multi-stage RL algorithm, with various data filtering strategies, to recover the accuracy while decreasing the longest path length. Across several benchmarks including AIME 2024 and HMMT 2025, DC-CoT achieves similar accuracy as DeepScaleR-1.5B-Preview while decreasing longest path length by 35-40%. Our code, SFT dataset and models are publicly available at https://github.com/amahankali10/DC_CoT_RL_for_Low_Latency_CoT_with_Parallel_Reasoning.

Kefan Dong, Tengyu Ma

Many machine learning applications require learning a function with a small worst-case error over the entire input domain, that is, the $L_\infty$-error, whereas most existing theoretical works only guarantee recovery in average errors such as the $L_2$-error. $L_\infty$-recovery from polynomial samples is even impossible for seemingly simple function classes such as constant-norm infinite-width two-layer neural nets. This paper makes some initial steps beyond the impossibility results by leveraging the randomness in the ground-truth functions. We prove a polynomial sample complexity bound for random ground-truth functions drawn from Gaussian random fields. Our key technical novelty is to prove that the degree-$k$ spherical harmonics components of a function from Gaussian random field cannot be spiky in that their $L_\infty$/$L_2$ ratios are upperbounded by $O(d \sqrt{\ln k})$ with high probability. In contrast, the worst-case $L_\infty$/$L_2$ ratio for degree-$k$ spherical harmonics is on the order of $Ω(\min\{d^{k/2},k^{d/2}\})$.

Daniel Bolya, Po-Yao Huang, Peize Sun et al. · meta-ai, mit

We introduce Perception Encoder (PE), a state-of-the-art vision encoder for image and video understanding trained via simple vision-language learning. Traditionally, vision encoders have relied on a variety of pretraining objectives, each tailored to specific downstream tasks such as classification, captioning, or localization. Surprisingly, after scaling our carefully tuned image pretraining recipe and refining with our robust video data engine, we find that contrastive vision-language training alone can produce strong, general embeddings for all of these downstream tasks. There is only one caveat: these embeddings are hidden within the intermediate layers of the network. To draw them out, we introduce two alignment methods: language alignment for multimodal language modeling, and spatial alignment for dense prediction. Together, our PE family of models achieves best-in-class results on a wide variety of tasks, including (1) zero-shot image and video classification and retrieval, simultaneously obtaining 86.6 average zero-shot ImageNet robustness and 76.9 zero-shot Kinetics-400 video classification; (2) document, image, and video Q&A, enabling 94.6 DocVQA, 80.9 InfographicVQA, and 82.7 PerceptionTest with an 8B LLM; and (3) spatial tasks such as detection, tracking, and depth estimation, setting a new COCO state-of-the-art of 66.0 box mAP. To foster further research, we release our models, code, and novel dataset of synthetically and human-annotated videos: https://github.com/facebookresearch/perception_models

Kefan Dong, Tengyu Ma

A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by alternating between LLM generating proofs and finetuning them on correctly generated ones, performance quickly plateaus due to the scarcity of correct proofs (sparse rewards). To keep improving the models with limited data, we draw inspiration from mathematicians, who continuously develop new results, partly by proposing novel conjectures or exercises (which are often variants of known results) and attempting to solve them. We design the Self-play Theorem Prover (STP) that simultaneously takes on two roles, conjecturer and prover, each providing training signals to the other. The conjecturer is trained iteratively on previously generated conjectures that are barely provable by the current prover, which incentivizes it to generate increasingly challenging conjectures over time. The prover attempts to prove the conjectures with standard expert iteration. We evaluate STP with both Lean and Isabelle formal versifiers. With 51.3 billion tokens generated during the training in Lean, STP proves 28.5% of the statements in the LeanWorkbook dataset, doubling the previous best result of 13.2% achieved through expert iteration. The final model achieves state-of-the-art performance among whole-proof generation methods on miniF2F-test (65.0%, pass@3200), Proofnet-test (23.9%, pass@3200) and PutnamBench (8/644, pass@3200). We release our code, model, and dataset in this URL: https://github.com/kfdong/STP.

Jang Hyun Cho, Andrea Madotto, Effrosyni Mavroudi et al.

Vision-language models are integral to computer vision research, yet many high-performing models remain closed-source, obscuring their data, design and training recipe. The research community has responded by using distillation from black-box models to label training data, achieving strong benchmark results, at the cost of measurable scientific progress. However, without knowing the details of the teacher model and its data sources, scientific progress remains difficult to measure. In this paper, we study building a Perception Language Model (PLM) in a fully open and reproducible framework for transparent research in image and video understanding. We analyze standard training pipelines without distillation from proprietary models and explore large-scale synthetic data to identify critical data gaps, particularly in detailed video understanding. To bridge these gaps, we release 2.8M human-labeled instances of fine-grained video question-answer pairs and spatio-temporally grounded video captions. Additionally, we introduce PLM-VideoBench, a suite for evaluating challenging video understanding tasks focusing on the ability to reason about "what", "where", "when", and "how" of a video. We make our work fully reproducible by providing data, training recipes, code & models. https://github.com/facebookresearch/perception_models

Luke Bailey, Kaiyue Wen, Kefan Dong et al.

LLM self-play algorithms are notable in that, in principle, nothing bounds their learning: a Conjecturer model creates problems for a Solver, and both improve together. However, in practice, existing LLM self-play methods do not scale well with large amounts of compute, instead hitting learning plateaus. We argue this is because over long training runs, the Conjecturer learns to hack its reward, collapsing to artificially complex problems that do not help the Solver improve. To overcome this, we introduce Self-Guided Self-Play (SGS), a self-play algorithm in which the language model itself guides the Conjecturer away from degeneracy. In SGS, the model takes on three roles: Solver, Conjecturer, and a Guide that scores synthetic problems by their relevance to unsolved target problems and how clean and natural they are, providing supervision against Conjecturer collapse. Our core hypothesis is that language models can assess whether a subproblem is useful for achieving a goal. We evaluate the scaling properties of SGS by running training for significantly longer than prior works and by fitting scaling laws to cumulative solve rate curves. Applying SGS to formal theorem proving in Lean4, we find that it surpasses the asymptotic solve rate of our strongest RL baseline in fewer than 80 rounds of self-play and enables a 7B parameter model, after 200 rounds of self-play, to solve more problems than a 671B parameter model pass@4.

Slim Barkallah, Luke Bailey, Kaiyue Wen et al.

Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most proofs, particularly those written by AI systems, have neither property, and translating them into formal languages remains challenging in many frontier math settings. We propose Pseudo-Formalization (PF), a proof format that captures the modularity and precision of formal proofs while retaining the flexibility of natural language. A Pseudo-Formal proof is decomposed into self-contained modules, each stating its premises, conclusion, and proof in natural language. To verify the correctness of a regular natural language proof, an LLM translates it to Pseudo-Formal and then verifies each module independently, an algorithm we call Block Verification (BV). We evaluate PF+BV on two benchmarks spanning olympiad and research-level mathematics, where it pareto-dominates LLM-as-judge baselines on error-finding precision and recall. To support future work, we release our research-level proof verification benchmark ArxivMathGradingBench.

Zhiyuan Li, Hong Liu, Denny Zhou et al.

Instructing the model to generate a sequence of intermediate steps, a.k.a., a chain of thought (CoT), is a highly effective method to improve the accuracy of large language models (LLMs) on arithmetics and symbolic reasoning tasks. However, the mechanism behind CoT remains unclear. This work provides a theoretical understanding of the power of CoT for decoder-only transformers through the lens of expressiveness. Conceptually, CoT empowers the model with the ability to perform inherently serial computation, which is otherwise lacking in transformers, especially when depth is low. Given input length $n$, previous works have shown that constant-depth transformers with finite precision $\mathsf{poly}(n)$ embedding size can only solve problems in $\mathsf{TC}^0$ without CoT. We first show an even tighter expressiveness upper bound for constant-depth transformers with constant-bit precision, which can only solve problems in $\mathsf{AC}^0$, a proper subset of $ \mathsf{TC}^0$. However, with $T$ steps of CoT, constant-depth transformers using constant-bit precision and $O(\log n)$ embedding size can solve any problem solvable by boolean circuits of size $T$. Empirically, enabling CoT dramatically improves the accuracy for tasks that are hard for parallel computation, including the composition of permutation groups, iterated squaring, and circuit value problems, especially for low-depth transformers.

Huaqing Zhang, Kaiyue Wen, Tengyu Ma

Researchers build scaling laws to forecast the training performance of expensive large-scale runs with larger model size N and data size D. These laws assume that other training hyperparameters are optimally chosen, which can require significant effort and, in some cases, be impossible due to external hardware constraints. To improve predictability across a broader set of hyperparameters and enable simpler tuning at scale, we propose learning a \textit{Configuration-to-Performance Scaling Law} (CPL): a mapping from the \textit{full training configuration} to training performance. Because no simple functional form can express this mapping, we parameterize it with a large language model (LLM), and fit it with diverse open-source pretraining logs across multiple sources, yielding a \textit{Neural} Configuration-to-Performance Scaling Law (NCPL). NCPL accurately predicts how training configurations influence the final pretraining loss, achieving 20-40% lower prediction error than the configuration-agnostic Chinchilla law and generalizing to runs using up to 10 x more compute than any run in the training set. It further supports joint tuning of multiple hyperparameters with performance comparable to hyperparameter scaling law baselines. Finally, NCPL naturally and effectively extends to richer prediction targets such as loss-curve prediction.

Long Ma, Tengyu Ma, Risheng Liu et al.

Existing low-light image enhancement techniques are mostly not only difficult to deal with both visual quality and computational efficiency but also commonly invalid in unknown complex scenarios. In this paper, we develop a new Self-Calibrated Illumination (SCI) learning framework for fast, flexible, and robust brightening images in real-world low-light scenarios. To be specific, we establish a cascaded illumination learning process with weight sharing to handle this task. Considering the computational burden of the cascaded pattern, we construct the self-calibrated module which realizes the convergence between results of each stage, producing the gains that only use the single basic block for inference (yet has not been exploited in previous works), which drastically diminishes computation cost. We then define the unsupervised training loss to elevate the model capability that can adapt to general scenes. Further, we make comprehensive explorations to excavate SCI's inherent properties (lacking in existing works) including operation-insensitive adaptability (acquiring stable performance under the settings of different simple operations) and model-irrelevant generality (can be applied to illumination-based existing works to improve performance). Finally, plenty of experiments and ablation studies fully indicate our superiority in both quality and efficiency. Applications on low-light face detection and nighttime semantic segmentation fully reveal the latent practical values for SCI. The source code is available at https://github.com/vis-opt-group/SCI.

Tianhe Yu, Garrett Thomas, Lantao Yu et al.

Offline reinforcement learning (RL) refers to the problem of learning policies entirely from a large batch of previously collected data. This problem setting offers the promise of utilizing such datasets to acquire policies without any costly or dangerous active exploration. However, it is also challenging, due to the distributional shift between the offline training data and those states visited by the learned policy. Despite significant recent progress, the most successful prior methods are model-free and constrain the policy to the support of data, precluding generalization to unseen states. In this paper, we first observe that an existing model-based RL algorithm already produces significant gains in the offline setting compared to model-free approaches. However, standard model-based RL methods, designed for the online setting, do not provide an explicit mechanism to avoid the offline setting's distributional shift issue. Instead, we propose to modify the existing model-based RL methods by applying them with rewards artificially penalized by the uncertainty of the dynamics. We theoretically show that the algorithm maximizes a lower bound of the policy's return under the true MDP. We also characterize the trade-off between the gain and risk of leaving the support of the batch data. Our algorithm, Model-based Offline Policy Optimization (MOPO), outperforms standard model-based RL algorithms and prior state-of-the-art model-free offline RL algorithms on existing offline RL benchmarks and two challenging continuous control tasks that require generalizing from data collected for a different task. The code is available at https://github.com/tianheyu927/mopo.

Neil Band, Xuechen Li, Tengyu Ma et al.

Language models (LMs) may lead their users to make suboptimal downstream decisions when they confidently hallucinate. This issue can be mitigated by having the LM verbally convey the probability that its claims are correct, but existing models cannot produce long-form text with calibrated confidence statements. Through the lens of decision-making, we define linguistic calibration for long-form generations: an LM is linguistically calibrated if its generations enable its users to make calibrated probabilistic predictions. This definition enables a training framework where a supervised finetuning step bootstraps an LM to emit long-form generations with confidence statements such as "I estimate a 30% chance of..." or "I am certain that...", followed by a reinforcement learning step which rewards generations that enable a user to provide calibrated answers to related questions. We linguistically calibrate Llama 2 7B and find in automated and human evaluations of long-form generations that it is significantly more calibrated than strong finetuned factuality baselines with comparable accuracy. These findings generalize under significant domain shifts to scientific and biomedical questions and to an entirely held-out person biography generation task. Our results demonstrate that long-form generations may be calibrated end-to-end by constructing an objective in the space of the predictions that users make in downstream decision-making.

Kaiyue Wen, David Hall, Tengyu Ma et al.

AdamW has long been the dominant optimizer in language model pretraining, despite numerous claims that alternative optimizers offer 1.4 to 2x speedup. We posit that two methodological shortcomings have obscured fair comparisons and hindered practical adoption: (i) unequal hyperparameter tuning and (ii) limited or misleading evaluation setups. To address these two issues, we conduct a systematic study of ten deep learning optimizers across four model scales (0.1B-1.2B parameters) and data-to-model ratios (1-8x the Chinchilla optimum). We find that fair and informative comparisons require rigorous hyperparameter tuning and evaluations across a range of model scales and data-to-model ratios, performed at the end of training. First, optimal hyperparameters for one optimizer may be suboptimal for another, making blind hyperparameter transfer unfair. Second, the actual speedup of many proposed optimizers over well-tuned baselines is lower than claimed and decreases with model size to only 1.1x for 1.2B parameter models. Thirdly, comparing intermediate checkpoints before reaching the target training budgets can be misleading, as rankings between two optimizers can flip during training due to learning rate decay. Through our thorough investigation, we find that all the fastest optimizers such as Muon and Soap, use matrices as preconditioners -- multiplying gradients with matrices rather than entry-wise scalars. However, the speedup of matrix-based optimizers is inversely proportional to model scale, decreasing from 1.4x over AdamW for 0.1B parameter models to merely 1.1x for 1.2B parameter models.

Kefan Dong, Arvind Mahankali, Tengyu Ma

Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof verification/evaluation. Most previous results provide human-written lemmas to the theorem prover, which is an arguably oversimplified setting that does not sufficiently test the provers' planning and decomposition capabilities. Instead, we work in a more natural setup where the lemmas that are directly relevant to the theorem are not given to the theorem prover at test time. We design an RL-based training algorithm that encourages the model to decompose a theorem into lemmas, prove the lemmas, and then prove the theorem by using the lemmas. Our reward mechanism is inspired by how mathematicians train themselves: even if a theorem is too challenging to be proved by the current model, a positive reward is still given to the model for any correct and novel lemmas that are proposed and proved in this process. During training, our model proposes and proves lemmas that are not in the training dataset. In fact, these newly-proposed correct lemmas consist of 37.7% of the training replay buffer when we train on the dataset extracted from Archive of Formal Proofs (AFP). The model trained by our RL algorithm outperforms that trained by supervised finetuning, improving the pass rate from 40.8% to 45.5% on AFP test set, and from 36.5% to 39.5% on an out-of-distribution test set.

Thomas Chen, Tengyu Ma, Zhiyuan Li

Length generalization is the ability of a learning algorithm to learn a hypothesis which generalizes to longer inputs than the inputs in the training set. In this paper, we provide provable guarantees of length generalization for various classes of functions in an idealized setting. First, we formalize the framework of non-asymptotic length generalization, which requires a computable upper bound for the minimum input length that guarantees length generalization, as a function of the complexity of ground-truth function under some given complexity measure. We refer to this minimum input length to length generalize as length complexity. We show the Minimum-Complexity Interpolator learning algorithm achieves optimal length complexity. We further show that whether a function class admits non-asymptotic length generalization is equivalent to the decidability of its language equivalence problem, which implies that there is no computable upper bound for the length complexity of Context-Free Grammars. On the positive side, we show that the length complexity of Deterministic Finite Automata is $2n - 2$ where $n$ is the number of states of the ground-truth automaton. Our main results are upper bounds of length complexity for a subset of a transformer-related function class called C-RASP (Yang & Chiang, 2024). We show that the length complexity of 1-layer C-RASP functions is $O(T^2)$ when the ground-truth function has precision $T$, and that the length complexity of 2-layer C-RASP functions is $O(T^{O(K)})$ when the ground-truth function has precision $T$ and $K$ heads.

Tianle Cai, Xuezhi Wang, Tengyu Ma et al.

Recent research has highlighted the potential of large language models (LLMs) to improve their problem-solving capabilities with the aid of suitable external tools. In our work, we further advance this concept by introducing a closed-loop framework, referred to as LLMs A s Tool Makers (LATM), where LLMs create their own reusable tools for problem-solving. Our approach consists of two phases: 1) tool making: an LLM acts as the tool maker that crafts tools for a set of tasks. 2) tool using: another LLM acts as the tool user, which applies the tool built by the tool maker for problem-solving. On the problem-solving server side, tool-making enables continual tool generation and caching as new requests emerge. This framework enables subsequent requests to access cached tools via their corresponding APIs, enhancing the efficiency of task resolution. Recognizing that tool-making requires more sophisticated capabilities, we assign this task to a powerful, albeit resource-intensive, model. Conversely, the simpler tool-using phase is delegated to a lightweight model. This strategic division of labor allows the once-off cost of tool-making to be spread over multiple instances of tool-using, significantly reducing average costs while maintaining strong performance. Furthermore, our method offers a functional cache through the caching and reuse of tools, which stores the functionality of a class of requests instead of the natural language responses from LLMs, thus extending the applicability of the conventional cache mechanism. We evaluate our approach across various complex reasoning tasks, including Big-Bench tasks. With GPT-4 as the tool maker and GPT-3.5 as the tool user, LATM demonstrates performance equivalent to using GPT-4 for both roles, but with a significantly reduced inference cost.

Hong Liu, Zhiyuan Li, David Hall et al.

Given the massive cost of language model pre-training, a non-trivial improvement of the optimization algorithm would lead to a material reduction on the time and cost of training. Adam and its variants have been state-of-the-art for years, and more sophisticated second-order (Hessian-based) optimizers often incur too much per-step overhead. In this paper, we propose Sophia, Second-order Clipped Stochastic Optimization, a simple scalable second-order optimizer that uses a light-weight estimate of the diagonal Hessian as the pre-conditioner. The update is the moving average of the gradients divided by the moving average of the estimated Hessian, followed by element-wise clipping. The clipping controls the worst-case update size and tames the negative impact of non-convexity and rapid change of Hessian along the trajectory. Sophia only estimates the diagonal Hessian every handful of iterations, which has negligible average per-step time and memory overhead. On language modeling with GPT models of sizes ranging from 125M to 1.5B, Sophia achieves a 2x speed-up compared to Adam in the number of steps, total compute, and wall-clock time, achieving the same perplexity with 50% fewer steps, less total compute, and reduced wall-clock time. Theoretically, we show that Sophia, in a much simplified setting, adapts to the heterogeneous curvatures in different parameter dimensions, and thus has a run-time bound that does not depend on the condition number of the loss.

Sang Michael Xie, Hieu Pham, Xuanyi Dong et al.

The mixture proportions of pretraining data domains (e.g., Wikipedia, books, web text) greatly affect language model (LM) performance. In this paper, we propose Domain Reweighting with Minimax Optimization (DoReMi), which first trains a small proxy model using group distributionally robust optimization (Group DRO) over domains to produce domain weights (mixture proportions) without knowledge of downstream tasks. We then resample a dataset with these domain weights and train a larger, full-sized model. In our experiments, we use DoReMi on a 280M-parameter proxy model to set the domain weights for training an 8B-parameter model (30x larger) more efficiently. On The Pile, DoReMi improves perplexity across all domains, even when it downweights a domain. DoReMi improves average few-shot downstream accuracy by 6.5% points over a baseline model trained using The Pile's default domain weights and reaches the baseline accuracy with 2.6x fewer training steps. On the GLaM dataset, DoReMi, which has no knowledge of downstream tasks, even matches the performance of using domain weights tuned on downstream tasks.

Jerry Wei, Le Hou, Andrew Lampinen et al.

We present symbol tuning - finetuning language models on in-context input-label pairs where natural language labels (e.g., "positive/negative sentiment") are replaced with arbitrary symbols (e.g., "foo/bar"). Symbol tuning leverages the intuition that when a model cannot use instructions or natural language labels to figure out a task, it must instead do so by learning the input-label mappings. We experiment with symbol tuning across Flan-PaLM models up to 540B parameters and observe benefits across various settings. First, symbol tuning boosts performance on unseen in-context learning tasks and is much more robust to underspecified prompts, such as those without instructions or without natural language labels. Second, symbol-tuned models are much stronger at algorithmic reasoning tasks, with up to 18.2% better performance on the List Functions benchmark and up to 15.3% better performance on the Simple Turing Concepts benchmark. Finally, symbol-tuned models show large improvements in following flipped-labels presented in-context, meaning that they are more capable of using in-context information to override prior semantic knowledge.

Ananya Kumar, Aditi Raghunathan, Robbie Jones et al.

When transferring a pretrained model to a downstream task, two popular methods are full fine-tuning (updating all the model parameters) and linear probing (updating only the last linear layer -- the "head"). It is well known that fine-tuning leads to better accuracy in-distribution (ID). However, in this paper, we find that fine-tuning can achieve worse accuracy than linear probing out-of-distribution (OOD) when the pretrained features are good and the distribution shift is large. On 10 distribution shift datasets (Breeds-Living17, Breeds-Entity30, DomainNet, CIFAR $\to$ STL, CIFAR10.1, FMoW, ImageNetV2, ImageNet-R, ImageNet-A, ImageNet-Sketch), fine-tuning obtains on average 2% higher accuracy ID but 7% lower accuracy OOD than linear probing. We show theoretically that this tradeoff between ID and OOD accuracy arises even in a simple setting: fine-tuning overparameterized two-layer linear networks. We prove that the OOD error of fine-tuning is high when we initialize with a fixed or random head -- this is because while fine-tuning learns the head, the lower layers of the neural network change simultaneously and distort the pretrained features. Our analysis suggests that the easy two-step strategy of linear probing then full fine-tuning (LP-FT), sometimes used as a fine-tuning heuristic, combines the benefits of both fine-tuning and linear probing. Empirically, LP-FT outperforms both fine-tuning and linear probing on the above datasets (1% better ID, 10% better OOD than full fine-tuning).

Garrett Thomas, Yuping Luo, Tengyu Ma

Safe reinforcement learning is a promising path toward applying reinforcement learning algorithms to real-world problems, where suboptimal behaviors may lead to actual negative consequences. In this work, we focus on the setting where unsafe states can be avoided by planning ahead a short time into the future. In this setting, a model-based agent with a sufficiently accurate model can avoid unsafe states. We devise a model-based algorithm that heavily penalizes unsafe trajectories, and derive guarantees that our algorithm can avoid unsafe states under certain assumptions. Experiments demonstrate that our algorithm can achieve competitive rewards with fewer safety violations in several continuous control tasks.

Risheng Liu, Long Ma, Tengyu Ma et al.

Images captured from low-light scenes often suffer from severe degradations, including low visibility, color cast and intensive noises, etc. These factors not only affect image qualities, but also degrade the performance of downstream Low-Light Vision (LLV) applications. A variety of deep learning methods have been proposed to enhance the visual quality of low-light images. However, these approaches mostly rely on significant architecture engineering to obtain proper low-light models and often suffer from high computational burden. Furthermore, it is still challenging to extend these enhancement techniques to handle other LLVs. To partially address above issues, we establish Retinex-inspired Unrolling with Architecture Search (RUAS), a general learning framework, which not only can address low-light enhancement task, but also has the flexibility to handle other more challenging downstream vision applications. Specifically, we first establish a nested optimization formulation, together with an unrolling strategy, to explore underlying principles of a series of LLV tasks. Furthermore, we construct a differentiable strategy to cooperatively search specific scene and task architectures for RUAS. Last but not least, we demonstrate how to apply RUAS for both low- and high-level LLV applications (e.g., enhancement, detection and segmentation). Extensive experiments verify the flexibility, effectiveness, and efficiency of RUAS.

Aviral Kumar, Rishabh Agarwal, Tengyu Ma et al.

Despite overparameterization, deep networks trained via supervised learning are easy to optimize and exhibit excellent generalization. One hypothesis to explain this is that overparameterized deep networks enjoy the benefits of implicit regularization induced by stochastic gradient descent, which favors parsimonious solutions that generalize well on test inputs. It is reasonable to surmise that deep reinforcement learning (RL) methods could also benefit from this effect. In this paper, we discuss how the implicit regularization effect of SGD seen in supervised learning could in fact be harmful in the offline deep RL setting, leading to poor generalization and degenerate feature representations. Our theoretical analysis shows that when existing models of implicit regularization are applied to temporal difference learning, the resulting derived regularizer favors degenerate solutions with excessive "aliasing", in stark contrast to the supervised learning case. We back up these findings empirically, showing that feature representations learned by a deep network value function trained via bootstrapping can indeed become degenerate, aliasing the representations for state-action pairs that appear on either side of the Bellman backup. To address this issue, we derive the form of this implicit regularizer and, inspired by this derivation, propose a simple and effective explicit regularizer, called DR3, that counteracts the undesirable effects of this implicit regularizer. When combined with existing offline RL methods, DR3 substantially improves performance and stability, alleviating unlearning in Atari 2600 games, D4RL domains and robotic manipulation from images.

Ling Pan, Longbo Huang, Tengyu Ma et al.

Conservatism has led to significant progress in offline reinforcement learning (RL) where an agent learns from pre-collected datasets. However, as many real-world scenarios involve interaction among multiple agents, it is important to resolve offline RL in the multi-agent setting. Given the recent success of transferring online RL algorithms to the multi-agent setting, one may expect that offline RL algorithms will also transfer to multi-agent settings directly. Surprisingly, we empirically observe that conservative offline RL algorithms do not work well in the multi-agent setting -- the performance degrades significantly with an increasing number of agents. Towards mitigating the degradation, we identify a key issue that non-concavity of the value function makes the policy gradient improvements prone to local optima. Multiple agents exacerbate the problem severely, since the suboptimal policy by any agent can lead to uncoordinated global failure. Following this intuition, we propose a simple yet effective method, Offline Multi-Agent RL with Actor Rectification (OMAR), which combines the first-order policy gradients and zeroth-order optimization methods to better optimize the conservative value functions over the actor parameters. Despite the simplicity, OMAR achieves state-of-the-art results in a variety of multi-agent control tasks.

Margalit Glasgow, Honglin Yuan, Tengyu Ma

Federated Averaging (FedAvg), also known as Local SGD, is one of the most popular algorithms in Federated Learning (FL). Despite its simplicity and popularity, the convergence rate of FedAvg has thus far been undetermined. Even under the simplest assumptions (convex, smooth, homogeneous, and bounded covariance), the best-known upper and lower bounds do not match, and it is not clear whether the existing analysis captures the capacity of the algorithm. In this work, we first resolve this question by providing a lower bound for FedAvg that matches the existing upper bound, which shows the existing FedAvg upper bound analysis is not improvable. Additionally, we establish a lower bound in a heterogeneous setting that nearly matches the existing upper bound. While our lower bounds show the limitations of FedAvg, under an additional assumption of third-order smoothness, we prove more optimistic state-of-the-art convergence results in both convex and non-convex settings. Our analysis stems from a notion we call iterate bias, which is defined by the deviation of the expectation of the SGD trajectory from the noiseless gradient descent trajectory with the same initialization. We prove novel sharp bounds on this quantity, and show intuitively how to analyze this quantity from a Stochastic Differential Equation (SDE) perspective.

Sang Michael Xie, Aditi Raghunathan, Percy Liang et al.

Large language models (LMs) such as GPT-3 have the surprising ability to do in-context learning, where the model learns to do a downstream task simply by conditioning on a prompt consisting of input-output examples. The LM learns from these examples without being explicitly pretrained to learn. Thus, it is unclear what enables in-context learning. In this paper, we study how in-context learning can emerge when pretraining documents have long-range coherence. Here, the LM must infer a latent document-level concept to generate coherent next tokens during pretraining. At test time, in-context learning occurs when the LM also infers a shared latent concept between examples in a prompt. We prove when this occurs despite a distribution mismatch between prompts and pretraining data in a setting where the pretraining distribution is a mixture of HMMs. In contrast to messy large-scale datasets used to train LMs capable of in-context learning, we generate a small-scale synthetic dataset (GINC) where Transformers and LSTMs both exhibit in-context learning. Beyond the theory, experiments on GINC exhibit large-scale real-world phenomena including improved in-context performance with model scaling (despite the same pretraining loss), sensitivity to example order, and instances where zero-shot is better than few-shot in-context learning.

Hong Liu, Jeff Z. HaoChen, Adrien Gaidon et al.

Self-supervised learning (SSL) is a scalable way to learn general visual representations since it learns without labels. However, large-scale unlabeled datasets in the wild often have long-tailed label distributions, where we know little about the behavior of SSL. In this work, we systematically investigate self-supervised learning under dataset imbalance. First, we find out via extensive experiments that off-the-shelf self-supervised representations are already more robust to class imbalance than supervised representations. The performance gap between balanced and imbalanced pre-training with SSL is significantly smaller than the gap with supervised learning, across sample sizes, for both in-domain and, especially, out-of-domain evaluation. Second, towards understanding the robustness of SSL, we hypothesize that SSL learns richer features from frequent data: it may learn label-irrelevant-but-transferable features that help classify the rare classes and downstream tasks. In contrast, supervised learning has no incentive to learn features irrelevant to the labels from frequent examples. We validate this hypothesis with semi-synthetic experiments and theoretical analyses on a simplified setting. Third, inspired by the theoretical insights, we devise a re-weighted regularization technique that consistently improves the SSL representation quality on imbalanced datasets with several evaluation criteria, closing the small gap between balanced and imbalanced datasets with the same number of examples.

Rishi Bommasani, Drew A. Hudson, Ehsan Adeli et al.

AI is undergoing a paradigm shift with the rise of models (e.g., BERT, DALL-E, GPT-3) that are trained on broad data at scale and are adaptable to a wide range of downstream tasks. We call these models foundation models to underscore their critically central yet incomplete character. This report provides a thorough account of the opportunities and risks of foundation models, ranging from their capabilities (e.g., language, vision, robotics, reasoning, human interaction) and technical principles(e.g., model architectures, training procedures, data, systems, security, evaluation, theory) to their applications (e.g., law, healthcare, education) and societal impact (e.g., inequity, misuse, economic and environmental impact, legal and ethical considerations). Though foundation models are based on standard deep learning and transfer learning, their scale results in new emergent capabilities,and their effectiveness across so many tasks incentivizes homogenization. Homogenization provides powerful leverage but demands caution, as the defects of the foundation model are inherited by all the adapted models downstream. Despite the impending widespread deployment of foundation models, we currently lack a clear understanding of how they work, when they fail, and what they are even capable of due to their emergent properties. To tackle these questions, we believe much of the critical research on foundation models will require deep interdisciplinary collaboration commensurate with their fundamentally sociotechnical nature.

Yuping Luo, Tengyu Ma

Training-time safety violations have been a major concern when we deploy reinforcement learning algorithms in the real world. This paper explores the possibility of safe RL algorithms with zero training-time safety violations in the challenging setting where we are only given a safe but trivial-reward initial policy without any prior knowledge of the dynamics model and additional offline data. We propose an algorithm, Co-trained Barrier Certificate for Safe RL (CRABS), which iteratively learns barrier certificates, dynamics models, and policies. The barrier certificates, learned via adversarial training, ensure the policy's safety assuming calibrated learned dynamics model. We also add a regularization term to encourage larger certified regions to enable better exploration. Empirical simulations show that zero safety violations are already challenging for a suite of simple environments with only 2-4 dimensional state space, especially if high-reward policies have to visit regions near the safety boundary. Prior methods require hundreds of violations to achieve decent rewards on these tasks, whereas our proposed algorithms incur zero violations.

Colin Wei, Yining Chen, Tengyu Ma

A common lens to theoretically study neural net architectures is to analyze the functions they can approximate. However, constructions from approximation theory may be unrealistic and therefore less meaningful. For example, a common unrealistic trick is to encode target function values using infinite precision. To address these issues, this work proposes a formal definition of statistically meaningful (SM) approximation which requires the approximating network to exhibit good statistical learnability. We study SM approximation for two function classes: boolean circuits and Turing machines. We show that overparameterized feedforward neural nets can SM approximate boolean circuits with sample complexity depending only polynomially on the circuit size, not the size of the network. In addition, we show that transformers can SM approximate Turing machines with computation time bounded by $T$ with sample complexity polynomial in the alphabet size, state space size, and $\log (T)$. We also introduce new tools for analyzing generalization which provide much tighter sample complexities than the typical VC-dimension or norm-based bounds, which may be of independent interest.