arXiv subjects

Tengyu Ma

Publications and source records attributed to Tengyu Ma.

At least 19 recordsLinked to original sources

arXiv2026

Anchored Self-Play for Code Repair

Code repair is an important capability for language models (LMs): given a buggy program and unit tests, an LM must produce a fixed program that passes the tests. Because code repair data is limited, we aim to scale supervision by using an LM to generate bug--fix tasks. We propose __generator--fixer self-play__, in which a single model is trained with reinforcement learning to generate bugs and fix them. As the fixer improves, the generator adapts to produce more difficult bugs, yielding an automatic curriculum. To test whether this curriculum generalizes, we introduce BugSourceBench, a repair benchmark spanning realistic bug sources: bugs in human-written code, LM-generated code, and human-edited LM-generated code. On BugSourceBench, we find that self-play drifts toward difficult but unrealistic bugs, improving on synthetic bugs but degrading on human-authored ones. We propose Anchored Self-Play (ASP), which anchors self-play with a small reference set by adding a code-embedding similarity reward for generation and mixing reference bugs into fixer training. Across bug sources, ASP achieves the best fix rates, improving average fix rate over standard self-play by $+24\%$ relative / $+7.0$ pp absolute, with gains on bugs from both LMs and humans.

cs.SE↗

arXiv2026

Fantastic Pretraining Optimizers and Where to Find Them II: Hyperball Optimization

Matrix based optimizers such as Muon can substantially speed up language model pretraining, but their gains over AdamW are observed to shrink as model size and data scale grow when using standard constant decoupled weight decay. We propose Hyperball, a simple optimizer wrapper that addresses this issue. Given a base optimizer such as Adam or Muon, Hyperball sets the Frobenius norms of weight matrices and their corresponding optimizer updates to fixed constants. On Qwen3 style models up to 1.2B parameters, Muon Hyperball achieves 20--30% token equivalent speedup over weight decay baselines. Hyperball also improves learning rate transfer across widths and depths compared to decoupled weight decay. This method is motivated by prior theory showing that training with weight decay leads to an equilibrium weight norm that only depends on the training hyperparameters. Through this mechanism, the weight decay then decides the angular learning rate, i.e. how fast the direction of the weight matrix changes.

cs.LG↗

arXiv2026

Pseudo-Formalization for Automatic Proof Verification

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.

cs.LO↗

arXiv2026

Scaling Self-Play with Self-Guidance

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.

cs.LG↗

arXiv2026

Configuration-to-Performance Scaling Law with Neural Ansatz

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.

cs.LG↗

arXiv2026

Divide-and-Conquer CoT: RL for Reducing Latency via Parallel Reasoning

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.

cs.LG↗

arXiv2025

SAM 3: Segment Anything with Concepts

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.

cs.CV↗

arXiv2025

Fantastic Pretraining Optimizers and Where to Find Them

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.

cs.LG↗

arXiv2025

Non-Asymptotic Length Generalization

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.

cs.LG↗

arXiv2025

PerceptionLM: Open-Access Data and Models for Detailed Visual Understanding

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

cs.CV↗

arXiv2025

Perception Encoder: The best visual embeddings are not at the output of the network

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

cs.CV↗

arXiv2025

STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving

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.

cs.LG↗

arXiv2024

Formal Theorem Proving by Rewarding LLMs to Decompose Proofs Hierarchically

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.

cs.LG↗

arXiv2024

Understanding Warmup-Stable-Decay Learning Rates: A River Valley Loss Landscape Perspective

Training language models currently requires pre-determining a fixed compute budget because the typical cosine learning rate schedule depends on the total number of steps. In contrast, the Warmup-Stable-Decay (WSD) schedule uses a constant learning rate to produce a main branch of iterates that can in principle continue indefinitely without a pre-specified compute budget. Then, given any compute budget, one can branch out from the main branch at a proper time with a rapidly decaying learning rate to produce a strong model. Empirically, WSD generates a non-traditional loss curve: the loss remains elevated during the stable phase but sharply declines during the decay phase. Towards explaining this phenomenon, we conjecture that pretraining loss exhibits a river valley landscape, which resembles a deep valley with a river at its bottom. Under this assumption, we show that during the stable phase, the iterate undergoes large oscillations due to the high learning rate, yet it progresses swiftly along the river. During the decay phase, the rapidly dropping learning rate minimizes the iterate's oscillations, moving it closer to the river and revealing true optimization progress. Therefore, the sustained high learning rate phase and fast decaying phase are responsible for progress in the river and the mountain directions respectively, and are both critical. Our analysis predicts phenomenons consistent with empirical observations and shows that this landscape can emerge from pretraining on a simple bi-gram dataset. Inspired by the theory, we introduce WSD-S, a variant of WSD that reuses previous checkpoints' decay phases and keeps only one main branch, where we resume from a decayed checkpoint. WSD-S empirically outperforms WSD and Cyclic-Cosine in obtaining multiple language model checkpoints across various compute budgets in a single run for parameters scaling from 0.1B to 1.2B.

cs.LG↗

arXiv2024

SAM 2: Segment Anything in Images and Videos

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.

cs.CV↗

arXiv2024

Linguistic Calibration of Long-Form Generations

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.

cs.LG↗

arXiv2024

Chain of Thought Empowers Transformers to Solve Inherently Serial Problems

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.

cs.LG↗

arXiv2023

Trash to Treasure: Low-Light Object Detection via Decomposition-and-Aggregation

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.

cs.CV↗