Daily Papers

Test-Time Scaling (TTS) is an important method for improving the performance of Large Language Models (LLMs) by using additional computation during the inference phase. However, current studies do not systematically analyze how policy models, Process Reward Models (PRMs), and problem difficulty influence TTS. This lack of analysis limits the understanding and practical use of TTS methods. In this paper, we focus on two core questions: (1) What is the optimal approach to scale test-time computation across different policy models, PRMs, and problem difficulty levels? (2) To what extent can extended computation improve the performance of LLMs on complex tasks, and can smaller language models outperform larger ones through this approach? Through comprehensive experiments on MATH-500 and challenging AIME24 tasks, we have the following observations: (1) The compute-optimal TTS strategy is highly dependent on the choice of policy model, PRM, and problem difficulty. (2) With our compute-optimal TTS strategy, extremely small policy models can outperform larger models. For example, a 1B LLM can exceed a 405B LLM on MATH-500. Moreover, on both MATH-500 and AIME24, a 0.5B LLM outperforms GPT-4o, a 3B LLM surpasses a 405B LLM, and a 7B LLM beats o1 and DeepSeek-R1, while with higher inference efficiency. These findings show the significance of adapting TTS strategies to the specific characteristics of each task and model and indicate that TTS is a promising approach for enhancing the reasoning abilities of LLMs.

Test-time scaling is a promising new approach to language modeling that uses extra test-time compute to improve performance. Recently, OpenAI's o1 model showed this capability but did not publicly share its methodology, leading to many replication efforts. We seek the simplest approach to achieve test-time scaling and strong reasoning performance. First, we curate a small dataset s1K of 1,000 questions paired with reasoning traces relying on three criteria we validate through ablations: difficulty, diversity, and quality. Second, we develop budget forcing to control test-time compute by forcefully terminating the model's thinking process or lengthening it by appending "Wait" multiple times to the model's generation when it tries to end. This can lead the model to double-check its answer, often fixing incorrect reasoning steps. After supervised finetuning the Qwen2.5-32B-Instruct language model on s1K and equipping it with budget forcing, our model s1 exceeds o1-preview on competition math questions by up to 27% (MATH and AIME24). Further, scaling s1 with budget forcing allows extrapolating beyond its performance without test-time intervention: from 50% to 57% on AIME24. Our model, data, and code are open-source at https://github.com/simplescaling/s1.

Increasing test-time compute for LLMs shows promise across domains but remains underexplored in code generation, despite extensive study in math. In this paper, we propose S*, the first hybrid test-time scaling framework that substantially improves the coverage and selection accuracy of generated code. S* extends the existing parallel scaling paradigm with sequential scaling to push performance boundaries. It further leverages a novel selection mechanism that adaptively generates distinguishing inputs for pairwise comparison, combined with execution-grounded information to robustly identify correct solutions. We evaluate across 12 Large Language Models and Large Reasoning Model and show: (1) S* consistently improves performance across model families and sizes, enabling a 3B model to outperform GPT-4o-mini; (2) S* enables non-reasoning models to surpass reasoning models - GPT-4o-mini with S* outperforms o1-preview by 3.7% on LiveCodeBench; (3) S* further boosts state-of-the-art reasoning models - DeepSeek-R1-Distill-Qwen-32B with S* achieves 85.7% on LiveCodeBench, approaching o1 (high) at 88.5%. Code will be available under https://github.com/NovaSky-AI/SkyThought.

Increasing test-time computation is a straightforward approach to enhancing the quality of responses in Large Language Models (LLMs). While Best-of-N sampling and Self-Consistency with majority voting are simple and effective, they require a fixed number of sampling responses for each query, regardless of its complexity. This could result in wasted computation for simpler questions and insufficient exploration for more challenging ones. In this work, we argue that model confidence of responses can be used for improving the efficiency of test-time scaling. Unfortunately, LLMs are known to be overconfident and provide unreliable confidence estimation. To address this limitation, we introduce Self-Calibration by distilling Self-Consistency-derived confidence into the model itself. This enables reliable confidence estimation at test time with one forward pass. We then design confidence-based efficient test-time scaling methods to handle queries of various difficulty, such as Early-Stopping for Best-of-N and Self-Consistency with calibrated confidence. Experiments on three LLMs across six datasets demonstrate the effectiveness of our approach. Specifically, applying confidence-based Early Stopping to Best-of-N improves MathQA accuracy from 81.0 to 83.6 with a sample budget of 16 responses, indicating the efficacy of confidence-based sampling strategy at inference time.

Scaling pre-training compute has proven effective for achieving mulitlinguality, but does the same hold for test-time scaling? In this work, we introduce MCLM, a multilingual math benchmark featuring competition-level problems in 55 languages. We test three test-time scaling methods-Outcome Reward Modeling (ORM), Process Reward Modeling (ORM), and Budget Forcing (BF)-on both Qwen2.5-1.5B Math and MR1-1.5B, a multilingual LLM we trained for extended reasoning. Our experiments show that using Qwen2.5-1.5B Math with ORM achieves a score of 35.8 on MCLM, while BF on MR1-1.5B attains 35.2. Although "thinking LLMs" have recently garnered significant attention, we find that their performance is comparable to traditional scaling methods like best-of-N once constrained to similar levels of inference FLOPs. Moreover, while BF yields a 20-point improvement on English AIME, it provides only a 1.94-point average gain across other languages-a pattern consistent across the other test-time scaling methods we studied-higlighting that test-time scaling may not generalize as effectively to multilingual tasks. To foster further research, we release MCLM, MR1-1.5B, and evaluation results.

Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give an answer to any question provided. This overlooks concerns about whether a model is confident in its answer, and whether it is appropriate to always provide a response. To address these concerns, we extract confidence scores during reasoning for thresholding model responses. We find that increasing compute budget at inference time not only helps models answer more questions correctly, but also increases confidence in correct responses. We then extend the current paradigm of zero-risk responses during evaluation by considering settings with non-zero levels of response risk, and suggest a recipe for reporting evaluations under these settings.

The advent of test-time scaling in large language models (LLMs), exemplified by OpenAI's o1 series, has advanced reasoning capabilities by scaling computational resource allocation during inference. While successors like QwQ, Deepseek-R1 (R1) and LIMO replicate these advancements, whether these models truly possess test-time scaling capabilities remains underexplored. This study found that longer CoTs of these o1-like models do not consistently enhance accuracy; in fact, correct solutions are often shorter than incorrect ones for the same questions. Further investigation shows this phenomenon is closely related to models' self-revision capabilities - longer CoTs contain more self-revisions, which often lead to performance degradation. We then compare sequential and parallel scaling strategies on QwQ, R1 and LIMO, finding that parallel scaling achieves better coverage and scalability. Based on these insights, we propose Shortest Majority Vote, a method that combines parallel scaling strategies with CoT length characteristics, significantly improving models' test-time scalability compared to conventional majority voting approaches.

The LLM-as-a-Judge paradigm shows promise for evaluating generative content but lacks reliability in reasoning-intensive scenarios, such as programming. Inspired by recent advances in reasoning models and shifts in scaling laws, we pioneer bringing test-time computation into LLM-as-a-Judge, proposing MCTS-Judge, a resource-efficient, System-2 thinking framework for code correctness evaluation. MCTS-Judge leverages Monte Carlo Tree Search (MCTS) to decompose problems into simpler, multi-perspective evaluations. Through a node-selection strategy that combines self-assessment based on historical actions in the current trajectory and the Upper Confidence Bound for Trees based on prior rollouts, MCTS-Judge balances global optimization and refinement of the current trajectory. We further designed a high-precision, unit-test-level reward mechanism to encourage the Large Language Model (LLM) to perform line-by-line analysis. Extensive experiments on three benchmarks and five LLMs demonstrate the effectiveness of MCTS-Judge, which improves the base model's accuracy from 41% to 80%, surpassing the o1-series models with 3x fewer tokens. Further evaluations validate the superiority of its reasoning trajectory in logic, analytics, thoroughness, and overall quality, while revealing the test-time scaling law of the LLM-as-a-Judge paradigm.

Recent studies have shown that making a model spend more time thinking through longer Chain of Thoughts (CoTs) enables it to gain significant improvements in complex reasoning tasks. While current researches continue to explore the benefits of increasing test-time compute by extending the CoT lengths of Large Language Models (LLMs), we are concerned about a potential issue hidden behind the current pursuit of test-time scaling: Would excessively scaling the CoT length actually bring adverse effects to a model's reasoning performance? Our explorations on mathematical reasoning tasks reveal an unexpected finding that scaling with longer CoTs can indeed impair the reasoning performance of LLMs in certain domains. Moreover, we discover that there exists an optimal scaled length distribution that differs across different domains. Based on these insights, we propose a Thinking-Optimal Scaling strategy. Our method first uses a small set of seed data with varying response length distributions to teach the model to adopt different reasoning efforts for deep thinking. Then, the model selects its shortest correct response under different reasoning efforts on additional problems for self-improvement. Our self-improved models built upon Qwen2.5-32B-Instruct outperform other distillation-based 32B o1-like models across various math benchmarks, and achieve performance on par with QwQ-32B-Preview.

Solving complex planning problems requires Large Language Models (LLMs) to explicitly model the state transition to avoid rule violations, comply with constraints, and ensure optimality-a task hindered by the inherent ambiguity of natural language. To overcome such ambiguity, Planning Domain Definition Language (PDDL) is leveraged as a planning abstraction that enables precise and formal state descriptions. With PDDL, we can generate a symbolic world model where classic searching algorithms, such as A*, can be seamlessly applied to find optimal plans. However, directly generating PDDL domains with current LLMs remains an open challenge due to the lack of PDDL training data. To address this challenge, we propose to scale up the test-time computation of LLMs to enhance their PDDL reasoning capabilities, thereby enabling the generation of high-quality PDDL domains. Specifically, we introduce a simple yet effective algorithm, which first employs a Best-of-N sampling approach to improve the quality of the initial solution and then refines the solution in a fine-grained manner with verbalized machine learning. Our method outperforms o1-mini by a considerable margin in the generation of PDDL domain, achieving over 50% success rate on two tasks (i.e., generating PDDL domains from natural language description or PDDL problems). This is done without requiring additional training. By taking advantage of PDDL as state abstraction, our method is able to outperform current state-of-the-art methods on almost all competition-level planning tasks.

Large Language Models (LLMs) achieve superior performance through training-time scaling, and test-time scaling further enhances their capabilities by conducting effective reasoning during inference. However, as the scale of reasoning increases, existing test-time scaling methods suffer from accumulated historical information, which not only wastes computational resources but also interferes with effective reasoning. To address this issue, we observe that complex reasoning progress is often achieved by solving a sequence of independent subquestions, each being self-contained and verifiable. These subquestions are essentially atomic questions, relying primarily on their current state rather than accumulated history, similar to the memoryless transitions in a Markov process. Based on this observation, we propose Atom of Thoughts (AoT), where each state transition in the reasoning process consists of decomposing the current question into a dependency-based directed acyclic graph and contracting its subquestions, forming a new atomic question state. This iterative decomposition-contraction process continues until reaching directly solvable atomic questions, naturally realizing Markov transitions between question states. Furthermore, these atomic questions can be seamlessly integrated into existing test-time scaling methods, enabling AoT to serve as a plug-in enhancement for improving reasoning capabilities. Experiments across six benchmarks demonstrate the effectiveness of AoT both as a standalone framework and a plug-in enhancement. Notably, on HotpotQA, when applied to gpt-4o-mini, AoT achieves an 80.6% F1 score, surpassing o3-mini by 3.4% and DeepSeek-R1 by 10.6%. The code will be available at https://github.com/qixucen/atom.

Recent advancements in Large Language Models (LLMs) have created new opportunities to enhance performance on complex reasoning tasks by leveraging test-time computation. However, conventional approaches such as repeated sampling with majority voting or reward model scoring, often face diminishing returns as test-time compute scales, in addition to requiring costly task-specific reward model training. In this paper, we present Self-Enhanced Test-Time Scaling (SETS), a novel method that leverages the self-verification and self-correction capabilities of recent advanced LLMs to overcome these limitations. SETS integrates sampling, self-verification, and self-correction into a unified framework, enabling efficient and scalable test-time computation for improved capabilities at complex tasks. Through extensive experiments on challenging planning and reasoning benchmarks, compared to the alternatives, we demonstrate that SETS achieves significant performance improvements and more favorable test-time scaling laws.

We introduce InternVL 2.5, an advanced multimodal large language model (MLLM) series that builds upon InternVL 2.0, maintaining its core model architecture while introducing significant enhancements in training and testing strategies as well as data quality. In this work, we delve into the relationship between model scaling and performance, systematically exploring the performance trends in vision encoders, language models, dataset sizes, and test-time configurations. Through extensive evaluations on a wide range of benchmarks, including multi-discipline reasoning, document understanding, multi-image / video understanding, real-world comprehension, multimodal hallucination detection, visual grounding, multilingual capabilities, and pure language processing, InternVL 2.5 exhibits competitive performance, rivaling leading commercial models such as GPT-4o and Claude-3.5-Sonnet. Notably, our model is the first open-source MLLMs to surpass 70% on the MMMU benchmark, achieving a 3.7-point improvement through Chain-of-Thought (CoT) reasoning and showcasing strong potential for test-time scaling. We hope this model contributes to the open-source community by setting new standards for developing and applying multimodal AI systems. HuggingFace demo see https://huggingface.co/spaces/OpenGVLab/InternVL

Large language models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks. However, existing approaches mainly rely on imitation learning and struggle to achieve effective test-time scaling. While reinforcement learning (RL) holds promise for enabling self-exploration and learning from feedback, recent attempts yield only modest improvements in complex reasoning. In this paper, we present T1 to scale RL by encouraging exploration and understand inference scaling. We first initialize the LLM using synthesized chain-of-thought data that integrates trial-and-error and self-verification. To scale RL training, we promote increased sampling diversity through oversampling. We further employ an entropy bonus as an auxiliary loss, alongside a dynamic anchor for regularization to facilitate reward optimization. We demonstrate that T1 with open LLMs as its base exhibits inference scaling behavior and achieves superior performance on challenging math reasoning benchmarks. For example, T1 with Qwen2.5-32B as the base model outperforms the recent Qwen QwQ-32B-Preview model on MATH500, AIME2024, and Omni-math-500. More importantly, we present a simple strategy to examine inference scaling, where increased inference budgets directly lead to T1's better performance without any additional verification. We will open-source the T1 models and the data used to train them at https://github.com/THUDM/T1.

Chain-of-thought (CoT) reasoning has been widely applied in the mathematical reasoning of Large Language Models (LLMs). Recently, the introduction of derivative process supervision on CoT trajectories has sparked discussions on enhancing scaling capabilities during test time, thereby boosting the potential of these models. However, in multimodal mathematical reasoning, the scarcity of high-quality CoT training data has hindered existing models from achieving high-precision CoT reasoning and has limited the realization of reasoning potential during test time. In this work, we propose a three-module synthesis strategy that integrates CoT distillation, trajectory-format rewriting, and format unification. It results in a high-quality CoT reasoning instruction fine-tuning dataset in multimodal mathematics, MMathCoT-1M. We comprehensively validate the state-of-the-art (SOTA) performance of the trained URSA-7B model on multiple multimodal mathematical benchmarks. For test-time scaling, we introduce a data synthesis strategy that automatically generates process annotation datasets, known as DualMath-1.1M, focusing on both interpretation and logic. By further training URSA-7B on DualMath-1.1M, we transition from CoT reasoning capabilities to robust supervision abilities. The trained URSA-RM-7B acts as a verifier, effectively enhancing the performance of URSA-7B at test time. URSA-RM-7B also demonstrates excellent out-of-distribution (OOD) verifying capabilities, showcasing its generalization. Model weights, training data and code will be open-sourced.

Ensuring the safety and harmlessness of Large Language Models (LLMs) has become equally critical as their performance in applications. However, existing safety alignment methods typically suffer from safety-performance trade-offs and the susceptibility to jailbreak attacks, primarily due to their reliance on direct refusals for malicious queries. In this paper, we propose STAIR, a novel framework that integrates SafeTy Alignment with Itrospective Reasoning. We enable LLMs to identify safety risks through step-by-step analysis by self-improving chain-of-thought (CoT) reasoning with safety awareness. STAIR first equips the model with a structured reasoning capability and then advances safety alignment via iterative preference optimization on step-level reasoning data generated using our newly proposed Safety-Informed Monte Carlo Tree Search (SI-MCTS). We further train a process reward model on this data to guide test-time searches for improved responses. Extensive experiments show that STAIR effectively mitigates harmful outputs while better preserving helpfulness, compared to instinctive alignment strategies. With test-time scaling, STAIR achieves a safety performance comparable to Claude-3.5 against popular jailbreak attacks. Relevant resources in this work are available at https://github.com/thu-ml/STAIR.

Medical language models (MLMs) have become pivotal in advancing medical natural language processing. However, prior models that rely on pre-training or supervised fine-tuning often exhibit low data efficiency and limited practicality in real-world clinical applications. While OpenAIs O1 highlights test-time scaling in mathematics, attempts to replicate this approach in medicine typically distill responses from GPT-series models to open-source models, focusing primarily on multiple-choice tasks. This strategy, though straightforward, neglects critical concerns like data privacy and realistic deployment in clinical settings. In this work, we present a deployable, small-scale medical language model, \mone, designed for long-chain reasoning in clinical tasks using a self-evolution paradigm. Starting with a seed dataset of around 8,000 instances spanning five domains and 16 datasets, we prompt a base policy model to perform Monte Carlo Tree Search (MCTS) to construct verifiable reasoning chains. Each reasoning step is assigned an evolution rollout value, allowing verified trajectories to train the policy model and the reward model. During inference, the policy model generates multiple responses, and the reward model selects the one with the highest reward score. Experiments on eleven evaluation datasets demonstrate that \mone outperforms prior open-source models by 2 points, with the addition of the reward model further boosting performance (sim13 points), surpassing GPT-4o-mini. Code and data are available at https://github.com/pixas/MedSSS.

Scaling data and model size has been proven effective for boosting the performance of large language models. In addition to training-time scaling, recent studies have revealed that increasing test-time computational resources can further improve performance. In this work, we introduce Aggregation Fine-Tuning (AFT), a supervised finetuning paradigm where the model learns to synthesize multiple draft responses, referred to as proposals, into a single, refined answer, termed aggregation. At inference time, a propose-and-aggregate strategy further boosts performance by iteratively generating proposals and aggregating them. Empirical evaluations on benchmark datasets show that AFT-trained models substantially outperform standard SFT. Notably, an AFT model, fine-tuned from Llama3.1-8B-Base with only 64k data, achieves a 41.3% LC win rate on AlpacaEval 2, surpassing significantly larger LLMs such as Llama3.1-405B-Instruct and GPT4. By combining sequential refinement and parallel sampling, the propose-and-aggregate framework scales inference-time computation in a flexible manner. Overall, These findings position AFT as a promising approach to unlocking additional capabilities of LLMs without resorting to increasing data volume or model size.

Large reasoning models (LRMs) like OpenAI-o1 and DeepSeek-R1 have demonstrated remarkable capabilities in complex reasoning tasks through the utilization of long Chain-of-thought (CoT). However, these models often suffer from hallucinations and inefficiencies due to their reliance solely on internal reasoning processes. In this paper, we introduce START (Self-Taught Reasoner with Tools), a novel tool-integrated long CoT reasoning LLM that significantly enhances reasoning capabilities by leveraging external tools. Through code execution, START is capable of performing complex computations, self-checking, exploring diverse methods, and self-debugging, thereby addressing the limitations of LRMs. The core innovation of START lies in its self-learning framework, which comprises two key techniques: 1) Hint-infer: We demonstrate that inserting artificially designed hints (e.g., ``Wait, maybe using Python here is a good idea.'') during the inference process of a LRM effectively stimulates its ability to utilize external tools without the need for any demonstration data. Hint-infer can also serve as a simple and effective sequential test-time scaling method; 2) Hint Rejection Sampling Fine-Tuning (Hint-RFT): Hint-RFT combines Hint-infer and RFT by scoring, filtering, and modifying the reasoning trajectories with tool invocation generated by a LRM via Hint-infer, followed by fine-tuning the LRM. Through this framework, we have fine-tuned the QwQ-32B model to achieve START. On PhD-level science QA (GPQA), competition-level math benchmarks (AMC23, AIME24, AIME25), and the competition-level code benchmark (LiveCodeBench), START achieves accuracy rates of 63.6%, 95.0%, 66.7%, 47.1%, and 47.3%, respectively. It significantly outperforms the base QwQ-32B and achieves performance comparable to the state-of-the-art open-weight model R1-Distill-Qwen-32B and the proprietary model o1-Preview.

Despite the promising performance of Large Vision Language Models (LVLMs) in visual understanding, they occasionally generate incorrect outputs. While reward models (RMs) with reinforcement learning or test-time scaling offer the potential for improving generation quality, a critical gap remains: publicly available multi-modal RMs for LVLMs are scarce, and the implementation details of proprietary models are often unclear. We bridge this gap with InternLM-XComposer2.5-Reward (IXC-2.5-Reward), a simple yet effective multi-modal reward model that aligns LVLMs with human preferences. To ensure the robustness and versatility of IXC-2.5-Reward, we set up a high-quality multi-modal preference corpus spanning text, image, and video inputs across diverse domains, such as instruction following, general understanding, text-rich documents, mathematical reasoning, and video understanding. IXC-2.5-Reward achieves excellent results on the latest multi-modal reward model benchmark and shows competitive performance on text-only reward model benchmarks. We further demonstrate three key applications of IXC-2.5-Reward: (1) Providing a supervisory signal for RL training. We integrate IXC-2.5-Reward with Proximal Policy Optimization (PPO) yields IXC-2.5-Chat, which shows consistent improvements in instruction following and multi-modal open-ended dialogue; (2) Selecting the best response from candidate responses for test-time scaling; and (3) Filtering outlier or noisy samples from existing image and video instruction tuning training data. To ensure reproducibility and facilitate further research, we have open-sourced all model weights and training recipes at https://github.com/InternLM/InternLM-XComposer

Recently, test-time scaling has garnered significant attention from the research community, largely due to the substantial advancements of the o1 model released by OpenAI. By allocating more computational resources during the inference phase, large language models~(LLMs) can extensively explore the solution space by generating more thought tokens or diverse solutions, thereby producing more accurate responses. However, developing an o1-like reasoning approach is challenging, and researchers have been making various attempts to advance this open area of research. In this paper, we present a preliminary exploration into enhancing the reasoning abilities of LLMs through reward-guided tree search algorithms. This framework is implemented by integrating the policy model, reward model, and search algorithm. It is primarily constructed around a tree search algorithm, where the policy model navigates a dynamically expanding tree guided by a specially trained reward model. We thoroughly explore various design considerations necessary for implementing this framework and provide a detailed report of the technical aspects. To assess the effectiveness of our approach, we focus on mathematical reasoning tasks and conduct extensive evaluations on four challenging datasets, significantly enhancing the reasoning abilities of LLMs.

Recent studies have demonstrated the effectiveness of LLM test-time scaling. However, existing approaches to incentivize LLMs' deep thinking abilities generally require large-scale data or significant training efforts. Meanwhile, it remains unclear how to improve the thinking abilities of less powerful base models. In this work, we introduce S^2R, an efficient framework that enhances LLM reasoning by teaching models to self-verify and self-correct during inference. Specifically, we first initialize LLMs with iterative self-verification and self-correction behaviors through supervised fine-tuning on carefully curated data. The self-verification and self-correction skills are then further strengthened by both outcome-level and process-level reinforcement learning, with minimized resource requirements, enabling the model to adaptively refine its reasoning process during inference. Our results demonstrate that, with only 3.1k self-verifying and self-correcting behavior initialization samples, Qwen2.5-math-7B achieves an accuracy improvement from 51.0\% to 81.6\%, outperforming models trained on an equivalent amount of long-CoT distilled data. Extensive experiments and analysis based on three base models across both in-domain and out-of-domain benchmarks validate the effectiveness of S^2R. Our code and data are available at https://github.com/NineAbyss/S2R.

Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers have moved beyond simple autoregressive token generation by introducing the concept of "thought" -- a sequence of tokens representing intermediate steps in the reasoning process. This innovative paradigm enables LLMs' to mimic complex human reasoning processes, such as tree search and reflective thinking. Recently, an emerging trend of learning to reason has applied reinforcement learning (RL) to train LLMs to master reasoning processes. This approach enables the automatic generation of high-quality reasoning trajectories through trial-and-error search algorithms, significantly expanding LLMs' reasoning capacity by providing substantially more training data. Furthermore, recent studies demonstrate that encouraging LLMs to "think" with more tokens during test-time inference can further significantly boost reasoning accuracy. Therefore, the train-time and test-time scaling combined to show a new research frontier -- a path toward Large Reasoning Model. The introduction of OpenAI's o1 series marks a significant milestone in this research direction. In this survey, we present a comprehensive review of recent progress in LLM reasoning. We begin by introducing the foundational background of LLMs and then explore the key technical components driving the development of large reasoning models, with a focus on automated data construction, learning-to-reason techniques, and test-time scaling. We also analyze popular open-source projects at building large reasoning models, and conclude with open challenges and future research directions.

The recent release of OpenAI's o1 models and other similar frameworks showcasing test-time scaling laws has demonstrated their exceptional capability to tackle complex reasoning tasks. Inspired by this, subsequent research has revealed that such test-time scaling laws hinge on the model's ability to search both within a single response (intra-response) and across multiple responses (inter-response) during training. Crucially, beyond selecting a single optimal response, the model must also develop robust self-correction capabilities within its own outputs. However, training models to achieve effective self-evaluation and self-correction remains a significant challenge, heavily dependent on the quality of self-reflection data. In this paper, we address this challenge by focusing on enhancing the quality of self-reflection data generation for complex problem-solving, which can subsequently improve the training of next-generation large language models (LLMs). Specifically, we explore how manually triggering a model's self-correction mechanisms can improve performance on challenging reasoning tasks. To this end, we propose a novel iterative deepening sampling algorithm framework designed to enhance self-correction and generate higher-quality samples. Through extensive experiments on Math500 and AIME benchmarks, we demonstrate that our method achieves a higher success rate on difficult tasks and provide detailed ablation studies to analyze its effectiveness across diverse settings.

Best-of-N (BoN) sampling, a common strategy for test-time scaling of Large Language Models (LLMs), relies on reward models to select the best candidate solution from multiple generations. However, traditional reward models often assign arbitrary and inconsistent scores, limiting their effectiveness. To address this, we propose a Pairwise Reward Model (Pairwise RM) combined with a knockout tournament for BoN sampling. Instead of assigning absolute scores, given one math problem, Pairwise RM evaluates two candidate solutions' correctness simultaneously. This approach eliminates the need for arbitrary scoring and enables cross-validation of solutions through parallel comparison. In the knockout tournament, Pairwise RM conducts pairwise comparisons between candidate solutions and eliminates the incorrect ones iteratively. We construct \ourdataset, a large-scale dataset of 443K pairwise comparisons derived from NumiaMath and annotated using gemini-1.5-flash, and train the Pairwise RM via supervised fine-tuning. Experiments on MATH-500 and the Olympiad Bench demonstrate significant improvements over traditional discriminative reward models. And a 40\% to 60\% relative improvement is achieved on the top 50\% challenging problems.

Teaching large language models (LLMs) to critique and refine their outputs is crucial for building systems that can iteratively improve, yet it is fundamentally limited by the ability to provide accurate judgments and actionable suggestions. In this work, we study LLM critics for code generation and propose CTRL, a framework for Critic Training via Reinforcement Learning, which trains a critic model to generate feedback that maximizes correction performance for a fixed generator model without human supervision. Our results demonstrate that critics trained with CTRL significantly enhance pass rates and mitigate compounding errors across both base and stronger generator models. Furthermore, we show that these critic models act as accurate generative reward models and enable test-time scaling through iterative critique-revision, achieving up to 106.1% relative improvements across challenging code generation benchmarks.

Understanding information from visually rich documents remains a significant challenge for traditional Retrieval-Augmented Generation (RAG) methods. Existing benchmarks predominantly focus on image-based question answering (QA), overlooking the fundamental challenges of efficient retrieval, comprehension, and reasoning within dense visual documents. To bridge this gap, we introduce ViDoSeek, a novel dataset designed to evaluate RAG performance on visually rich documents requiring complex reasoning. Based on it, we identify key limitations in current RAG approaches: (i) purely visual retrieval methods struggle to effectively integrate both textual and visual features, and (ii) previous approaches often allocate insufficient reasoning tokens, limiting their effectiveness. To address these challenges, we propose ViDoRAG, a novel multi-agent RAG framework tailored for complex reasoning across visual documents. ViDoRAG employs a Gaussian Mixture Model (GMM)-based hybrid strategy to effectively handle multi-modal retrieval. To further elicit the model's reasoning capabilities, we introduce an iterative agent workflow incorporating exploration, summarization, and reflection, providing a framework for investigating test-time scaling in RAG domains. Extensive experiments on ViDoSeek validate the effectiveness and generalization of our approach. Notably, ViDoRAG outperforms existing methods by over 10% on the competitive ViDoSeek benchmark.

Recently, there has been growing interest in leveraging large language models (LLMs) to generate symbolic world models from textual descriptions. Although LLMs have been extensively explored in the context of world modeling, prior studies encountered several challenges, including evaluation randomness, dependence on indirect metrics, and a limited domain scope. To address these limitations, we introduce a novel benchmark, Text2World, based on planning domain definition language (PDDL), featuring hundreds of diverse domains and employing multi-criteria, execution-based metrics for a more robust evaluation. We benchmark current LLMs using Text2World and find that reasoning models trained with large-scale reinforcement learning outperform others. However, even the best-performing model still demonstrates limited capabilities in world modeling. Building on these insights, we examine several promising strategies to enhance the world modeling capabilities of LLMs, including test-time scaling, agent training, and more. We hope that Text2World can serve as a crucial resource, laying the groundwork for future research in leveraging LLMs as world models. The project page is available at https://text-to-world.github.io/.

Large multimodal models (LMMs) have demonstrated significant potential as generalists in vision-language (VL) tasks. However, there remains a significant gap between state-of-the-art LMMs and human performance when it comes to complex tasks that require a combination of fundamental VL capabilities, as well as tasks involving the grounding of complex instructions. To thoroughly investigate the human-LMM gap and its underlying causes, we propose MOAT, a diverse benchmark with complex real-world VL tasks that are challenging for LMMs. Specifically, the tasks in MOAT require LMMs to engage in generalist problem solving by integrating fundamental VL capabilities such as reading text, counting, understanding spatial relations, grounding textual and visual instructions, etc. All these abilities fit into a taxonomy proposed by us that contains 10 fundamental VL capabilities, enabling MOAT to provide a fine-grained view of LMMs' strengths and weaknesses. Besides, MOAT is the first benchmark to explicitly evaluate LMMs' ability to ground complex text and visual instructions, which is essential to many real-world applications. We evaluate over 20 proprietary and open source LMMs, as well as humans, on MOAT, and found that humans achieved 82.7% accuracy while the best performing LMM (OpenAI o1) achieved only 38.8%. To guide future model development, we analyze common trends in our results and discuss the underlying causes of observed performance gaps between LMMs and humans, focusing on which VL capability forms the bottleneck in complex tasks, whether test time scaling improves performance on MOAT, and how tiling harms LMMs' capability to count. Code and data are available at https://cambrian-yzt.github.io/MOAT.

Retrieval-Augmented Generation (RAG) systems for Large Language Models (LLMs) hold promise in knowledge-intensive tasks but face limitations in complex multi-step reasoning. While recent methods have integrated RAG with chain-of-thought reasoning or test-time search using Process Reward Models (PRMs), these approaches encounter challenges such as a lack of explanations, bias in PRM training data, early-step bias in PRM scores, and insufficient post-training optimization of reasoning potential. To address these issues, we propose Retrieval-Augmented Reasoning through Trustworthy Process Rewarding (ReARTeR), a framework that enhances RAG systems' reasoning capabilities through post-training and test-time scaling. At test time, ReARTeR introduces Trustworthy Process Rewarding via a Process Reward Model for accurate scalar scoring and a Process Explanation Model (PEM) for generating natural language explanations, enabling step refinement. During post-training, it utilizes Monte Carlo Tree Search guided by Trustworthy Process Rewarding to collect high-quality step-level preference data, optimized through Iterative Preference Optimization. ReARTeR addresses three core challenges: (1) misalignment between PRM and PEM, tackled through off-policy preference learning; (2) bias in PRM training data, mitigated by balanced annotation methods and stronger annotations for challenging examples; and (3) early-step bias in PRM, resolved through a temporal-difference-based look-ahead search strategy. Experimental results on multi-step reasoning benchmarks demonstrate significant improvements, underscoring ReARTeR's potential to advance the reasoning capabilities of RAG systems.

Monocular depth estimation is scale-ambiguous, and thus requires scale supervision to produce metric predictions. Even so, the resulting models will be geometry-specific, with learned scales that cannot be directly transferred across domains. Because of that, recent works focus instead on relative depth, eschewing scale in favor of improved up-to-scale zero-shot transfer. In this work we introduce ZeroDepth, a novel monocular depth estimation framework capable of predicting metric scale for arbitrary test images from different domains and camera parameters. This is achieved by (i) the use of input-level geometric embeddings that enable the network to learn a scale prior over objects; and (ii) decoupling the encoder and decoder stages, via a variational latent representation that is conditioned on single frame information. We evaluated ZeroDepth targeting both outdoor (KITTI, DDAD, nuScenes) and indoor (NYUv2) benchmarks, and achieved a new state-of-the-art in both settings using the same pre-trained model, outperforming methods that train on in-domain data and require test-time scaling to produce metric estimates.

Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of inference-time computation in LLMs, with a focus on answering the question: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on the achievable performance of LLMs, but also on the future of LLM pretraining and how one should tradeoff inference-time and pre-training compute. Despite its importance, little research attempted to understand the scaling behaviors of various test-time inference methods. Moreover, current work largely provides negative results for a number of these strategies. In this work, we analyze two primary mechanisms to scale test-time computation: (1) searching against dense, process-based verifier reward models; and (2) updating the model's distribution over a response adaptively, given the prompt at test time. We find that in both cases, the effectiveness of different approaches to scaling test-time compute critically varies depending on the difficulty of the prompt. This observation motivates applying a "compute-optimal" scaling strategy, which acts to most effectively allocate test-time compute adaptively per prompt. Using this compute-optimal strategy, we can improve the efficiency of test-time compute scaling by more than 4x compared to a best-of-N baseline. Additionally, in a FLOPs-matched evaluation, we find that on problems where a smaller base model attains somewhat non-trivial success rates, test-time compute can be used to outperform a 14x larger model.

The remarkable performance of the o1 model in complex reasoning demonstrates that test-time computing scaling can further unlock the model's potential, enabling powerful System-2 thinking. However, there is still a lack of comprehensive surveys for test-time computing scaling. We trace the concept of test-time computing back to System-1 models. In System-1 models, test-time computing addresses distribution shifts and improves robustness and generalization through parameter updating, input modification, representation editing, and output calibration. In System-2 models, it enhances the model's reasoning ability to solve complex problems through repeated sampling, self-correction, and tree search. We organize this survey according to the trend of System-1 to System-2 thinking, highlighting the key role of test-time computing in the transition from System-1 models to weak System-2 models, and then to strong System-2 models. We also point out a few possible future directions.

Large language models have demonstrated remarkable progress in mathematical reasoning, leveraging chain-of-thought and test-time compute scaling. However, many open questions remain regarding the interplay between reasoning token usage and accuracy gains. In particular, when comparing models across generations, it is unclear whether improved performance results from longer reasoning chains or more efficient reasoning. We systematically analyze chain-of-thought length across o1-mini and o3-mini variants on the Omni-MATH benchmark, finding that o3-mini (m) achieves superior accuracy without requiring longer reasoning chains than o1-mini. Moreover, we show that accuracy generally declines as reasoning chains grow across all models and compute settings, even when controlling for difficulty of the questions. This accuracy drop is significantly smaller in more proficient models, suggesting that new generations of reasoning models use test-time compute more effectively. Finally, we highlight that while o3-mini (h) achieves a marginal accuracy gain over o3-mini (m), it does so by allocating substantially more reasoning tokens across all problems, even the ones that o3-mini (m) can already solve. These findings provide new insights into the relationship between model capability and reasoning length, with implications for efficiency, scaling, and evaluation methodologies.

The ability to organically reason over and with both text and images is a pillar of human intelligence, yet the ability of Multimodal Large Language Models (MLLMs) to perform such multimodal reasoning remains under-explored. Existing benchmarks often emphasize text-dominant reasoning or rely on shallow visual cues, failing to adequately assess integrated visual and textual reasoning. We introduce EMMA (Enhanced MultiModal reAsoning), a benchmark targeting organic multimodal reasoning across mathematics, physics, chemistry, and coding. EMMA tasks demand advanced cross-modal reasoning that cannot be addressed by reasoning independently in each modality, offering an enhanced test suite for MLLMs' reasoning capabilities. Our evaluation of state-of-the-art MLLMs on EMMA reveals significant limitations in handling complex multimodal and multi-step reasoning tasks, even with advanced techniques like Chain-of-Thought prompting and test-time compute scaling underperforming. These findings underscore the need for improved multimodal architectures and training paradigms to close the gap between human and model reasoning in multimodality.

Scaling test-time compute is a promising axis for improving LLM capabilities. However, test-time compute can be scaled in a variety of ways, and effectively combining different approaches remains an active area of research. Here, we explore this problem in the context of solving real-world GitHub issues from the SWE-bench dataset. Our system, named CodeMonkeys, allows models to iteratively edit a codebase by jointly generating and running a testing script alongside their draft edit. We sample many of these multi-turn trajectories for every issue to generate a collection of candidate edits. This approach lets us scale "serial" test-time compute by increasing the number of iterations per trajectory and "parallel" test-time compute by increasing the number of trajectories per problem. With parallel scaling, we can amortize up-front costs across multiple downstream samples, allowing us to identify relevant codebase context using the simple method of letting an LLM read every file. In order to select between candidate edits, we combine voting using model-generated tests with a final multi-turn trajectory dedicated to selection. Overall, CodeMonkeys resolves 57.4% of issues from SWE-bench Verified using a budget of approximately 2300 USD. Our selection method can also be used to combine candidates from different sources. Selecting over an ensemble of edits from existing top SWE-bench Verified submissions obtains a score of 66.2% and outperforms the best member of the ensemble on its own. We fully release our code and data at https://scalingintelligence.stanford.edu/pubs/codemonkeys.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Large Language Models (LLMs) have shown remarkable abilities across various language tasks, but solving complex reasoning problems remains a challenge. While existing methods like Chain-of-Thought (CoT) and Tree-of-Thought (ToT) enhance reasoning by decomposing problems or structuring prompts, they typically perform a single pass of reasoning and may fail to revisit flawed paths, compromising accuracy. To address this, we propose a novel reasoning framework called Forest-of-Thought (FoT), which integrates multiple reasoning trees to leverage collective decision-making for solving complex logical problems. FoT utilizes sparse activation strategies to select the most relevant reasoning paths, improving both efficiency and accuracy. Additionally, we introduce a dynamic self-correction strategy that enables real-time error correction and learning from past mistakes, as well as consensus-guided decision making strategies to optimize correctness and computational resources. Experimental results demonstrate that the FoT framework, combined with these strategies, significantly enhances the reasoning capabilities of LLMs, enabling them to solve complex tasks with greater precision and efficiency.

We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This stands in contrast to mainstream reasoning models that scale up compute by producing more tokens. Unlike approaches based on chain-of-thought, our approach does not require any specialized training data, can work with small context windows, and can capture types of reasoning that are not easily represented in words. We scale a proof-of-concept model to 3.5 billion parameters and 800 billion tokens. We show that the resulting model can improve its performance on reasoning benchmarks, sometimes dramatically, up to a computation load equivalent to 50 billion parameters.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

Training large language models (LLMs) to spend more time thinking and reflection before responding is crucial for effectively solving complex reasoning tasks in fields such as science, coding, and mathematics. However, the effectiveness of mechanisms like self-reflection and self-correction depends on the model's capacity to accurately assess its own performance, which can be limited by factors such as initial accuracy, question difficulty, and the lack of external feedback. In this paper, we delve into a two-player paradigm that separates the roles of reasoning and critique models, where the critique model provides step-level feedback to supervise the reasoning (actor) model during both test-time and train-time. We first propose AutoMathCritique, an automated and scalable framework for collecting critique data, resulting in a dataset of 76,321 responses paired with step-level feedback. Fine-tuning language models with this dataset enables them to generate natural language feedback for mathematical reasoning. We demonstrate that the critique models consistently improve the actor's performance on difficult queries at test-time, especially when scaling up inference-time computation. Motivated by these findings, we introduce the critique-based supervision to the actor's self-training process, and propose a critique-in-the-loop self-improvement method. Experiments show that the method improves the actor's exploration efficiency and solution diversity, especially on challenging queries, leading to a stronger reasoning model. Lastly, we take the preliminary step to explore training self-talk reasoning models via critique supervision and showcase its potential. Our code and datasets are at https://mathcritique.github.io/{https://mathcritique.github.io/}.

Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by verifying each response for correctness. In this paper, we study the scaling trends governing sampling-based search. Among our findings is that simply scaling up a minimalist implementation that uses only random sampling and direct self-verification results in sustained performance improvements that, for example, elevate the Gemini v1.5 Pro model's reasoning capabilities past that of o1-Preview on popular benchmarks. We partially attribute the scalability of sampling-based search to a phenomenon of implicit scaling, where sampling a larger pool of responses in turn improves verification accuracy. We further identify two useful principles for improving self-verification capabilities with test-time compute: (1) comparing across responses provides helpful signals about the locations of errors and hallucinations, and (2) different model output styles are useful for different contexts -- chains of thought are useful for reasoning but harder to verify. We also find that, though accurate verification can be elicited, frontier models demonstrate remarkably weak out-of-box verification capabilities and introduce a benchmark to measure progress on these deficiencies.

Chain-of-Thought (CoT) reasoning has been extensively explored in large models to tackle complex understanding tasks. However, it still remains an open question whether such strategies can be applied to verifying and reinforcing image generation scenarios. In this paper, we provide the first comprehensive investigation of the potential of CoT reasoning to enhance autoregressive image generation. We focus on three techniques: scaling test-time computation for verification, aligning model preferences with Direct Preference Optimization (DPO), and integrating these techniques for complementary effects. Our results demonstrate that these approaches can be effectively adapted and combined to significantly improve image generation performance. Furthermore, given the pivotal role of reward models in our findings, we propose the Potential Assessment Reward Model (PARM) and PARM++, specialized for autoregressive image generation. PARM adaptively assesses each generation step through a potential assessment approach, merging the strengths of existing reward models, and PARM++ further introduces a reflection mechanism to self-correct the generated unsatisfactory image. Using our investigated reasoning strategies, we enhance a baseline model, Show-o, to achieve superior results, with a significant +24% improvement on the GenEval benchmark, surpassing Stable Diffusion 3 by +15%. We hope our study provides unique insights and paves a new path for integrating CoT reasoning with autoregressive image generation. Code and models are released at https://github.com/ZiyuGuo99/Image-Generation-CoT

Recent advancements in the field of large language models, particularly through the Chain of Thought (CoT) approach, have demonstrated significant improvements in solving complex problems. However, existing models either tend to sacrifice detailed reasoning for brevity due to user preferences, or require extensive and expensive training data to learn complicated reasoning ability, limiting their potential in solving complex tasks. To bridge this gap, following the concept of scaling test-time, we propose a simple method by encouraging models to adopt a more patient reasoning style without the need of introducing new knowledge or skills. To employ a preference optimization approach, we generate detailed reasoning processes as positive examples and simple answers as negative examples, thereby training the model to favor thoroughness in its responses. Our results demonstrate a performance increase of up to 6.7% on GSM8k with training just on a lightweight dataset.

Large language models (LLMs) such as OpenAI's o1 have demonstrated remarkable abilities in complex reasoning tasks by scaling test-time compute and exhibiting human-like deep thinking. However, we identify a phenomenon we term underthinking, where o1-like LLMs frequently switch between different reasoning thoughts without sufficiently exploring promising paths to reach a correct solution. This behavior leads to inadequate depth of reasoning and decreased performance, particularly on challenging mathematical problems. To systematically analyze this issue, we conduct experiments on three challenging test sets and two representative open-source o1-like models, revealing that frequent thought switching correlates with incorrect responses. We introduce a novel metric to quantify underthinking by measuring token efficiency in incorrect answers. To address underthinking, we propose a decoding strategy with thought switching penalty TIP that discourages premature transitions between thoughts, encouraging deeper exploration of each reasoning path. Experimental results demonstrate that our approach improves accuracy across challenging datasets without requiring model fine-tuning. Our findings contribute to understanding reasoning inefficiencies in o1-like LLMs and offer a practical solution to enhance their problem-solving capabilities.

Scientific discovery relies on scientists generating novel hypotheses that undergo rigorous experimental validation. To augment this process, we introduce an AI co-scientist, a multi-agent system built on Gemini 2.0. The AI co-scientist is intended to help uncover new, original knowledge and to formulate demonstrably novel research hypotheses and proposals, building upon prior evidence and aligned to scientist-provided research objectives and guidance. The system's design incorporates a generate, debate, and evolve approach to hypothesis generation, inspired by the scientific method and accelerated by scaling test-time compute. Key contributions include: (1) a multi-agent architecture with an asynchronous task execution framework for flexible compute scaling; (2) a tournament evolution process for self-improving hypotheses generation. Automated evaluations show continued benefits of test-time compute, improving hypothesis quality. While general purpose, we focus development and validation in three biomedical areas: drug repurposing, novel target discovery, and explaining mechanisms of bacterial evolution and anti-microbial resistance. For drug repurposing, the system proposes candidates with promising validation findings, including candidates for acute myeloid leukemia that show tumor inhibition in vitro at clinically applicable concentrations. For novel target discovery, the AI co-scientist proposed new epigenetic targets for liver fibrosis, validated by anti-fibrotic activity and liver cell regeneration in human hepatic organoids. Finally, the AI co-scientist recapitulated unpublished experimental results via a parallel in silico discovery of a novel gene transfer mechanism in bacterial evolution. These results, detailed in separate, co-timed reports, demonstrate the potential to augment biomedical and scientific discovery and usher an era of AI empowered scientists.

The advent of Large Language Models (LLMs) has paved the way for AI search engines, e.g., SearchGPT, showcasing a new paradigm in human-internet interaction. However, most current AI search engines are limited to text-only settings, neglecting the multimodal user queries and the text-image interleaved nature of website information. Recently, Large Multimodal Models (LMMs) have made impressive strides. Yet, whether they can function as AI search engines remains under-explored, leaving the potential of LMMs in multimodal search an open question. To this end, we first design a delicate pipeline, MMSearch-Engine, to empower any LMMs with multimodal search capabilities. On top of this, we introduce MMSearch, a comprehensive evaluation benchmark to assess the multimodal search performance of LMMs. The curated dataset contains 300 manually collected instances spanning 14 subfields, which involves no overlap with the current LMMs' training data, ensuring the correct answer can only be obtained within searching. By using MMSearch-Engine, the LMMs are evaluated by performing three individual tasks (requery, rerank, and summarization), and one challenging end-to-end task with a complete searching process. We conduct extensive experiments on closed-source and open-source LMMs. Among all tested models, GPT-4o with MMSearch-Engine achieves the best results, which surpasses the commercial product, Perplexity Pro, in the end-to-end task, demonstrating the effectiveness of our proposed pipeline. We further present error analysis to unveil current LMMs still struggle to fully grasp the multimodal search tasks, and conduct ablation study to indicate the potential of scaling test-time computation for AI search engine. We hope MMSearch may provide unique insights to guide the future development of multimodal AI search engine. Project Page: https://mmsearch.github.io

We propose a general two-stage algorithm that enjoys a provable scaling law for the test-time compute of large language models (LLMs). Given an input problem, the proposed algorithm first generates N candidate solutions, and then chooses the best one via a multiple-round knockout tournament where each pair of candidates are compared for K times and only the winners move on to the next round. In a minimalistic implementation, both stages can be executed with a black-box LLM alone and nothing else (e.g., no external verifier or reward model), and a total of N times (K + 1) highly parallelizable LLM calls are needed for solving an input problem. Assuming that a generated candidate solution is correct with probability p_{gen} > 0 and a comparison between a pair of correct and incorrect solutions identifies the right winner with probability p_{comp} > 0.5 (i.e., better than a random guess), we prove theoretically that the failure probability of the proposed algorithm decays to zero exponentially with respect to N and K: $P(final output is incorrect) le (1 - p_{gen})^N + lceil log_2 N rceil e^{-2 K (p_{comp} - 0.5)^2}.$ Our empirical results with the challenging MMLU-Pro benchmark validate the technical assumptions, as well as the efficacy of the proposed algorithm and the gains from scaling up its test-time compute.

We present Puppet-Master, an interactive video generative model that can serve as a motion prior for part-level dynamics. At test time, given a single image and a sparse set of motion trajectories (i.e., drags), Puppet-Master can synthesize a video depicting realistic part-level motion faithful to the given drag interactions. This is achieved by fine-tuning a large-scale pre-trained video diffusion model, for which we propose a new conditioning architecture to inject the dragging control effectively. More importantly, we introduce the all-to-first attention mechanism, a drop-in replacement for the widely adopted spatial attention modules, which significantly improves generation quality by addressing the appearance and background issues in existing models. Unlike other motion-conditioned video generators that are trained on in-the-wild videos and mostly move an entire object, Puppet-Master is learned from Objaverse-Animation-HQ, a new dataset of curated part-level motion clips. We propose a strategy to automatically filter out sub-optimal animations and augment the synthetic renderings with meaningful motion trajectories. Puppet-Master generalizes well to real images across various categories and outperforms existing methods in a zero-shot manner on a real-world benchmark. See our project page for more results: vgg-puppetmaster.github.io.

The scaling of inference computation has unlocked the potential of long-context large language models (LLMs) across diverse settings. For knowledge-intensive tasks, the increased compute is often allocated to incorporate more external knowledge. However, without effectively utilizing such knowledge, solely expanding context does not always enhance performance. In this work, we investigate inference scaling for retrieval augmented generation (RAG), exploring strategies beyond simply increasing the quantity of knowledge. We focus on two inference scaling strategies: in-context learning and iterative prompting. These strategies provide additional flexibility to scale test-time computation (e.g., by increasing retrieved documents or generation steps), thereby enhancing LLMs' ability to effectively acquire and utilize contextual information. We address two key questions: (1) How does RAG performance benefit from the scaling of inference computation when optimally configured? (2) Can we predict the optimal test-time compute allocation for a given budget by modeling the relationship between RAG performance and inference parameters? Our observations reveal that increasing inference computation leads to nearly linear gains in RAG performance when optimally allocated, a relationship we describe as the inference scaling laws for RAG. Building on this, we further develop the computation allocation model to estimate RAG performance across different inference configurations. The model predicts optimal inference parameters under various computation constraints, which align closely with the experimental results. By applying these optimal configurations, we demonstrate that scaling inference compute on long-context LLMs achieves up to 58.9% gains on benchmark datasets compared to standard RAG.

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

The largest experiments in machine learning now require resources far beyond the budget of all but a few institutions. Fortunately, it has recently been shown that the results of these huge experiments can often be extrapolated from the results of a sequence of far smaller, cheaper experiments. In this work, we show that not only can the extrapolation be done based on the size of the model, but on the size of the problem as well. By conducting a sequence of experiments using AlphaZero and Hex, we show that the performance achievable with a fixed amount of compute degrades predictably as the game gets larger and harder. Along with our main result, we further show that the test-time and train-time compute available to an agent can be traded off while maintaining performance.

We show that the YOLOv4 object detection neural network based on the CSP approach, scales both up and down and is applicable to small and large networks while maintaining optimal speed and accuracy. We propose a network scaling approach that modifies not only the depth, width, resolution, but also structure of the network. YOLOv4-large model achieves state-of-the-art results: 55.5% AP (73.4% AP50) for the MS COCO dataset at a speed of ~16 FPS on Tesla V100, while with the test time augmentation, YOLOv4-large achieves 56.0% AP (73.3 AP50). To the best of our knowledge, this is currently the highest accuracy on the COCO dataset among any published work. The YOLOv4-tiny model achieves 22.0% AP (42.0% AP50) at a speed of 443 FPS on RTX 2080Ti, while by using TensorRT, batch size = 4 and FP16-precision the YOLOv4-tiny achieves 1774 FPS.

Pre-trained models produce strong generic representations that can be adapted via fine-tuning. The learned weight difference relative to the pre-trained model, known as a task vector, characterises the direction and stride of fine-tuning. The significance of task vectors is such that simple arithmetic operations on them can be used to combine diverse representations from different domains. This paper builds on these properties of task vectors and aims to answer (1) whether components of task vectors, particularly parameter blocks, exhibit similar characteristics, and (2) how such blocks can be used to enhance knowledge composition and transfer. To this end, we introduce aTLAS, an algorithm that linearly combines parameter blocks with different learned coefficients, resulting in anisotropic scaling at the task vector level. We show that such linear combinations explicitly exploit the low intrinsic dimensionality of pre-trained models, with only a few coefficients being the learnable parameters. Furthermore, composition of parameter blocks leverages the already learned representations, thereby reducing the dependency on large amounts of data. We demonstrate the effectiveness of our method in task arithmetic, few-shot recognition and test-time adaptation, with supervised or unsupervised objectives. In particular, we show that (1) learned anisotropic scaling allows task vectors to be more disentangled, causing less interference in composition; (2) task vector composition excels with scarce or no labeled data and is less prone to domain shift, thus leading to better generalisability; (3) mixing the most informative parameter blocks across different task vectors prior to training can reduce the memory footprint and improve the flexibility of knowledge transfer. Moreover, we show the potential of aTLAS as a PEFT method, particularly with less data, and demonstrate that its scalibility.

Scaling laws for large language models (LLMs) predict model performance based on parameters like size and training data. However, differences in training configurations and data processing across model families lead to significant variations in benchmark performance, making it difficult for a single scaling law to generalize across all LLMs. On the other hand, training family-specific scaling laws requires training models of varying sizes for every family. In this work, we propose Skills Scaling Laws (SSLaws, pronounced as Sloth), a novel scaling law that leverages publicly available benchmark data and assumes LLM performance is driven by low-dimensional latent skills, such as reasoning and instruction following. These latent skills are influenced by computational resources like model size and training tokens but with varying efficiencies across model families. Sloth exploits correlations across benchmarks to provide more accurate and interpretable predictions while alleviating the need to train multiple LLMs per family. We present both theoretical results on parameter identification and empirical evaluations on 12 prominent benchmarks, from Open LLM Leaderboard v1/v2, demonstrating that Sloth predicts LLM performance efficiently and offers insights into scaling behaviors for complex downstream tasks and increased test-time compute.

In this paper, we argue that iterative computation with diffusion models offers a powerful paradigm for not only generation but also visual perception tasks. We unify tasks such as depth estimation, optical flow, and segmentation under image-to-image translation, and show how diffusion models benefit from scaling training and test-time compute for these perception tasks. Through a careful analysis of these scaling behaviors, we present various techniques to efficiently train diffusion models for visual perception tasks. Our models achieve improved or comparable performance to state-of-the-art methods using significantly less data and compute. To use our code and models, see https://scaling-diffusion-perception.github.io .

We present PointInfinity, an efficient family of point cloud diffusion models. Our core idea is to use a transformer-based architecture with a fixed-size, resolution-invariant latent representation. This enables efficient training with low-resolution point clouds, while allowing high-resolution point clouds to be generated during inference. More importantly, we show that scaling the test-time resolution beyond the training resolution improves the fidelity of generated point clouds and surfaces. We analyze this phenomenon and draw a link to classifier-free guidance commonly used in diffusion models, demonstrating that both allow trading off fidelity and variability during inference. Experiments on CO3D show that PointInfinity can efficiently generate high-resolution point clouds (up to 131k points, 31 times more than Point-E) with state-of-the-art quality.

Large language models are usually fine-tuned to align with human preferences. However, fine-tuning a large language model can be challenging. In this work, we introduce weak-to-strong search, framing the alignment of a large language model as a test-time greedy search to maximize the log-likelihood difference between small tuned and untuned models while sampling from the frozen large model. This method serves both as (i) a compute-efficient model up-scaling strategy that avoids directly tuning the large model and as (ii) an instance of weak-to-strong generalization that enhances a strong model with weak test-time guidance. Empirically, we demonstrate the flexibility of weak-to-strong search across different tasks. In controlled-sentiment generation and summarization, we use tuned and untuned gpt2s to effectively improve the alignment of large models without additional training. Crucially, in a more difficult instruction-following benchmark, AlpacaEval 2.0, we show that reusing off-the-shelf small model pairs (e.g., zephyr-7b-beta and its untuned version) can significantly improve the length-controlled win rates of both white-box and black-box large models against gpt-4-turbo (e.g., 34.4 rightarrow 37.9 for Llama-3-70B-Instruct and 16.0 rightarrow 20.1 for gpt-3.5-turbo-instruct), despite the small models' low win rates approx 10.0.

Recent advancements in language models (LMs) have demonstrated strong capabilities in semantic understanding and contextual modeling, which have flourished in generative speech enhancement (SE). However, many LM-based SE approaches primarily focus on semantic information, often neglecting the critical role of acoustic information, which leads to acoustic inconsistency after enhancement and limited generalization across diverse SE tasks. In this paper, we introduce LLaSE-G1, a LLaMA-based language model that incentivizes generalization capabilities for speech enhancement. LLaSE-G1 offers the following key contributions: First, to mitigate acoustic inconsistency, LLaSE-G1 employs continuous representations from WavLM as input and predicts speech tokens from X-Codec2, maximizing acoustic preservation. Second, to promote generalization capability, LLaSE-G1 introduces dual-channel inputs and outputs, unifying multiple SE tasks without requiring task-specific IDs. Third, LLaSE-G1 outperforms prior task-specific discriminative and generative SE models, demonstrating scaling effects at test time and emerging capabilities for unseen SE tasks. Additionally, we release our code and models to support further research in this area.

The sequential nature of modern LLMs makes them expensive and slow, and speculative sampling has proven to be an effective solution to this problem. Methods like EAGLE perform autoregression at the feature level, reusing top-layer features from the target model to achieve better results than vanilla speculative sampling. A growing trend in the LLM community is scaling up training data to improve model intelligence without increasing inference costs. However, we observe that scaling up data provides limited improvements for EAGLE. We identify that this limitation arises from EAGLE's feature prediction constraints. In this paper, we introduce EAGLE-3, which abandons feature prediction in favor of direct token prediction and replaces reliance on top-layer features with multi-layer feature fusion via a technique named training-time test. These improvements significantly enhance performance and enable the draft model to fully benefit from scaling up training data. Our experiments include both chat models and reasoning models, evaluated on five tasks. The results show that EAGLE-3 achieves a speedup ratio up to 6.5x, with about 1.4x improvement over EAGLE-2. The code is available at https://github.com/SafeAILab/EAGLE.

This paper studies how to synthesize face images of non-existent persons, to create a dataset that allows effective training of face recognition (FR) models. Two important goals are (1) the ability to generate a large number of distinct identities (inter-class separation) with (2) a wide variation in appearance of each identity (intra-class variation). However, existing works 1) are typically limited in how many well-separated identities can be generated and 2) either neglect or use a separate editing model for attribute augmentation. We propose Vec2Face, a holistic model that uses only a sampled vector as input and can flexibly generate and control face images and their attributes. Composed of a feature masked autoencoder and a decoder, Vec2Face is supervised by face image reconstruction and can be conveniently used in inference. Using vectors with low similarity among themselves as inputs, Vec2Face generates well-separated identities. Randomly perturbing an input identity vector within a small range allows Vec2Face to generate faces of the same identity with robust variation in face attributes. It is also possible to generate images with designated attributes by adjusting vector values with a gradient descent method. Vec2Face has efficiently synthesized as many as 300K identities with 15 million total images, whereas 60K is the largest number of identities created in the previous works. FR models trained with the generated HSFace datasets, from 10k to 300k identities, achieve state-of-the-art accuracy, from 92% to 93.52%, on five real-world test sets. For the first time, our model created using a synthetic training set achieves higher accuracy than the model created using a same-scale training set of real face images (on the CALFW test set).

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is the compute-optimal scaling law, which reports the performance as a function of units of compute when choosing model sizes optimally. We analyze a random feature model trained with gradient descent as a solvable model of network training and generalization. This reproduces many observations about neural scaling laws. First, our model makes a prediction about why the scaling of performance with training time and with model size have different power law exponents. Consequently, the theory predicts an asymmetric compute-optimal scaling rule where the number of training steps are increased faster than model parameters, consistent with recent empirical observations. Second, it has been observed that early in training, networks converge to their infinite-width dynamics at a rate 1/width but at late time exhibit a rate width^{-c}, where c depends on the structure of the architecture and task. We show that our model exhibits this behavior. Lastly, our theory shows how the gap between training and test loss can gradually build up over time due to repeated reuse of data.

Scaling law principles indicate a power-law correlation between loss and variables such as model size, dataset size, and computational resources utilized during training. These principles play a vital role in optimizing various aspects of model pre-training, ultimately contributing to the success of large language models such as GPT-4, Llama and Gemini. However, the original scaling law paper by OpenAI did not disclose the complete details necessary to derive the precise scaling law formulas, and their conclusions are only based on models containing up to 1.5 billion parameters. Though some subsequent works attempt to unveil these details and scale to larger models, they often neglect the training dependency of important factors such as the learning rate, context length and batch size, leading to their failure to establish a reliable formula for predicting the test loss trajectory. In this technical report, we confirm that the scaling law formulations proposed in the original OpenAI paper remain valid when scaling the model size up to 33 billion, but the constant coefficients in these formulas vary significantly with the experiment setup. We meticulously identify influential factors and provide transparent, step-by-step instructions to estimate all constant terms in scaling-law formulas by training on models with only 1M~60M parameters. Using these estimated formulas, we showcase the capability to accurately predict various attributes for models with up to 33B parameters before their training, including (1) the minimum possible test loss; (2) the minimum required training steps and processed tokens to achieve a specific loss; (3) the critical batch size with an optimal time/computation trade-off at any loss value; and (4) the complete test loss trajectory with arbitrary batch size.

Test-Time Adaptation (TTA) has recently emerged as a promising approach for tackling the robustness challenge under distribution shifts. However, the lack of consistent settings and systematic studies in prior literature hinders thorough assessments of existing methods. To address this issue, we present TTAB, a test-time adaptation benchmark that encompasses ten state-of-the-art algorithms, a diverse array of distribution shifts, and two evaluation protocols. Through extensive experiments, our benchmark reveals three common pitfalls in prior efforts. First, selecting appropriate hyper-parameters, especially for model selection, is exceedingly difficult due to online batch dependency. Second, the effectiveness of TTA varies greatly depending on the quality and properties of the model being adapted. Third, even under optimal algorithmic conditions, none of the existing methods are capable of addressing all common types of distribution shifts. Our findings underscore the need for future research in the field to conduct rigorous evaluations on a broader set of models and shifts, and to re-examine the assumptions behind the empirical success of TTA. Our code is available at https://github.com/lins-lab/ttab.

Test-time adaptation (TTA) intends to adapt the pretrained model to test distributions with only unlabeled test data streams. Most of the previous TTA methods have achieved great success on simple test data streams such as independently sampled data from single or multiple distributions. However, these attempts may fail in dynamic scenarios of real-world applications like autonomous driving, where the environments gradually change and the test data is sampled correlatively over time. In this work, we explore such practical test data streams to deploy the model on the fly, namely practical test-time adaptation (PTTA). To do so, we elaborate a Robust Test-Time Adaptation (RoTTA) method against the complex data stream in PTTA. More specifically, we present a robust batch normalization scheme to estimate the normalization statistics. Meanwhile, a memory bank is utilized to sample category-balanced data with consideration of timeliness and uncertainty. Further, to stabilize the training procedure, we develop a time-aware reweighting strategy with a teacher-student model. Extensive experiments prove that RoTTA enables continual testtime adaptation on the correlatively sampled data streams. Our method is easy to implement, making it a good choice for rapid deployment. The code is publicly available at https://github.com/BIT-DA/RoTTA

Test-time adaptation (TTA) seeks to tackle potential distribution shifts between training and testing data by adapting a given model w.r.t. any testing sample. This task is particularly important for deep models when the test environment changes frequently. Although some recent attempts have been made to handle this task, we still face two practical challenges: 1) existing methods have to perform backward computation for each test sample, resulting in unbearable prediction cost to many applications; 2) while existing TTA solutions can significantly improve the test performance on out-of-distribution data, they often suffer from severe performance degradation on in-distribution data after TTA (known as catastrophic forgetting). In this paper, we point out that not all the test samples contribute equally to model adaptation, and high-entropy ones may lead to noisy gradients that could disrupt the model. Motivated by this, we propose an active sample selection criterion to identify reliable and non-redundant samples, on which the model is updated to minimize the entropy loss for test-time adaptation. Furthermore, to alleviate the forgetting issue, we introduce a Fisher regularizer to constrain important model parameters from drastic changes, where the Fisher importance is estimated from test samples with generated pseudo labels. Extensive experiments on CIFAR-10-C, ImageNet-C, and ImageNet-R verify the effectiveness of our proposed method.

Training models to effectively use test-time compute is crucial for improving the reasoning performance of LLMs. Current methods mostly do so via fine-tuning on search traces or running RL with 0/1 outcome reward, but do these approaches efficiently utilize test-time compute? Would these approaches continue to scale as the budget improves? In this paper, we try to answer these questions. We formalize the problem of optimizing test-time compute as a meta-reinforcement learning (RL) problem, which provides a principled perspective on spending test-time compute. This perspective enables us to view the long output stream from the LLM as consisting of several episodes run at test time and leads us to use a notion of cumulative regret over output tokens as a way to measure the efficacy of test-time compute. Akin to how RL algorithms can best tradeoff exploration and exploitation over training, minimizing cumulative regret would also provide the best balance between exploration and exploitation in the token stream. While we show that state-of-the-art models do not minimize regret, one can do so by maximizing a dense reward bonus in conjunction with the outcome 0/1 reward RL. This bonus is the ''progress'' made by each subsequent block in the output stream, quantified by the change in the likelihood of eventual success. Using these insights, we develop Meta Reinforcement Fine-Tuning, or MRT, a new class of fine-tuning methods for optimizing test-time compute. MRT leads to a 2-3x relative gain in performance and roughly a 1.5x gain in token efficiency for math reasoning compared to outcome-reward RL.

Vision-Language Models (VLMs) have demonstrated great potential in interpreting remote sensing (RS) images through language-guided semantic understanding. However, the effectiveness of these VLMs critically depends on high-quality image-text training data that captures rich semantic relationships between visual content and language descriptions. Unlike natural images, RS lacks large-scale interleaved image-text pairs from web data, making data collection challenging. While current approaches rely primarily on rule-based methods or flagship VLMs for data synthesis, a systematic framework for automated quality assessment of such synthetically generated RS visionlanguage data is notably absent. To fill this gap, we propose a novel score model trained on large-scale RS visionlanguage preference data for automated quality assessment. Our empirical results demonstrate that fine-tuning CLIP or advanced VLMs (e.g., Qwen2-VL) with the top 30% of data ranked by our score model achieves superior interpretation accuracy compared to both full-data fine-tuning and CLIP-score-based ranking approaches. Furthermore, we demonstrate applications of our scoring model for reinforcement learning (RL) training and best-of-N (BoN) testtime scaling, enabling significant improvements in VLM performance for RS tasks.

In this paper, we propose Test-Time Training, a general approach for improving the performance of predictive models when training and test data come from different distributions. We turn a single unlabeled test sample into a self-supervised learning problem, on which we update the model parameters before making a prediction. This also extends naturally to data in an online stream. Our simple approach leads to improvements on diverse image classification benchmarks aimed at evaluating robustness to distribution shifts.

Prior work has established test-time training (TTT) as a general framework to further improve a trained model at test time. Before making a prediction on each test instance, the model is trained on the same instance using a self-supervised task, such as image reconstruction with masked autoencoders. We extend TTT to the streaming setting, where multiple test instances - video frames in our case - arrive in temporal order. Our extension is online TTT: The current model is initialized from the previous model, then trained on the current frame and a small window of frames immediately before. Online TTT significantly outperforms the fixed-model baseline for four tasks, on three real-world datasets. The relative improvement is 45% and 66% for instance and panoptic segmentation. Surprisingly, online TTT also outperforms its offline variant that accesses more information, training on all frames from the entire test video regardless of temporal order. This differs from previous findings using synthetic videos. We conceptualize locality as the advantage of online over offline TTT. We analyze the role of locality with ablations and a theory based on bias-variance trade-off.

Recently, test-time adaptation (TTA) has been proposed as a promising solution for addressing distribution shifts. It allows a base model to adapt to an unforeseen distribution during inference by leveraging the information from the batch of (unlabeled) test data. However, we uncover a novel security vulnerability of TTA based on the insight that predictions on benign samples can be impacted by malicious samples in the same batch. To exploit this vulnerability, we propose Distribution Invading Attack (DIA), which injects a small fraction of malicious data into the test batch. DIA causes models using TTA to misclassify benign and unperturbed test data, providing an entirely new capability for adversaries that is infeasible in canonical machine learning pipelines. Through comprehensive evaluations, we demonstrate the high effectiveness of our attack on multiple benchmarks across six TTA methods. In response, we investigate two countermeasures to robustify the existing insecure TTA implementations, following the principle of "security by design". Together, we hope our findings can make the community aware of the utility-security tradeoffs in deploying TTA and provide valuable insights for developing robust TTA approaches.

Test-time adaptation harnesses test inputs to improve the accuracy of a model trained on source data when tested on shifted target data. Existing methods update the source model by (re-)training on each target domain. While effective, re-training is sensitive to the amount and order of the data and the hyperparameters for optimization. We instead update the target data, by projecting all test inputs toward the source domain with a generative diffusion model. Our diffusion-driven adaptation method, DDA, shares its models for classification and generation across all domains. Both models are trained on the source domain, then fixed during testing. We augment diffusion with image guidance and self-ensembling to automatically decide how much to adapt. Input adaptation by DDA is more robust than prior model adaptation approaches across a variety of corruptions, architectures, and data regimes on the ImageNet-C benchmark. With its input-wise updates, DDA succeeds where model adaptation degrades on too little data in small batches, dependent data in non-uniform order, or mixed data with multiple corruptions.

Inference-Time Scaling has been critical to the success of recent models such as OpenAI o1 and DeepSeek R1. However, many techniques used to train models for inference-time scaling require tasks to have answers that can be verified, limiting their application to domains such as math, coding and logical reasoning. We take inspiration from how humans make first attempts, ask for detailed feedback from others and make improvements based on such feedback across a wide spectrum of open-ended endeavors. To this end, we collect data for and train dedicated Feedback and Edit Models that are capable of performing inference-time scaling for open-ended general-domain tasks. In our setup, one model generates an initial response, which are given feedback by a second model, that are then used by a third model to edit the response. We show that performance on Arena Hard, a benchmark strongly predictive of Chatbot Arena Elo can be boosted by scaling the number of initial response drafts, effective feedback and edited responses. When scaled optimally, our setup based on 70B models from the Llama 3 family can reach SoTA performance on Arena Hard at 92.7 as of 5 Mar 2025, surpassing OpenAI o1-preview-2024-09-12 with 90.4 and DeepSeek R1 with 92.3.

A primary cost driver for training large models is wall-clock training time. We show that popular time estimates based on FLOPs are poor estimates, and construct a more accurate proxy based on memory copies. We show that with some simple accounting, we can estimate the training speed of a transformer model from its hyperparameters. Combined with a scaling law curve like Chinchilla, this lets us estimate the final loss of the model. We fit our estimate to real data with a linear regression, and apply the result to rewrite Chinchilla in terms of a model's estimated training time as opposed to the amount of training data. This gives an expression for the loss in terms of the model's hyperparameters alone. We show that this expression is accurate across a wide range of model hyperparameter values, enabling us to analytically make architectural decisions and train models more efficiently.

Test-time adaptation (TTA) addresses distribution shifts for streaming test data in unsupervised settings. Currently, most TTA methods can only deal with minor shifts and rely heavily on heuristic and empirical studies. To advance TTA under domain shifts, we propose the novel problem setting of active test-time adaptation (ATTA) that integrates active learning within the fully TTA setting. We provide a learning theory analysis, demonstrating that incorporating limited labeled test instances enhances overall performances across test domains with a theoretical guarantee. We also present a sample entropy balancing for implementing ATTA while avoiding catastrophic forgetting (CF). We introduce a simple yet effective ATTA algorithm, known as SimATTA, using real-time sample selection techniques. Extensive experimental results confirm consistency with our theoretical analyses and show that the proposed ATTA method yields substantial performance improvements over TTA methods while maintaining efficiency and shares similar effectiveness to the more demanding active domain adaptation (ADA) methods. Our code is available at https://github.com/divelab/ATTA

Generalizing deep learning models to unknown target domain distribution with low latency has motivated research into test-time training/adaptation (TTT/TTA). Existing approaches often focus on improving test-time training performance under well-curated target domain data. As figured out in this work, many state-of-the-art methods fail to maintain the performance when the target domain is contaminated with strong out-of-distribution (OOD) data, a.k.a. open-world test-time training (OWTTT). The failure is mainly due to the inability to distinguish strong OOD samples from regular weak OOD samples. To improve the robustness of OWTTT we first develop an adaptive strong OOD pruning which improves the efficacy of the self-training TTT method. We further propose a way to dynamically expand the prototypes to represent strong OOD samples for an improved weak/strong OOD data separation. Finally, we regularize self-training with distribution alignment and the combination yields the state-of-the-art performance on 5 OWTTT benchmarks. The code is available at https://github.com/Yushu-Li/OWTTT.

Most recent test-time adaptation methods focus on only classification tasks, use specialized network architectures, destroy model calibration or rely on lightweight information from the source domain. To tackle these issues, this paper proposes a novel Test-time Self-Learning method with automatic Adversarial augmentation dubbed TeSLA for adapting a pre-trained source model to the unlabeled streaming test data. In contrast to conventional self-learning methods based on cross-entropy, we introduce a new test-time loss function through an implicitly tight connection with the mutual information and online knowledge distillation. Furthermore, we propose a learnable efficient adversarial augmentation module that further enhances online knowledge distillation by simulating high entropy augmented images. Our method achieves state-of-the-art classification and segmentation results on several benchmarks and types of domain shifts, particularly on challenging measurement shifts of medical images. TeSLA also benefits from several desirable properties compared to competing methods in terms of calibration, uncertainty metrics, insensitivity to model architectures, and source training strategies, all supported by extensive ablations. Our code and models are available on GitHub.

The scientific scale-up of large language models (LLMs) necessitates a comprehensive understanding of their scaling properties. However, the existing literature on the scaling properties only yields an incomplete answer: optimization loss decreases predictably as the model size increases, in line with established scaling law; yet no scaling law for task has been established and the task performances are far from predictable during scaling. Task performances typically show minor gains on small models until they improve dramatically once models exceed a size threshold, exemplifying the ``emergent abilities''. In this study, we discover that small models, although they exhibit minor performance, demonstrate critical and consistent task performance improvements that are not captured by conventional evaluation strategies due to insufficient measurement resolution. To measure such improvements, we introduce PassUntil, an evaluation strategy through massive sampling in the decoding phase. We conduct quantitative investigations into the scaling law of task performance. Firstly, a strict task scaling law is identified, enhancing the predictability of task performances. Remarkably, we are able to predict the performance of the 2.4B model on code generation with merely 0.05\% deviation before training starts. Secondly, underpinned by PassUntil, we observe concrete evidence of emergent abilities and ascertain that they are not in conflict with the continuity of performance improvement. Their semblance to break-through is that their scaling curve cannot be fitted by standard scaling law function. We then introduce a mathematical definition for the emergent abilities. Through the definition, we refute a prevalent ``multi-step reasoning hypothesis'' regarding the genesis of emergent abilities and propose a new hypothesis with a satisfying fit to the observed scaling curve.

Current large language models (LLMs) often struggle to produce accurate responses on the first attempt for complex reasoning tasks like code generation. Prior research tackles this challenge by generating multiple candidate solutions and validating them with LLM-generated unit tests. The execution results of unit tests serve as reward signals to identify correct solutions. As LLMs always confidently make mistakes, these unit tests are not reliable, thereby diminishing the quality of reward signals. Motivated by the observation that scaling the number of solutions improves LLM performance, we explore the impact of scaling unit tests to enhance reward signal quality. Our pioneer experiment reveals a positive correlation between the number of unit tests and reward signal quality, with greater benefits observed in more challenging problems. Based on these insights, we propose CodeRM-8B, a lightweight yet effective unit test generator that enables efficient and high-quality unit test scaling. Additionally, we implement a dynamic scaling mechanism that adapts the number of unit tests based on problem difficulty, further improving efficiency. Experimental results show that our approach significantly improves performance across various models on three benchmarks (e.g., with gains of 18.43% for Llama3-8B and 3.42% for GPT-4o-mini on HumanEval Plus).

Scaling laws offer valuable insights into the design of time series foundation models (TSFMs). However, previous research has largely focused on the scaling laws of TSFMs for in-distribution (ID) data, leaving their out-of-distribution (OOD) scaling behavior and the influence of model architectures less explored. In this work, we examine two common TSFM architectures, encoder-only and decoder-only Transformers, and investigate their scaling behavior on both ID and OOD data. These models are trained and evaluated across varying parameter counts, compute budgets, and dataset sizes. Our experiments reveal that the log-likelihood loss of TSFMs exhibits similar scaling behavior in both OOD and ID settings. We further compare the scaling properties across different architectures, incorporating two state-of-the-art TSFMs as case studies, showing that model architecture plays a significant role in scaling. The encoder-only Transformers demonstrate better scalability than the decoder-only Transformers, while the architectural enhancements in the two advanced TSFMs primarily improve ID performance but reduce OOD scalability. While scaling up TSFMs is expected to drive performance breakthroughs, the lack of a comprehensive understanding of TSFM scaling laws has hindered the development of a robust framework to guide model scaling. We fill this gap in this work by synthesizing our findings and providing practical guidelines for designing and scaling larger TSFMs with enhanced model capabilities.

The main challenge in domain generalization (DG) is to handle the distribution shift problem that lies between the training and test data. Recent studies suggest that test-time training (TTT), which adapts the learned model with test data, might be a promising solution to the problem. Generally, a TTT strategy hinges its performance on two main factors: selecting an appropriate auxiliary TTT task for updating and identifying reliable parameters to update during the test phase. Both previous arts and our experiments indicate that TTT may not improve but be detrimental to the learned model if those two factors are not properly considered. This work addresses those two factors by proposing an Improved Test-Time Adaptation (ITTA) method. First, instead of heuristically defining an auxiliary objective, we propose a learnable consistency loss for the TTT task, which contains learnable parameters that can be adjusted toward better alignment between our TTT task and the main prediction task. Second, we introduce additional adaptive parameters for the trained model, and we suggest only updating the adaptive parameters during the test phase. Through extensive experiments, we show that the proposed two strategies are beneficial for the learned model (see Figure 1), and ITTA could achieve superior performance to the current state-of-the-art methods on several DG benchmarks. Code is available at https://github.com/liangchen527/ITTA.

Building upon our previous investigations of O1 replication (Part 1: Journey Learning [Qin et al., 2024] and Part 2: Distillation [Huang et al., 2024]), this work explores the potential of inference-time scaling in large language models (LLMs) for medical reasoning tasks, ranging from diagnostic decision-making to treatment planning. Through extensive experiments on medical benchmarks of varying complexity (MedQA, Medbullets, and JAMA Clinical Challenges), our investigation reveals several key insights: (1) Increasing inference time does lead to improved performance. With a modest training set of 500 samples, our model yields substantial performance improvements of 6%-11%. (2) Task complexity directly correlates with the required length of reasoning chains, confirming the necessity of extended thought processes for challenging problems. (3) The differential diagnoses generated by our model adhere to the principles of the hypothetico-deductive method, producing a list of potential conditions that may explain a patient's symptoms and systematically narrowing these possibilities by evaluating the evidence. These findings demonstrate the promising synergy between inference-time scaling and journey learning in advancing LLMs' real-world clinical reasoning capabilities.

Recent work has identified simple empirical scaling laws for language models, linking compute budget, dataset size, model size, and autoregressive modeling loss. The validity of these simple power laws across orders of magnitude in model scale provides compelling evidence that larger models are also more capable models. However, scaling up models under the constraints of hardware and infrastructure is no easy feat, and rapidly becomes a hard and expensive engineering problem. We investigate ways to tentatively cheat scaling laws, and train larger models for cheaper. We emulate an increase in effective parameters, using efficient approximations: either by doping the models with frozen random parameters, or by using fast structured transforms in place of dense linear layers. We find that the scaling relationship between test loss and compute depends only on the actual number of trainable parameters; scaling laws cannot be deceived by spurious parameters.

Test-time adaptation (TTA) aims to address the distribution shift between the training and test data with only unlabeled data at test time. Existing TTA methods often focus on improving recognition performance specifically for test data associated with classes in the training set. However, during the open-world inference process, there are inevitably test data instances from unknown classes, commonly referred to as outliers. This paper pays attention to the problem that conducts both sample recognition and outlier rejection during inference while outliers exist. To address this problem, we propose a new approach called STAble Memory rePlay (STAMP), which performs optimization over a stable memory bank instead of the risky mini-batch. In particular, the memory bank is dynamically updated by selecting low-entropy and label-consistent samples in a class-balanced manner. In addition, we develop a self-weighted entropy minimization strategy that assigns higher weight to low-entropy samples. Extensive results demonstrate that STAMP outperforms existing TTA methods in terms of both recognition and outlier detection performance. The code is released at https://github.com/yuyongcan/STAMP.

Test-time adaptation (TTA) is the problem of updating a pre-trained source model at inference time given test input(s) from a different target domain. Most existing TTA approaches assume the setting in which the target domain is stationary, i.e., all the test inputs come from a single target domain. However, in many practical settings, the test input distribution might exhibit a lifelong/continual shift over time. Moreover, existing TTA approaches also lack the ability to provide reliable uncertainty estimates, which is crucial when distribution shifts occur between the source and target domain. To address these issues, we present PETAL (Probabilistic lifElong Test-time Adaptation with seLf-training prior), which solves lifelong TTA using a probabilistic approach, and naturally results in (1) a student-teacher framework, where the teacher model is an exponential moving average of the student model, and (2) regularizing the model updates at inference time using the source model as a regularizer. To prevent model drift in the lifelong/continual TTA setting, we also propose a data-driven parameter restoration technique which contributes to reducing the error accumulation and maintaining the knowledge of recent domains by restoring only the irrelevant parameters. In terms of predictive error rate as well as uncertainty based metrics such as Brier score and negative log-likelihood, our method achieves better results than the current state-of-the-art for online lifelong test-time adaptation across various benchmarks, such as CIFAR-10C, CIFAR-100C, ImageNetC, and ImageNet3DCC datasets. The source code for our approach is accessible at https://github.com/dhanajitb/petal.

Deploying models on target domain data subject to distribution shift requires adaptation. Test-time training (TTT) emerges as a solution to this adaptation under a realistic scenario where access to full source domain data is not available and instant inference on target domain is required. Despite many efforts into TTT, there is a confusion over the experimental settings, thus leading to unfair comparisons. In this work, we first revisit TTT assumptions and categorize TTT protocols by two key factors. Among the multiple protocols, we adopt a realistic sequential test-time training (sTTT) protocol, under which we further develop a test-time anchored clustering (TTAC) approach to enable stronger test-time feature learning. TTAC discovers clusters in both source and target domain and match the target clusters to the source ones to improve generalization. Pseudo label filtering and iterative updating are developed to improve the effectiveness and efficiency of anchored clustering. We demonstrate that under all TTT protocols TTAC consistently outperforms the state-of-the-art methods on six TTT datasets. We hope this work will provide a fair benchmarking of TTT methods and future research should be compared within respective protocols. A demo code is available at https://github.com/Gorilla-Lab-SCUT/TTAC.

Large language models (LLMs) have achieved significant performance gains via scaling up model sizes and/or data. However, recent evidence suggests diminishing returns from such approaches, motivating scaling the computation spent at inference time. Existing inference-time scaling methods, usually with reward models, cast the task as a search problem, which tends to be vulnerable to reward hacking as a consequence of approximation errors in reward models. In this paper, we instead cast inference-time scaling as a probabilistic inference task and leverage sampling-based techniques to explore the typical set of the state distribution of a state-space model with an approximate likelihood, rather than optimize for its mode directly. We propose a novel inference-time scaling approach by adapting particle-based Monte Carlo methods to this task. Our empirical evaluation demonstrates that our methods have a 4-16x better scaling rate over our deterministic search counterparts on various challenging mathematical reasoning tasks. Using our approach, we show that Qwen2.5-Math-1.5B-Instruct can surpass GPT-4o accuracy in only 4 rollouts, while Qwen2.5-Math-7B-Instruct scales to o1 level accuracy in only 32 rollouts. Our work not only presents an effective method to inference-time scaling, but also connects the rich literature in probabilistic inference with inference-time scaling of LLMs to develop more robust algorithms in future work. Code and further information is available at https://probabilistic-inference-scaling.github.io.

Time series models face significant challenges in scaling to handle large and complex datasets, akin to the scaling achieved by large language models (LLMs). The unique characteristics of time series data and the computational demands of model scaling necessitate innovative approaches. While researchers have explored various architectures such as Transformers, LSTMs, and GRUs to address these challenges, we propose a novel solution using RWKV-7, which incorporates meta-learning into its state update mechanism. By integrating RWKV-7's time mix and channel mix components into the transformer-based time series model Timer, we achieve a substantial performance improvement of approximately 1.13 to 43.3x and a 4.5x reduction in training time with 1/23 parameters, all while utilizing fewer parameters. Our code and model weights are publicly available for further research and development at https://github.com/Alic-Li/BlackGoose_Rimer.

LLM test-time compute (or LLM inference) via search has emerged as a promising research area with rapid developments. However, current frameworks often adopt distinct perspectives on three key aspects (task definition, LLM profiling, and search procedures), making direct comparisons challenging. Moreover, the search algorithms employed often diverge from standard implementations, and their specific characteristics are not thoroughly specified. In this survey, we provide a comprehensive technical review that unifies task definitions and provides modular definitions of LLM profiling and search procedures. The definitions enable precise comparisons of various LLM inference frameworks while highlighting their departures from conventional search algorithms. We also discuss the applicability, performance, and efficiency of these methods. For further details and ongoing updates, please refer to our GitHub repository: https://github.com/xinzhel/LLM-Agent-Survey/blob/main/search.md

Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can be used to accelerate model development. In this work, we perform such an empirical investigation across a wide range of language understanding tasks, starting from models with as few as 10K parameters, and evaluate downstream performance across 9 language understanding tasks. We find that scaling laws emerge at finetuning time in some NLP tasks, and that they can also be exploited for debugging convergence when training large models. Moreover, for tasks where scaling laws exist, they can be used to predict the performance of larger models, which enables effective model selection. However, revealing scaling laws requires careful hyperparameter tuning and multiple runs for the purpose of uncertainty estimation, which incurs additional overhead, partially offsetting the computational benefits.

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative - constant learning rate and cooldowns - and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs.

Recent test-time adaptation methods heavily rely on nuanced adjustments of batch normalization (BN) parameters. However, one critical assumption often goes overlooked: that of independently and identically distributed (i.i.d.) test batches with respect to unknown labels. This oversight leads to skewed BN statistics and undermines the reliability of the model under non-i.i.d. scenarios. To tackle this challenge, this paper presents a novel method termed 'Un-Mixing Test-Time Normalization Statistics' (UnMix-TNS). Our method re-calibrates the statistics for each instance within a test batch by mixing it with multiple distinct statistics components, thus inherently simulating the i.i.d. scenario. The core of this method hinges on a distinctive online unmixing procedure that continuously updates these statistics components by incorporating the most similar instances from new test batches. Remarkably generic in its design, UnMix-TNS seamlessly integrates with a wide range of leading test-time adaptation methods and pre-trained architectures equipped with BN layers. Empirical evaluations corroborate the robustness of UnMix-TNS under varied scenarios-ranging from single to continual and mixed domain shifts, particularly excelling with temporally correlated test data and corrupted non-i.i.d. real-world streams. This adaptability is maintained even with very small batch sizes or single instances. Our results highlight UnMix-TNS's capacity to markedly enhance stability and performance across various benchmarks. Our code is publicly available at https://github.com/devavratTomar/unmixtns.

Predictable behavior from scaling advanced AI systems is an extremely desirable property. Although a well-established literature exists on how pretraining performance scales, the literature on how particular downstream capabilities scale is significantly muddier. In this work, we take a step back and ask: why has predicting specific downstream capabilities with scale remained elusive? While many factors are certainly responsible, we identify a new factor that makes modeling scaling behavior on widely used multiple-choice question-answering benchmarks challenging. Using five model families and twelve well-established multiple-choice benchmarks, we show that downstream performance is computed from negative log likelihoods via a sequence of transformations that progressively degrade the statistical relationship between performance and scale. We then reveal the mechanism causing this degradation: downstream metrics require comparing the correct choice against a small number of specific incorrect choices, meaning accurately predicting downstream capabilities requires predicting not just how probability mass concentrates on the correct choice with scale, but also how probability mass fluctuates on specific incorrect choices with scale. We empirically study how probability mass on the correct choice co-varies with probability mass on incorrect choices with increasing compute, suggesting that scaling laws for incorrect choices might be achievable. Our work also explains why pretraining scaling laws are commonly regarded as more predictable than downstream capabilities and contributes towards establishing scaling-predictable evaluations of frontier AI models.

The Languini Kitchen serves as both a research collective and codebase designed to empower researchers with limited computational resources to contribute meaningfully to the field of language modelling. We introduce an experimental protocol that enables model comparisons based on equivalent compute, measured in accelerator hours. The number of tokens on which a model is trained is defined by the model's throughput and the chosen compute class. Notably, this approach avoids constraints on critical hyperparameters which affect total parameters or floating-point operations. For evaluation, we pre-process an existing large, diverse, and high-quality dataset of books that surpasses existing academic benchmarks in quality, diversity, and document length. On it, we compare methods based on their empirical scaling trends which are estimated through experiments at various levels of compute. This work also provides two baseline models: a feed-forward model derived from the GPT-2 architecture and a recurrent model in the form of a novel LSTM with ten-fold throughput. While the GPT baseline achieves better perplexity throughout all our levels of compute, our LSTM baseline exhibits a predictable and more favourable scaling law. This is due to the improved throughput and the need for fewer training tokens to achieve the same decrease in test perplexity. Extrapolating the scaling laws leads of both models results in an intersection at roughly 50,000 accelerator hours. We hope this work can serve as the foundation for meaningful and reproducible language modelling research.

Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship between, loss, or task performance, and scale. All components of this process vary, from the specific equation being fit, to the training setup, to the optimization method. Each of these factors may affect the fitted law, and therefore, the conclusions of a given study. We discuss discrepancies in the conclusions that several prior works reach, on questions such as the optimal token to parameter ratio. We augment this discussion with our own analysis of the critical impact that changes in specific details may effect in a scaling study, and the resulting altered conclusions. Additionally, we survey over 50 papers that study scaling trends: while 45 of these papers quantify these trends using a power law, most under-report crucial details needed to reproduce their findings. To mitigate this, we we propose a checklist for authors to consider while contributing to scaling law research.

Kaplan et al. and Hoffmann et al. developed influential scaling laws for the optimal model size as a function of the compute budget, but these laws yield substantially different predictions. We explain the discrepancy by reproducing the Kaplan scaling law on two datasets (OpenWebText2 and RefinedWeb) and identifying three factors causing the difference: last layer computational cost, warmup duration, and scale-dependent optimizer tuning. With these factors corrected, we obtain excellent agreement with the Hoffmann et al. (i.e., "Chinchilla") scaling law. Counter to a hypothesis of Hoffmann et al., we find that careful learning rate decay is not essential for the validity of their scaling law. As a secondary result, we derive scaling laws for the optimal learning rate and batch size, finding that tuning the AdamW beta_2 parameter is essential at lower batch sizes.

Machine learning models can make critical errors that are easily hidden within vast amounts of data. Such errors often run counter to rules based on human intuition. However, rules based on human knowledge are challenging to scale or to even formalize. We thereby seek to infer statistical rules from the data and quantify the extent to which a model has learned them. We propose a framework SQRL that integrates logic-based methods with statistical inference to derive these rules from a model's training data without supervision. We further show how to adapt models at test time to reduce rule violations and produce more coherent predictions. SQRL generates up to 300K rules over datasets from vision, tabular, and language settings. We uncover up to 158K violations of those rules by state-of-the-art models for classification, object detection, and data imputation. Test-time adaptation reduces these violations by up to 68.7% with relative performance improvement up to 32%. SQRL is available at https://github.com/DebugML/sqrl.

Scaling laws are typically fit using a family of models with a narrow range of frozen hyper-parameter choices. In this work we study scaling laws using a wide range of architecture and hyper-parameter choices, and highlight their impact on resulting prescriptions. As a primary artifact of our research, we release the Gemstones: the most comprehensive open-source scaling law dataset to date, consisting of over 4000 checkpoints from transformers with up to 2 billion parameters; these models have been trained with different learning rates, cooldown schedules, and architectural shapes. Our checkpoints enable more complex studies of scaling, such as a law that predicts language modeling performance as a function of model width and depth. By examining the various facets of our model suite, we find that the prescriptions of scaling laws can be highly sensitive to the experimental design process and the specific model checkpoints used during fitting. Code: https://github.com/mcleish7/gemstone-scaling-laws

While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we derive a strategy for predicting one loss from another and apply it to predict across different pre-training datasets and from pre-training data to downstream task data. Our predictions extrapolate well even at 20x the largest FLOP budget used to fit the curves. More precisely, we find that there are simple shifted power law relationships between (1) the train losses of two models trained on two separate datasets when the models are paired by training compute (train-to-train), (2) the train loss and the test loss on any downstream distribution for a single model (train-to-test), and (3) the test losses of two models trained on two separate train datasets (test-to-test). The results hold up for pre-training datasets that differ substantially (some are entirely code and others have no code at all) and across a variety of downstream tasks. Finally, we find that in some settings these shifted power law relationships can yield more accurate predictions than extrapolating single-dataset scaling laws.

Scaling up language models has been empirically shown to improve performance on a wide range of downstream tasks. However, if we were to observe worse performance as a function of scale ("inverse scaling") on certain tasks, this would indicate that scaling can also encourage behaviors that are misaligned with human preferences. The Inverse Scaling Prize (McKenzie et al. 2022) identified eleven such inverse scaling tasks, evaluated on models of up to 280B parameters and up to 500 zettaFLOPs of training compute. This paper takes a closer look at these inverse scaling tasks. We evaluate models of up to 540B parameters, trained on five times more compute than those evaluated in the Inverse Scaling Prize. With this increased range of model sizes and training compute, only four out of the eleven tasks remain inverse scaling. Six out of the eleven tasks exhibit "U-shaped scaling", where performance decreases up to a certain size, and then increases again up to the largest model evaluated (the one remaining task displays positive scaling). In addition, we find that 1-shot examples and chain-of-thought can help mitigate undesirable scaling patterns even further. U-shaped scaling suggests that the inverse scaling trend observed in McKenzie et al. (2022) may not continue to hold for larger models, which we attribute to the presence of distractor tasks that only sufficiently large models can avoid.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

The remarkable performance of models like the OpenAI o1 can be attributed to their ability to emulate human-like long-time thinking during inference. These models employ extended chain-of-thought (CoT) processes, exploring multiple strategies to enhance problem-solving capabilities. However, a critical question remains: How to intelligently and efficiently scale computational resources during testing. This paper presents the first comprehensive study on the prevalent issue of overthinking in these models, where excessive computational resources are allocated for simple problems with minimal benefit. We introduce novel efficiency metrics from both outcome and process perspectives to evaluate the rational use of computational resources by o1-like models. Using a self-training paradigm, we propose strategies to mitigate overthinking, streamlining reasoning processes without compromising accuracy. Experimental results show that our approach successfully reduces computational overhead while preserving model performance across a range of testsets with varying difficulty levels, such as GSM8K, MATH500, GPQA, and AIME.

Test-time adaptation (TTA) fine-tunes pre-trained deep neural networks for unseen test data. The primary challenge of TTA is limited access to the entire test dataset during online updates, causing error accumulation. To mitigate it, TTA methods have utilized the model output's entropy as a confidence metric that aims to determine which samples have a lower likelihood of causing error. Through experimental studies, however, we observed the unreliability of entropy as a confidence metric for TTA under biased scenarios and theoretically revealed that it stems from the neglect of the influence of latent disentangled factors of data on predictions. Building upon these findings, we introduce a novel TTA method named Destroy Your Object (DeYO), which leverages a newly proposed confidence metric named Pseudo-Label Probability Difference (PLPD). PLPD quantifies the influence of the shape of an object on prediction by measuring the difference between predictions before and after applying an object-destructive transformation. DeYO consists of sample selection and sample weighting, which employ entropy and PLPD concurrently. For robust adaptation, DeYO prioritizes samples that dominantly incorporate shape information when making predictions. Our extensive experiments demonstrate the consistent superiority of DeYO over baseline methods across various scenarios, including biased and wild. Project page is publicly available at https://whitesnowdrop.github.io/DeYO/.

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 442 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting.

Large Language Models (LLMs) are often described as being instances of foundation models - that is, models that transfer strongly across various tasks and conditions in few-show or zero-shot manner, while exhibiting scaling laws that predict function improvement when increasing the pre-training scale. These claims of excelling in different functions and tasks rely on measurements taken across various sets of standardized benchmarks showing high scores for such models. We demonstrate here a dramatic breakdown of function and reasoning capabilities of state-of-the-art models trained at the largest available scales which claim strong function, using a simple, short, conventional common sense problem formulated in concise natural language, easily solvable by humans. The breakdown is dramatic, as models also express strong overconfidence in their wrong solutions, while providing often non-sensical "reasoning"-like explanations akin to confabulations to justify and backup the validity of their clearly failed responses, making them sound plausible. Various standard interventions in an attempt to get the right solution, like various type of enhanced prompting, or urging the models to reconsider the wrong solutions again by multi step re-evaluation, fail. We take these initial observations to the scientific and technological community to stimulate urgent re-assessment of the claimed capabilities of current generation of LLMs, Such re-assessment also requires common action to create standardized benchmarks that would allow proper detection of such basic reasoning deficits that obviously manage to remain undiscovered by current state-of-the-art evaluation procedures and benchmarks. Code for reproducing experiments in the paper and raw experiments data can be found at https://github.com/LAION-AI/AIW

Continual Test Time Adaptation (CTTA) is required to adapt efficiently to continuous unseen domains while retaining previously learned knowledge. However, despite the progress of CTTA, forgetting-adaptation trade-offs and efficiency are still unexplored. Moreover, current CTTA scenarios assume only the disjoint situation, even though real-world domains are seamlessly changed. To tackle these challenges, this paper proposes BECoTTA, an input-dependent yet efficient framework for CTTA. We propose Mixture-of-Domain Low-rank Experts (MoDE) that contains two core components: (i) Domain-Adaptive Routing, which aids in selectively capturing the domain-adaptive knowledge with multiple domain routers, and (ii) Domain-Expert Synergy Loss to maximize the dependency between each domain and expert. We validate our method outperforms multiple CTTA scenarios including disjoint and gradual domain shits, while only requiring ~98% fewer trainable parameters. We also provide analyses of our method, including the construction of experts, the effect of domain-adaptive experts, and visualizations.

Independence testing is a fundamental and classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the complexity of a problem at hand instead of setting sample size in advance. Ideally, such procedures should (a) allow stopping earlier on easy tasks (and later on harder tasks), hence making better use of available resources, and (b) continuously monitor the data and efficiently incorporate statistical evidence after collecting new data, while controlling the false alarm rate. It is well known that classical batch tests are not tailored for streaming data settings: valid inference after data peeking requires correcting for multiple testing but such corrections generally result in low power. Following the principle of testing by betting, we design sequential kernelized independence tests (SKITs) that overcome such shortcomings. We exemplify our broad framework using bets inspired by kernelized dependence measures, e.g, the Hilbert-Schmidt independence criterion. Our test is valid under non-i.i.d. time-varying settings, for which there exist no batch tests. We demonstrate the power of our approaches on both simulated and real data.

We examine the reasoning and planning capabilities of large language models (LLMs) in solving complex tasks. Recent advances in inference-time techniques demonstrate the potential to enhance LLM reasoning without additional training by exploring intermediate steps during inference. Notably, OpenAI's o1 model shows promising performance through its novel use of multi-step reasoning and verification. Here, we explore how scaling inference-time techniques can improve reasoning and planning, focusing on understanding the tradeoff between computational cost and performance. To this end, we construct a comprehensive benchmark, known as Sys2Bench, and perform extensive experiments evaluating existing inference-time techniques on eleven diverse tasks across five categories, including arithmetic reasoning, logical reasoning, common sense reasoning, algorithmic reasoning, and planning. Our findings indicate that simply scaling inference-time computation has limitations, as no single inference-time technique consistently performs well across all reasoning and planning tasks.

Scaling the amount of compute used to train language models has dramatically improved their capabilities. However, when it comes to inference, we often limit the amount of compute to only one attempt per problem. Here, we explore inference compute as another axis for scaling by increasing the number of generated samples. Across multiple tasks and models, we observe that coverage - the fraction of problems solved by any attempt - scales with the number of samples over four orders of magnitude. In domains like coding and formal proofs, where all answers can be automatically verified, these increases in coverage directly translate into improved performance. When we apply repeated sampling to SWE-bench Lite, the fraction of issues solved with DeepSeek-V2-Coder-Instruct increases from 15.9% with one sample to 56% with 250 samples, outperforming the single-attempt state-of-the-art of 43% which uses more capable frontier models. Moreover, using current API pricing, amplifying the cheaper DeepSeek model with five samples is more cost-effective and solves more issues than paying a premium for one sample from GPT-4o or Claude 3.5 Sonnet. Interestingly, the relationship between coverage and the number of samples is often log-linear and can be modelled with an exponentiated power law, suggesting the existence of inference-time scaling laws. Finally, we find that identifying correct samples out of many generations remains an important direction for future research in domains without automatic verifiers. When solving math word problems from GSM8K and MATH, coverage with Llama-3 models grows to over 95% with 10,000 samples. However, common methods to pick correct solutions from a sample collection, such as majority voting or reward models, plateau beyond several hundred samples and fail to fully scale with the sample budget.

Evaluation benchmarks are the cornerstone of measuring capabilities of large language models (LLMs), as well as driving progress in said capabilities. Originally designed to make claims about capabilities (or lack thereof) in fully pretrained models, evaluation benchmarks are now also extensively used to decide between various training choices. Despite this widespread usage, we rarely quantify the variance in our evaluation benchmarks, which dictates whether differences in performance are meaningful. Here, we define and measure a range of metrics geared towards measuring variance in evaluation benchmarks, including seed variance across initialisations, and monotonicity during training. By studying a large number of models -- both openly available and pretrained from scratch -- we provide empirical estimates for a variety of variance metrics, with considerations and recommendations for practitioners. We also evaluate the utility and tradeoffs of continuous versus discrete performance measures and explore options for better understanding and reducing this variance. We find that simple changes, such as framing choice tasks (like MMLU) as completion tasks, can often reduce variance for smaller scale (sim7B) models, while more involved methods inspired from human testing literature (such as item analysis and item response theory) struggle to meaningfully reduce variance. Overall, our work provides insights into variance in evaluation benchmarks, suggests LM-specific techniques to reduce variance, and more generally encourages practitioners to carefully factor in variance when comparing models.

Scaling laws are useful guides for developing language models, but there are still gaps between current scaling studies and how language models are ultimately trained and evaluated. For instance, scaling is usually studied in the compute-optimal training regime (i.e., "Chinchilla optimal" regime); however, in practice, models are often over-trained to reduce inference costs. Moreover, scaling laws mostly predict loss on next-token prediction, but ultimately models are compared based on downstream task performance. In this paper, we address both shortcomings. To do so, we create a testbed of 104 models with 0.011B to 6.9B parameters trained with various numbers of tokens on three data distributions. First, we investigate scaling in the over-trained regime. We fit scaling laws that extrapolate in both the number of model parameters and the ratio of training tokens to parameters. This enables us to predict the validation loss of a 1.4B parameter, 900B token run (i.e., 32times over-trained) and a 6.9B parameter, 138B token runx2014each from experiments that take 300times less compute. Second, we relate the perplexity of a language model to its downstream task performance via a power law. We use this law to predict top-1 error averaged over downstream tasks for the two aforementioned models using experiments that take 20times less compute. Our experiments are available at https://github.com/mlfoundations/scaling.

Traditionally, data selection has been studied in settings where all samples from prospective sources are fully revealed to a machine learning developer. However, in practical data exchange scenarios, data providers often reveal only a limited subset of samples before an acquisition decision is made. Recently, there have been efforts to fit scaling laws that predict model performance at any size and data source composition using the limited available samples. However, these scaling functions are black-box, computationally expensive to fit, highly susceptible to overfitting, or/and difficult to optimize for data selection. This paper proposes a framework called <projektor>, which predicts model performance and supports data selection decisions based on partial samples of prospective data sources. Our approach distinguishes itself from existing work by introducing a novel *two-stage* performance inference process. In the first stage, we leverage the Optimal Transport distance to predict the model's performance for any data mixture ratio within the range of disclosed data sizes. In the second stage, we extrapolate the performance to larger undisclosed data sizes based on a novel parameter-free mapping technique inspired by neural scaling laws. We further derive an efficient gradient-based method to select data sources based on the projected model performance. Evaluation over a diverse range of applications demonstrates that <projektor> significantly improves existing performance scaling approaches in terms of both the accuracy of performance inference and the computation costs associated with constructing the performance predictor. Also, <projektor> outperforms by a wide margin in data selection effectiveness compared to a range of other off-the-shelf solutions.

Developing an educational test can be expensive and time-consuming, as each item must be written by experts and then evaluated by collecting hundreds of student responses. Moreover, many tests require multiple distinct sets of questions administered throughout the school year to closely monitor students' progress, known as parallel tests. In this study, we focus on tests of silent sentence reading efficiency, used to assess students' reading ability over time. To generate high-quality parallel tests, we propose to fine-tune large language models (LLMs) to simulate how previous students would have responded to unseen items. With these simulated responses, we can estimate each item's difficulty and ambiguity. We first use GPT-4 to generate new test items following a list of expert-developed rules and then apply a fine-tuned LLM to filter the items based on criteria from psychological measurements. We also propose an optimal-transport-inspired technique for generating parallel tests and show the generated tests closely correspond to the original test's difficulty and reliability based on crowdworker responses. Our evaluation of a generated test with 234 students from grades 2 to 8 produces test scores highly correlated (r=0.93) to those of a standard test form written by human experts and evaluated across thousands of K-12 students.

Uncovering early-stage metrics that reflect final model performance is one core principle for large-scale pretraining. The existing scaling law demonstrates the power-law correlation between pretraining loss and training flops, which serves as an important indicator of the current training state for large language models. However, this principle only focuses on the model's compression properties on the training data, resulting in an inconsistency with the ability improvements on the downstream tasks. Some follow-up works attempted to extend the scaling-law to more complex metrics (such as hyperparameters), but still lacked a comprehensive analysis of the dynamic differences among various capabilities during pretraining. To address the aforementioned limitations, this paper undertakes a comprehensive comparison of model capabilities at various pretraining intermediate checkpoints. Through this analysis, we confirm that specific downstream metrics exhibit similar training dynamics across models of different sizes, up to 67 billion parameters. In addition to our core findings, we've reproduced Amber and OpenLLaMA, releasing their intermediate checkpoints. This initiative offers valuable resources to the research community and facilitates the verification and exploration of LLM pretraining by open-source researchers. Besides, we provide empirical summaries, including performance comparisons of different models and capabilities, and tuition of key metrics for different training phases. Based on these findings, we provide a more user-friendly strategy for evaluating the optimization state, offering guidance for establishing a stable pretraining process.

Work on scaling laws has found that large language models (LMs) show predictable improvements to overall loss with increased scale (model size, training data, and compute). Here, we present evidence for the claim that LMs may show inverse scaling, or worse task performance with increased scale, e.g., due to flaws in the training objective and data. We present empirical evidence of inverse scaling on 11 datasets collected by running a public contest, the Inverse Scaling Prize, with a substantial prize pool. Through analysis of the datasets, along with other examples found in the literature, we identify four potential causes of inverse scaling: (i) preference to repeat memorized sequences over following in-context instructions, (ii) imitation of undesirable patterns in the training data, (iii) tasks containing an easy distractor task which LMs could focus on, rather than the harder real task, and (iv) correct but misleading few-shot demonstrations of the task. We release the winning datasets at https://inversescaling.com/data to allow for further investigation of inverse scaling. Our tasks have helped drive the discovery of U-shaped and inverted-U scaling trends, where an initial trend reverses, suggesting that scaling trends are less reliable at predicting the behavior of larger-scale models than previously understood. Overall, our results suggest that there are tasks for which increased model scale alone may not lead to progress, and that more careful thought needs to go into the data and objectives for training language models.

Offline reinforcement learning (RL) methodologies enforce constraints on the policy to adhere closely to the behavior policy, thereby stabilizing value learning and mitigating the selection of out-of-distribution (OOD) actions during test time. Conventional approaches apply identical constraints for both value learning and test time inference. However, our findings indicate that the constraints suitable for value estimation may in fact be excessively restrictive for action selection during test time. To address this issue, we propose a Mildly Constrained Evaluation Policy (MCEP) for test time inference with a more constrained target policy for value estimation. Since the target policy has been adopted in various prior approaches, MCEP can be seamlessly integrated with them as a plug-in. We instantiate MCEP based on TD3-BC [Fujimoto and Gu, 2021] and AWAC [Nair et al., 2020] algorithms. The empirical results on MuJoCo locomotion tasks show that the MCEP significantly outperforms the target policy and achieves competitive results to state-of-the-art offline RL methods. The codes are open-sourced at https://github.com/egg-west/MCEP.git.

Testing is an integral part of the software development process. Yet, writing tests is time-consuming and therefore often neglected. Classical test generation tools such as EvoSuite generate behavioral test suites by optimizing for coverage, but tend to produce tests that are hard to understand. Language models trained on code can generate code that is highly similar to that written by humans, but current models are trained to generate each file separately, as is standard practice in natural language processing, and thus fail to consider the code-under-test context when producing a test file. In this work, we propose the Aligned Code And Tests Language Model (CAT-LM), a GPT-style language model with 2.7 Billion parameters, trained on a corpus of Python and Java projects. We utilize a novel pretraining signal that explicitly considers the mapping between code and test files when available. We also drastically increase the maximum sequence length of inputs to 8,192 tokens, 4x more than typical code generation models, to ensure that the code context is available to the model when generating test code. We analyze its usefulness for realistic applications, showing that sampling with filtering (e.g., by compilability, coverage) allows it to efficiently produce tests that achieve coverage similar to ones written by developers while resembling their writing style. By utilizing the code context, CAT-LM generates more valid tests than even much larger language models trained with more data (CodeGen 16B and StarCoder) and substantially outperforms a recent test-specific model (TeCo) at test completion. Overall, our work highlights the importance of incorporating software-specific insights when training language models for code and paves the way to more powerful automated test generation.

Code generation models can help improve many common software tasks ranging from code completion to defect prediction. Most of the existing benchmarks for code generation LLMs focus on code authoring or code completion. Surprisingly, there has been far less effort dedicated to benchmarking software testing, despite the strong correlation between well-tested software and effective bug detection. To address this gap, we create and release TestGenEval, a large-scale benchmark to measure test generation performance. Based on SWEBench, TestGenEval comprises 68,647 tests from 1,210 code and test file pairs across 11 well-maintained Python repositories. It covers initial tests authoring, test suite completion, and code coverage improvements. Test authoring simulates the process of a developer writing a test suite from scratch, while test completion mimics the scenario where a developer aims to improve the coverage of an existing test suite. We evaluate several popular models, with sizes ranging from 7B to 405B parameters. Our detailed analysis highlights TestGenEval's contribution to a comprehensive evaluation of test generation performance. In particular, models struggle to generate high-coverage test suites, with the best model, GPT-4o, achieving an average coverage of only 35.2%. This is primarily due to models struggling to reason about execution, and their frequent assertion errors when addressing complex code paths.

The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their parameters while processing an input. For these models, parameter count and computational requirement form two independent axes along which an increase leads to better performance. In this work we derive and justify scaling laws defined on these two variables which generalize those known for standard language models and describe the performance of a wide range of routing architectures trained via three different techniques. Afterwards we provide two applications of these laws: first deriving an Effective Parameter Count along which all models scale at the same rate, and then using the scaling coefficients to give a quantitative comparison of the three routing techniques considered. Our analysis derives from an extensive evaluation of Routing Networks across five orders of magnitude of size, including models with hundreds of experts and hundreds of billions of parameters.

The ever-growing ecosystem of LLMs has posed a challenge in selecting the most appropriate pre-trained model to fine-tune amidst a sea of options. Given constrained resources, fine-tuning all models and making selections afterward is unrealistic. In this work, we formulate this resource-constrained selection task into predicting fine-tuning performance and illustrate its natural connection with scaling laws. Unlike pre-training, We find that the fine-tuning scaling curve includes not just the well-known "power phase" but also the previously unobserved "pre-power phase". We also explain why existing scaling laws fail to capture this phase transition phenomenon both theoretically and empirically. To address this, we introduce the concept of "pre-learned data size" into our rectified scaling law, which overcomes theoretical limitations and fits experimental results much better. By leveraging our law, we propose a novel LLM selection algorithm that selects the near-optimal model with hundreds of times less resource consumption, while other methods may provide negatively correlated selection.

This paper describes an AI agent that plays the popular first-person-shooter (FPS) video game `Counter-Strike; Global Offensive' (CSGO) from pixel input. The agent, a deep neural network, matches the performance of the medium difficulty built-in AI on the deathmatch game mode, whilst adopting a humanlike play style. Unlike much prior work in games, no API is available for CSGO, so algorithms must train and run in real-time. This limits the quantity of on-policy data that can be generated, precluding many reinforcement learning algorithms. Our solution uses behavioural cloning - training on a large noisy dataset scraped from human play on online servers (4 million frames, comparable in size to ImageNet), and a smaller dataset of high-quality expert demonstrations. This scale is an order of magnitude larger than prior work on imitation learning in FPS games.

The recent rapid progress in (self) supervised learning models is in large part predicted by empirical scaling laws: a model's performance scales proportionally to its size. Analogous scaling laws remain elusive for reinforcement learning domains, however, where increasing the parameter count of a model often hurts its final performance. In this paper, we demonstrate that incorporating Mixture-of-Expert (MoE) modules, and in particular Soft MoEs (Puigcerver et al., 2023), into value-based networks results in more parameter-scalable models, evidenced by substantial performance increases across a variety of training regimes and model sizes. This work thus provides strong empirical evidence towards developing scaling laws for reinforcement learning.

We find that the cross-entropy loss curves of neural language models empirically adhere to a scaling law with learning rate (LR) annealing over training steps (s): $L(s) = L_0 + Acdot S_1^{-alpha} - Ccdot S_2 Where S_1 is forward area and S_2$ is learning rate annealing area. This formulation takes into account two factors: (1) The forward scaling defined as typical scaling law, and (2) the additional loss drop brought by LR annealing. Therefore, this formulation can describe the full loss curve at each step, rather than the single loss point at the end of training. Applying the scaling law with LR annealing and fitting only one or two training curves, we can accurately predict the loss of language model training at any given step and across any learning rate scheduler (LRS). Furthermore, this equation accurately describes the dynamics during training process, and provides a theoretical verification and explanation for numerous experimental findings of previous studies, particularly those focusing on LR schedule and LR annealing. The resulting insights, also serve as a guide for researchers to select critical LRS in advance by prediction using our equation. Most significantly, since all the points in a full training curve follow the equation, we can achieve accurate loss prediction at any given step across any learning rate scheduler, while expending less than 1\% of the computational cost required by the chinchilla scaling law to fit language modeling loss. This approach extremely democratizes scaling law fitting and predicting in developing large language models.

Insertion of hardware Trojans (HTs) in integrated circuits is a pernicious threat. Since HTs are activated under rare trigger conditions, detecting them using random logic simulations is infeasible. In this work, we design a reinforcement learning (RL) agent that circumvents the exponential search space and returns a minimal set of patterns that is most likely to detect HTs. Experimental results on a variety of benchmarks demonstrate the efficacy and scalability of our RL agent, which obtains a significant reduction (169times) in the number of test patterns required while maintaining or improving coverage (95.75%) compared to the state-of-the-art techniques.

It is a common belief that large language models (LLMs) are better than smaller-sized ones. However, larger models also require significantly more time and compute during inference. This begs the question: what happens when both models operate under the same budget? (e.g., compute, run-time). To address this question, we analyze code generation LLMs of various sizes and make comparisons such as running a 70B model once vs. generating five outputs from a 13B model. We consider a standard unit-test setup, which can be used to select the correct output from the smaller model. Our findings reveal that the repeated use of smaller models can yield consistent improvements, with gains of up to 15% across five tasks. On the other hand, in scenarios where unit-tests are unavailable, a ranking-based selection of candidates from the smaller model falls short of the performance of a single output from larger ones. Our results highlight the potential of using smaller models instead of larger ones, and the importance of studying approaches for ranking LLM outputs.

Testing and evaluation is a critical step in the development and deployment of connected and automated vehicles (CAVs). Due to the black-box property and various types of CAVs, how to test and evaluate CAVs adaptively remains a major challenge. Many approaches have been proposed to adaptively generate testing scenarios during the testing process. However, most existing approaches cannot be applied to complex scenarios, where the variables needed to define such scenarios are high dimensional. Towards filling this gap, the adaptive testing with sparse control variates method is proposed in this paper. Instead of adaptively generating testing scenarios, our approach evaluates CAVs' performances by adaptively utilizing the testing results. Specifically, each testing result is adjusted using multiple linear regression techniques based on control variates. As the regression coefficients can be adaptively optimized for the CAV under test, using the adjusted results can reduce the estimation variance, compared with using the testing results directly. To overcome the high dimensionality challenge, sparse control variates are utilized only for the critical variables of testing scenarios. To validate the proposed method, the high-dimensional overtaking scenarios are investigated, and the results demonstrate that our approach can further accelerate the evaluation process by about 30 times.

In recent years, language models have drastically grown in size, and the abilities of these models have been shown to improve with scale. The majority of recent scaling laws studies focused on high-compute high-parameter count settings, leaving the question of when these abilities begin to emerge largely unanswered. In this paper, we investigate whether the effects of pre-training can be observed when the problem size is reduced, modeling a smaller, reduced-vocabulary language. We show the benefits of pre-training with masked language modeling (MLM) objective in models as small as 1.25M parameters, and establish a strong correlation between pre-training perplexity and downstream performance (GLUE benchmark). We examine downscaling effects, extending scaling laws to models as small as ~1M parameters. At this scale, we observe a break of the power law for compute-optimal models and show that the MLM loss does not scale smoothly with compute-cost (FLOPs) below 2.2 times 10^{15} FLOPs. We also find that adding layers does not always benefit downstream performance.

Training algorithms, broadly construed, are an essential part of every deep learning pipeline. Training algorithm improvements that speed up training across a wide variety of workloads (e.g., better update rules, tuning protocols, learning rate schedules, or data selection schemes) could save time, save computational resources, and lead to better, more accurate, models. Unfortunately, as a community, we are currently unable to reliably identify training algorithm improvements, or even determine the state-of-the-art training algorithm. In this work, using concrete experiments, we argue that real progress in speeding up training requires new benchmarks that resolve three basic challenges faced by empirical comparisons of training algorithms: (1) how to decide when training is complete and precisely measure training time, (2) how to handle the sensitivity of measurements to exact workload details, and (3) how to fairly compare algorithms that require hyperparameter tuning. In order to address these challenges, we introduce a new, competitive, time-to-result benchmark using multiple workloads running on fixed hardware, the AlgoPerf: Training Algorithms benchmark. Our benchmark includes a set of workload variants that make it possible to detect benchmark submissions that are more robust to workload changes than current widely-used methods. Finally, we evaluate baseline submissions constructed using various optimizers that represent current practice, as well as other optimizers that have recently received attention in the literature. These baseline results collectively demonstrate the feasibility of our benchmark, show that non-trivial gaps between methods exist, and set a provisional state-of-the-art for future benchmark submissions to try and surpass.

Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.

Neural network scaling has been critical for improving the model quality in many real-world machine learning applications with vast amounts of training data and compute. Although this trend of scaling is affirmed to be a sure-fire approach for better model quality, there are challenges on the path such as the computation cost, ease of programming, and efficient implementation on parallel devices. GShard is a module composed of a set of lightweight annotation APIs and an extension to the XLA compiler. It provides an elegant way to express a wide range of parallel computation patterns with minimal changes to the existing model code. GShard enabled us to scale up multilingual neural machine translation Transformer model with Sparsely-Gated Mixture-of-Experts beyond 600 billion parameters using automatic sharding. We demonstrate that such a giant model can efficiently be trained on 2048 TPU v3 accelerators in 4 days to achieve far superior quality for translation from 100 languages to English compared to the prior art.

Time is an important dimension in our physical world. Lots of facts can evolve with respect to time. For example, the U.S. President might change every four years. Therefore, it is important to consider the time dimension and empower the existing QA models to reason over time. However, the existing QA datasets contain rather few time-sensitive questions, hence not suitable for diagnosing or benchmarking the model's temporal reasoning capability. In order to promote research in this direction, we propose to construct a time-sensitive QA dataset. The dataset is constructed by 1) mining time-evolving facts from WikiData and aligning them to their corresponding Wikipedia page, 2) employing crowd workers to verify and calibrate these noisy facts, 3) generating question-answer pairs based on the annotated time-sensitive facts. Our dataset poses challenges in the aspect of both temporal understanding and temporal reasoning. We evaluate different SoTA long-document QA systems like BigBird and FiD on our dataset. The best-performing model FiD can only achieve 46\% accuracy, still far behind the human performance of 87\%. We demonstrate that these models are still lacking the ability to perform consistent temporal reasoning. Therefore, we believe that our dataset could serve as a benchmark to develop NLP models more sensitive to temporal shifts. The dataset and code are released in~https://github.com/wenhuchen/Time-Sensitive-QA.

We present a self-supervised, time-to-event (TTE) foundation model called MOTOR (Many Outcome Time Oriented Representations) which is pretrained on timestamped sequences of events in electronic health records (EHR) and health insurance claims. TTE models are used for estimating the probability distribution of the time until a specific event occurs, which is an important task in medical settings. TTE models provide many advantages over classification using fixed time horizons, including naturally handling censored observations, but are challenging to train with limited labeled data. MOTOR addresses this challenge by pretraining on up to 55M patient records (9B clinical events). We evaluate MOTOR's transfer learning performance on 19 tasks, across 3 patient databases (a private EHR system, MIMIC-IV, and Merative claims data). Task-specific models adapted from MOTOR improve time-dependent C statistics by 4.6% over state-of-the-art, improve label efficiency by up to 95% ,and are more robust to temporal distributional shifts. We further evaluate cross-site portability by adapting our MOTOR foundation model for six prediction tasks on the MIMIC-IV dataset, where it outperforms all baselines. MOTOR is the first foundation model for medical TTE predictions and we release a 143M parameter pretrained model for research use at [redacted URL].

We investigate the rate at which algorithms for pre-training language models have improved since the advent of deep learning. Using a dataset of over 200 language model evaluations on Wikitext and Penn Treebank spanning 2012-2023, we find that the compute required to reach a set performance threshold has halved approximately every 8 months, with a 95% confidence interval of around 5 to 14 months, substantially faster than hardware gains per Moore's Law. We estimate augmented scaling laws, which enable us to quantify algorithmic progress and determine the relative contributions of scaling models versus innovations in training algorithms. Despite the rapid pace of algorithmic progress and the development of new architectures such as the transformer, our analysis reveals that the increase in compute made an even larger contribution to overall performance improvements over this time period. Though limited by noisy benchmark data, our analysis quantifies the rapid progress in language modeling, shedding light on the relative contributions from compute and algorithms.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

We introduce MOMENT, a family of open-source foundation models for general-purpose time-series analysis. Pre-training large models on time-series data is challenging due to (1) the absence of a large and cohesive public time-series repository, and (2) diverse time-series characteristics which make multi-dataset training onerous. Additionally, (3) experimental benchmarks to evaluate these models, especially in scenarios with limited resources, time, and supervision, are still in their nascent stages. To address these challenges, we compile a large and diverse collection of public time-series, called the Time-series Pile, and systematically tackle time-series-specific challenges to unlock large-scale multi-dataset pre-training. Finally, we build on recent work to design a benchmark to evaluate time-series foundation models on diverse tasks and datasets in limited supervision settings. Experiments on this benchmark demonstrate the effectiveness of our pre-trained models with minimal data and task-specific fine-tuning. Finally, we present several interesting empirical observations about large pre-trained time-series models. Our code is available anonymously at anonymous.4open.science/r/BETT-773F/.

Program synthesis methods aim to automatically generate programs restricted to a language that can explain a given specification of input-output pairs. While purely symbolic approaches suffer from a combinatorial search space, recent methods leverage neural networks to learn distributions over program structures to narrow this search space significantly, enabling more efficient search. However, for challenging problems, it remains difficult to train models to perform program synthesis in one shot, making test-time search essential. Most neural methods lack structured search mechanisms during inference, relying instead on stochastic sampling or gradient updates, which can be inefficient. In this work, we propose the Latent Program Network (LPN), a general algorithm for program induction that learns a distribution over latent programs in a continuous space, enabling efficient search and test-time adaptation. We explore how to train these networks to optimize for test-time computation and demonstrate the use of gradient-based search both during training and at test time. We evaluate LPN on ARC-AGI, a program synthesis benchmark that evaluates performance by generalizing programs to new inputs rather than explaining the underlying specification. We show that LPN can generalize beyond its training distribution and adapt to unseen tasks by utilizing test-time computation, outperforming algorithms without test-time adaptation mechanisms.

The remarkable success of large language pretraining and the discovery of scaling laws signify a paradigm shift in machine learning. Notably, the primary objective has evolved from minimizing generalization error to reducing approximation error, and the most effective strategy has transitioned from regularization (in a broad sense) to scaling up models. This raises a critical question: Do the established principles that proved successful in the generalization-centric era remain valid in this new era of scaling? This paper examines several influential regularization-based principles that may no longer hold true in the scaling-centric, large language model (LLM) era. These principles include explicit L2 regularization and implicit regularization through small batch sizes and large learning rates. Additionally, we identify a new phenomenon termed ``scaling law crossover,'' where two scaling curves intersect at a certain scale, implying that methods effective at smaller scales may not generalize to larger ones. Together, these observations highlight two fundamental questions within this new paradigm: bullet Guiding Principles for Scaling: If regularization is no longer the primary guiding principle for model design, what new principles are emerging to guide scaling? bullet Model Comparison at Scale: How to reliably and effectively compare models at the scale where only a single experiment is feasible?

Traditional fixed test sets fall short in evaluating open-ended capabilities of foundation models. To address this, we propose ONEBench(OpeN-Ended Benchmarking), a new testing paradigm that consolidates individual evaluation datasets into a unified, ever-expanding sample pool. ONEBench allows users to generate custom, open-ended evaluation benchmarks from this pool, corresponding to specific capabilities of interest. By aggregating samples across test sets, ONEBench enables the assessment of diverse capabilities beyond those covered by the original test sets, while mitigating overfitting and dataset bias. Most importantly, it frames model evaluation as a collective process of selecting and aggregating sample-level tests. The shift from task-specific benchmarks to ONEBench introduces two challenges: (1)heterogeneity and (2)incompleteness. Heterogeneity refers to the aggregation over diverse metrics, while incompleteness describes comparing models evaluated on different data subsets. To address these challenges, we explore algorithms to aggregate sparse measurements into reliable model scores. Our aggregation algorithm ensures identifiability(asymptotically recovering ground-truth scores) and rapid convergence, enabling accurate model ranking with less data. On homogenous datasets, we show our aggregation algorithm provides rankings that highly correlate with those produced by average scores. We also demonstrate robustness to ~95% of measurements missing, reducing evaluation cost by up to 20x with little-to-no change in model rankings. We introduce ONEBench-LLM for language models and ONEBench-LMM for vision-language models, unifying evaluations across these domains. Overall, we present a technique for open-ended evaluation, which can aggregate over incomplete, heterogeneous sample-level measurements to continually grow a benchmark alongside the rapidly developing foundation models.

Training large neural networks is known to be time-consuming, with the learning duration taking days or even weeks. To address this problem, large-batch optimization was introduced. This approach demonstrated that scaling mini-batch sizes with appropriate learning rate adjustments can speed up the training process by orders of magnitude. While long training time was not typically a major issue for model-free deep offline RL algorithms, recently introduced Q-ensemble methods achieving state-of-the-art performance made this issue more relevant, notably extending the training duration. In this work, we demonstrate how this class of methods can benefit from large-batch optimization, which is commonly overlooked by the deep offline RL community. We show that scaling the mini-batch size and naively adjusting the learning rate allows for (1) a reduced size of the Q-ensemble, (2) stronger penalization of out-of-distribution actions, and (3) improved convergence time, effectively shortening training duration by 3-4x times on average.

Continuous-time event sequences play a vital role in real-world domains such as healthcare, finance, online shopping, social networks, and so on. To model such data, temporal point processes (TPPs) have emerged as the most natural and competitive models, making a significant impact in both academic and application communities. Despite the emergence of many powerful models in recent years, there hasn't been a central benchmark for these models and future research endeavors. This lack of standardization impedes researchers and practitioners from comparing methods and reproducing results, potentially slowing down progress in this field. In this paper, we present EasyTPP, the first central repository of research assets (e.g., data, models, evaluation programs, documentations) in the area of event sequence modeling. Our EasyTPP makes several unique contributions to this area: a unified interface of using existing datasets and adding new datasets; a wide range of evaluation programs that are easy to use and extend as well as facilitate reproducible research; implementations of popular neural TPPs, together with a rich library of modules by composing which one could quickly build complex models. All the data and implementation can be found at https://github.com/ant-research/EasyTemporalPointProcess. We will actively maintain this benchmark and welcome contributions from other researchers and practitioners. Our benchmark will help promote reproducible research in this field, thus accelerating research progress as well as making more significant real-world impacts.

Hoffmann et al. (2022) propose three methods for estimating a compute-optimal scaling law. We attempt to replicate their third estimation procedure, which involves fitting a parametric loss function to a reconstruction of data from their plots. We find that the reported estimates are inconsistent with their first two estimation methods, fail at fitting the extracted data, and report implausibly narrow confidence intervals--intervals this narrow would require over 600,000 experiments, while they likely only ran fewer than 500. In contrast, our rederivation of the scaling law using the third approach yields results that are compatible with the findings from the first two estimation procedures described by Hoffmann et al.

Scaling data and compute is critical to the success of machine learning. However, scaling demands predictability: we want methods to not only perform well with more compute or data, but also have their performance be predictable from small-scale runs, without running the large-scale experiment. In this paper, we show that value-based off-policy RL methods are predictable despite community lore regarding their pathological behavior. First, we show that data and compute requirements to attain a given performance level lie on a Pareto frontier, controlled by the updates-to-data (UTD) ratio. By estimating this frontier, we can predict this data requirement when given more compute, and this compute requirement when given more data. Second, we determine the optimal allocation of a total resource budget across data and compute for a given performance and use it to determine hyperparameters that maximize performance for a given budget. Third, this scaling behavior is enabled by first estimating predictable relationships between hyperparameters, which is used to manage effects of overfitting and plasticity loss unique to RL. We validate our approach using three algorithms: SAC, BRO, and PQL on DeepMind Control, OpenAI gym, and IsaacGym, when extrapolating to higher levels of data, compute, budget, or performance.

Context: Test-driven development (TDD) is a widely employed software development practice that involves developing test cases based on requirements prior to writing the code. Although various methods for automated test case generation have been proposed, they are not specifically tailored for TDD, where requirements instead of code serve as input. Objective: In this paper, we introduce a text-to-testcase generation approach based on a large language model (GPT-3.5) that is fine-tuned on our curated dataset with an effective prompt design. Method: Our approach involves enhancing the capabilities of basic GPT-3.5 for text-to-testcase generation task that is fine-tuned on our curated dataset with an effective prompting design. We evaluated the effectiveness of our approach using a span of five large-scale open-source software projects. Results: Our approach generated 7k test cases for open source projects, achieving 78.5% syntactic correctness, 67.09% requirement alignment, and 61.7% code coverage, which substantially outperforms all other LLMs (basic GPT-3.5, Bloom, and CodeT5). In addition, our ablation study demonstrates the substantial performance improvement of the fine-tuning and prompting components of the GPT-3.5 model. Conclusions: These findings lead us to conclude that fine-tuning and prompting should be considered in the future when building a language model for the text-to-testcase generation task

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.

Testing plays a crucial role in the software development cycle, enabling the detection of bugs, vulnerabilities, and other undesirable behaviors. To perform software testing, testers need to write code snippets that execute the program under test. Recently, researchers have recognized the potential of large language models (LLMs) in software testing. However, there remains a lack of fair comparisons between different LLMs in terms of test case generation capabilities. In this paper, we propose TESTEVAL, a novel benchmark for test case generation with LLMs. We collect 210 Python programs from an online programming platform, LeetCode, and design three different tasks: overall coverage, targeted line/branch coverage, and targeted path coverage. We further evaluate sixteen popular LLMs, including both commercial and open-source ones, on TESTEVAL. We find that generating test cases to cover specific program lines/branches/paths is still challenging for current LLMs, indicating a lack of ability to comprehend program logic and execution paths. We have open-sourced our dataset and benchmark pipelines at https://llm4softwaretesting.github.io to contribute and accelerate future research on LLMs for software testing.

In unsupervised learning, collecting more data is not always a costly process unlike the training. For example, it is not hard to enlarge the 40GB WebText used for training GPT-2 by modifying its sampling methodology considering how many webpages there are in the Internet. On the other hand, given that training on this dataset already costs tens of thousands of dollars, training on a larger dataset naively is not cost-wise feasible. In this paper, we suggest to train on a larger dataset for only one epoch unlike the current practice, in which the unsupervised models are trained for from tens to hundreds of epochs. Furthermore, we suggest to adjust the model size and the number of iterations to be performed appropriately. We show that the performance of Transformer language model becomes dramatically improved in this way, especially if the original number of epochs is greater. For example, by replacing the training for 10 epochs with the one epoch training, this translates to 1.9-3.3x speedup in wall-clock time in our settings and more if the original number of epochs is greater. Under one epoch training, no overfitting occurs, and regularization method does nothing but slows down the training. Also, the curve of test loss over iterations follows power-law extensively. We compare the wall-clock time of the training of models with different parameter budget under one epoch training, and we show that size/iteration adjustment based on our proposed heuristics leads to 1-2.7x speedup in our cases. With the two methods combined, we achieve 3.3-5.1x speedup. Finally, we speculate various implications of one epoch training and size/iteration adjustment. In particular, based on our analysis we believe that we can reduce the cost to train the state-of-the-art models as BERT and GPT-2 dramatically, maybe even by the factor of 10.

The process of creating training data to teach models is currently driven by humans, who manually analyze model weaknesses and plan how to create data that improves a student model. Recent approaches using LLMs as annotators reduce human effort, but still require humans to interpret feedback from evaluations and control the LLM to produce data the student needs. Automating this labor-intensive process by creating autonomous data generation agents - or teachers - is desirable, but requires environments that can simulate the feedback-driven, iterative, closed loop of data creation. To enable rapid and scalable testing for such agents and their modules, we introduce DataEnvGym, a testbed of teacher environments for data generation agents. DataEnvGym frames data generation as a sequential decision-making task, involving an agent consisting of a data generation policy (which generates a plan for creating training data) and a data generation engine (which transforms the plan into data), inside an environment that provides student feedback. The agent's goal is to improve student performance. Students are iteratively trained and evaluated on generated data, with their feedback (in the form of errors or weak skills) being reported to the agent after each iteration. DataEnvGym includes multiple teacher environment instantiations across 3 levels of structure in the state representation and action space. More structured environments are based on inferred skills and offer more interpretability and curriculum control. We support 3 diverse tasks (math, code, and VQA) and test multiple students and teachers. Example agents in our teaching environments can iteratively improve students across tasks and settings. Moreover, we show that environments teach different skill levels and test variants of key modules, pointing to future work in improving data generation agents, engines, and feedback mechanisms.

Many studies on scaling laws consider basic factors such as model size, model shape, dataset size, and compute power. These factors are easily tunable and represent the fundamental elements of any machine learning setup. But researchers have also employed more complex factors to estimate the test error and generalization performance with high predictability. These factors are generally specific to the domain or application. For example, feature diversity was primarily used for promoting syn-to-real transfer by Chen et al. (2021). With numerous scaling factors defined in previous works, it would be interesting to investigate how these factors may affect overall generalization performance in the context of self-supervised learning with CNN models. How do individual factors promote generalization, which includes varying depth, width, or the number of training epochs with early stopping? For example, does higher feature diversity result in higher accuracy held in complex settings other than a syn-to-real transfer? How do these factors depend on each other? We found that the last layer is the most diversified throughout the training. However, while the model's test error decreases with increasing epochs, its diversity drops. We also discovered that diversity is directly related to model width.

Evaluating anomaly detection algorithms in time series data is critical as inaccuracies can lead to flawed decision-making in various domains where real-time analytics and data-driven strategies are essential. Traditional performance metrics assume iid data and fail to capture the complex temporal dynamics and specific characteristics of time series anomalies, such as early and delayed detections. We introduce Proximity-Aware Time series anomaly Evaluation (PATE), a novel evaluation metric that incorporates the temporal relationship between prediction and anomaly intervals. PATE uses proximity-based weighting considering buffer zones around anomaly intervals, enabling a more detailed and informed assessment of a detection. Using these weights, PATE computes a weighted version of the area under the Precision and Recall curve. Our experiments with synthetic and real-world datasets show the superiority of PATE in providing more sensible and accurate evaluations than other evaluation metrics. We also tested several state-of-the-art anomaly detectors across various benchmark datasets using the PATE evaluation scheme. The results show that a common metric like Point-Adjusted F1 Score fails to characterize the detection performances well, and that PATE is able to provide a more fair model comparison. By introducing PATE, we redefine the understanding of model efficacy that steers future studies toward developing more effective and accurate detection models.

Inference-time techniques are emerging as highly effective tools to enhance large language model (LLM) capabilities. However, best practices for developing systems that combine these techniques remain underdeveloped due to our limited understanding of the utility of individual inference-time techniques and the interactions between them. Additionally, efficiently and automatically searching the space of model choices, inference-time techniques, and their compositions is challenging due to the large design space. To address these challenges, we introduce Archon, a modular framework for selecting, combining, and stacking layers of inference-time techniques to construct optimized LLM systems for target benchmarks. Rather than relying on a single LLM called once, we leverage a diverse set of LLMs and inference-time techniques, creating LLM systems greater than the sum of their parts. Archon defines an extensible design space, encompassing techniques such as generation ensembling, repeated sampling, ranking, fusion, critiquing, verification, and unit testing. It transforms the problem of building LLM systems into a hyperparameter optimization objective. Given the available LLMs, inference-time techniques, and compute budget, Archon utilizes hyperparameter search techniques to discover optimized architectures for target benchmark(s). We evaluate Archon architectures across a range of instruction-following, reasoning, and coding benchmarks, including MT-Bench, Arena-Hard-Auto, AlpacaEval 2.0, MixEval, MixEval Hard, MATH, and CodeContests. Archon architectures outperform frontier models, such as GPT-4o and Claude 3.5 Sonnet, on these benchmarks, achieving an average accuracy increase of 15.1 percentage points by using all available LLMs. We make our code and datasets available publicly on Github: https://github.com/ScalingIntelligence/Archon.

Alternatives to backpropagation have long been studied to better understand how biological brains may learn. Recently, they have also garnered interest as a way to train neural networks more efficiently. By relaxing constraints inherent to backpropagation (e.g., symmetric feedforward and feedback weights, sequential updates), these methods enable promising prospects, such as local learning. However, the tradeoffs between different methods in terms of final task performance, convergence speed, and ultimately compute and data requirements are rarely outlined. In this work, we use scaling laws to study the ability of Direct Feedback Alignment~(DFA) to train causal decoder-only Transformers efficiently. Scaling laws provide an overview of the tradeoffs implied by a modeling decision, up to extrapolating how it might transfer to increasingly large models. We find that DFA fails to offer more efficient scaling than backpropagation: there is never a regime for which the degradation in loss incurred by using DFA is worth the potential reduction in compute budget. Our finding comes at variance with previous beliefs in the alternative training methods community, and highlights the need for holistic empirical approaches to better understand modeling decisions.

Mathematical capabilities were previously believed to emerge in common language models only at a very large scale or require extensive math-related pre-training. This paper shows that the LLaMA-2 7B model with common pre-training already exhibits strong mathematical abilities, as evidenced by its impressive accuracy of 97.7% and 72.0% on the GSM8K and MATH benchmarks, respectively, when selecting the best response from 256 random generations. The primary issue with the current base model is the difficulty in consistently eliciting its inherent mathematical capabilities. Notably, the accuracy for the first answer drops to 49.5% and 7.9% on the GSM8K and MATH benchmarks, respectively. We find that simply scaling up the SFT data can significantly enhance the reliability of generating correct answers. However, the potential for extensive scaling is constrained by the scarcity of publicly available math questions. To overcome this limitation, we employ synthetic data, which proves to be nearly as effective as real data and shows no clear saturation when scaled up to approximately one million samples. This straightforward approach achieves an accuracy of 82.6% on GSM8K and 40.6% on MATH using LLaMA-2 7B models, surpassing previous models by 14.2% and 20.8%, respectively. We also provide insights into scaling behaviors across different reasoning complexities and error types.

Neural scaling laws (NSL) refer to the phenomenon where model performance improves with scale. Sharma & Kaplan analyzed NSL using approximation theory and predict that MSE losses decay as N^{-alpha}, alpha=4/d, where N is the number of model parameters, and d is the intrinsic input dimension. Although their theory works well for some cases (e.g., ReLU networks), we surprisingly find that a simple 1D problem y=x^2 manifests a different scaling law (alpha=1) from their predictions (alpha=4). We opened the neural networks and found that the new scaling law originates from lottery ticket ensembling: a wider network on average has more "lottery tickets", which are ensembled to reduce the variance of outputs. We support the ensembling mechanism by mechanistically interpreting single neural networks, as well as studying them statistically. We attribute the N^{-1} scaling law to the "central limit theorem" of lottery tickets. Finally, we discuss its potential implications for large language models and statistical physics-type theories of learning.

In domain generalization (DG), the target domain is unknown when the model is being trained, and the trained model should successfully work on an arbitrary (and possibly unseen) target domain during inference. This is a difficult problem, and despite active studies in recent years, it remains a great challenge. In this paper, we take a simple yet effective approach to tackle this issue. We propose test-time style shifting, which shifts the style of the test sample (that has a large style gap with the source domains) to the nearest source domain that the model is already familiar with, before making the prediction. This strategy enables the model to handle any target domains with arbitrary style statistics, without additional model update at test-time. Additionally, we propose style balancing, which provides a great platform for maximizing the advantage of test-time style shifting by handling the DG-specific imbalance issues. The proposed ideas are easy to implement and successfully work in conjunction with various other DG schemes. Experimental results on different datasets show the effectiveness of our methods.

Offline reinforcement learning (RL) allows agents to learn effective, return-maximizing policies from a static dataset. Three popular algorithms for offline RL are Conservative Q-Learning (CQL), Behavior Cloning (BC), and Decision Transformer (DT), from the class of Q-Learning, Imitation Learning, and Sequence Modeling respectively. A key open question is: which algorithm is preferred under what conditions? We study this question empirically by exploring the performance of these algorithms across the commonly used D4RL and Robomimic benchmarks. We design targeted experiments to understand their behavior concerning data suboptimality, task complexity, and stochasticity. Our key findings are: (1) DT requires more data than CQL to learn competitive policies but is more robust; (2) DT is a substantially better choice than both CQL and BC in sparse-reward and low-quality data settings; (3) DT and BC are preferable as task horizon increases, or when data is obtained from human demonstrators; and (4) CQL excels in situations characterized by the combination of high stochasticity and low data quality. We also investigate architectural choices and scaling trends for DT on Atari and D4RL and make design/scaling recommendations. We find that scaling the amount of data for DT by 5x gives a 2.5x average score improvement on Atari.

The success of large pretrained models in natural language processing (NLP) and computer vision (CV) has opened new avenues for constructing foundation models for time series forecasting (TSF). Traditional TSF foundation models rely heavily on numerical data fitting. In contrast, the human brain is inherently skilled at processing visual information, prefer predicting future trends by observing visualized sequences. From a biomimetic perspective, utilizing models to directly process numerical sequences might not be the most effective route to achieving Artificial General Intelligence (AGI). This paper proposes ViTime, a novel Visual Intelligence-based foundation model for TSF. ViTime overcomes the limitations of numerical time series data fitting by utilizing visual data processing paradigms and employs a innovative data synthesis method during training, called Real Time Series (RealTS). Experiments on a diverse set of previously unseen forecasting datasets demonstrate that ViTime achieves state-of-the-art zero-shot performance, even surpassing the best individually trained supervised models in some situations. These findings suggest that visual intelligence can significantly enhance time series analysis and forecasting, paving the way for more advanced and versatile models in the field. The code for our framework is accessible at https://github.com/IkeYang/ViTime.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.

Large language model pre-training has become increasingly expensive, with most practitioners relying on scaling laws to allocate compute budgets for model size and training tokens, commonly referred to as Compute-Optimal or Chinchilla Optimal. In this paper, we hypothesize a new scaling law that suggests model performance depends mostly on the amount of compute spent for transformer-based models, independent of the specific allocation to model size and dataset size. Using this unified scaling law, we predict that (a) for inference efficiency, training should prioritize smaller model sizes and larger training datasets, and (b) assuming the exhaustion of available web datasets, scaling the model size might be the only way to further improve model performance.

Large language model (LLM) scaling laws are empirical formulas that estimate changes in model quality as a result of increasing parameter count and training data. However, these formulas, including the popular DeepMind Chinchilla scaling laws, neglect to include the cost of inference. We modify the Chinchilla scaling laws to calculate the optimal LLM parameter count and pre-training data size to train and deploy a model of a given quality and inference demand. We conduct our analysis both in terms of a compute budget and real-world costs and find that LLM researchers expecting reasonably large inference demand (~1B requests) should train models smaller and longer than Chinchilla-optimal.

Benchmarks play an important role in the development of machine learning algorithms. For example, research in reinforcement learning (RL) has been heavily influenced by available environments and benchmarks. However, RL environments are traditionally run on the CPU, limiting their scalability with typical academic compute. Recent advancements in JAX have enabled the wider use of hardware acceleration to overcome these computational hurdles, enabling massively parallel RL training pipelines and environments. This is particularly useful for multi-agent reinforcement learning (MARL) research. First of all, multiple agents must be considered at each environment step, adding computational burden, and secondly, the sample complexity is increased due to non-stationarity, decentralised partial observability, or other MARL challenges. In this paper, we present JaxMARL, the first open-source code base that combines ease-of-use with GPU enabled efficiency, and supports a large number of commonly used MARL environments as well as popular baseline algorithms. When considering wall clock time, our experiments show that per-run our JAX-based training pipeline is up to 12500x faster than existing approaches. This enables efficient and thorough evaluations, with the potential to alleviate the evaluation crisis of the field. We also introduce and benchmark SMAX, a vectorised, simplified version of the popular StarCraft Multi-Agent Challenge, which removes the need to run the StarCraft II game engine. This not only enables GPU acceleration, but also provides a more flexible MARL environment, unlocking the potential for self-play, meta-learning, and other future applications in MARL. We provide code at https://github.com/flairox/jaxmarl.

Time series has been left behind in the era of pre-training and transfer learning. While research in the fields of natural language processing and computer vision are enjoying progressively larger datasets to train massive models, the most popular time series datasets consist of only tens of thousands of time steps, limiting our ability to study the effectiveness of pre-training and scaling. Recent studies have also cast doubt on the need for expressive models and scale. To alleviate these issues, we introduce three large-scale time series forecasting datasets from the cloud operations (CloudOps) domain, the largest having billions of observations, enabling further study into pre-training and scaling of time series models. We build the empirical groundwork for studying pre-training and scaling of time series models and pave the way for future research by identifying a promising candidate architecture. We show that it is a strong zero-shot baseline and benefits from further scaling, both in model and dataset size. Accompanying these datasets and results is a suite of comprehensive benchmark results comparing classical and deep learning baselines to our pre-trained method - achieving a 27% reduction in error on the largest dataset. Code and datasets will be released.