Vision-language models (VLMs) trained via reinforcement learning with verifiable reward (RLVR) have shown notable progress in scaling test-time compute effectively. In this work, we investigate how synthesized RL data can further improve RLVR. To this end, we propose \textbf{SynthRL}-a scalable and guaranteed pipeline for automatic data scaling in reasoning-oriented RL training. SynthRL comprises three key stages: (1) selecting seed questions with appropriate distribution, (2) augmenting them into more challenging variants while preserving the original answers, and (3) a guaranteed verification stage that ensures near-perfect correctness and difficulty enhancement. Our empirical experiments demonstrate SynthRL's scalability and effectiveness. When applied to the MMK12 dataset, SynthRL synthesizes over 3.3K additional verifiable, challenging questions from approximately 8K seed samples. Models trained with our synthesized data achieve consistent gains across five out-of-domain visual math reasoning benchmarks, with a significant improvement over baseline models trained on seed data alone. Notably, detailed analysis reveals that the gains are more pronounced on the most challenging evaluation samples, highlighting SynthRL's effectiveness in eliciting deeper and more complex reasoning patterns.
Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training language models (LMs) on reasoning tasks that elicit emergent long chains of thought (CoTs). Unlike supervised learning, it updates the model using both correct and incorrect samples via policy gradients. To better understand its mechanism, we decompose the learning signal into reinforcing correct responses and penalizing incorrect ones, referred to as Positive and Negative Sample Reinforcement (PSR and NSR), respectively. We train Qwen2.5-Math-7B and Qwen3-4B on a mathematical reasoning dataset and uncover a surprising result: training with only negative samples -- without reinforcing correct responses -- can be highly effective: it consistently improves performance over the base model across the entire Pass@$k$ spectrum ($k$ up to $256$), often matching or surpassing PPO and GRPO. In contrast, reinforcing only correct responses improves Pass@$1$ but degrades performance at higher $k$, due to reduced diversity. These inference-scaling trends highlight that solely penalizing incorrect responses may contribute more to performance than previously recognized. Through gradient analysis, we show that NSR works by suppressing incorrect generations and redistributing probability mass toward other plausible candidates, guided by the model's prior beliefs. It refines the model's existing knowledge rather than introducing entirely new behaviors. Building on this insight, we propose a simple variant of the RL objective that upweights NSR, and show that it consistently improves overall Pass@$k$ performance on MATH, AIME 2025, and AMC23. Our code is available at https://github.com/TianHongZXY/RLVR-Decomposed.
The recent paradigm shift towards training large language models (LLMs) using DeepSeek-R1-Zero-style reinforcement learning (RL) on verifiable rewards has led to impressive advancements in code and mathematical reasoning. However, this methodology is limited to tasks where rule-based answer verification is possible and does not naturally extend to real-world domains such as chemistry, healthcare, engineering, law, biology, business, and economics. Current practical workarounds use an additional LLM as a model-based verifier; however, this introduces issues such as reliance on a strong verifier LLM, susceptibility to reward hacking, and the practical burden of maintaining the verifier model in memory during training. To address this and extend DeepSeek-R1-Zero-style training to general reasoning domains, we propose a verifier-free method (VeriFree) that bypasses answer verification and instead uses RL to directly maximize the probability of generating the reference answer. We compare VeriFree with verifier-based methods and demonstrate that, in addition to its significant practical benefits and reduced compute requirements, VeriFree matches and even surpasses verifier-based methods on extensive evaluations across MMLU-Pro, GPQA, SuperGPQA, and math-related benchmarks. Moreover, we provide insights into this method from multiple perspectives: as an elegant integration of training both the policy and implicit verifier in a unified model, and as a variational optimization approach. Code is available at https://github.com/sail-sg/VeriFree.
As test-time scaling becomes a pivotal research frontier in Large Language Models (LLMs) development, contemporary and advanced post-training methodologies increasingly focus on extending the generation length of long Chain-of-Thought (CoT) responses to enhance reasoning capabilities toward DeepSeek R1-like performance. However, recent studies reveal a persistent overthinking phenomenon in state-of-the-art reasoning models, manifesting as excessive redundancy or repetitive thinking patterns in long CoT responses. To address this issue, in this paper, we propose a simple yet effective two-stage reinforcement learning framework for achieving concise reasoning in LLMs, named ConciseR. Specifically, the first stage, using more training steps, aims to incentivize the model's reasoning capabilities via Group Relative Policy Optimization with clip-higher and dynamic sampling components (GRPO++), and the second stage, using fewer training steps, explicitly enforces conciseness and improves efficiency via Length-aware Group Relative Policy Optimization (L-GRPO). Significantly, ConciseR only optimizes response length once all rollouts of a sample are correct, following the "walk before you run" principle. Extensive experimental results demonstrate that our ConciseR model, which generates more concise CoT reasoning responses, outperforms recent state-of-the-art reasoning models with zero RL paradigm across AIME 2024, MATH-500, AMC 2023, Minerva, and Olympiad benchmarks.
Reasoning models have made rapid progress on many benchmarks involving math, code, and science. Yet, there are still many open questions about the best training recipes for reasoning since state-of-the-art models often rely on proprietary datasets with little to no public information available. To address this, the goal of the OpenThoughts project is to create open-source datasets for training reasoning models. After initial explorations, our OpenThoughts2-1M dataset led to OpenThinker2-32B, the first model trained on public reasoning data to match DeepSeek-R1-Distill-32B on standard reasoning benchmarks such as AIME and LiveCodeBench. We then improve our dataset further by systematically investigating each step of our data generation pipeline with 1,000+ controlled experiments, which led to OpenThoughts3. Scaling the pipeline to 1.2M examples and using QwQ-32B as teacher yields our OpenThoughts3-7B model, which achieves state-of-the-art results: 53% on AIME 2025, 51% on LiveCodeBench 06/24-01/25, and 54% on GPQA Diamond - improvements of 15.3, 17.2, and 20.5 percentage points compared to the DeepSeek-R1-Distill-Qwen-7B. All of our datasets and models are available on https://openthoughts.ai.
Large language models can exhibit unexpected behavior in the blink of an eye. In a recent computer use demo, a language model switched from coding to Googling pictures of Yellowstone, and these sudden shifts in behavior have also been observed in reasoning patterns and jailbreaks. This phenomenon is not unique to autoregressive models: in diffusion models, key features of the final output are decided in narrow ``critical windows'' of the generation process. In this work we develop a simple, unifying theory to explain this phenomenon using the formalism of stochastic localization samplers. We show that it emerges generically as the generation process localizes to a sub-population of the distribution it models. While critical windows have been studied at length in diffusion models, existing theory heavily relies on strong distributional assumptions and the particulars of Gaussian diffusion. In contrast to existing work our theory (1) applies to autoregressive and diffusion models; (2) makes no distributional assumptions; (3) quantitatively improves previous bounds even when specialized to diffusions; and (4) requires basic tools and no stochastic calculus or statistical-physics-based machinery. We also identify an intriguing connection to the all-or-nothing phenomenon from statistical inference. Finally, we validate our predictions empirically for LLMs and find that critical windows often coincide with failures in problem solving for various math and reasoning benchmarks.
Large Language Models (LLMs) have shown remarkable reasoning capabilities through Reinforcement Learning with Verifiable Rewards (RLVR) methods. However, a key limitation of existing approaches is that rewards defined at the full trajectory level provide insufficient guidance for optimizing the intermediate steps of a reasoning process. To address this, we introduce \textbf{\name}, a novel method that estimates the mathematical expectations of rewards at various reasoning steps using tree sampling. Unlike prior methods that rely on a separate step reward model, \name directly estimates these rewards through this sampling process. Building on the group-relative reward training mechanism of GRPO, \name innovatively computes rewards based on step-level groups generated during tree sampling. This advancement allows \name to produce fine-grained and dense reward signals, significantly enhancing the learning process and overall performance of LLMs. Experimental results demonstrate that our \name algorithm substantially improves the average Pass@1 accuracy of Qwen-2.5-Math on test benchmarks, increasing it from 19.0\% to 35.5\%. Furthermore, \name significantly outperforms GRPO by 2.9\% in performance while simultaneously reducing the average response length by 18.1\%, showcasing its effectiveness and efficiency. Our code will be available at \href{https://github.com/yangzhch6/TreeRPO}{https://github.com/yangzhch6/TreeRPO}.
Autonomous UAV operation necessitates reliable mathematical reasoning for tasks such as trajectory planning and power management. While traditional flight control relies on hardcoded equations, recent Large Language Models (LLMs) offer potential for more flexible problem-solving but struggle with reliably selecting and applying correct mathematical formulations and executing precise multi-step arithmetic. We propose RAG-UAV, a retrieval-augmented generation framework designed to improve the mathematical reasoning of several LLMs (including GPT o1/Turbo, Llama-3.2/3.3, Mistral, and DeepSeek R1) in UAV-specific contexts by providing access to relevant domain literature. To conduct an initial assessment, we introduce the UAV-Math-Bench, a small problem set comprising 20 UAV-centric mathematical problems across four difficulty levels. Our experiments demonstrate that incorporating retrieval substantially increases exact answer accuracy (achieving up to 75% with o1), reduces instances of incorrect formulation selection (from 25% without RAG to 5% with RAG), decreases numerical errors, reducing Mean Squared Error (MSE) by orders of magnitude for the best-performing models. This pilot study indicates that RAG can enable general-purpose LLMs to function as more reliable tools for engineering analysis, although direct real-time flight control requires further investigation and validation on a larger scale. All benchmark data, question and answer are publicly available.
Efficient long-sequence generation is a critical challenge for Large Language Models. While recent sparse decoding methods improve efficiency, they suffer from KV cache misalignment, where approximation errors accumulate and degrade generation quality. In this work, we propose Rectified Sparse Attention (ReSA), a simple yet effective method that combines block-sparse attention with periodic dense rectification. By refreshing the KV cache at fixed intervals using a dense forward pass, ReSA bounds error accumulation and preserves alignment with the pretraining distribution. Experiments across math reasoning, language modeling, and retrieval tasks demonstrate that ReSA achieves near-lossless generation quality with significantly improved efficiency. Notably, ReSA delivers up to 2.42$\times$ end-to-end speedup under decoding at 256K sequence length, making it a practical solution for scalable long-context inference. Code is available at https://aka.ms/ReSA-LM.
We have witnessed that strong LLMs like Qwen-Math, MiMo, and Phi-4 possess immense reasoning potential inherited from the pre-training stage. With reinforcement learning (RL), these models can improve dramatically on reasoning tasks. Recent studies have shown that even RL on a single problem can unleash these models' reasoning capabilities. However, RL is not only expensive but also unstable. Even one-shot RL requires hundreds of GPU hours. This raises a critical question: Is there a more efficient way to unleash the reasoning potential of these powerful base LLMs? In this work, we demonstrate that Critique Fine-Tuning (CFT) on only one problem can effectively unleash the reasoning potential of LLMs. Our method constructs critique data by collecting diverse model-generated solutions to a single problem and using teacher LLMs to provide detailed critiques. We fine-tune Qwen and Llama family models, ranging from 1.5B to 14B parameters, on the CFT data and observe significant performance gains across diverse reasoning tasks. For example, with just 5 GPU hours of training, Qwen-Math-7B-CFT show an average improvement of 15% on six math benchmarks and 16% on three logic reasoning benchmarks. These results are comparable to or even surpass the results from RL with 20x less compute. Ablation studies reveal the robustness of one-shot CFT across different prompt problems. These results highlight one-shot CFT as a simple, general, and compute-efficient approach to unleashing the reasoning capabilities of modern LLMs.
Large language models (LLMs) have achieved distinguished performance on various reasoning-intensive tasks. However, LLMs might still face the challenges of robustness issues and fail unexpectedly in some simple reasoning tasks. Previous works evaluate the LLM robustness with hand-crafted templates or a limited set of perturbation rules, indicating potential data contamination in pre-training or fine-tuning datasets. In this work, inspired by stress testing in software engineering, we propose a novel framework, Automatic Robustness Checker (AR-Checker), to generate mathematical problem variants that maintain the semantic meanings of the original one but might fail the LLMs. The AR-Checker framework generates mathematical problem variants through multi-round parallel streams of LLM-based rewriting and verification. Our framework can generate benchmark variants dynamically for each LLM, thus minimizing the risk of data contamination. Experiments on GSM8K and MATH-500 demonstrate the strong performance of AR-Checker on mathematical tasks. We also evaluate AR-Checker on benchmarks beyond mathematics, including MMLU, MMLU-Pro, and CommonsenseQA, where it also achieves strong performance, further proving the effectiveness of AR-Checker.
Large language models (LLMs) have demonstrated the ability to generate formative feedback and instructional hints in English, making them increasingly relevant for AI-assisted education. However, their ability to provide effective instructional support across different languages, especially for mathematically grounded reasoning tasks, remains largely unexamined. In this work, we present the first large-scale simulation of multilingual tutor-student interactions using LLMs. A stronger model plays the role of the tutor, generating feedback in the form of hints, while a weaker model simulates the student. We explore 352 experimental settings across 11 typologically diverse languages, four state-of-the-art LLMs, and multiple prompting strategies to assess whether language-specific feedback leads to measurable learning gains. Our study examines how student input language, teacher feedback language, model choice, and language resource level jointly influence performance. Results show that multilingual hints can significantly improve learning outcomes, particularly in low-resource languages when feedback is aligned with the student's native language. These findings offer practical insights for developing multilingual, LLM-based educational tools that are both effective and inclusive.
Chain-of-Thought (CoT) has widely enhanced mathematical reasoning in Large Language Models (LLMs), but it still remains challenging for extending it to multimodal domains. Existing works either adopt a similar textual reasoning for image input, or seek to interleave visual signals into mathematical CoT. However, they face three key limitations for math problem-solving: reliance on coarse-grained box-shaped image regions, limited perception of vision encoders on math content, and dependence on external capabilities for visual modification. In this paper, we propose MINT-CoT, introducing Mathematical INterleaved Tokens for Chain-of-Thought visual reasoning. MINT-CoT adaptively interleaves relevant visual tokens into textual reasoning steps via an Interleave Token, which dynamically selects visual regions of any shapes within math figures. To empower this capability, we construct the MINT-CoT dataset, containing 54K mathematical problems aligning each reasoning step with visual regions at the token level, accompanied by a rigorous data generation pipeline. We further present a three-stage MINT-CoT training strategy, progressively combining text-only CoT SFT, interleaved CoT SFT, and interleaved CoT RL, which derives our MINT-CoT-7B model. Extensive experiments demonstrate the effectiveness of our method for effective visual interleaved reasoning in mathematical domains, where MINT-CoT-7B outperforms the baseline model by +34.08% on MathVista, +28.78% on GeoQA, and +23.2% on MMStar, respectively. Our code and data are available at https://github.com/xinyan-cxy/MINT-CoT
Recent advances in slow-thinking language models (e.g., OpenAI-o1 and DeepSeek-R1) have demonstrated remarkable abilities in complex reasoning tasks by emulating human-like reflective cognition. However, extending such capabilities to multi-modal large language models (MLLMs) remains challenging due to the high cost of retraining vision-language alignments when upgrading the underlying reasoner LLMs. A straightforward solution is to decouple perception from reasoning, i.e., converting visual inputs into language representations (e.g., captions) that are then passed to a powerful text-only reasoner. However, this decoupling introduces a critical challenge: the visual extractor must generate descriptions that are both faithful to the image and informative enough to support accurate downstream reasoning. To address this, we propose Reasoning-Aligned Perceptual Decoupling via Caption Reward Optimization (RACRO) - a reasoning-guided reinforcement learning strategy that aligns the extractor's captioning behavior with the reasoning objective. By closing the perception-reasoning loop via reward-based optimization, RACRO significantly enhances visual grounding and extracts reasoning-optimized representations. Experiments on multi-modal math and science benchmarks show that the proposed RACRO method achieves state-of-the-art average performance while enabling superior scalability and plug-and-play adaptation to more advanced reasoning LLMs without the necessity for costly multi-modal re-alignment.
Visuals are valuable tools for teaching math word problems (MWPs), helping young learners interpret textual descriptions into mathematical expressions before solving them. However, creating such visuals is labor-intensive and there is a lack of automated methods to support this process. In this paper, we present Math2Visual, an automatic framework for generating pedagogically meaningful visuals from MWP text descriptions. Math2Visual leverages a pre-defined visual language and a design space grounded in interviews with math teachers, to illustrate the core mathematical relationships in MWPs. Using Math2Visual, we construct an annotated dataset of 1,903 visuals and evaluate Text-to-Image (TTI) models for their ability to generate visuals that align with our design. We further fine-tune several TTI models with our dataset, demonstrating improvements in educational visual generation. Our work establishes a new benchmark for automated generation of pedagogically meaningful visuals and offers insights into key challenges in producing multimodal educational content, such as the misrepresentation of mathematical relationships and the omission of essential visual elements.
High-quality math datasets are crucial for advancing the reasoning abilities of large language models (LLMs). However, existing datasets often suffer from three key issues: outdated and insufficient challenging content, neglecting human-like reasoning, and limited reliability due to single-LLM generation. To address these, we introduce $\textbf{STORM-BORN}$, an ultra-challenging dataset of mathematical derivations sourced from cutting-edge academic papers, which includes dense human-like approximations and heuristic cues. To ensure the reliability and quality, we propose a novel human-in-the-loop, multi-agent data generation framework, integrating reasoning-dense filters, multi-agent collaboration, and human mathematicians' evaluations. We curated a set of 2,000 synthetic samples and deliberately selected the 100 most difficult problems. Even most advanced models like GPT-o1 solved fewer than $5\%$ of them. Fine-tuning on STORM-BORN boosts accuracy by $7.84\%$ (LLaMA3-8B) and $9.12\%$ (Qwen2.5-7B). As AI approaches mathematician-level reasoning, STORM-BORN provides both a high-difficulty benchmark and a human-like reasoning training resource. Our code and dataset are publicly available at https://github.com/lwhere/STORM-BORN.
Recent advances in test-time optimization have led to remarkable reasoning capabilities in Large Language Models (LLMs), enabling them to solve highly complex problems in math and coding. However, the reasoning capabilities of multimodal LLMs (MLLMs) still significantly lag, especially for complex video-language tasks. To address this issue, we present SiLVR, a Simple Language-based Video Reasoning framework that decomposes complex video understanding into two stages. In the first stage, SiLVR transforms raw video into language-based representations using multisensory inputs, such as short clip captions and audio/speech subtitles. In the second stage, language descriptions are fed into a powerful reasoning LLM to solve complex video-language understanding tasks. To handle long-context multisensory inputs, we use an adaptive token reduction scheme, which dynamically determines the temporal granularity with which to sample the tokens. Our simple, modular, and training-free video reasoning framework achieves the best-reported results on Video-MME (long), Video-MMMU (comprehension), Video-MMLU, CGBench, and EgoLife. Furthermore, our empirical study focused on video reasoning capabilities shows that, despite not being explicitly trained on video, strong reasoning LLMs can effectively aggregate multisensory input information from video, speech, and audio for complex temporal, causal, long-context, and knowledge acquisition reasoning tasks in video. Code is available at https://github.com/CeeZh/SILVR.
Deep reasoning is fundamental for solving complex tasks, especially in vision-centric scenarios that demand sequential, multimodal understanding. However, existing benchmarks typically evaluate agents with fully synthetic, single-turn queries, limited visual modalities, and lack a framework to assess reasoning quality over multiple steps as required in real-world settings. To address this, we introduce Agent-X, a large-scale benchmark for evaluating vision-centric agents multi-step and deep reasoning capabilities in real-world, multimodal settings. Agent- X features 828 agentic tasks with authentic visual contexts, including images, multi-image comparisons, videos, and instructional text. These tasks span six major agentic environments: general visual reasoning, web browsing, security and surveillance, autonomous driving, sports, and math reasoning. Our benchmark requires agents to integrate tool use with explicit, stepwise decision-making in these diverse settings. In addition, we propose a fine-grained, step-level evaluation framework that assesses the correctness and logical coherence of each reasoning step and the effectiveness of tool usage throughout the task. Our results reveal that even the best-performing models, including GPT, Gemini, and Qwen families, struggle to solve multi-step vision tasks, achieving less than 50% full-chain success. These findings highlight key bottlenecks in current LMM reasoning and tool-use capabilities and identify future research directions in vision-centric agentic reasoning models. Our data and code are publicly available at https://github.com/mbzuai-oryx/Agent-X
We explore a method for improving the performance of large language models through self-reflection and reinforcement learning. By incentivizing the model to generate better self-reflections when it answers incorrectly, we demonstrate that a model's ability to solve complex, verifiable tasks can be enhanced even when generating synthetic data is infeasible and only binary feedback is available. Our framework operates in two stages: first, upon failing a given task, the model generates a self-reflective commentary analyzing its previous attempt; second, the model is given another attempt at the task with the self-reflection in context. If the subsequent attempt succeeds, the tokens generated during the self-reflection phase are rewarded. Our experimental results show substantial performance gains across a variety of model architectures, as high as 34.7% improvement at math equation writing and 18.1% improvement at function calling. Notably, smaller fine-tuned models (1.5 billion to 7 billion parameters) outperform models in the same family that are 10 times larger. Our novel paradigm is thus an exciting pathway to more useful and reliable language models that can self-improve on challenging tasks with limited external feedback.
Large Reasoning Models (LRMs) achieve superior performance by extending the thought length. However, a lengthy thinking trajectory leads to reduced efficiency. Most of the existing methods are stuck in the assumption of overthinking and attempt to reason efficiently by compressing the Chain-of-Thought, but this often leads to performance degradation. To address this problem, we introduce A*-Thought, an efficient tree search-based unified framework designed to identify and isolate the most essential thoughts from the extensive reasoning chains produced by these models. It formulates the reasoning process of LRMs as a search tree, where each node represents a reasoning span in the giant reasoning space. By combining the A* search algorithm with a cost function specific to the reasoning path, it can efficiently compress the chain of thought and determine a reasoning path with high information density and low cost. In addition, we also propose a bidirectional importance estimation mechanism, which further refines this search process and enhances its efficiency beyond uniform sampling. Extensive experiments on several advanced math tasks show that A*-Thought effectively balances performance and efficiency over a huge search space. Specifically, A*-Thought can improve the performance of QwQ-32B by 2.39$\times$ with low-budget and reduce the length of the output token by nearly 50% with high-budget. The proposed method is also compatible with several other LRMs, demonstrating its generalization capability. The code can be accessed at: https://github.com/AI9Stars/AStar-Thought.