Daily Papers

Supervised Fine-Tuning (SFT) is commonly used to train language models to imitate annotated responses for given instructions. In this paper, we challenge this paradigm and propose Critique Fine-Tuning (CFT), a strategy where models learn to critique noisy responses rather than simply imitate correct ones. Inspired by human learning processes that emphasize critical thinking, CFT encourages deeper analysis and nuanced understanding-traits often overlooked by standard SFT. To validate the effectiveness of CFT, we construct a 50K-sample dataset from WebInstruct, using GPT-4o as the teacher to generate critiques in the form of (input=[query; noisy response], output=critique). CFT on this dataset yields a consistent 4-10% improvement over SFT on six math benchmarks with different base models like Qwen2.5, Qwen2.5-Math and DeepSeek-Math. We further expand to MetaMath and NuminaMath datasets and observe similar gains over SFT. Notably, our Qwen2.5-Math-CFT model-trained on just 50K samples-matches or outperforms competitive models such as AceMath and Qwen2.5-Math-Instruct on most benchmarks, both of which use over 2M samples. Ablation studies show that CFT is robust to the source of noisy response and teacher critique model. Through these findings, we argue that critique-based training offers a more effective alternative to advance the reasoning of language models.

Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO). However, the training pipelines behind these systems remain largely undisclosed, and their reliance on large "internal" models and scaffolds makes them expensive to run, difficult to reproduce, and hard to study or improve upon. This raises a central question: can small, open models also be trained to achieve competitive reasoning performance on difficult Olympiad-level math? In this paper, we answer this question by building QED-Nano, a 4B model post-trained for Olympiad-level proofs. Our training recipe has three stages: (1) supervised fine-tuning to imbue good proof-writing styles by distilling from DeepSeek-Math-V2, (2) reinforcement learning (RL) with rubric-based rewards, and (3) expanding RL with a reasoning cache, which decomposes long proofs into iterative summarize-and-refine cycles and enables stronger test-time reasoning. QED-Nano surpasses the proof-generation performance of much larger open models, including Nomos-1 and GPT-OSS-120B, and approaches the performance of proprietary models like Gemini 3 Pro, at a fraction of the inference cost. To support further research on open mathematical reasoning, we release the full QED-Nano pipeline, including the QED-Nano and QED-Nano-SFT models, the FineProofs-SFT and FineProofs-RL datasets, and the training and evaluation code.

DeepSeek-R1 has shown that long chain-of-thought (CoT) reasoning can naturally emerge through a simple reinforcement learning (RL) framework with rule-based rewards, where the training may directly start from the base models-a paradigm referred to as zero RL training. Most recent efforts to reproduce zero RL training have primarily focused on the Qwen2.5 model series, which may not be representative as we find the base models already exhibit strong instruction-following and self-reflection abilities. In this work, we investigate zero RL training across 10 diverse base models, spanning different families and sizes including LLama3-8B, Mistral-7B/24B, DeepSeek-Math-7B, Qwen2.5-math-7B, and all Qwen2.5 models from 0.5B to 32B. Leveraging several key design strategies-such as adjusting format reward and controlling query difficulty-we achieve substantial improvements in both reasoning accuracy and response length across most settings. However, by carefully monitoring the training dynamics, we observe that different base models exhibit distinct patterns during training. For instance, the increased response length does not always correlate with the emergence of certain cognitive behaviors such as verification (i.e., the "aha moment"). Notably, we observe the "aha moment" for the first time in small models not from the Qwen family. We share the key designs that enable successful zero RL training, along with our findings and practices. To facilitate further research, we open-source the code, models, and analysis tools.

Chain-of-thought (CoT) has emerged as a critical mechanism for enhancing reasoning capabilities in large language models (LLMs), with self-consistency demonstrating notable promise in boosting performance. However, inherent linguistic biases in multilingual training corpora frequently cause semantic drift and logical inconsistencies, especially in sub-10B parameter LLMs handling complex inference tasks. To overcome these constraints, we propose the Cross-Lingual Consistency (CLC) framework, an innovative inference paradigm that integrates multilingual reasoning paths through majority voting to elevate LLMs' reasoning capabilities. Empirical evaluations on the CMATH dataset reveal CLC's superiority over the conventional self-consistency method, delivering 9.5%, 6.5%, and 6.0% absolute accuracy gains for DeepSeek-Math-7B-Instruct, Qwen2.5-Math-7B-Instruct, and Gemma2-9B-Instruct respectively. Expanding CLC's linguistic scope to 11 diverse languages implies two synergistic benefits: 1) neutralizing linguistic biases in multilingual training corpora through multilingual ensemble voting, 2) escaping monolingual reasoning traps by exploring the broader multilingual solution space. This dual benefits empirically enables more globally optimal reasoning paths compared to monolingual self-consistency baselines, as evidenced by the 4.1%-18.5% accuracy gains using Gemma2-9B-Instruct on the MGSM dataset.

Large Language Models (LLMs) have exhibited remarkable performance on reasoning tasks. They utilize autoregressive token generation to construct reasoning trajectories, enabling the development of a coherent chain of thought. In this work, we explore the impact of individual tokens on the final outcomes of reasoning tasks. We identify the existence of ``critical tokens'' that lead to incorrect reasoning trajectories in LLMs. Specifically, we find that LLMs tend to produce positive outcomes when forced to decode other tokens instead of critical tokens. Motivated by this observation, we propose a novel approach - cDPO - designed to automatically recognize and conduct token-level rewards for the critical tokens during the alignment process. Specifically, we develop a contrastive estimation approach to automatically identify critical tokens. It is achieved by comparing the generation likelihood of positive and negative models. To achieve this, we separately fine-tune the positive and negative models on various reasoning trajectories, consequently, they are capable of identifying identify critical tokens within incorrect trajectories that contribute to erroneous outcomes. Moreover, to further align the model with the critical token information during the alignment process, we extend the conventional DPO algorithms to token-level DPO and utilize the differential likelihood from the aforementioned positive and negative model as important weight for token-level DPO learning.Experimental results on GSM8K and MATH500 benchmarks with two-widely used models Llama-3 (8B and 70B) and deepseek-math (7B) demonstrate the effectiveness of the propsoed approach cDPO.

Corruption studies, the primary tool for evaluating chain-of-thought (CoT) faithfulness, identify which chain positions are "computationally important" by measuring accuracy when steps are replaced with errors. We identify a systematic confound: for chains with explicit terminal answer statements, the dominant format in standard benchmarks, corruption studies detect where the answer text appears, not where computation occurs. A within-dataset format ablation provides the key evidence: on standard GSM8K chains ending with "the answer is X," removing only the answer statement, preserving all reasoning, collapses suffix sensitivity ~19x at 3B (N=300, p=0.022). Conflicting-answer experiments quantify the causal mechanism: at 7B, CC accuracy drops to near-zero (<=0.02) across five architecture families; the followed-wrong rate spans 0.63-1.00 at 3B-7B and attenuates at larger scales (0.300 at Phi-4-14B, ~0.01 at 32B). A within-stable 7B replication (9.3x attenuation, N=76, p=7.8e-3; Qwen3-8B N=299, p=0.004) provides converging evidence, and the pattern replicates on MATH (DeepSeek-R1-7B: 10.9x suffix-survival recovery). On chains without answer suffixes the same protocol identifies the prefix as load-bearing (Delta=-0.77, p<10^-12). Generation-time probes confirm a dissociation: the answer is not early-determined during generation (early commitment <5%), yet at consumption time model outputs systematically follow the explicit answer text. The format-determination effect persists through 14B (8.5x ratio, p=0.001) and converges toward zero at 32B. We propose a three-prerequisite protocol (question-only control, format characterization, all-position sweep) as a minimum standard for corruption-based faithfulness studies.

We present Future-KL Influenced Policy Optimization (FIPO), a reinforcement learning algorithm designed to overcome reasoning bottlenecks in large language models. While GRPO style training scales effectively, it typically relies on outcome-based rewards (ORM) that distribute a global advantage uniformly across every token in a trajectory. We argue that this coarse-grained credit assignment imposes a performance ceiling by failing to distinguish critical logical pivots from trivial tokens. FIPO addresses this by incorporating discounted future-KL divergence into the policy update, creating a dense advantage formulation that re-weights tokens based on their influence on subsequent trajectory behavior. Empirically, FIPO enables models to break through the length stagnation seen in standard baselines. Evaluated on Qwen2.5-32B, FIPO extends the average chain-of-thought length from roughly 4,000 to over 10,000 tokens and increases AIME 2024 Pass@1 accuracy from 50.0% to a peak of 58.0% (converging at approximately 56.0\%). This outperforms both DeepSeek-R1-Zero-Math-32B (around 47.0%) and o1-mini (approximately 56.0%). Our results suggest that establishing dense advantage formulations is a vital path for evolving ORM-based algorithms to unlock the full reasoning potential of base models. We open-source our training system, built on the verl framework.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an indispensable paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard policy optimization methods, such as Group Relative Policy Optimization (GRPO), often converge to low-entropy policies, leading to severe mode collapse and limited output diversity. We analyze this issue from the perspective of sampling probability dynamics, identifying that the standard objective disproportionately reinforces the highest-likelihood paths, thereby suppressing valid alternative reasoning chains. To address this, we propose a novel Advantage Re-weighting Mechanism (ARM) designed to equilibrate the confidence levels across all correct responses. By incorporating Prompt Perplexity and Answer Confidence into the advantage estimation, our method dynamically reshapes the reward signal to attenuate the gradient updates of over-confident reasoning paths, while redistributing probability mass toward under-explored correct solutions. Empirical results demonstrate that our approach significantly enhances generative diversity and response entropy while maintaining competitive accuracy, effectively achieving a superior trade-off between exploration and exploitation in reasoning tasks. Empirical results on Qwen2.5 and DeepSeek models across mathematical and coding benchmarks show that ProGRPO significantly mitigates entropy collapse. Specifically, on Qwen2.5-7B, our method outperforms GRPO by 5.7% in Pass@1 and, notably, by 13.9% in Pass@32, highlighting its superior capability in generating diverse correct reasoning paths.

Reinforcement learning, such as PPO and GRPO, has powered recent breakthroughs in LLM reasoning. Scaling rollout to sample more prompts enables models to selectively use higher-quality data for training, which can stabilize RL training and improve model performance. However, this comes at the cost of significant computational overhead. In this paper, we show that a substantial portion of this overhead can be avoided by skipping uninformative prompts before rollout. Our analysis of reward dynamics reveals a strong temporal consistency in prompt value: prompts that are uninformative in one epoch of training are likely to remain uninformative in future epochs. Based on these insights, we propose GRESO (GRPO with Efficient Selective Rollout), an online, lightweight pre-rollout filtering algorithm that predicts and skips uninformative prompts using reward training dynamics. By evaluating GRESO on a broad range of math reasoning benchmarks and models, such as Qwen2.5-Math-1.5B, DeepSeek-R1-Distill-Qwen-1.5B, and Qwen2.5-Math-7B, we show that GRESO achieves up to 2.4x wall-clock time speedup in rollout and up to 2.0x speedup in total training time without accuracy degradation.

We introduce DeepSeek-Prover-V2, an open-source large language model designed for formal theorem proving in Lean 4, with initialization data collected through a recursive theorem proving pipeline powered by DeepSeek-V3. The cold-start training procedure begins by prompting DeepSeek-V3 to decompose complex problems into a series of subgoals. The proofs of resolved subgoals are synthesized into a chain-of-thought process, combined with DeepSeek-V3's step-by-step reasoning, to create an initial cold start for reinforcement learning. This process enables us to integrate both informal and formal mathematical reasoning into a unified model. The resulting model, DeepSeek-Prover-V2-671B, achieves state-of-the-art performance in neural theorem proving, reaching 88.9% pass ratio on the MiniF2F-test and solving 49 out of 658 problems from PutnamBench. In addition to standard benchmarks, we introduce ProverBench, a collection of 325 formalized problems, to enrich our evaluation, including 15 selected problems from the recent AIME competitions (years 24-25). Further evaluation on these 15 AIME problems shows that the model successfully solves 6 of them. In comparison, DeepSeek-V3 solves 8 of these problems using majority voting, highlighting that the gap between formal and informal mathematical reasoning in large language models is substantially narrowing.

Large Language Models (LLMs) have achieved impressive results across a broad array of tasks, yet their capacity for complex, domain-specific mathematical reasoning-particularly in wireless communications-remains underexplored. In this work, we introduce WirelessMathBench, a novel benchmark specifically designed to evaluate LLMs on mathematical modeling challenges to wireless communications engineering. Our benchmark consists of 587 meticulously curated questions sourced from 40 state-of-the-art research papers, encompassing a diverse spectrum of tasks ranging from basic multiple-choice questions to complex equation completion tasks, including both partial and full completions, all of which rigorously adhere to physical and dimensional constraints. Through extensive experimentation with leading LLMs, we observe that while many models excel in basic recall tasks, their performance degrades significantly when reconstructing partially or fully obscured equations, exposing fundamental limitations in current LLMs. Even DeepSeek-R1, the best performer on our benchmark, achieves an average accuracy of only 38.05%, with a mere 7.83% success rate in full equation completion. By publicly releasing WirelessMathBench along with the evaluation toolkit, we aim to advance the development of more robust, domain-aware LLMs for wireless system analysis and broader engineering applications.

With the advent of DeepSeek-R1, a new wave of reinforcement learning (RL) methods has emerged that seem to unlock stronger mathematical reasoning. However, a closer look at the open-source ecosystem reveals a critical limitation: with sufficiently many draws (e.g., pass@1024), many existing base models already solve nearly all questions on widely used math benchmarks such as MATH-500 and AIME 2024. This suggests that the RL fine-tuning methods prevalent in the LLM reasoning literature largely sharpen existing solution modes rather than discovering entirely new ones. Such sharpening stands in contrast to the broader promise of RL: to foster exploration and to acquire new skills. To move beyond this plateau, we introduce MATH-Beyond (MATH-B), a benchmark deliberately constructed to defeat common open-source models of up to 8B parameters even under large sampling budgets. Improving performance on our benchmark via RL requires methods that learn to reason in ways that go beyond base model capabilities in repeated sampling. Since the problems are drawn from subsets of DAPO-Math-17K and DeepScaleR datasets, they remain topically equivalent to standard high-school math. Validating our premise, RL fine-tuned models such as Nemotron-Research-Reasoning-Qwen-1.5B and DeepScaleR-1.5B-Preview perform poorly on MATH-B at pass@1024, showing how existing approaches fall short on tackling harder instances. We hope MATH-B will catalyze exploration-driven RL approaches that elicit deeper reasoning capabilities. We release MATH-B at https://huggingface.co/datasets/brendel-group/MATH-Beyond.

Proof assistants like Lean have revolutionized mathematical proof verification, ensuring high accuracy and reliability. Although large language models (LLMs) show promise in mathematical reasoning, their advancement in formal theorem proving is hindered by a lack of training data. To address this issue, we introduce an approach to generate extensive Lean 4 proof data derived from high-school and undergraduate-level mathematical competition problems. This approach involves translating natural language problems into formal statements, filtering out low-quality statements, and generating proofs to create synthetic data. After fine-tuning the DeepSeekMath 7B model on this synthetic dataset, which comprises 8 million formal statements with proofs, our model achieved whole-proof generation accuracies of 46.3% with 64 samples and 52% cumulatively on the Lean 4 miniF2F test, surpassing the baseline GPT-4 at 23.0% with 64 samples and a tree search reinforcement learning method at 41.0%. Additionally, our model successfully proved 5 out of 148 problems in the Lean 4 Formalized International Mathematical Olympiad (FIMO) benchmark, while GPT-4 failed to prove any. These results demonstrate the potential of leveraging large-scale synthetic data to enhance theorem-proving capabilities in LLMs. Both the synthetic dataset and the model will be made available to facilitate further research in this promising field.

We introduce DeepSeek-Prover-V1.5, an open-source language model designed for theorem proving in Lean 4, which enhances DeepSeek-Prover-V1 by optimizing both training and inference processes. Pre-trained on DeepSeekMath-Base with specialization in formal mathematical languages, the model undergoes supervised fine-tuning using an enhanced formal theorem proving dataset derived from DeepSeek-Prover-V1. Further refinement is achieved through reinforcement learning from proof assistant feedback (RLPAF). Beyond the single-pass whole-proof generation approach of DeepSeek-Prover-V1, we propose RMaxTS, a variant of Monte-Carlo tree search that employs an intrinsic-reward-driven exploration strategy to generate diverse proof paths. DeepSeek-Prover-V1.5 demonstrates significant improvements over DeepSeek-Prover-V1, achieving new state-of-the-art results on the test set of the high school level miniF2F benchmark (63.5%) and the undergraduate level ProofNet benchmark (25.3%).

This paper presents a practical investigation into fine-tuning model parameters for mathematical reasoning tasks through experimenting with various configurations including randomness control, reasoning depth, and sampling strategies, careful tuning demonstrates substantial improvements in efficiency as well as performance. A holistically optimized framework is introduced for five state-of-the-art models on mathematical reasoning tasks, exhibiting significant performance boosts while maintaining solution correctness. Through systematic parameter optimization across Qwen2.5-72B, Llama-3.1-70B, DeepSeek-V3, Mixtral-8x22B, and Yi-Lightning, consistent efficiency gains are demonstrated with 100% optimization success rate. The methodology achieves an average 29.4% reduction in computational cost and 23.9% improvement in inference speed across all tested models. This framework systematically searches parameter spaces including temperature (0.1-0.5), reasoning steps (4-12), planning periods (1-4), and nucleus sampling (0.85-0.98), determining optimal configurations through testing on mathematical reasoning benchmarks. Critical findings show that lower temperature regimes (0.1-0.4) and reduced reasoning steps (4-6) consistently enhance efficiency without compromising accuracy. DeepSeek-V3 achieves the highest accuracy at 98%, while Mixtral-8x22B delivers the most cost-effective performance at 361.5 tokens per accurate response. Key contributions include: (1) the first comprehensive optimization study for five diverse SOTA models in mathematical reasoning, (2) a standardized production-oriented parameter optimization framework, (3) discovery of universal optimization trends applicable across model architectures, and (4) production-ready configurations with extensive performance characterization.

Large Reasoning Models (LRMs) like o3 and DeepSeek-R1 have achieved remarkable progress in natural language reasoning with long chain-of-thought. However, they remain computationally inefficient and struggle with accuracy when solving problems requiring complex mathematical operations. In this work, we present AgentMath, an agent framework that seamlessly integrates language models' reasoning capabilities with code interpreters' computational precision to efficiently tackle complex mathematical problems. Our approach introduces three key innovations: (1) An automated method that converts natural language chain-of-thought into structured tool-augmented trajectories, generating high-quality supervised fine-tuning (SFT) data to alleviate data scarcity; (2) A novel agentic reinforcement learning (RL) paradigm that dynamically interleaves natural language generation with real-time code execution. This enables models to autonomously learn optimal tool-use strategies through multi-round interactive feedback, while fostering emergent capabilities in code refinement and error correction; (3) An efficient training system incorporating innovative techniques, including request-level asynchronous rollout scheduling, agentic partial rollout, and prefix-aware weighted load balancing, achieving 4-5x speedup and making efficient RL training feasible on ultra-long sequences with scenarios with massive tool invocation. The evaluations show that AgentMath achieves state-of-the-art performance on challenging mathematical competition benchmarks including AIME24, AIME25, and HMMT25. Specifically, AgentMath-30B-A3B attains 90.6%, 86.4%, and 73.8% accuracy respectively, achieving advanced performance. The results validate the effectiveness of our approach and pave the way for building more sophisticated and scalable mathematical reasoning agents.

Reasoning-enabled large language models (LLMs) have recently demonstrated impressive performance in complex logical and mathematical tasks, yet their effectiveness in evaluating natural language generation remains unexplored. This study systematically compares reasoning-based LLMs (DeepSeek-R1 and OpenAI o3) with their non-reasoning counterparts across machine translation (MT) and text summarization (TS) evaluation tasks. We evaluate eight models across three architectural categories, including state-of-the-art reasoning models, their distilled variants (ranging from 8B to 70B parameters), and equivalent conventional, non-reasoning LLMs. Our experiments on WMT23 and SummEval benchmarks reveal that the benefits of reasoning capabilities are highly model and task-dependent: while OpenAI o3-mini models show consistent performance improvements with increased reasoning intensity, DeepSeek-R1 underperforms compared to its non-reasoning variant, with exception to certain aspects of TS evaluation. Correlation analysis demonstrates that increased reasoning token usage positively correlates with evaluation quality in o3-mini models. Furthermore, our results show that distillation of reasoning capabilities maintains reasonable performance in medium-sized models (32B) but degrades substantially in smaller variants (8B). This work provides the first comprehensive assessment of reasoning LLMs for NLG evaluation and offers insights into their practical use.

With the rapid development of large language models (LLMs), the quality of training data has become crucial. Among the various types of training data, mathematical data plays a key role in enabling LLMs to acquire strong reasoning abilities. While high-quality open-source data is important, it is often insufficient for pre-training, necessitating the addition of synthetic math problems. However, synthetic math questions and answers can introduce inaccuracies, which may degrade both the training data and web data. Therefore, an effective method for cleaning synthetic math data is essential. In this paper, we propose the MathClean benchmark to evaluate the effectiveness of math data cleaning models. The MathClean benchmark consists of 2,000 correct questions and 2,000 erroneous questions with additional 2,000 correct and erroneous answers sourced from augmented data based on GSM8K and MATH. Moreover, we also annotate error types for each question or answer, since it can assess whether models can correctly identify the error categories for future improvements. Finally, we present comprehensive evaluations using state-of-the-art (SOTA) models. Our results demonstrate that even strong models like GPT-o1 and DeepSeek-R1 perform poorly on this benchmark, highlighting the utility of MathClean. Our code and data is available at https://github.com/YuYingLi0/MathClean.

We present DeepSeek-Coder-V2, an open-source Mixture-of-Experts (MoE) code language model that achieves performance comparable to GPT4-Turbo in code-specific tasks. Specifically, DeepSeek-Coder-V2 is further pre-trained from an intermediate checkpoint of DeepSeek-V2 with additional 6 trillion tokens. Through this continued pre-training, DeepSeek-Coder-V2 substantially enhances the coding and mathematical reasoning capabilities of DeepSeek-V2, while maintaining comparable performance in general language tasks. Compared to DeepSeek-Coder-33B, DeepSeek-Coder-V2 demonstrates significant advancements in various aspects of code-related tasks, as well as reasoning and general capabilities. Additionally, DeepSeek-Coder-V2 expands its support for programming languages from 86 to 338, while extending the context length from 16K to 128K. In standard benchmark evaluations, DeepSeek-Coder-V2 achieves superior performance compared to closed-source models such as GPT4-Turbo, Claude 3 Opus, and Gemini 1.5 Pro in coding and math benchmarks.

In this paper, we introduce PolyMath, a multilingual mathematical reasoning benchmark covering 18 languages and 4 easy-to-hard difficulty levels. Our benchmark ensures difficulty comprehensiveness, language diversity, and high-quality translation, making it a highly discriminative multilingual mathematical benchmark in the era of reasoning LLMs. We conduct a comprehensive evaluation for advanced LLMs and find that even Deepseek-R1-671B and Qwen-QwQ-32B, achieve only 43.4 and 41.8 benchmark scores, with less than 30% accuracy under the highest level. From a language perspective, our benchmark reveals several key challenges of LLMs in multilingual reasoning: (1) Reasoning performance varies widely across languages for current LLMs; (2) Input-output language consistency is low in reasoning LLMs and may be correlated with performance; (3) The thinking length differs significantly by language for current LLMs. Additionally, we demonstrate that controlling the output language in the instructions has the potential to affect reasoning performance, especially for some low-resource languages, suggesting a promising direction for improving multilingual capabilities in LLMs.

Chain-of-Thought (CoT) significantly enhances formal reasoning capabilities in Large Language Models (LLMs) by training them to explicitly generate intermediate reasoning steps. While LLMs readily benefit from such techniques, improving reasoning in Small Language Models (SLMs) remains challenging due to their limited model capacity. Recent work by Deepseek-R1 demonstrates that distillation from LLM-generated synthetic data can substantially improve the reasoning ability of SLM. However, the detailed modeling recipe is not disclosed. In this work, we present a systematic training recipe for SLMs that consists of four steps: (1) large-scale mid-training on diverse distilled long-CoT data, (2) supervised fine-tuning on high-quality long-CoT data, (3) Rollout DPO leveraging a carefully curated preference dataset, and (4) Reinforcement Learning (RL) with Verifiable Reward. We apply our method on Phi-4-Mini, a compact 3.8B-parameter model. The resulting Phi-4-Mini-Reasoning model exceeds, on math reasoning tasks, much larger reasoning models, e.g., outperforming DeepSeek-R1-Distill-Qwen-7B by 3.2 points and DeepSeek-R1-Distill-Llama-8B by 7.7 points on Math-500. Our results validate that a carefully designed training recipe, with large-scale high-quality CoT data, is effective to unlock strong reasoning capabilities even in resource-constrained small models.

Despite recent progress in large-scale reinforcement learning (RL) for reasoning, the training recipe for building high-performing reasoning models remains elusive. Key implementation details of frontier models, such as DeepSeek-R1, including data curation strategies and RL training recipe, are often omitted. Moreover, recent research indicates distillation remains more effective than RL for smaller models. In this work, we demonstrate that large-scale RL can significantly enhance the reasoning capabilities of strong, small- and mid-sized models, achieving results that surpass those of state-of-the-art distillation-based models. We systematically study the RL training process through extensive ablations and propose a simple yet effective approach: first training on math-only prompts, then on code-only prompts. Notably, we find that math-only RL not only significantly enhances the performance of strong distilled models on math benchmarks (e.g., +14.6% / +17.2% on AIME 2025 for the 7B / 14B models), but also code reasoning tasks (e.g., +6.8% / +5.8% on LiveCodeBench for the 7B / 14B models). In addition, extended code-only RL iterations further improve performance on code benchmarks with minimal or no degradation in math results. We develop a robust data curation pipeline to collect challenging prompts with high-quality, verifiable answers and test cases to enable verification-based RL across both domains. Finally, we identify key experimental insights, including curriculum learning with progressively increasing response lengths and the stabilizing effect of on-policy parameter updates. We find that RL not only elicits the foundational reasoning capabilities acquired during pretraining and supervised fine-tuning (e.g., distillation), but also pushes the limits of the model's reasoning ability, enabling it to solve problems that were previously unsolvable.

We introduce DeepSeek-V3.2, a model that harmonizes high computational efficiency with superior reasoning and agent performance. The key technical breakthroughs of DeepSeek-V3.2 are as follows: (1) DeepSeek Sparse Attention (DSA): We introduce DSA, an efficient attention mechanism that substantially reduces computational complexity while preserving model performance in long-context scenarios. (2) Scalable Reinforcement Learning Framework: By implementing a robust reinforcement learning protocol and scaling post-training compute, DeepSeek-V3.2 performs comparably to GPT-5. Notably, our high-compute variant, DeepSeek-V3.2-Speciale, surpasses GPT-5 and exhibits reasoning proficiency on par with Gemini-3.0-Pro, achieving gold-medal performance in both the 2025 International Mathematical Olympiad (IMO) and the International Olympiad in Informatics (IOI). (3) Large-Scale Agentic Task Synthesis Pipeline: To integrate reasoning into tool-use scenarios, we developed a novel synthesis pipeline that systematically generates training data at scale. This methodology facilitates scalable agentic post-training, yielding substantial improvements in generalization and instruction-following robustness within complex, interactive environments.

The rapid development of open-source large language models (LLMs) has been truly remarkable. However, the scaling law described in previous literature presents varying conclusions, which casts a dark cloud over scaling LLMs. We delve into the study of scaling laws and present our distinctive findings that facilitate scaling of large scale models in two commonly used open-source configurations, 7B and 67B. Guided by the scaling laws, we introduce DeepSeek LLM, a project dedicated to advancing open-source language models with a long-term perspective. To support the pre-training phase, we have developed a dataset that currently consists of 2 trillion tokens and is continuously expanding. We further conduct supervised fine-tuning (SFT) and Direct Preference Optimization (DPO) on DeepSeek LLM Base models, resulting in the creation of DeepSeek Chat models. Our evaluation results demonstrate that DeepSeek LLM 67B surpasses LLaMA-2 70B on various benchmarks, particularly in the domains of code, mathematics, and reasoning. Furthermore, open-ended evaluations reveal that DeepSeek LLM 67B Chat exhibits superior performance compared to GPT-3.5.

Large language models (LLMs) have made impressive progress in handling simple math problems, yet they still struggle with more challenging and complex mathematical tasks. In this paper, we introduce a series of LLMs that employs the Decomposition of thought with code assistance and self-correction for mathematical reasoning, dubbed as DotaMath. DotaMath models tackle complex mathematical tasks by decomposing them into simpler logical subtasks, leveraging code to solve these subtasks, obtaining fine-grained feedback from the code interpreter, and engaging in self-reflection and correction. By annotating diverse interactive tool-use trajectories and employing query evolution on GSM8K and MATH datasets, we generate an instruction fine-tuning dataset called DotaMathQA with 574K query-response pairs. We train a series of base LLMs using imitation learning on DotaMathQA, resulting in DotaMath models that achieve remarkable performance compared to open-source LLMs across various in-domain and out-of-domain benchmarks. Notably, DotaMath-deepseek-7B showcases an outstanding performance of 64.8% on the competitive MATH dataset and 86.7% on GSM8K. Besides, DotaMath-deepseek-7B maintains strong competitiveness on a series of in-domain and out-of-domain benchmarks (Avg. 80.1%). Looking forward, we anticipate that the DotaMath paradigm will open new pathways for addressing intricate mathematical problems. Our code is publicly available at https://github.com/ChengpengLi1003/DotaMath.

Recent large-scale language models (LLMs) with long Chain-of-Thought reasoning-such as DeepSeek-R1-have achieved impressive results on Olympiad-level mathematics benchmarks. However, they often rely on a narrow set of strategies and struggle with problems that require a novel way of thinking. To systematically investigate these limitations, we introduce OMEGA-Out-of-distribution Math Problems Evaluation with 3 Generalization Axes-a controlled yet diverse benchmark designed to evaluate three axes of out-of-distribution generalization, inspired by Boden's typology of creativity: (1) Exploratory-applying known problem solving skills to more complex instances within the same problem domain; (2) Compositional-combining distinct reasoning skills, previously learned in isolation, to solve novel problems that require integrating these skills in new and coherent ways; and (3) Transformative-adopting novel, often unconventional strategies by moving beyond familiar approaches to solve problems more effectively. OMEGA consists of programmatically generated training-test pairs derived from templated problem generators across geometry, number theory, algebra, combinatorics, logic, and puzzles, with solutions verified using symbolic, numerical, or graphical methods. We evaluate frontier (or top-tier) LLMs and observe sharp performance degradation as problem complexity increases. Moreover, we fine-tune the Qwen-series models across all generalization settings and observe notable improvements in exploratory generalization, while compositional generalization remains limited and transformative reasoning shows little to no improvement. By isolating and quantifying these fine-grained failures, OMEGA lays the groundwork for advancing LLMs toward genuine mathematical creativity beyond mechanical proficiency.

Test-time scaling, which leverages additional computation during inference to improve model accuracy, has enabled a new class of Large Language Models (LLMs) that are able to reason through complex problems by understanding the goal, turning this goal into a plan, working through intermediate steps, and checking their own work before answering . Frontier large language models with reasoning capabilities, such as DeepSeek-R1 and OpenAI's gpt-oss, follow the same procedure when solving complex problems by generating intermediate reasoning traces before giving the final answer. Today, these models are being increasingly used to generate reasoning traces that serve as high-quality supervised data for post-training of small and medium-sized language models to teach reasoning capabilities without requiring expensive human curation. In this work, we compare the performance of medium-sized LLMs on Math problems after post-training on two kinds of reasoning traces. We compare the impact of reasoning traces generated by DeepSeek-R1 and gpt-oss LLMs in terms of accuracy and inference efficiency.

Large language models (LLMs) excel at general mathematical reasoning but fail catastrophically on specialized technical mathematics. In wireless communications, where problems require precise manipulation of information-theoretic bounds, optimization constraints, and signal processing formulations, even state-of-the-art models struggle to achieve competent performance. We present WirelessMathLM, demonstrating that compact models (0.5B-7B parameters) can match or exceed much larger models through domain-specific reinforcement learning with verifiable rewards. Our key insight is that wireless mathematics problems possess a unique property--verifiable correctness--that enables effective reinforcement learning without human feedback. We construct WirelessMathBench-XL, a comprehensive benchmark of 4,027 problems from 970 papers. Using Group Relative Policy Optimization (GRPO) with binary verification rewards, we train models directly from base checkpoints without supervised warm-start. Our 7B model achieves 39.5% accuracy on WirelessMathBench-XL, approaching GPT-4o (40.4%) while using about 100 times fewer parameters than DeepSeek-R1 (671B, 57.4%). Remarkably, GRPO training nearly doubles performance across all model scales (0.5B +11%, 3B +103%, 7B +81%), with positive transfer to general mathematics benchmarks--our models gain +8.4 points on average across MATH, Minerva-Math, OlympiadBench, AMC, and AIME without any training on these tasks.

Mathematical problem solving remains a challenging test of reasoning for large language and multimodal models, yet existing benchmarks are limited in size, language coverage, and task diversity. We introduce MathNet, a high-quality, large-scale, multimodal, and multilingual dataset of Olympiad-level math problems together with a benchmark for evaluating mathematical reasoning in generative models and mathematical retrieval in embedding-based systems. MathNet spans 47 countries, 17 languages, and two decades of competitions, comprising 30,676 expert-authored problems with solutions across diverse domains. In addition to the core dataset, we construct a retrieval benchmark consisting of mathematically equivalent and structurally similar problem pairs curated by human experts. MathNet supports three tasks: (i) Problem Solving, (ii) Math-Aware Retrieval, and (iii) Retrieval-Augmented Problem Solving. Experimental results show that even state-of-the-art reasoning models (78.4% for Gemini-3.1-Pro and 69.3% for GPT-5) remain challenged, while embedding models struggle to retrieve equivalent problems. We further show that retrieval-augmented generation performance is highly sensitive to retrieval quality; for example, DeepSeek-V3.2-Speciale achieves gains of up to 12%, obtaining the highest scores on the benchmark. MathNet provides the largest high-quality Olympiad dataset together with the first benchmark for evaluating mathematical problem retrieval, and we publicly release both the dataset and benchmark at https://mathnet.mit.edu.

Large language models (LLMs) have shown promising first-order logic (FOL) reasoning capabilities with applications in various areas. However, their effectiveness in complex mathematical reasoning involving multi-step FOL deductions is still under-researched. While LLMs perform competitively on established mathematical reasoning benchmarks, they struggle with multi-step FOL tasks, as demonstrated by Deepseek-Prover-V2-7B's low accuracy (4.2%) on our proposed theorem proving dataset. This issue arises from the limited exploration of diverse proof strategies and the potential for early reasoning mistakes to undermine entire proofs. To address these issues, we propose DREAM, a self-adaptive solution that enhances the Diversity and REAsonability of LLMs' generation strategies. DREAM incorporates an Axiom-Driven Strategy Diversification mechanism to promote varied strategic outcomes and a Sub-Proposition Error Feedback to help LLMs reflect on and correct their proofs. Our contributions include pioneering advancements in LLMs' mathematical reasoning through FOL theorem proving, introducing a novel inference stage solution that improves performance by 0.6% to 6.4%, and providing a curated dataset of 447 mathematical theorems in Lean 4 format for evaluation.

Mathematical reasoning poses a significant challenge for language models due to its complex and structured nature. In this paper, we introduce DeepSeekMath 7B, which continues pre-training DeepSeek-Coder-Base-v1.5 7B with 120B math-related tokens sourced from Common Crawl, together with natural language and code data. DeepSeekMath 7B has achieved an impressive score of 51.7% on the competition-level MATH benchmark without relying on external toolkits and voting techniques, approaching the performance level of Gemini-Ultra and GPT-4. Self-consistency over 64 samples from DeepSeekMath 7B achieves 60.9% on MATH. The mathematical reasoning capability of DeepSeekMath is attributed to two key factors: First, we harness the significant potential of publicly available web data through a meticulously engineered data selection pipeline. Second, we introduce Group Relative Policy Optimization (GRPO), a variant of Proximal Policy Optimization (PPO), that enhances mathematical reasoning abilities while concurrently optimizing the memory usage of PPO.

In recent years, the rapid development of large reasoning models has resulted in the saturation of existing benchmarks for evaluating mathematical reasoning, highlighting the urgent need for more challenging and rigorous evaluation frameworks. To address this gap, we introduce OlymMATH, a novel Olympiad-level mathematical benchmark, designed to rigorously test the complex reasoning capabilities of LLMs. OlymMATH features 200 meticulously curated problems, each manually verified and available in parallel English and Chinese versions. The problems are systematically organized into two distinct difficulty tiers: (1) AIME-level problems (easy) that establish a baseline for mathematical reasoning assessment, and (2) significantly more challenging problems (hard) designed to push the boundaries of current state-of-the-art models. In our benchmark, these problems span four core mathematical fields, each including a verifiable numerical solution to enable objective, rule-based evaluation. Empirical results underscore the significant challenge presented by OlymMATH, with state-of-the-art models including DeepSeek-R1 and OpenAI's o3-mini demonstrating notably limited accuracy on the hard subset. Furthermore, the benchmark facilitates comprehensive bilingual assessment of mathematical reasoning abilities-a critical dimension that remains largely unaddressed in mainstream mathematical reasoning benchmarks. We release the OlymMATH benchmark at the STILL project: https://github.com/RUCAIBox/Slow_Thinking_with_LLMs.

The irruption of DeepSeek-R1 constitutes a turning point for the AI industry in general and the LLMs in particular. Its capabilities have demonstrated outstanding performance in several tasks, including creative thinking, code generation, maths and automated program repair, at apparently lower execution cost. However, LLMs must adhere to an important qualitative property, i.e., their alignment with safety and human values. A clear competitor of DeepSeek-R1 is its American counterpart, OpenAI's o3-mini model, which is expected to set high standards in terms of performance, safety and cost. In this paper we conduct a systematic assessment of the safety level of both, DeepSeek-R1 (70b version) and OpenAI's o3-mini (beta version). To this end, we make use of our recently released automated safety testing tool, named ASTRAL. By leveraging this tool, we automatically and systematically generate and execute a total of 1260 unsafe test inputs on both models. After conducting a semi-automated assessment of the outcomes provided by both LLMs, the results indicate that DeepSeek-R1 is highly unsafe as compared to OpenAI's o3-mini. Based on our evaluation, DeepSeek-R1 answered unsafely to 11.98% of the executed prompts whereas o3-mini only to 1.19%.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

A paraphrase-quality audit of MathCheck (ICLR 2025) detected 4 semantically incorrect paraphrases in 129 groups (3.1%); removing them drops GPT-4o from rank 2 to rank 4 and elevates Claude Haiku and DeepSeek V3 above it; these ranking changes are invisible to any single-model evaluation. Cross-model unanimity found these errors automatically (>= 3/4 models for MathCheck; >= 6/9 for our primary evaluation) for under $10; in our own dataset the same protocol found that 47% of auto-generated connective-variation paraphrases were semantically incorrect. That flaw compounds a deeper measurement gap: Claude Haiku 4.5 achieves 86% accuracy yet SCR=50%, meaning half its theorems are answered differently under semantically equivalent restatements, while aggregate accuracy across 9 models spans only 86-96% yet Semantic Consistency Rates (SCR) span 50-82% -- a 32-point gap invisible to standard benchmarks. Formally, for any target ranking over 9 frontier models there exists a weighting over paraphrase families that realizes it (No-Free-Benchmark corollary), because no model Pareto-dominates all families -- so benchmark designers who select families are implicitly choosing which model wins. FormInv supplies the audit protocol (replicated on external benchmarks at 100% recall), SCR and per-theorem Cochran's Q as primary invariance measures evaluated on 9 models across 366-811 items (on Lean4-verified theorems), and FormInvSelector for regime-aware model selection.

Autoformalisation, the task of expressing informal mathematical statements in formal language, is often viewed as a direct translation process. This, however, disregards a critical preceding step: conjecturing. Many mathematical problems cannot be formalised directly without first conjecturing a conclusion such as an explicit answer, or a specific bound. Since Large Language Models (LLMs) already struggle with autoformalisation, and the evaluation of their conjecturing ability is limited and often entangled within autoformalisation or proof, it is particularly challenging to understand its effect. To address this gap, we augment existing datasets to create ConjectureBench, and redesign the evaluation framework and metric specifically to measure the conjecturing capabilities of LLMs both as a distinct task and within the autoformalisation pipeline. Our evaluation of foundational models, including GPT-4.1 and DeepSeek-V3.1, reveals that their autoformalisation performance is substantially overestimated when the conjecture is accounted for during evaluation. However, the conjecture should not be assumed to be provided. We design an inference-time method, Lean-FIRe to improve conjecturing and autoformalisation, which, to the best of our knowledge, achieves the first successful end-to-end autoformalisation of 13 PutnamBench problems with GPT-4.1 and 7 with DeepSeek-V3.1. We demonstrate that while LLMs possess the requisite knowledge to generate accurate conjectures, improving autoformalisation performance requires treating conjecturing as an independent task, and investigating further how to correctly integrate it within autoformalisation. Finally, we provide forward-looking guidance to steer future research toward improving conjecturing, an overlooked step of formal mathematical reasoning.

Large Reasoning Models (LRMs), such as OpenAI o1 and DeepSeek-R1, have been rapidly progressing and achieving breakthrough performance on complex reasoning tasks such as mathematics and coding. However, the open-source R1 models have raised safety concerns in wide applications, such as the tendency to comply with malicious queries, which greatly impacts the utility of these powerful models in their applications. In this paper, we introduce RealSafe-R1 as safety-aligned versions of DeepSeek-R1 distilled models. To train these models, we construct a dataset of 15k safety-aware reasoning trajectories generated by DeepSeek-R1, under explicit instructions for expected refusal behavior. Both quantitative experiments and qualitative case studies demonstrate the models' improvements, which are shown in their safety guardrails against both harmful queries and jailbreak attacks. Importantly, unlike prior safety alignment efforts that often compromise reasoning performance, our method preserves the models' reasoning capabilities by maintaining the training data within the original distribution of generation. Model weights of RealSafe-R1 are open-source at https://huggingface.co/RealSafe.

Solving Bengali Math Word Problems (MWPs) remains a major challenge in natural language processing (NLP) due to the language's low-resource status and the multi-step reasoning required. Existing models struggle with complex Bengali MWPs, largely because no human-annotated Bengali dataset has previously addressed this task. This gap has limited progress in Bengali mathematical reasoning. To address this, we created SOMADHAN, a dataset of 8792 complex Bengali MWPs with manually written, step-by-step solutions. We designed this dataset to support reasoning-focused evaluation and model development in a linguistically underrepresented context. Using SOMADHAN, we evaluated a range of large language models (LLMs) - including GPT-4o, GPT-3.5 Turbo, LLaMA series models, Deepseek, and Qwen - through both zero-shot and few-shot prompting with and without Chain of Thought (CoT) reasoning. CoT prompting consistently improved performance over standard prompting, especially in tasks requiring multi-step logic. LLaMA-3.3 70B achieved the highest accuracy of 88% with few-shot CoT prompting. We also applied Low-Rank Adaptation (LoRA) to fine-tune models efficiently, enabling them to adapt to Bengali MWPs with minimal computational cost. Our work fills a critical gap in Bengali NLP by providing a high-quality reasoning dataset and a scalable framework for solving complex MWPs. We aim to advance equitable research in low-resource languages and enhance reasoning capabilities in educational and language technologies.

Mathematical reasoning lies at the heart of artificial intelligence, underpinning applications in education, program verification, and research-level mathematical discovery. Mathematical competitions, in particular, present two challenging problem types: theorem proving, which requires rigorous proofs of stated conclusions, and answer construction, which involves hypothesizing and formally verifying mathematical objects. Large Language Models (LLMs) effectively generate creative candidate answers but struggle with formal verification, while symbolic provers ensure rigor but cannot efficiently handle creative conjecture generation. We introduce the Enumerate-Conjecture-Prove (ECP) framework, a modular neuro-symbolic method integrating LLM-based enumeration and pattern-driven conjecturing with formal theorem proving. We present ConstructiveBench, a dataset of 3,431 answer-construction problems in various math competitions with verified Lean formalizations. On the ConstructiveBench dataset, ECP improves the accuracy of answer construction from a Chain-of-Thought (CoT) baseline of 14.54% to 45.06% with the gpt-4.1-mini model. Moreover, combined with ECP's constructed answers, the state-of-the-art DeepSeek-Prover-V2-7B model generates correct proofs for 858 of the 3,431 constructive problems in Lean, achieving 25.01% accuracy compared to 9.86% for symbolic-only baselines. Our code and dataset are publicly available at https://github.com/JackSun200312/ECP.

Large language models (LLMs) have achieved significant progress in solving complex reasoning tasks by Reinforcement Learning with Verifiable Rewards (RLVR). This advancement is also inseparable from the oversight automated by reliable verifiers. However, current outcome-based verifiers (OVs) are unable to inspect the unreliable intermediate steps in the long reasoning chains of thought (CoTs). Meanwhile, current process-based verifiers (PVs) have difficulties in reliably detecting errors in the complex long CoTs, limited by the scarcity of high-quality annotations due to the prohibitive costs of human annotations. Therefore, we propose the Outcome-based Process Verifier (OPV), which verifies the rationale process of summarized outcomes from long CoTs to achieve both accurate and efficient verification and enable large-scale annotation. To empower the proposed verifier, we adopt an iterative active learning framework with expert annotations to progressively improve the verification capability of OPV with fewer annotation costs. Specifically, in each iteration, the most uncertain cases of the current best OPV are annotated and then subsequently used to train a new OPV through Rejection Fine-Tuning (RFT) and RLVR for the next round. Extensive experiments demonstrate OPV's superior performance and broad applicability. It achieves new state-of-the-art results on our held-out \thisbench, outperforming much larger open-source models such as Qwen3-Max-Preview with an F1 score of 83.1 compared to 76.3. Furthermore, OPV effectively detects false positives within synthetic dataset, closely align with expert assessment. When collaborating with policy models, OPV consistently yields performance gains, e.g., raising the accuracy of DeepSeek-R1-Distill-Qwen-32B from 55.2\% to 73.3\% on AIME2025 as the compute budget scales.

Recent advances in large language models (LLMs) for mathematical reasoning have largely focused on tasks with easily verifiable final answers; however, generating and verifying natural language math proofs remains an open challenge. We identify the absence of a reliable, fine-grained evaluator for LLM-generated math proofs as a critical gap. To address this, we propose a systematic methodology for developing and validating evaluators that assign fine-grained scores on a 0-7 scale to model-generated math proofs. To enable this study, we introduce ProofBench, the first expert-annotated dataset of fine-grained proof ratings, spanning 145 problems from six major math competitions (USAMO, IMO, Putnam, etc) and 435 LLM-generated solutions from Gemini-2.5-pro, o3, and DeepSeek-R1. %with expert gradings. Using ProofBench as a testbed, we systematically explore the evaluator design space across key axes: the backbone model, input context, instructions and evaluation workflow. Our analysis delivers ProofGrader, an evaluator that combines a strong reasoning backbone LM, rich context from reference solutions and marking schemes, and a simple ensembling method; it achieves a low Mean Absolute Error (MAE) of 0.926 against expert scores, significantly outperforming naive baselines. Finally, we demonstrate its practical utility in a best-of-n selection task: at n=16, ProofGrader achieves an average score of 4.14 (out of 7), closing 78% of the gap between a naive binary evaluator (2.48) and the human oracle (4.62), highlighting its potential to advance downstream proof generation.

Full-parameter post-training of trillion-parameter-scale MoE models introduces substantial system-level challenges for large-scale distributed training, including severe memory pressure, non-overlapped communication overhead, and inefficient kernel execution. While most large-scale LLM training systems are built around GPU-based clusters, this report presents an end-to-end optimization practice on the Ascend NPU SuperPOD. Using the DeepSeek-V4 model family as the target workload, we develop a hierarchical optimization framework spanning model-level parallelism, computation-communication orchestration, and low-level kernel execution. The resulting system achieves 34.22% Model FLOPs Utilization (MFU) with a 2.93x improvement over the open-source baseline recipe while maintaining training stability. Building on this optimized infrastructure, we further establish a CPT and SFT workflow for complex Operations Research (OR) tasks. We refer to the integrated framework as SLAI T-Rex. Using DeepSeek-V4-Flash, we develop OR-oriented CPT and SFT data pipelines that combine collected domain resources with solver-verified synthetic optimization documents. The resulting dataset contains 10K high-quality SFT samples spanning four task categories and three problem representations. The specialized model achieves the highest average zero-shot Pass@1 score among the evaluated models, reaching 71.81% and outperforming GPT-5.4-Mini and the base DeepSeek-V4-Flash model by 3.98 and 11.27 percentage points, respectively. Overall, this work demonstrates a full-stack pathway from efficient trillion-parameter model post-training on Ascend infra to domain-specialized Flash models for solver-grounded mathematical modeling, advancing frontier-model systems for complex reasoning.

Trustworthy verifiers are essential for the success of reinforcement learning with verifiable reward (RLVR), which is the core methodology behind various large reasoning models such as DeepSeek-R1. In complex domains like mathematical reasoning, rule-based verifiers have been widely adopted in previous works to train strong reasoning models. However, the reliability of these verifiers and their impact on the RL training process remain poorly understood. In this work, we take mathematical reasoning as a case study and conduct a comprehensive analysis of various verifiers in both static evaluation and RL training scenarios. First, we find that current open-source rule-based verifiers often fail to recognize equivalent answers presented in different formats across multiple commonly used mathematical datasets, resulting in non-negligible false negative rates. This limitation adversely affects RL training performance and becomes more pronounced as the policy model gets stronger. Subsequently, we investigate model-based verifiers as a potential solution to address these limitations. While the static evaluation shows that model-based verifiers achieve significantly higher verification accuracy, further analysis and RL training results imply that they are highly susceptible to hacking, where they misclassify certain patterns in responses as correct (i.e., false positives). This vulnerability is exploited during policy model optimization, leading to artificially inflated rewards. Our findings underscore the unique risks inherent to both rule-based and model-based verifiers, aiming to offer valuable insights to develop more robust reward systems in reinforcement learning.

As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that standard "LLM-as-a-Judge" protocols suffer from a systematic Alignment Gap when applied to upper-undergraduate to early graduate level mathematics. To quantify this, we introduce QEDBench, the first large-scale dual-rubric alignment benchmark to systematically measure alignment with human experts on university-level math proofs by contrasting course-specific rubrics against expert common knowledge criteria. By deploying a dual-evaluation matrix (7 judges x 5 solvers) against 1,000+ hours of human evaluation, we reveal that certain frontier evaluators like Claude Opus 4.5, DeepSeek-V3, Qwen 2.5 Max, and Llama 4 Maverick exhibit significant positive bias (up to +0.18, +0.20, +0.30, +0.36 mean score inflation, respectively). Furthermore, we uncover a critical reasoning gap in the discrete domain: while Gemini 3.0 Pro achieves state-of-the-art performance (0.91 average human evaluation score), other reasoning models like GPT-5 Pro and Claude Sonnet 4.5 see their performance significantly degrade in discrete domains. Specifically, their average human evaluation scores drop to 0.72 and 0.63 in Discrete Math, and to 0.74 and 0.50 in Graph Theory. In addition to these research results, we also release QEDBench as a public benchmark for evaluating and improving AI judges. Our benchmark is publicly published at https://github.com/qqliu/Yale-QEDBench.

The rapid advancement of large language models (LLMs) demands robust, unbiased, and scalable evaluation methods. However, human annotations are costly to scale, model-based evaluations are susceptible to stylistic biases, and target-answer-based benchmarks are vulnerable to data contamination and cheating. To address these limitations, we propose StructTest, a novel benchmark that evaluates LLMs on their ability to follow compositional instructions and generate structured outputs, providing an unbiased, cost-effective, and difficult-to-cheat evaluation framework. Assessments are conducted deterministically using a rule-based evaluator, which can be easily extended to new tasks and datasets. By testing structured outputs across diverse domains including Summarization, Code, HTML, and Math, and evaluating 17 popular LLMs, we demonstrate that StructTest remains challenging even for top-performing models like Deepseek-V3/R1 and GPT-4o, establishing it as a robust proxy for measuring reasoning capabilities. We believe StructTest offers a critical and complementary approach to achieving objective and comprehensive model evaluation.

Mixture-of-experts (MoE) architectures enable scaling large language models (LLMs) to vast parameter counts without a proportional rise in computational costs. However, the significant memory demands of large MoE models hinder their deployment across various computational environments, from cloud servers to consumer devices. This study first demonstrates pronounced task-specific specialization in expert activation patterns within MoE layers. Building on this, we introduce PreMoe, a novel framework that enables efficient deployment of massive MoE models in memory-constrained environments. PreMoe features two main components: probabilistic expert pruning (PEP) and task-adaptive expert retrieval (TAER). PEP employs a new metric, the task-conditioned expected selection score (TCESS), derived from router logits to quantify expert importance for specific tasks, thereby identifying a minimal set of critical experts. TAER leverages these task-specific expert importance profiles for efficient inference. It pre-computes and stores compact expert patterns for diverse tasks. When a user query is received, TAER rapidly identifies the most relevant stored task pattern and reconstructs the model by loading only the small subset of experts crucial for that task. This approach dramatically reduces the memory footprint across all deployment scenarios. DeepSeek-R1 671B maintains 97.2\% accuracy on MATH500 when pruned to 8/128 configuration (50\% expert reduction), and still achieves 72.0\% with aggressive 8/32 pruning (87.5\% expert reduction). Pangu-Ultra-MoE 718B achieves 97.15\% on MATH500 and 81.3\% on AIME24 with 8/128 pruning, while even more aggressive pruning to 4/64 (390GB memory) preserves 96.95\% accuracy on MATH500. We make our code publicly available at https://github.com/JarvisPei/PreMoe.

When a large language model under reinforcement learning commits a wrong reasoning step early in a trajectory, standard algorithms force it to keep generating until the maximum horizon, spending compute on tokens that never receive positive reward and polluting advantage estimates with post-failure noise. We propose ESPO (Early-Stopping Proximal Policy Optimization), which detects trajectory failure on-the-fly and terminates rollouts early. At each generation step, ESPO computes a surrogate regret using only the logits already computed during sampling, and terminates when the smoothed cumulative regret significantly exceeds its estimated values. Truncated trajectories are treated as absorbing failure states with a terminal reward, concentrating negative temporal-difference (TD) errors near the detected failure step without any additional reward model or human annotation. On DeepSeek-R1-Distill-Qwen-7B trained for mathematical reasoning, ESPO surpasses PPO on AIME~2024 (46.28% vs. 45.25%), AMC~2023 (85.83% vs. 82.94%), and MATH-500 (87.42% vs. 85.43%), while saving more than 20% rollout tokens cumulatively.

Group Relative Policy Optimization (GRPO) is effective when the current policy already samples useful reasoning trajectories, but it stalls on hard prompts whose correct solution modes lie outside the student's on-policy support. We propose TREK (Teacher-Routed Exploration via Forward KL), a simple staged procedure that uses distillation not for imitation but for exploration support expansion. A key advantage of TREK is its generality: because it only consumes verified output trajectories, it can use an external black-box teacher, a white-box teacher, or the same model given additional inference-time context, and it can efficiently identify which hard-prompt samples are most worth consolidating even when teacher internals are unavailable. TREK first identifies prompts where the unaided student has very low pass rate, queries a proposal source to produce verified candidate solutions, keeps the top-r proposals ranked by current student likelihood, applies a short forward-KL phase to pull those verified modes into the student's support, and then returns to standard on-policy GRPO refinement. On mathematical reasoning, TREK with DeepSeek-V4 proposals improves Qwen3 models across all tested scales on AIME 2024 and AIME 2025; for Qwen3-8B, it improves AIME 2025 from 36.9 to 40.3 and AIME 2024 from 47.9 to 51.1 (avg@16), while the self-context variant reaches 38.5 and 49.6 without an external teacher. On agentic tasks, TREK raises ALFWorld success rate from 75.8 to 82.8 and ScienceWorld success rate from 12.5 to 26.7; notably, on the hardest task types, TREK achieves high success rates early in training while unaided GRPO requires substantially more optimization steps to reach comparable levels.

Reinforcement learning with verifiable rewards (RLVR) for Large Reasoning Models hinges on baseline estimation for variance reduction, but existing approaches pay a heavy price: PPO requires a policy-model scale critic, while GRPO needs multiple rollouts per prompt to keep its empirical group mean stable. We introduce Policy Optimization with Internal State Value Estimation), which obtains a baseline at negligible cost by using the policy model's internal signals already computed during the policy forward pass. A lightweight probe predicts the expected verifiable reward from the hidden states of the prompt and generated trajectory, as well as token-entropy statistics, and is trained online alongside the policy. To preserve gradient unbiasedness despite using trajectory-conditioned features, we introduce a cross-rollout construction that predicts each rollout's value from an independent rollout's internal states. Because POISE estimates prompt value using only a single rollout, it enables higher prompt diversity for a fixed compute budget during training. This reduces gradient variance for more stable learning and also eliminates the compute overhead of sampling costs for detecting zero-advantage prompts. On Qwen3-4B and DeepSeek-R1-Distill-Qwen-1.5B across math reasoning benchmarks, POISE matches DAPO while requiring less compute. Moreover, its value estimator shows similar performance to a separate LLM-scale value model and generalizes to various verifiable tasks. By leveraging the model's own internal representations, POISE enables more stable and efficient policy optimization.

Generative reward models with parallel sampling have enabled effective test-time scaling for reasoning tasks. Current approaches employ pointwise scoring of individual solutions or pairwise comparisons. However, pointwise methods underutilize LLMs' comparative abilities, while pairwise methods scale inefficiently with larger sampling budgets. We introduce GenSelect, where the LLM uses long reasoning to select the best solution among N candidates. This leverages LLMs' comparative strengths while scaling efficiently across parallel sampling budgets. For math reasoning, we demonstrate that reasoning models, such as QwQ and DeepSeek-R1-0528, excel at GenSelect, outperforming existing scoring approaches with simple prompting.

The recent DeepSeek-R1 release has demonstrated the immense potential of reinforcement learning (RL) in enhancing the general reasoning capabilities of large language models (LLMs). While DeepSeek-R1 and other follow-up work primarily focus on applying RL to competitive coding and math problems, this paper introduces SWE-RL, the first approach to scale RL-based LLM reasoning for real-world software engineering. Leveraging a lightweight rule-based reward (e.g., the similarity score between ground-truth and LLM-generated solutions), SWE-RL enables LLMs to autonomously recover a developer's reasoning processes and solutions by learning from extensive open-source software evolution data -- the record of a software's entire lifecycle, including its code snapshots, code changes, and events such as issues and pull requests. Trained on top of Llama 3, our resulting reasoning model, Llama3-SWE-RL-70B, achieves a 41.0% solve rate on SWE-bench Verified -- a human-verified collection of real-world GitHub issues. To our knowledge, this is the best performance reported for medium-sized (<100B) LLMs to date, even comparable to leading proprietary LLMs like GPT-4o. Surprisingly, despite performing RL solely on software evolution data, Llama3-SWE-RL has even emerged with generalized reasoning skills. For example, it shows improved results on five out-of-domain tasks, namely, function coding, library use, code reasoning, mathematics, and general language understanding, whereas a supervised-finetuning baseline even leads to performance degradation on average. Overall, SWE-RL opens up a new direction to improve the reasoning capabilities of LLMs through reinforcement learning on massive software engineering data.

Recent advances in Large Language Model (LLM) agents have demonstrated their promising general capabilities. However, their performance in specialized real-world domains often degrades due to challenges in effectively integrating external tools and specific prompting strategies. While methods like agentic reinforcement learning have been proposed to address this, they typically rely on costly parameter updates, for example, through a process that uses Supervised Fine-Tuning (SFT) followed by a Reinforcement Learning (RL) phase with Group Relative Policy Optimization (GRPO) to alter the output distribution. However, we argue that LLMs can achieve a similar effect on the output distribution by learning experiential knowledge as a token prior, which is a far more lightweight approach that not only addresses practical data scarcity but also avoids the common issue of overfitting. To this end, we propose Training-Free Group Relative Policy Optimization (Training-Free GRPO), a cost-effective solution that enhances LLM agent performance without any parameter updates. Our method leverages the group relative semantic advantage instead of numerical ones within each group of rollouts, iteratively distilling high-quality experiential knowledge during multi-epoch learning on a minimal ground-truth data. Such knowledge serves as the learned token prior, which is seamlessly integrated during LLM API calls to guide model behavior. Experiments on mathematical reasoning and web searching tasks demonstrate that Training-Free GRPO, when applied to DeepSeek-V3.1-Terminus, significantly improves out-of-domain performance. With just a few dozen training samples, Training-Free GRPO outperforms fine-tuned small LLMs with marginal training data and cost.

Large Reasoning Models (LRMs) have demonstrated remarkable performance on complex reasoning tasks by employing test-time scaling. However, they often generate over-long chains-of-thought that, driven by substantial reflections such as repetitive self-questioning and circular reasoning, lead to high token consumption, substantial computational overhead, and increased latency without improving accuracy, particularly in smaller models. Our observation reveals that increasing problem complexity induces more excessive and unnecessary reflection, which in turn reduces accuracy and increases token overhead. To address this challenge, we propose Adaptive Reflection and Length Coordinated Penalty (ARLCP), a novel reinforcement learning framework designed to dynamically balance reasoning efficiency and solution accuracy. ARLCP introduces two key innovations: (1) a reflection penalty that adaptively curtails unnecessary reflective steps while preserving essential reasoning, and (2) a length penalty calibrated to the estimated complexity of the problem. By coordinating these penalties, ARLCP encourages the model to generate more concise and effective reasoning paths. We evaluate our method on five mathematical reasoning benchmarks using DeepSeek-R1-Distill-Qwen-1.5B and DeepSeek-R1-Distill-Qwen-7B models. Experimental results show that ARLCP achieves a superior efficiency-accuracy trade-off compared to existing approaches. For the 1.5B model, it reduces the average response length by 53.1% while simultaneously improving accuracy by 5.8%. For the 7B model, it achieves a 35.0% reduction in length with a 2.7% accuracy gain. The code is released at https://github.com/ZeweiYu1/ARLCP .

Entropy-based deep reasoning has emerged as a promising direction for improving the reasoning capabilities of Large Language Models (LLMs), but existing methods often either increase response length indiscriminately or shorten responses at the cost of accuracy. To better balance this trade-off, we introduce Conditional Entropy Shaping (CES), a framework that dynamically controls token-level response entropy, enabling LLMs to produce concise solutions on simple problems while encouraging deeper exploration on hard ones. Built on DAPO, CES uses token-level entropy as an uncertainty signal and applies a conditional bidirectional policy: it penalizes high-entropy "forking point" tokens on correct reasoning paths to improve conciseness, and rewards them on incorrect paths to encourage exploration and error correction. We implement CES on DeepSeek-R1-Distill-7B and evaluate it on 12 mathematical benchmarks. CES consistently improves average accuracy while reducing response length relative to DAPO, and supplementary experiments show similar trends on a smaller 1.5B backbone and on out-of-domain benchmarks.

Large Reasoning Models (LRMs) excel at complex tasks using Chain-of-Thought (CoT) reasoning. However, their tendency to overthinking leads to unnecessarily lengthy reasoning chains, dramatically increasing inference costs. To mitigate this issue, we introduce VeriThinker, a novel approach for CoT compression. Unlike conventional methods that fine-tune LRMs directly on the original reasoning task using synthetic concise CoT data, we innovatively fine-tune the model solely through an auxiliary verification task. By training LRMs to accurately verify the correctness of CoT solutions, the LRMs inherently become more discerning about the necessity of subsequent self-reflection steps, thereby effectively suppressing overthinking. Extensive experiments validate that VeriThinker substantially reduces reasoning chain lengths while maintaining or even slightly improving accuracy. When applied to DeepSeek-R1-Distill-Qwen-7B, our approach reduces reasoning tokens on MATH500 from 3790 to 2125 while improving accuracy by 0.8% (94.0% to 94.8%), and on AIME25, tokens decrease from 14321 to 10287 with a 2.1% accuracy gain (38.7% to 40.8%). Additionally, our experiments demonstrate that VeriThinker can also be zero-shot generalized to speculative reasoning. Code is available at https://github.com/czg1225/VeriThinker

OpenAI o1 and DeepSeek R1 achieve or even surpass human expert-level performance in complex domains like mathematics and science, with reinforcement learning (RL) and reasoning playing a crucial role. In autonomous driving, recent end-to-end models have greatly improved planning performance but still struggle with long-tailed problems due to limited common sense and reasoning abilities. Some studies integrate vision-language models (VLMs) into autonomous driving, but they typically rely on pre-trained models with simple supervised fine-tuning (SFT) on driving data, without further exploration of training strategies or optimizations specifically tailored for planning. In this paper, we propose AlphaDrive, a RL and reasoning framework for VLMs in autonomous driving. AlphaDrive introduces four GRPO-based RL rewards tailored for planning and employs a two-stage planning reasoning training strategy that combines SFT with RL. As a result, AlphaDrive significantly improves both planning performance and training efficiency compared to using only SFT or without reasoning. Moreover, we are also excited to discover that, following RL training, AlphaDrive exhibits some emergent multimodal planning capabilities, which is critical for improving driving safety and efficiency. To the best of our knowledge, AlphaDrive is the first to integrate GRPO-based RL with planning reasoning into autonomous driving. Code will be released to facilitate future research.

Reinforcement Learning with Verifiable Rewards (RLVR) has become the standard paradigm for LLM mathematical reasoning, with Group Relative Policy Optimization (GRPO) serving as the dominant algorithm. We identify two overlooked inefficiencies inherent in GRPO. First, a fixed KL coefficient overly restricts policy exploration at moments when the model needs to diverge significantly from the reference policy. Second, uniform question sampling overlooks that moderately difficult problems produce the most informative gradient signals. We propose FG-ExPO, short for Frontier-Guided Exploration-Prioritized Policy Optimization, which integrates two lightweight components. Accuracy-Conditioned KL Scaling (AKL) adjusts the KL penalty strength through a smooth nonlinear function of batch average accuracy, loosening the constraint when the model performs poorly and strengthening it when the model achieves satisfactory results. Gaussian Curriculum Sampling (GCS) assigns sampling weights to questions following a Gaussian distribution centered at a moderate accuracy level around 0.5, focusing model training on its learning frontier. We conduct evaluations on DeepSeek-R1-Distill-Qwen-1.5B and Qwen3-8B-Base across six mainstream mathematical reasoning benchmarks. Experimental results demonstrate that FG-ExPO consistently outperforms vanilla GRPO. It delivers an absolute improvement of 13.34 on the AIME 2025 pass@32 metric, rising from 63.33 percent to 76.67 percent, and obtains an average pass@32 gain of 2.66 on the 8B model. The substantially larger performance gains observed on pass@32 compared to pass@1 verify that FG-ExPO enlarges the model's effective exploration space under a fixed inference budget.

We aim to improve the reasoning capabilities of language models via reinforcement learning (RL). Recent RL post-trained models like DeepSeek-R1 have demonstrated reasoning abilities on mathematical and coding tasks. However, prior studies suggest that using RL alone to improve reasoning on inherently difficult tasks is less effective. Here, we draw inspiration from curriculum learning and propose to schedule tasks from easy to hard (E2H), allowing LLMs to build reasoning skills gradually. Our method is termed E2H Reasoner. Empirically, we observe that, although easy tasks are important initially, fading them out through appropriate scheduling is essential in preventing overfitting. Theoretically, we establish convergence guarantees for E2H Reasoner within an approximate policy iteration framework. We derive finite-sample complexity bounds and show that when tasks are appropriately decomposed and conditioned, learning through curriculum stages requires fewer total samples than direct learning. Experiments across multiple domains show that E2H Reasoner significantly improves the reasoning ability of small LLMs (1.5B to 3B), which otherwise struggle when trained with vanilla RL alone, highlighting the effectiveness of our method. Our code can be found on https://github.com/divelab/E2H-Reasoning.

Large Language Models (LLMs), such as OpenAI's o1-series have demonstrated compelling capabilities for complex reasoning tasks via the extended chain-of-thought (CoT) reasoning mechanism. However, recent studies reveal substantial redundancy in the CoT reasoning traces, which not only increases inference latency but also negatively impacts model performance by diverting attention to unnecessary reasoning paths. To address this issue, we investigate the internal reasoning structures of LLMs and categorize them into three primary thought types: execution, reflection, and transition thoughts. Moreover, our analysis reveals that excessive reflection and transition thoughts are strongly correlated with failure cases and these thought categories exhibit clear separation in the latent space. Based on these, we introduce SEAL (Steerable reasoning calibration), a training-free approach that seamlessly calibrates the CoT process, improving accuracy while demonstrating significant efficiency gains. SEAL consists of an offline stage for extracting the reasoning steering vector in the latent space, followed by an on-the-fly calibration of the reasoning trace through representation intervention using the steering vector. Notably, the steering vector exhibits strong transferability across various tasks. Extensive experiments across multiple models (DeepSeek-R1-Distill and QwQ-32B-Preview) and benchmarks (Math500, GSM8K, LiveCodeBench) validate the effectiveness of SEAL, up to a 11% improvement in accuracy while reducing reasoning tokens by 11.8% to 50.4%. Our code is publicly available at https://github.com/VITA-Group/SEAL.

The success of Large Language Models in mathematical reasoning relies heavily on the generation of diverse and valid solution paths during the rollout phase. However, current rollout techniques face a fundamental trade-off: token-level sampling often yields redundant trajectories that differ only in rephrasing, while embedding-level methods utilizing random noise frequently disrupt semantic consistency. To resolve this, we introduce N-GRPO, a novel exploration strategy integrated into the Group Relative Policy Optimization (GRPO) framework. Rather than relying on token-level sampling or native embedding-level noise, our approach leverages Semantic Neighbor Mixing. This mechanism dynamically constructs input representations by mixing the embeddings of an anchor token and its nearest semantic neighbors, thereby injecting diversity while strictly adhering to the local semantic manifold. Experimental evaluations on the DeepSeek-R1-Distill-Qwen models across different sizes show that N-GRPO not only achieves consistent improvements over strong baselines on math reasoning benchmarks but also exhibits robust generalization capabilities on out-of-distribution tasks.

We present that hierarchical LLM reasoning via scaling thought templates can effectively optimize the reasoning search space and outperform the mathematical reasoning capabilities of powerful LLMs like OpenAI o1-preview and DeepSeek V3. We train our ReasonFlux-32B model with only 8 GPUs and introduces three innovations: (i) a structured and generic thought template library, containing around 500 high-level thought templates capable of generalizing to similar or relevant reasoning problems; (ii) performing hierarchical reinforcement learning on a sequence of thought templates instead of long CoTs, optimizing a base LLM to plan out an optimal template trajectory for gradually handling complex problems; (iii) a brand new inference scaling system that enables hierarchical LLM reasoning by adaptively scaling thought templates at inference time. With a template trajectory containing sequential thought templates, our ReasonFlux-32B significantly advances math reasoning capabilities to state-of-the-art levels. Notably, on the MATH benchmark, it achieves an accuracy of 91.2% and surpasses o1-preview by 6.7%. On the USA Math Olympiad (AIME) benchmark, ReasonFlux-32B solves an average of 56.7% of problems, surpassing o1-preview and DeepSeek-V3 by 27% and 45%, respectively. Code: https://github.com/Gen-Verse/ReasonFlux

Large language models (LLMs) have exhibited impressive reasoning abilities on a wide range of complex tasks. However, enhancing these capabilities through post-training remains resource intensive, particularly in terms of data and computational cost. Although recent efforts have sought to improve sample efficiency through selective data curation, existing methods often rely on heuristic or task-specific strategies that hinder scalability. In this work, we introduce InfiAlign, a scalable and sample-efficient post-training framework that integrates supervised fine-tuning (SFT) with Direct Preference Optimization (DPO) to align LLMs for enhanced reasoning. At the core of InfiAlign is a robust data selection pipeline that automatically curates high-quality alignment data from open-source reasoning datasets using multidimensional quality metrics. This pipeline enables significant performance gains while drastically reducing data requirements and remains extensible to new data sources. When applied to the Qwen2.5-Math-7B-Base model, our SFT model achieves performance on par with DeepSeek-R1-Distill-Qwen-7B, while using only approximately 12% of the training data, and demonstrates strong generalization across diverse reasoning tasks. Additional improvements are obtained through the application of DPO, with particularly notable gains in mathematical reasoning tasks. The model achieves an average improvement of 3.89% on AIME 24/25 benchmarks. Our results highlight the effectiveness of combining principled data selection with full-stage post-training, offering a practical solution for aligning large reasoning models in a scalable and data-efficient manner. The model checkpoints are available at https://huggingface.co/InfiX-ai/InfiAlign-Qwen-7B-SFT.

Large reasoning models (LRMs) aim to solve diverse and complex problems through structured reasoning. Recent advances in group-based policy optimization methods have shown promise in enabling stable advantage estimation without reliance on process-level annotations. However, these methods rely on advantage gaps induced by high-quality samples within the same batch, which makes the training process fragile and inefficient when intra-group advantages collapse under challenging tasks. To address these problems, we propose a reinforcement learning mechanism named \textbf{R^3} that along three directions: (1) a cross-context \underline{\textbf{R}eplay} strategy that maintains the intra-group advantage by recalling valuable examples from historical trajectories of the same query, (2) an in-context self-\underline{\textbf{R}eflection} mechanism enabling models to refine outputs by leveraging past failures, and (3) a structural entropy \underline{\textbf{R}anking reward}, which assigns relative rewards to truncated or failed samples by ranking responses based on token-level entropy patterns, capturing both local exploration and global stability. We implement our method on Deepseek-R1-Distill-Qwen-1.5B and train it on the DeepscaleR-40k in the math domain. Experiments demonstrate our method achieves SoTA performance on several math benchmarks, representing significant improvements and fewer reasoning tokens over the base models. Code and model will be released.

Large Language Models (LLMs) have demonstrated remarkable progress in complex reasoning tasks through both post-training and test-time scaling laws. While prevalent test-time scaling approaches are often realized by using external reward models to guide the model generation process, we find only marginal gains can be acquired when scaling a model post-trained on specific reasoning tasks. We identify that the limited improvement stems from distribution discrepancies between the specific post-trained generator and the general reward model. To address this, we propose a framework that incentivizes LLMs to self-verify their own answers. By unifying answer generation and verification within a single reinforcement learning (RL) process, we train models that can effectively assess the correctness of their own solutions. The trained model can further scale its performance during inference time by verifying its generations, without the need for external verifiers. We train our self-verification models based on Qwen2.5-Math-7B and DeepSeek-R1-Distill-Qwen-1.5B, demonstrating its capabilities across varying reasoning context lengths. Experiments on multiple mathematical reasoning benchmarks show that our models can not only improve post-training performance but also enable effective test-time scaling. Our code is available at https://github.com/mansicer/self-verification.

Language Reasoning Models (LRMs) achieve strong performance by scaling test-time computation but often suffer from ``overthinking'', producing excessively long reasoning traces that increase latency and memory usage. Existing LRMs typically enforce conciseness with uniform length penalties, which over-compress crucial early deduction steps at the sequence level and indiscriminately penalize all queries at the group level. To solve these limitations, we propose \model, a dual-level framework for prefix-protected and difficulty-aware compression under hierarchical supervision. At the sequence level, prefix-protected optimization employs decaying mixed rollouts to maintain valid reasoning paths while promoting conciseness. At the group level, difficulty-aware penalty dynamically scales length constraints based on query complexity, maintaining exploration for harder questions while curbing redundancy on easier ones. Extensive experiments on DeepSeek-R1-Distill-Qwen (1.5B/7B) demonstrate that \model achieves a substantial reduction in token usage (up to 55.7\%) while simultaneously improving accuracy (up to 4.1\%) on math benchmarks, with generalization ability to code, science, and general domains.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for enhancing reasoning in Large Language Models (LLMs). However, it frequently encounters challenges such as entropy collapse, excessive verbosity, and insufficient exploration for hard problems. Crucially, existing reward schemes fail to distinguish between the need for extensive search during problem-solving and the efficiency required for mastered knowledge. In this work, we introduce T2T(Thickening-to-Thinning), a dynamic reward framework inspired by human learning processes. Specifically, it implements a dual-phase mechanism: (1) On incorrect attempts, T2T incentivizes "thickening" (longer trajectories) to broaden the search space and explore novel solution paths; (2) Upon achieving correctness, it shifts to "thinning", imposing length penalties to discourage redundancy, thereby fostering model confidence and crystallizing reasoning capabilities. Extensive experiments on mathematical benchmarks (MATH-500, AIME, AMC) across Qwen-series and Deepseek models demonstrate that T2T significantly outperforms standard GRPO and recent baselines, achieving superior performance.

Inference-time scaling enhances the reasoning ability of a language model (LM) by extending its chain-of-thought (CoT). However, existing approaches typically generate the entire reasoning chain in a single forward pass, which often leads to CoT derailment, i.e., the reasoning trajectory drifting off course due to compounding errors. This problem is particularly severe for smaller LMs with long CoTs due to their limited capacity. To address this, we analyze raw long CoTs and uncover a reasoning hierarchy consisting of planning and execution steps. Our analysis reveals that most reasoning errors stem from incorrect planning. Motivated by this observation, we propose Multi-Path Plan Aggregation (MPPA), a framework that augments single-pass reasoning with plan exploration and aggregation. Following a variable interval schedule based on the token position, MPPA generates multiple candidate plans and aggregates them into a refined planning step. To maintain efficiency, we adopt a minimal design in which the base LM serves as the primary policy, while a lightweight LoRA module implements the plan aggregation policy. We further observe that outcome-reward RL is inefficient for long trajectories (e.g., exceeding 4K tokens). To overcome this, we introduce online Step-DPO, a process-level preference optimization scheme that leverages Twisted Sequential Monte Carlo (TSMC) to provide scalable stepwise supervision using small LMs. This yields more efficient training, improved stability, and higher accuracy. Extensive experiments on challenging math, science, and logical reasoning benchmarks demonstrate that, with only 10% SFT data and 5% of preference pairs, our method outperforms both the DeepSeek-R1 distillation baseline and the outcome-reward RL baseline across multiple base models and tasks.

Sparse Mixture-of-Experts (MoE) has become a key architecture for scaling large language models (LLMs) efficiently. Recent fine-grained MoE designs introduce hundreds of experts per layer, with multiple experts activated per token, enabling stronger specialization. However, during pre-training, routers are optimized mainly for stability and robustness: they converge prematurely and enforce balanced usage, limiting the full potential of model performance and efficiency at inference. In this work, we uncover two overlooked issues: (i) a few highly influential experts are underutilized due to premature and balanced routing decisions; and (ii) enforcing a fixed number of active experts per token introduces substantial redundancy. Instead of retraining models or redesigning MoE architectures, we introduce Ban&Pick, a post-training, plug-and-play strategy for smarter routing. Pick discovers and reinforces key experts-a small group with outsized impact on performance-leading to notable accuracy gains across domains. Ban further dynamically prunes redundant experts based on layer and token sensitivity, delivering faster inference with minimal accuracy loss. Experiments on fine-grained MoE-LLMs (DeepSeek, Qwen3) across math, code, and general reasoning benchmarks demonstrate that Ban\&Pick delivers free performance gains and inference acceleration without retraining or architectural changes. For instance, on Qwen3-30B-A3B, it improves accuracy from 80.67 to 84.66 on AIME2024 and from 65.66 to 68.18 on GPQA-Diamond, while accelerating inference by 1.25x under the vLLM.

Large reasoning language models such as OpenAI-o1 and Deepseek-R1 have recently attracted widespread attention due to their impressive task-solving abilities. However, the enormous model size and the generation of lengthy thought chains introduce significant reasoning costs and response latency. Existing methods for efficient reasoning mainly focus on reducing the number of model parameters or shortening the chain-of-thought length. In this paper, we introduce Speculative Chain-of-Thought (SCoT), which reduces reasoning latency from another perspective by accelerated average reasoning speed through large and small model collaboration. SCoT conducts thought-level drafting using a lightweight draft model. Then it selects the best CoT draft and corrects the error cases with the target model. The proposed thinking behavior alignment improves the efficiency of drafting and the draft selection strategy maintains the prediction accuracy for complex problems. Experimental results on GSM8K, MATH, GaoKao, CollegeMath and Olympiad datasets show that SCoT reduces reasoning latency by 48\%sim66\% for Deepseek-R1-Distill-Qwen-32B while achieving near-target-model-level performance. Our code is available at https://github.com/Jikai0Wang/Speculative_CoT.

We present AM-Thinking-v1, a 32B dense language model that advances the frontier of reasoning, embodying the collaborative spirit of open-source innovation. Outperforming DeepSeek-R1 and rivaling leading Mixture-of-Experts (MoE) models like Qwen3-235B-A22B and Seed1.5-Thinking, AM-Thinking-v1 achieves impressive scores of 85.3 on AIME 2024, 74.4 on AIME 2025, and 70.3 on LiveCodeBench, showcasing state-of-the-art mathematical and coding capabilities among open-source models of similar scale. Built entirely from the open-source Qwen2.5-32B base model and publicly available queries, AM-Thinking-v1 leverages a meticulously crafted post-training pipeline - combining supervised fine-tuning and reinforcement learning - to deliver exceptional reasoning capabilities. This work demonstrates that the open-source community can achieve high performance at the 32B scale, a practical sweet spot for deployment and fine-tuning. By striking a balance between top-tier performance and real-world usability, we hope AM-Thinking-v1 inspires further collaborative efforts to harness mid-scale models, pushing reasoning boundaries while keeping accessibility at the core of innovation. We have open-sourced our model on https://huggingface.co/a-m-team/AM-Thinking-v1{Hugging Face}.

Recent advances in model distillation demonstrate that data from advanced reasoning models (e.g., DeepSeek-R1, OpenAI's o1) can effectively transfer complex reasoning abilities to smaller, efficient student models. However, standard practices employ rejection sampling, discarding incorrect reasoning examples -- valuable, yet often underutilized data. This paper addresses the critical question: How can both positive and negative distilled reasoning traces be effectively leveraged to maximize LLM reasoning performance in an offline setting? To this end, We propose Reinforcement Distillation (REDI), a two-stage framework. Stage 1 learns from positive traces via Supervised Fine-Tuning (SFT). Stage 2 further refines the model using both positive and negative traces through our proposed REDI objective. This novel objective is a simple, reference-free loss function that outperforms established methods like DPO and SimPO in this distillation context. Our empirical evaluations demonstrate REDI's superiority over baseline Rejection Sampling SFT or SFT combined with DPO/SimPO on mathematical reasoning tasks. Notably, the Qwen-REDI-1.5B model, post-trained on just 131k positive and negative examples from the open Open-R1 dataset, achieves an 83.1% score on MATH-500 (pass@1). Its performance matches or surpasses that of DeepSeek-R1-Distill-Qwen-1.5B (a model post-trained on 800k proprietary data) across various mathematical reasoning benchmarks, establishing a new state-of-the-art for 1.5B models post-trained offline with openly available data.

Large language models (LLMs) have demonstrated impressive reasoning capabilities by scaling test-time compute via long Chain-of-Thought (CoT). However, recent findings suggest that raw token counts are unreliable proxies for reasoning quality: increased generation length does not consistently correlate with accuracy and may instead signal "overthinking," leading to performance degradation. In this work, we quantify inference-time effort by identifying deep-thinking tokens -- tokens where internal predictions undergo significant revisions in deeper model layers prior to convergence. Across four challenging mathematical and scientific benchmarks (AIME 24/25, HMMT 25, and GPQA-diamond) and a diverse set of reasoning-focused models (GPT-OSS, DeepSeek-R1, and Qwen3), we show that deep-thinking ratio (the proportion of deep-thinking tokens in a generated sequence) exhibits a robust and consistently positive correlation with accuracy, substantially outperforming both length-based and confidence-based baselines. Leveraging this insight, we introduce Think@n, a test-time scaling strategy that prioritizes samples with high deep-thinking ratios. We demonstrate that Think@n matches or exceeds standard self-consistency performance while significantly reducing inference costs by enabling the early rejection of unpromising generations based on short prefixes.

Existing approaches typically rely on fixed length penalties, but such penalties are hard to tune and fail to adapt to the evolving reasoning abilities of LLMs, leading to suboptimal trade-offs between accuracy and conciseness. To address this challenge, we propose Leash (adaptive LEngth penAlty and reward SHaping), a reinforcement learning framework for efficient reasoning in LLMs. We formulate length control as a constrained optimization problem and employ a Lagrangian primal-dual method to dynamically adjust the penalty coefficient. When generations exceed the target length, the penalty is intensified; when they are shorter, it is relaxed. This adaptive mechanism guides models toward producing concise reasoning without sacrificing task performance. Experiments on Deepseek-R1-Distill-Qwen-1.5B and Qwen3-4B-Thinking-2507 show that Leash reduces the average reasoning length by 60% across diverse tasks - including in-distribution mathematical reasoning and out-of-distribution domains such as coding and instruction following - while maintaining competitive performance. Our work thus presents a practical and effective paradigm for developing controllable and efficient LLMs that balance reasoning capabilities with computational budgets.

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model Qwen2.5-Math-1.5B, we identify a single example that elevates model performance on MATH500 from 36.0% to 73.6%, and improves the average performance across six common mathematical reasoning benchmarks from 17.6% to 35.7%. This result matches the performance obtained using the 1.2k DeepScaleR subset (MATH500: 73.6%, average: 35.9%), which includes the aforementioned example. Similar substantial improvements are observed across various models (Qwen2.5-Math-7B, Llama3.2-3B-Instruct, DeepSeek-R1-Distill-Qwen-1.5B), RL algorithms (GRPO and PPO), and different math examples (many of which yield approximately 30% or greater improvement on MATH500 when employed as a single training example). In addition, we identify some interesting phenomena during 1-shot RLVR, including cross-domain generalization, increased frequency of self-reflection, and sustained test performance improvement even after the training accuracy has saturated, a phenomenon we term post-saturation generalization. Moreover, we verify that the effectiveness of 1-shot RLVR primarily arises from the policy gradient loss, distinguishing it from the "grokking" phenomenon. We also show the critical role of promoting exploration (e.g., by adding entropy loss with an appropriate coefficient) in 1-shot RLVR training. As a bonus, we observe that applying entropy loss alone, without any outcome reward, significantly enhances Qwen2.5-Math-1.5B's performance on MATH500 by 27.4%. These findings can inspire future work on RLVR data efficiency and encourage a re-examination of both recent progress and the underlying mechanisms in RLVR. Our code, model, and data are open source at https://github.com/ypwang61/One-Shot-RLVR

Recently, large reasoning models have achieved impressive performance on various tasks by employing human-like deep thinking. However, the lengthy thinking process substantially increases inference overhead, making efficiency a critical bottleneck. In this work, we first demonstrate that NoThinking, which prompts the reasoning model to skip thinking and directly generate the final solution, is a better choice for relatively simple tasks in terms of both performance and efficiency. Motivated by this, we propose AdaptThink, a novel RL algorithm to teach reasoning models to choose the optimal thinking mode adaptively based on problem difficulty. Specifically, AdaptThink features two core components: (1) a constrained optimization objective that encourages the model to choose NoThinking while maintaining the overall performance; (2) an importance sampling strategy that balances Thinking and NoThinking samples during on-policy training, thereby enabling cold start and allowing the model to explore and exploit both thinking modes throughout the training process. Our experiments indicate that AdaptThink significantly reduces the inference costs while further enhancing performance. Notably, on three math datasets, AdaptThink reduces the average response length of DeepSeek-R1-Distill-Qwen-1.5B by 53% and improves its accuracy by 2.4%, highlighting the promise of adaptive thinking-mode selection for optimizing the balance between reasoning quality and efficiency. Our codes and models are available at https://github.com/THU-KEG/AdaptThink.

Effective reasoning is crucial to solving complex mathematical problems. Recent large language models (LLMs) have boosted performance by scaling test-time computation through long chain-of-thought reasoning. However, transformer-based models are inherently limited in extending context length due to their quadratic computational complexity and linear memory requirements. In this paper, we introduce a novel hybrid linear RNN reasoning model, M1, built on the Mamba architecture, which allows memory-efficient inference. Our approach leverages a distillation process from existing reasoning models and is further enhanced through RL training. Experimental results on the AIME and MATH benchmarks show that M1 not only outperforms previous linear RNN models but also matches the performance of state-of-the-art Deepseek R1 distilled reasoning models at a similar scale. We also compare our generation speed with a highly performant general purpose inference engine, vLLM, and observe more than a 3x speedup compared to a same size transformer. With throughput speedup, we are able to achieve higher accuracy compared to DeepSeek R1 distilled transformer reasoning models under a fixed generation time budget using self-consistency voting. Overall, we introduce a hybrid Mamba reasoning model and provide a more effective approach to scaling test-time generation using self-consistency or long chain of thought reasoning.

Building on the success of text-based reasoning models like DeepSeek-R1, extending these capabilities to multimodal reasoning holds great promise. While recent works have attempted to adapt DeepSeek-R1-style reinforcement learning (RL) training paradigms to multimodal large language models (MLLM), focusing on domain-specific tasks like math and visual perception, a critical question remains: How can we achieve the general-purpose visual-language reasoning through RL? To address this challenge, we make three key efforts: (1) A novel Scalable Multimodal QA Synthesis pipeline that autonomously generates context-aware, reasoning-centric question-answer (QA) pairs directly from the given images. (2) The open-source WeThink dataset containing over 120K multimodal QA pairs with annotated reasoning paths, curated from 18 diverse dataset sources and covering various question domains. (3) A comprehensive exploration of RL on our dataset, incorporating a hybrid reward mechanism that combines rule-based verification with model-based assessment to optimize RL training efficiency across various task domains. Across 14 diverse MLLM benchmarks, we demonstrate that our WeThink dataset significantly enhances performance, from mathematical reasoning to diverse general multimodal tasks. Moreover, we show that our automated data pipeline can continuously increase data diversity to further improve model performance.

While scaling the length of responses at test-time has been shown to markedly improve the reasoning abilities and performance of large language models (LLMs), it often results in verbose outputs and increases inference cost. Prior approaches for efficient test-time scaling, typically using universal budget constraints or query-level length optimization, do not leverage historical information from previous encounters with the same problem during training. We hypothesize that this limits their ability to progressively make solutions more concise over time. To address this, we present History-Aware Policy Optimization (HAPO), which keeps track of a history state (e.g., the minimum length over previously generated correct responses) for each problem. HAPO employs a novel length reward function based on this history state to incentivize the discovery of correct solutions that are more concise than those previously found. Crucially, this reward structure avoids overly penalizing shorter incorrect responses with the goal of facilitating exploration towards more efficient solutions. By combining this length reward with a correctness reward, HAPO jointly optimizes for correctness and efficiency. We use HAPO to train DeepSeek-R1-Distill-Qwen-1.5B, DeepScaleR-1.5B-Preview, and Qwen-2.5-1.5B-Instruct, and evaluate HAPO on several math benchmarks that span various difficulty levels. Experiment results demonstrate that HAPO effectively induces LLMs' concise reasoning abilities, producing length reductions of 33-59% with accuracy drops of only 2-5%.

We introduce Open-Reasoner-Zero, the first open source implementation of large-scale reasoning-oriented RL training focusing on scalability, simplicity and accessibility. Through extensive experiments, we demonstrate that a minimalist approach, vanilla PPO with GAE (lambda=1, gamma=1) and straightforward rule-based rewards, without any KL regularization, is sufficient to scale up both response length and benchmark performance, similar to the phenomenon observed in DeepSeek-R1-Zero. Using the same base model as DeepSeek-R1-Zero-Qwen-32B, our implementation achieves superior performance on AIME2024, MATH500, and the GPQA Diamond benchmark while demonstrating remarkable efficiency -- requiring only a tenth of the training steps, compared to DeepSeek-R1-Zero pipeline. In the spirit of open source, we release our source code, parameter settings, training data, and model weights across various sizes.

Post-training of reasoning LLMs is a holistic process that typically consists of an offline SFT stage followed by an online reinforcement learning (RL) stage. However, SFT is often optimized in isolation to maximize SFT performance alone. We show that, after identical RL training, models initialized from stronger SFT checkpoints can significantly underperform those initialized from weaker ones. We attribute this to a mismatch typical in current SFT-RL pipelines: the distribution that generates the offline SFT data can differ substantially from the policy optimized during online RL, which learns from its own rollouts. We propose PEAR (Policy Evaluation-inspired Algorithm for Offline Learning Loss Re-weighting), an SFT-stage method that corrects this mismatch and better prepares the model for RL. PEAR uses importance sampling to reweight the SFT loss, with three variants operating at the token, block, and sequence levels. It can be used to augment standard SFT objectives and incurs little additional training overhead once probabilities for the offline data are collected. We conduct controlled experiments on verifiable reasoning games and mathematical reasoning tasks on Qwen 2.5 and 3 and DeepSeek-distilled models. PEAR consistently improves post-RL performance over canonical SFT, with pass at 8 gains up to a 14.6 percent on AIME2025. Our results suggest that PEAR is an effective step toward more holistic LLM post-training by designing and evaluating SFT with downstream RL in mind rather than in isolation.

Reasoning models represented by the Deepseek-R1-Distill series have been widely adopted by the open-source community due to their strong performance in mathematics, science, programming, and other domains. However, our study reveals that their benchmark evaluation results are subject to significant fluctuations caused by various factors. Subtle differences in evaluation conditions can lead to substantial variations in results. Similar phenomena are observed in other open-source inference models fine-tuned based on the Deepseek-R1-Distill series, as well as in the QwQ-32B model, making their claimed performance improvements difficult to reproduce reliably. Therefore, we advocate for the establishment of a more rigorous paradigm for model performance evaluation and present our empirical assessments of the Deepseek-R1-Distill series models.

Large Reasoning Models (LRMs) like o1 and DeepSeek-R1 have shown remarkable progress in natural language reasoning with long chain-of-thought (CoT), yet they remain inefficient or inaccurate when handling complex mathematical operations. Addressing these limitations through computational tools (e.g., computation libraries and symbolic solvers) is promising, but it introduces a technical challenge: Code Interpreter (CI) brings external knowledge beyond the model's internal text representations, thus the direct combination is not efficient. This paper introduces CoRT, a post-training framework for teaching LRMs to leverage CI effectively and efficiently. As a first step, we address the data scarcity issue by synthesizing code-integrated reasoning data through Hint-Engineering, which strategically inserts different hints at appropriate positions to optimize LRM-CI interaction. We manually create 30 high-quality samples, upon which we post-train models ranging from 1.5B to 32B parameters, with supervised fine-tuning, rejection fine-tuning and reinforcement learning. Our experimental results demonstrate that Hint-Engineering models achieve 4\% and 8\% absolute improvements on DeepSeek-R1-Distill-Qwen-32B and DeepSeek-R1-Distill-Qwen-1.5B respectively, across five challenging mathematical reasoning datasets. Furthermore, Hint-Engineering models use about 30\% fewer tokens for the 32B model and 50\% fewer tokens for the 1.5B model compared with the natural language models. The models and code are available at https://github.com/ChengpengLi1003/CoRT.

Large reasoning models (LRMs) like OpenAI o1 and DeepSeek R1 have demonstrated impressive performance on complex reasoning tasks like mathematics and programming with long Chain-of-Thought (CoT) reasoning sequences (slow-thinking), compared with traditional large language models (fast-thinking). However, these reasoning models also face a huge challenge that generating unnecessarily lengthy and redundant reasoning chains even for trivial questions. This phenomenon leads to a significant waste of inference resources, increases the response time for simple queries, and hinders the practical application of LRMs in real-world products. To this end, it is crucial to shorten lengthy reasoning chains and learn adaptive reasoning between fast and slow thinking based on input difficulty. In this survey, we provide a comprehensive overview of recent progress in concise and adaptive thinking for efficient reasoning of LRMs, including methodologies, benchmarks, and challenges for future exploration. We hope this survey can help researchers quickly understand the landscape of this field and inspire novel adaptive thinking ideas to facilitate better usage of LRMs.

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.

Challenging the prevailing consensus that small models inherently lack robust reasoning, this report introduces VibeThinker-1.5B, a 1.5B-parameter dense model developed via our Spectrum-to-Signal Principle (SSP). This challenges the prevailing approach of scaling model parameters to enhance capabilities, as seen in models like DeepSeek R1 (671B) and Kimi k2 (>1T). The SSP framework first employs a Two-Stage Diversity-Exploring Distillation (SFT) to generate a broad spectrum of solutions, followed by MaxEnt-Guided Policy Optimization (RL) to amplify the correct signal. With a total training cost of only $7,800, VibeThinker-1.5B demonstrates superior reasoning capabilities compared to closed-source models like Magistral Medium and Claude Opus 4, and performs on par with open-source models like GPT OSS-20B Medium. Remarkably, it surpasses the 400x larger DeepSeek R1 on three math benchmarks: AIME24 (80.3 vs. 79.8), AIME25 (74.4 vs. 70.0), and HMMT25 (50.4 vs. 41.7). This is a substantial improvement over its base model (6.7, 4.3, and 0.6, respectively). On LiveCodeBench V6, it scores 51.1, outperforming Magistral Medium's 50.3 and its base model's 0.0. These findings demonstrate that small models can achieve reasoning capabilities comparable to large models, drastically reducing training and inference costs and thereby democratizing advanced AI research.

Recent advances in large language models (LLMs), such as OpenAI-o1 and DeepSeek-R1, have demonstrated the effectiveness of test-time scaling, where extended reasoning processes substantially enhance model performance. Despite this, current models are constrained by limitations in handling long texts and reinforcement learning (RL) training efficiency. To address these issues, we propose a simple yet effective test-time scaling approach Multi-round Thinking. This method iteratively refines model reasoning by leveraging previous answers as prompts for subsequent rounds. Extensive experiments across multiple models, including QwQ-32B and DeepSeek-R1, consistently show performance improvements on various benchmarks such as AIME 2024, MATH-500, GPQA-diamond, and LiveCodeBench. For instance, the accuracy of QwQ-32B improved from 80.3% (Round 1) to 82.1% (Round 2) on the AIME 2024 dataset, while DeepSeek-R1 showed a similar increase from 79.7% to 82.0%. These results confirm that Multi-round Thinking is a broadly applicable, straightforward approach to achieving stable enhancements in model performance, underscoring its potential for future developments in test-time scaling techniques. The key prompt: {Original question prompt} The assistant's previous answer is: <answer> {last round answer} </answer>, and please re-answer.

While reasoning models are increasingly ubiquitous, the effects of reasoning training on a model's internal mechanisms remain poorly understood. In this work, we introduce transcoder adapters, a technique for learning an interpretable approximation of the difference in MLP computation before and after fine-tuning. We apply transcoder adapters to characterize the differences between Qwen2.5-Math-7B and its reasoning-distilled variant, DeepSeek-R1-Distill-Qwen-7B. Learned adapters are faithful to the target model's internal computation and next-token predictions. When evaluated on reasoning benchmarks, adapters match the reasoning model's response lengths and typically recover 50-90% of the accuracy gains from reasoning fine-tuning. Adapter features are sparsely activating and interpretable. When examining adapter features, we find that only ~8% have activating examples directly related to reasoning behaviors. We deeply study one such behavior -- the production of hesitation tokens (e.g., "wait"). Using attribution graphs, we trace hesitation to only ~2.4% of adapter features (5.6k total) performing one of two functions. These features are necessary and sufficient for producing hesitation tokens; removing them reduces response length, often without affecting accuracy. Overall, our results provide insight into reasoning training and suggest transcoder adapters may be useful for studying fine-tuning more broadly.

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.

We introduce LADDER (Learning through Autonomous Difficulty-Driven Example Recursion), a framework which enables Large Language Models to autonomously improve their problem-solving capabilities through self-guided learning by recursively generating and solving progressively simpler variants of complex problems. Unlike prior approaches that require curated datasets or human feedback, LADDER leverages a model's own capabilities to generate easier question variants. We demonstrate LADDER's effectiveness in the subject of mathematical integration, improving Llama 3.2 3B's accuracy from 1% to 82% on undergraduate-level problems and enabling Qwen2.5 7B Deepseek-R1 Distilled to achieve 73% on the MIT Integration Bee qualifying examination. We also introduce TTRL (Test-Time Reinforcement Learning), where we perform reinforcement learning on variants of test problems at inference time. TTRL enables Qwen2.5 7B Deepseek-R1 Distilled to achieve a state-of-the-art score of 90% on the MIT Integration Bee qualifying examination, surpassing OpenAI o1's performance. These results show how self-directed strategic learning can achieve significant capability improvements without relying on architectural scaling or human supervision.

Reasoning LLMs such as OpenAI o1, o3 and DeepSeek R1 have made significant progress in mathematics and coding, yet find challenging advanced tasks such as International Mathematical Olympiad (IMO) combinatorics problems, Abstraction and Reasoning Corpus (ARC) puzzles, and Humanity's Last Exam (HLE) questions. We use a diverse inference approach that combines multiple models and methods at test time. We find that verifying mathematics and code problems, and rejection sampling on other problems is simple and effective. We automatically verify correctness of solutions to IMO problems by Lean, and ARC puzzles by code, and find that best-of-N effectively answers HLE questions. Our approach increases answer accuracy on IMO combinatorics problems from 33.3% to 77.8%, accuracy on HLE questions from 8% to 37%, and solves 80% of ARC puzzles that 948 humans could not and 26.5% of ARC puzzles that o3 high compute does not. Test-time simulations, reinforcement learning, and meta-learning with inference feedback improve generalization by adapting agent graph representations and varying prompts, code, and datasets. Our approach is reliable, robust, and scalable, and in the spirit of reproducible research, we will make it publicly available upon publication.

Test-time scaling has been shown to substantially improve large language models' (LLMs) mathematical reasoning. However, for a large portion of mathematical corpora, especially theorem proving, RLVR's scalability is limited: intermediate reasoning is crucial, while final answers are difficult to directly and reliably verify. Meanwhile, token-level SFT often degenerates into rote memorization rather than inducing longer chains of thought. Inspired by BERT's self-supervised tasks, we propose MR-RLVR (Masked-and-Reordered RLVR), which constructs process-level self-supervised rewards via "masked-then-fill" and "step reordering" to extract learnable signals from intermediate reasoning. Our training pipeline comprises two stages: we first perform self-supervised training on sampled mathematical calculation and proof data; we then conduct RLVR fine-tuning on mathematical calculation datasets where only outcomes are verifiable. We implement MR-RLVR on Qwen2.5-3B and DeepSeek-R1-Distill-Qwen-1.5B, and evaluate on AIME24, AIME25, AMC23, and MATH500. Under a fixed sampling and decoding budget, MR-RLVR achieves average relative gains over the original RLVR of +9.86% Pass@1, +5.27% Pass@5, and +4.00% Pass@8. These results indicate that incorporating process-aware self-supervised signals can effectively enhance RLVR's scalability and performance in only outcome-verifiable settings.

The development of reasoning capabilities represents a critical frontier in large language models (LLMs) research, where reinforcement learning (RL) and process reward models (PRMs) have emerged as predominant methodological frameworks. Contrary to conventional wisdom, empirical evidence from DeepSeek-R1 demonstrates that pure RL training focused on mathematical problem-solving can progressively enhance reasoning abilities without PRM integration, challenging the perceived necessity of process supervision. In this study, we conduct a systematic investigation of the relationship between RL training and PRM capabilities. Our findings demonstrate that problem-solving proficiency and process supervision capabilities represent complementary dimensions of reasoning that co-evolve synergistically during pure RL training. In particular, current PRMs underperform simple baselines like majority voting when applied to state-of-the-art models such as DeepSeek-R1 and QwQ-32B. To address this limitation, we propose Self-PRM, an introspective framework in which models autonomously evaluate and rerank their generated solutions through self-reward mechanisms. Although Self-PRM consistently improves the accuracy of the benchmark (particularly with larger sample sizes), analysis exposes persistent challenges: The approach exhibits low precision (<10\%) on difficult problems, frequently misclassifying flawed solutions as valid. These analyses underscore the need for continued RL scaling to improve reward alignment and introspective accuracy. Overall, our findings suggest that PRM may not be essential for enhancing complex reasoning, as pure RL not only improves problem-solving skills but also inherently fosters robust PRM capabilities. We hope these findings provide actionable insights for building more reliable and self-aware complex reasoning models.

Large Language Models (LLMs) achieve impressive reasoning capabilities at the cost of substantial inference overhead, posing substantial deployment challenges. Although distilled Small Language Models (SLMs) significantly enhance efficiency, their performance suffers as they fail to follow LLMs' reasoning paths. Luckily, we reveal that only a small fraction of tokens genuinely diverge reasoning paths between LLMs and SLMs. Most generated tokens are either identical or exhibit neutral differences, such as minor variations in abbreviations or expressions. Leveraging this insight, we introduce **Roads to Rome (R2R)**, a neural token routing method that selectively utilizes LLMs only for these critical, path-divergent tokens, while leaving the majority of token generation to the SLM. We also develop an automatic data generation pipeline that identifies divergent tokens and generates token-level routing labels to train the lightweight router. We apply R2R to combine R1-1.5B and R1-32B models from the DeepSeek family, and evaluate on challenging math, coding, and QA benchmarks. With an average activated parameter size of 5.6B, R2R surpasses the average accuracy of R1-7B by 1.6x, outperforming even the R1-14B model. Compared to R1-32B, it delivers a 2.8x wall-clock speedup with comparable performance, advancing the Pareto frontier of test-time scaling efficiency. Our code is available at https://github.com/thu-nics/R2R.

Recently, DeepSeek-R1 (671B) (DeepSeek-AIet al., 2025) has demonstrated its excellent reasoning ability in complex tasks and has publiclyshared its methodology. This provides potentially high-quality chain-of-thought (CoT) data for stimulating the reasoning abilities of small-sized large language models (LLMs). To generate high-quality CoT data for different LLMs, we seek an efficient method for generating high-quality CoT data with LLM-Adaptive questiondifficulty levels. First, we grade the difficulty of the questions according to the reasoning ability of the LLMs themselves and construct a LLM-Adaptive question database. Second, we sample the problem database based on a distribution of difficulty levels of the questions and then use DeepSeek-R1 (671B) (DeepSeek-AI et al., 2025) to generate the corresponding high-quality CoT data with correct answers. Thanks to the construction of CoT data with LLM-Adaptive difficulty levels, we have significantly reduced the cost of data generation and enhanced the efficiency of model supervised fine-tuning (SFT). Finally, we have validated the effectiveness and generalizability of the proposed method in the fields of complex mathematical competitions and code generation tasks. Notably, with only 2k high-quality mathematical CoT data, our ZMath-32B surpasses DeepSeek-Distill-32B in math reasoning task. Similarly, with only 2k high-quality code CoT data, our ZCode-32B surpasses DeepSeek-Distill-32B in code reasoning tasks.

Despite rapid advancements in large language models (LLMs), the token-level autoregressive nature constrains their complex reasoning capabilities. To enhance LLM reasoning, inference-time techniques, including Chain/Tree/Graph-of-Thought(s), successfully improve the performance, as they are fairly cost-effective by guiding reasoning through sophisticated logical structures without modifying LLMs' parameters. However, these manually predefined, task-agnostic frameworks are applied uniformly across diverse tasks, lacking adaptability. To improve this, we propose RL-of-Thoughts (RLoT), where we train a lightweight navigator model with reinforcement learning (RL) to adaptively enhance LLM reasoning at inference time. Specifically, we design five basic logic blocks from the perspective of human cognition. During the reasoning process, the trained RL navigator dynamically selects the suitable logic blocks and combines them into task-specific logical structures according to problem characteristics. Experiments across multiple reasoning benchmarks (AIME, MATH, GPQA, etc.) with multiple LLMs (GPT, Llama, Qwen, and DeepSeek) illustrate that RLoT outperforms established inference-time techniques by up to 13.4%. Remarkably, with less than 3K parameters, our RL navigator is able to make sub-10B LLMs comparable to 100B-scale counterparts. Moreover, the RL navigator demonstrates strong transferability: a model trained on one specific LLM-task pair can effectively generalize to unseen LLMs and tasks. Our code is open-source at https://anonymous.4open.science/r/RL-LLM-Reasoning-1A30 for reproducibility.

We present ZAYA1-8B, a reasoning-focused mixture-of-experts (MoE) model with 700M active and 8B total parameters, built on Zyphra's MoE++ architecture. ZAYA1-8B's core pretraining, midtraining, and supervised fine-tuning (SFT) were performed on a full-stack AMD compute, networking, and software platform. With under 1B active parameters, ZAYA1-8B matches or exceeds DeepSeek-R1-0528 on several challenging mathematics and coding benchmarks, and remains competitive with substantially larger open-weight reasoning models. ZAYA1-8B was trained from scratch for reasoning, with reasoning data included from pretraining onward using an answer-preserving trimming scheme. Post-training uses a four-stage RL cascade: reasoning warmup on math and puzzles; a 400-task RLVE-Gym curriculum; math and code RL with test-time compute traces and synthetic code environments built from competitive-programming references; and behavioral RL for chat and instruction following. We also introduce Markovian RSA, a test-time compute method that recursively aggregates parallel reasoning traces while carrying forward only bounded-length reasoning tails between rounds. In TTC evaluation, Markovian RSA raises ZAYA1-8B to 91.9\% on AIME'25 and 89.6\% on HMMT'25 while carrying forward only a 4K-token tail, narrowing the gap to much larger reasoning models including Gemini-2.5 Pro, DeepSeek-V3.2, and GPT-5-High.

Reinforcement learning (RL) has emerged as a dominant paradigm for eliciting long-horizon reasoning in Large Language Models (LLMs). However, scaling Tool-Integrated Reasoning (TIR) via RL remains challenging due to interaction collapse: a pathological state where models fail to sustain multi-turn tool usage, instead degenerating into heavy internal reasoning with only trivial, post-hoc code verification. We systematically study three questions: (i) how cold-start SFT induces an agentic, tool-using behavioral prior, (ii) how the interaction density of cold-start trajectories shapes exploration and downstream RL outcomes, and (iii) how the RL interaction budget affects learning dynamics and generalization under varying inference-time budgets. We then introduce ASTER (Agentic Scaling with Tool-integrated Extended Reasoning), a framework that circumvents this collapse through a targeted cold-start strategy prioritizing interaction-dense trajectories. We find that a small expert cold-start set of just 4K interaction-dense trajectories yields the strongest downstream performance, establishing a robust prior that enables superior exploration during extended RL training. Extensive evaluations demonstrate that ASTER-4B achieves state-of-the-art results on competitive mathematical benchmarks, reaching 90.0% on AIME 2025, surpassing leading frontier open-source models, including DeepSeek-V3.2-Exp.

Large language models (LLMs) benefit from increased test-time compute, a phenomenon known as test-time scaling. However, reasoning-optimized models often overthink even simple problems, producing excessively verbose outputs and leading to low token efficiency. By comparing these models with equally sized instruct models, we identify two key causes of this verbosity: (1) reinforcement learning reduces the information density of forward reasoning, and (2) backward chain-of thought training encourages redundant and often unnecessary verification steps. Since LLMs cannot assess the difficulty of a given problem, they tend to apply the same cautious reasoning strategy across all tasks, resulting in inefficient overthinking. To address this, we propose CoThink, an embarrassingly simple pipeline: an instruct model first drafts a high-level solution outline; a reasoning model then works out the solution. We observe that CoThink enables dynamic adjustment of reasoning depth based on input difficulty. Evaluated with three reasoning models DAPO, DeepSeek-R1, and QwQ on three datasets GSM8K, MATH500, and AIME24, CoThink reduces total token generation by 22.3% while maintaining pass@1 accuracy within a 0.42% margin on average. With reference to the instruct model, we formally define reasoning efficiency and observe a potential reasoning efficiency scaling law in LLMs.

Recent advancements in reasoning-focused language models such as OpenAI's O1 and DeepSeek-R1 have shown that scaling test-time computation-through chain-of-thought reasoning and iterative exploration-can yield substantial improvements on complex tasks like mathematics and code generation. These breakthroughs have been driven by large-scale reinforcement learning (RL), particularly when combined with verifiable reward signals that provide objective and grounded supervision. In this report, we investigate the effects of prolonged reinforcement learning on a small language model across a diverse set of reasoning domains. Our work identifies several key ingredients for effective training, including the use of verifiable reward tasks, enhancements to Group Relative Policy Optimization (GRPO), and practical techniques to improve training stability and generalization. We introduce controlled KL regularization, clipping ratio, and periodic reference policy resets as critical components for unlocking long-term performance gains. Our model achieves significant improvements over strong baselines, including +14.7% on math, +13.9% on coding, and +54.8% on logic puzzle tasks. To facilitate continued research, we release our model publicly.

The combination of verifiable languages and LLMs has significantly influenced both the mathematical and computer science communities because it provides a rigorous foundation for theorem proving. Recent advancements in the field provide foundation models and sophisticated agentic systems pushing the boundaries of formal mathematical reasoning to approach the natural language capability of LLMs. However, little attention has been given to the formal physics reasoning, which also heavily relies on similar problem-solving and theorem-proving frameworks. To solve this problem, this paper presents, to the best of our knowledge, the first approach to enhance formal theorem proving in the physics domain. We compose a dedicated dataset PhysLeanData for the task. It is composed of theorems sampled from PhysLean and data generated by a conjecture-based formal data generation pipeline. In the training pipeline, we leverage DeepSeek-Prover-V2-7B, a strong open-source mathematical theorem prover, and apply Reinforcement Learning with Verifiable Rewards (RLVR) to train our model PhysProver. Comprehensive experiments demonstrate that, using only sim5K training samples, PhysProver achieves an overall 2.4\% improvement in multiple sub-domains. Furthermore, after formal physics training, we observe 1.3\% gains on the MiniF2F-Test benchmark, which indicates non-trivial generalization beyond physics domains and enhancement for formal math capability as well. The results highlight the effectiveness and efficiency of our approach, which provides a paradigm for extending formal provers outside mathematical domains. To foster further research, we will release both our dataset and model to the community.

Recently, deep reasoning large language models(LLMs) like DeepSeek-R1 have made significant progress in tasks such as mathematics and coding. Inspired by this, several studies have employed reinforcement learning(RL) to enhance models' deep reasoning capabilities and improve machine translation(MT) quality. However, the terminology translation, an essential task in MT, remains unexplored in deep reasoning LLMs. In this paper, we propose TAT-R1, a terminology-aware translation model trained with reinforcement learning and word alignment. Specifically, we first extract the keyword translation pairs using a word alignment model. Then we carefully design three types of rule-based alignment rewards with the extracted alignment relationships. With those alignment rewards, the RL-trained translation model can learn to focus on the accurate translation of key information, including terminology in the source text. Experimental results show the effectiveness of TAT-R1. Our model significantly improves terminology translation accuracy compared to the baseline models while maintaining comparable performance on general translation tasks. In addition, we conduct detailed ablation studies of the DeepSeek-R1-like training paradigm for machine translation and reveal several key findings.

Large Reasoning Models (LRMs) demonstrate exceptional capability in tackling complex mathematical, logical, and coding tasks by leveraging extended Chain-of-Thought (CoT) reasoning. Test-time scaling methods, such as prolonging CoT with explicit token-level exploration, can push LRMs' accuracy boundaries, but they incur significant decoding overhead. A key inefficiency source is LRMs often generate redundant thinking CoTs, which demonstrate clear structured overthinking and underthinking patterns. Inspired by human cognitive reasoning processes and numerical optimization theories, we propose TrimR, a verifier-based, training-free, efficient framework for dynamic CoT compression to trim reasoning and enhance test-time scaling, explicitly tailored for production-level deployment. Our method employs a lightweight, pretrained, instruction-tuned verifier to detect and truncate redundant intermediate thoughts of LRMs without any LRM or verifier fine-tuning. We present both the core algorithm and asynchronous online system engineered for high-throughput industrial applications. Empirical evaluations on Ascend NPUs and vLLM show that our framework delivers substantial gains in inference efficiency under large-batch workloads. In particular, on the four MATH500, AIME24, AIME25, and GPQA benchmarks, the reasoning runtime of Pangu Pro MoE, Pangu-R-38B, QwQ-32B, and DeepSeek-R1-Distill-Qwen-32B is improved by up to 70% with negligible impact on accuracy.

Recent open-source large reasoning models (LRMs) exhibit strong performance on complex reasoning tasks, but their large parameter count makes them prohibitively expensive for individuals. The compression of large language models (LLMs) offers an effective solution to reduce cost of computational resources. However, systematic studies on the performance of compressed LLMs in complex reasoning tasks, especially for LRMs, are lacking. Most works on quantization and pruning focus on preserving language modeling performance, while existing distillation works do not comprehensively benchmark student models based on reasoning difficulty or compression impact on knowledge and reasoning. In this paper, we benchmark compressed DeepSeek-R1 models on four different reasoning datasets (AIME 2024, FOLIO, Temporal Sequences of BIG-Bench Hard, and MuSiQue), ranging from mathematical to multihop reasoning, using quantization, distillation, and pruning methods. We benchmark 2.51-, 1.73-, and 1.58-bit R1 models that adopt dynamic quantization. We also benchmark distilled R1 models that are based on LLaMA or Qwen and run SparseGPT on them to obtain various sparsity levels. Studying the performance and behavior of compressed LRMs, we report their performance scores and test-time compute (number of tokens spent on each question). Notably, using MuSiQue, we find that parameter count has a much greater impact on LRMs' knowledge memorization than on their reasoning capability, which can inform the choice of compression techniques. Through our empirical analysis of test-time compute, we find that shorter model outputs generally achieve better performance than longer ones across several benchmarks for both R1 and its compressed variants, highlighting the need for more concise reasoning chains.

Large Language Models (LLMs), such as OpenAI's o1 and DeepSeek's R1, excel at advanced reasoning tasks like math and coding via Reinforcement Learning with Verifiable Rewards (RLVR), but still struggle with puzzles solvable by humans without domain knowledge. We introduce Enigmata, the first comprehensive suite tailored for improving LLMs with puzzle reasoning skills. It includes 36 tasks across seven categories, each with 1) a generator that produces unlimited examples with controllable difficulty and 2) a rule-based verifier for automatic evaluation. This generator-verifier design supports scalable, multi-task RL training, fine-grained analysis, and seamless RLVR integration. We further propose Enigmata-Eval, a rigorous benchmark, and develop optimized multi-task RLVR strategies. Our trained model, Qwen2.5-32B-Enigmata, consistently surpasses o3-mini-high and o1 on the puzzle reasoning benchmarks like Enigmata-Eval, ARC-AGI (32.8%), and ARC-AGI 2 (0.6%). It also generalizes well to out-of-domain puzzle benchmarks and mathematical reasoning, with little multi-tasking trade-off. When trained on larger models like Seed1.5-Thinking (20B activated parameters and 200B total parameters), puzzle data from Enigmata further boosts SoTA performance on advanced math and STEM reasoning tasks such as AIME (2024-2025), BeyondAIME and GPQA (Diamond), showing nice generalization benefits of Enigmata. This work offers a unified, controllable framework for advancing logical reasoning in LLMs. Resources of this work can be found at https://seed-enigmata.github.io.

In this paper, we propose a simple and efficient method for value model training on long-context reasoning traces. Compared to existing process reward models (PRMs), our method does not require a fine-grained notion of "step," which is difficult to define for long-context reasoning models. By collecting a dataset of 2.5 million reasoning traces, we train a 1.5B token-level value model and apply it to DeepSeek models for improved performance with test-time compute scaling. We find that block-wise value-guided search (VGS) with a final weighted majority vote achieves better test-time scaling than standard methods such as majority voting or best-of-n. With an inference budget of 64 generations, VGS with DeepSeek-R1-Distill-1.5B achieves an average accuracy of 45.7% across four competition math benchmarks (AIME 2024 & 2025, HMMT Feb 2024 & 2025), reaching parity with o3-mini-medium. Moreover, VGS significantly reduces the inference FLOPs required to achieve the same performance of majority voting. Our dataset, model and codebase are open-sourced.

In this paper, we address post-training quantization (PTQ) for large language models (LLMs) from an overlooked perspective: given a pre-trained high-precision LLM, the predominant sequential quantization framework treats different layers equally, but this may be not optimal in challenging bit-width settings. We empirically study the quantization impact of different layers on model accuracy, and observe that: (1) shallow/deep layers are usually more sensitive to quantization than intermediate layers; (2) among shallow/deep layers, the most sensitive one is the first/last layer, which exhibits significantly larger quantization error than others. These empirical observations imply that the quantization design for different layers of LLMs is required on multiple levels instead of a single level shared to all layers. Motivated by this, we propose a new PTQ framework termed Sliding-layer Quantization (SliderQuant) that relies on a simple adaptive sliding quantization concept facilitated by few learnable parameters. The base component of SliderQuant is called inter-layer sliding quantization, which incorporates three types of novel sliding window designs tailored for addressing the varying quantization sensitivity of shallow, intermediate and deep layers. The other component is called intra-layer sliding quantization that leverages an incremental strategy to quantize each window. As a result, SliderQuant has a strong ability to reduce quantization errors across layers. Extensive experiments on basic language generation, zero-shot commonsense reasoning and challenging math and code tasks with various LLMs, including Llama/Llama2/Llama3/Qwen2.5 model families, DeepSeek-R1 distilled models and large MoE models, show that our method outperforms existing PTQ methods (including the latest PTQ methods using rotation transformations) for both weight-only quantization and weight-activation quantization.

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex tasks. Recent advancements in Large Reasoning Models (LRMs), such as OpenAI o1 and DeepSeek-R1, have further improved performance in System-2 reasoning domains like mathematics and programming by harnessing supervised fine-tuning (SFT) and reinforcement learning (RL) techniques to enhance the Chain-of-Thought (CoT) reasoning. However, while longer CoT reasoning sequences improve performance, they also introduce significant computational overhead due to verbose and redundant outputs, known as the "overthinking phenomenon". In this paper, we provide the first structured survey to systematically investigate and explore the current progress toward achieving efficient reasoning in LLMs. Overall, relying on the inherent mechanism of LLMs, we categorize existing works into several key directions: (1) model-based efficient reasoning, which considers optimizing full-length reasoning models into more concise reasoning models or directly training efficient reasoning models; (2) reasoning output-based efficient reasoning, which aims to dynamically reduce reasoning steps and length during inference; (3) input prompts-based efficient reasoning, which seeks to enhance reasoning efficiency based on input prompt properties such as difficulty or length control. Additionally, we introduce the use of efficient data for training reasoning models, explore the reasoning capabilities of small language models, and discuss evaluation methods and benchmarking.

Large language models (LLMs), especially Explicit Long Chain-of-Thought (CoT) reasoning models like DeepSeek-R1 and QWQ, have demonstrated powerful reasoning capabilities, achieving impressive performance in commonsense reasoning and mathematical inference. Despite their effectiveness, Long-CoT reasoning models are often criticized for their limited ability and low efficiency in knowledge-intensive domains such as molecule discovery. Success in this field requires a precise understanding of domain knowledge, including molecular structures and chemical principles, which is challenging due to the inherent complexity of molecular data and the scarcity of high-quality expert annotations. To bridge this gap, we introduce Mol-R1, a novel framework designed to improve explainability and reasoning performance of R1-like Explicit Long-CoT reasoning LLMs in text-based molecule generation. Our approach begins with a high-quality reasoning dataset curated through Prior Regulation via In-context Distillation (PRID), a dedicated distillation strategy to effectively generate paired reasoning traces guided by prior regulations. Building upon this, we introduce MoIA, Molecular Iterative Adaptation, a sophisticated training strategy that iteratively combines Supervised Fine-tuning (SFT) with Reinforced Policy Optimization (RPO), tailored to boost the reasoning performance of R1-like reasoning models for molecule discovery. Finally, we examine the performance of Mol-R1 in the text-based molecule reasoning generation task, showing superior performance against existing baselines.

We systematically evaluate Parameter-Efficient Fine-Tuning (PEFT) methods under the paradigm of Reinforcement Learning with Verifiable Rewards (RLVR). RLVR incentivizes language models to enhance their reasoning capabilities through verifiable feedback; however, while methods like LoRA are commonly used, the optimal PEFT architecture for RLVR remains unidentified. In this work, we conduct the first comprehensive evaluation of over 12 PEFT methodologies across the DeepSeek-R1-Distill families on mathematical reasoning benchmarks. Our empirical results challenge the default adoption of standard LoRA with three main findings. First, we demonstrate that structural variants, such as DoRA, AdaLoRA, and MiSS, consistently outperform LoRA. Second, we uncover a spectral collapse phenomenon in SVD-informed initialization strategies (e.g., PiSSA, MiLoRA), attributing their failure to a fundamental misalignment between principal-component updates and RL optimization. Furthermore, our ablations reveal that extreme parameter reduction (e.g., VeRA, Rank-1) severely bottlenecks reasoning capacity. We further conduct ablation studies and scaling experiments to validate our findings. This work provides a definitive guide for advocating for more exploration for parameter-efficient RL methods.

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical reasoning for more accurate judgments and reduced biases. Foundational Large Language Models (LLMs) excel at fast decision-making but lack the depth for complex reasoning, as they have not yet fully embraced the step-by-step analysis characteristic of true System 2 thinking. Recently, reasoning LLMs like OpenAI's o1/o3 and DeepSeek's R1 have demonstrated expert-level performance in fields such as mathematics and coding, closely mimicking the deliberate reasoning of System 2 and showcasing human-like cognitive abilities. This survey begins with a brief overview of the progress in foundational LLMs and the early development of System 2 technologies, exploring how their combination has paved the way for reasoning LLMs. Next, we discuss how to construct reasoning LLMs, analyzing their features, the core methods enabling advanced reasoning, and the evolution of various reasoning LLMs. Additionally, we provide an overview of reasoning benchmarks, offering an in-depth comparison of the performance of representative reasoning LLMs. Finally, we explore promising directions for advancing reasoning LLMs and maintain a real-time https://github.com/zzli2022/Awesome-Slow-Reason-System{GitHub Repository} to track the latest developments. We hope this survey will serve as a valuable resource to inspire innovation and drive progress in this rapidly evolving field.

On-policy reinforcement learning (RL), particularly Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO), has become the dominant paradigm for fine-tuning large language models (LLMs). While policy ratio clipping stabilizes training, this heuristic hard constraint incurs a fundamental cost: it indiscriminately truncates gradients from high-return yet high-divergence actions, suppressing rare but highly informative "eureka moments" in complex reasoning. Moreover, once data becomes slightly stale, hard clipping renders it unusable, leading to severe sample inefficiency. In this work, we revisit the trust-region objective in policy optimization and show that explicitly constraining the variance (second central moment) of the policy ratio provides a principled and smooth relaxation of hard clipping. This distributional constraint stabilizes policy updates while preserving gradient signals from valuable trajectories. Building on this insight, we propose R^2VPO (Ratio-Variance Regularized Policy Optimization), a novel primal-dual framework that supports stable on-policy learning and enables principled off-policy data reuse by dynamically reweighting stale samples rather than discarding them. We extensively evaluate R^2VPO on fine-tuning state-of-the-art LLMs, including DeepSeek-Distill-Qwen-1.5B and the openPangu-Embedded series (1B and 7B), across challenging mathematical reasoning benchmarks. Experimental results show that R^2VPO consistently achieves superior asymptotic performance, with average relative gains of up to 17% over strong clipping-based baselines, while requiring approximately 50% fewer rollouts to reach convergence. These findings establish ratio-variance control as a promising direction for improving both stability and data efficiency in RL-based LLM alignment.

Compressing long chain-of-thought (CoT) from large language models (LLMs) is an emerging strategy to improve the reasoning efficiency of LLMs. Despite its promising benefits, existing studies equally compress all thoughts within a long CoT, hindering more concise and effective reasoning. To this end, we first investigate the importance of different thoughts by examining their effectiveness and efficiency in contributing to reasoning through automatic long CoT chunking and Monte Carlo rollouts. Building upon the insights, we propose a theoretically bounded metric to jointly measure the effectiveness and efficiency of different thoughts. We then propose LongotimesShort, an efficient reasoning framework that enables two LLMs to collaboratively solve the problem: a long-thought LLM for more effectively generating important thoughts, while a short-thought LLM for efficiently generating remaining thoughts. Specifically, we begin by synthesizing a small amount of cold-start data to fine-tune LLMs for long-thought and short-thought reasoning styles, respectively. Furthermore, we propose a synergizing-oriented multi-turn reinforcement learning, focusing on the model self-evolution and collaboration between long-thought and short-thought LLMs. Experimental results show that our method enables Qwen2.5-7B and Llama3.1-8B to achieve comparable performance compared to DeepSeek-R1-Distill-Qwen-7B and DeepSeek-R1-Distill-Llama-8B, while reducing token length by over 80% across the MATH500, AIME24/25, AMC23, and GPQA Diamond benchmarks. Our data and code are available at https://github.com/yasNing/Long-otimes-Short/.

Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-O1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "test-time scaling." This survey seeks to fill this gap by offering a unified perspective on Long CoT. (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and test-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of logical reasoning in artificial intelligence.

Large reasoning models (LRMs) like OpenAI-o1 have shown impressive capabilities in natural language reasoning. However, these models frequently demonstrate inefficiencies or inaccuracies when tackling complex mathematical operations. While integrating computational tools such as Code Interpreters (CIs) offers a promising solution, it introduces a critical challenge: a conflict between the model's internal, probabilistic reasoning and the external, deterministic knowledge provided by the CI, which often leads models to unproductive deliberation. To overcome this, we introduce CoRT (Code-Optimized Reasoning Training), a post-training framework designed to teach LRMs to effectively utilize CIs. We propose Hint-Engineering, a new data synthesis strategy that strategically injects diverse hints at optimal points within reasoning paths. This approach generates high-quality, code-integrated reasoning data specifically tailored to optimize LRM-CI interaction. Using this method, we have synthesized 30 high-quality samples to post-train models ranging from 1.5B to 32B parameters through supervised fine-tuning. CoRT further refines the multi-round interleaving of external CI usage and internal thinking by employing rejection sampling and reinforcement learning. Our experimental evaluations demonstrate CoRT's effectiveness, yielding absolute improvements of 4\% and 8\% on DeepSeek-R1-Distill-Qwen-32B and DeepSeek-R1-Distill-Qwen-1.5B, respectively, across five challenging mathematical reasoning datasets. Moreover, CoRT significantly enhances efficiency, reducing token usage by approximately 30\% for the 32B model and 50\% for the 1.5B model compared to pure natural language reasoning baselines. The models and code are available at: https://github.com/ChengpengLi1003/CoRT.

Large language models (LLMs) have shown emerging potential in spatiotemporal reasoning, making them promising candidates for building urban agents that support diverse urban downstream applications. Despite these benefits, existing studies primarily focus on evaluating urban LLM agent on outcome-level metrics (e.g., prediction accuracy, traffic efficiency), offering limited insight into their underlying reasoning processes. As a result, the strengths and limitations of urban LLM agents in spatiotemporal reasoning remain poorly understood. To this end, we introduce USTBench, the first benchmark to evaluate LLMs' spatiotemporal reasoning abilities as urban agents across four decomposed dimensions: spatiotemporal understanding, forecasting, planning, and reflection with feedback. Specifically, USTBench supports five diverse urban decision-making and four spatiotemporal prediction tasks, all running within our constructed interactive city environment UAgentEnv. The benchmark includes 62,466 structured QA pairs for process-level evaluation and standardized end-to-end task assessments, enabling fine-grained diagnostics and broad task-level comparison across diverse urban scenarios. Through extensive evaluation of thirteen leading LLMs, we reveal that although LLMs show promising potential across various urban downstream tasks, they still struggle in long-horizon planning and reflective adaptation in dynamic urban contexts. Notably, recent advanced reasoning models (e.g., DeepSeek-R1) trained on general logic or mathematical problems do not consistently outperform non-reasoning LLMs. This discrepancy highlights the need for domain-specialized adaptation methods to enhance urban spatiotemporal reasoning. Overall, USTBench provides a foundation to build more adaptive and effective LLM-based urban agents and broad smart city applications.

Large Reasoning Models (LRMs) have the ability to self-correct even when they make mistakes in their reasoning paths. However, our study reveals that when the reasoning process starts with a short but poor beginning, it becomes difficult for the model to recover. We refer to this phenomenon as the "Prefix Dominance Trap". Inspired by psychological findings that peer interaction can promote self-correction without negatively impacting already accurate individuals, we propose **Learning from Peers** (LeaP) to address this phenomenon. Specifically, every tokens, each reasoning path summarizes its intermediate reasoning and shares it with others through a routing mechanism, enabling paths to incorporate peer insights during inference. However, we observe that smaller models sometimes fail to follow summarization and reflection instructions effectively. To address this, we fine-tune them into our **LeaP-T** model series. Experiments on AIME 2024, AIME 2025, AIMO 2025, and GPQA Diamond show that LeaP provides substantial improvements. For instance, QwQ-32B with LeaP achieves nearly 5 absolute points higher than the baseline on average, and surpasses DeepSeek-R1-671B on three math benchmarks with an average gain of 3.3 points. Notably, our fine-tuned LeaP-T-7B matches the performance of DeepSeek-R1-Distill-Qwen-14B on AIME 2024. In-depth analysis reveals LeaP's robust error correction by timely peer insights, showing strong error tolerance and handling varied task difficulty. LeaP marks a milestone by enabling LRMs to collaborate during reasoning. Our code, datasets, and models are available at https://learning-from-peers.github.io/ .

This paper presents our work on the Light-R1 series, with models, data, and code all released. We first focus on training long COT models from scratch, specifically starting from models initially lacking long COT capabilities. Using a curriculum training recipe consisting of two-stage SFT and semi-on-policy DPO, we train our model Light-R1-32B from Qwen2.5-32B-Instruct, resulting in superior math performance compared to DeepSeek-R1-Distill-Qwen-32B. Despite being trained exclusively on math data, Light-R1-32B shows strong generalization across other domains. In the subsequent phase of this work, we highlight the significant benefit of the 3k dataset constructed for the second SFT stage on enhancing other models. By fine-tuning DeepSeek-R1-Distilled models using this dataset, we obtain new SOTA models in 7B and 14B, while the 32B model, Light-R1-32B-DS performed comparably to QwQ-32B and DeepSeek-R1. Furthermore, we extend our work by applying reinforcement learning, specifically GRPO, on long-COT models to further improve reasoning performance. We successfully train our final Light-R1-14B-DS with RL, achieving SOTA performance among 14B parameter models in math. With AIME24 & 25 scores of 74.0 and 60.2 respectively, Light-R1-14B-DS surpasses even many 32B models and DeepSeek-R1-Distill-Llama-70B. Its RL training also exhibits well expected behavior, showing simultaneous increase in response length and reward score. The Light-R1 series of work validates training long-COT models from scratch, showcases the art in SFT data and releases SOTA models from RL.

Test-time compute has emerged as a promising strategy to enhance the reasoning abilities of large language models (LLMs). However, this strategy has in turn increased how much users pay cloud-based providers offering LLM-as-a-service, since providers charge users for the amount of test-time compute they use to generate an output. In our work, we show that the market of LLM-as-a-service is socially inefficient: providers have a financial incentive to increase the amount of test-time compute, even if this increase contributes little to the quality of the outputs. To address this inefficiency, we introduce a reverse second-price auction mechanism where providers bid their offered price and (expected) quality for the opportunity to serve a user, and users pay proportionally to the marginal value generated by the winning provider relative to the second-highest bidder. To illustrate and complement our theoretical results, we conduct experiments with multiple instruct models from the Llama and Qwen families, as well as reasoning models distilled from DeepSeek-R1, on math and science benchmark datasets.

Speculative decoding accelerates large language model (LLM) inference by letting a lightweight draft model propose multiple tokens that the target model verifies in parallel. Yet existing training objectives optimize only a single greedy draft path, while decoding follows a tree policy that re-ranks and verifies multiple branches. This draft policy misalignment limits achievable speedups. We introduce Group Tree Optimization (GTO), which aligns training with the decoding-time tree policy through two components: (i) Draft Tree Reward, a sampling-free objective equal to the expected acceptance length of the draft tree under the target model, directly measuring decoding performance; (ii) Group-based Draft Policy Training, a stable optimization scheme that contrasts trees from the current and a frozen reference draft model, forming debiased group-standardized advantages and applying a PPO-style surrogate along the longest accepted sequence for robust updates. We further prove that increasing our Draft Tree Reward provably improves acceptance length and speedup. Across dialogue (MT-Bench), code (HumanEval), and math (GSM8K), and multiple LLMs (e.g., LLaMA-3.1-8B, LLaMA-3.3-70B, Vicuna-1.3-13B, DeepSeek-R1-Distill-LLaMA-8B, Qwen3-8B), GTO increases acceptance length by (7.4%) and yields an additional (7.7%) speedup over prior state-of-the-art EAGLE-3. By bridging draft policy misalignment, GTO offers a practical, general solution for efficient LLM inference. Code and draft models are available at https://github.com/hsj576/GTO.

The AM-DeepSeek-R1-Distilled is a large-scale dataset with thinking traces for general reasoning tasks, composed of high-quality and challenging reasoning problems. These problems are collected from a multitude of open-source datasets, subjected to semantic deduplication and meticulous cleaning to eliminate test set contamination. All responses within the dataset are distilled from reasoning models (predominantly DeepSeek-R1) and have undergone rigorous verification procedures. Mathematical problems are validated by checking against reference answers, code problems are verified using test cases, and other tasks are evaluated with the aid of a reward model. The AM-Distill-Qwen-32B model, which was trained through only simple Supervised Fine-Tuning (SFT) using this batch of data, outperformed the DeepSeek-R1-Distill-Qwen-32B model on four benchmarks: AIME2024, MATH-500, GPQA-Diamond, and LiveCodeBench. Additionally, the AM-Distill-Qwen-72B model surpassed the DeepSeek-R1-Distill-Llama-70B model on all benchmarks as well. We are releasing these 1.4 million problems and their corresponding responses to the research community with the objective of fostering the development of powerful reasoning-oriented Large Language Models (LLMs). The dataset was published in https://huggingface.co/datasets/a-m-team/AM-DeepSeek-R1-Distilled-1.4M{https://huggingface.co/datasets/a-m-team/AM-DeepSeek-R1-Distilled-1.4M}.