DeepMath-103K is a new 103K-problem mathematical dataset with high difficulty, rigorous decontamination, and verifiable answers to support RL training of language-model reasoning.
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Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs
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abstract
Test-time inference has emerged as a powerful paradigm for enabling language models to ``think'' longer and more carefully about complex challenges, much like skilled human experts. While reinforcement learning (RL) can drive self-improvement in language models on verifiable tasks, some models exhibit substantial gains while others quickly plateau. For instance, we find that Qwen-2.5-3B far exceeds Llama-3.2-3B under identical RL training for the game of Countdown. This discrepancy raises a critical question: what intrinsic properties enable effective self-improvement? We introduce a framework to investigate this question by analyzing four key cognitive behaviors -- verification, backtracking, subgoal setting, and backward chaining -- that both expert human problem solvers and successful language models employ. Our study reveals that Qwen naturally exhibits these reasoning behaviors, whereas Llama initially lacks them. In systematic experimentation with controlled behavioral datasets, we find that priming Llama with examples containing these reasoning behaviors enables substantial improvements during RL, matching or exceeding Qwen's performance. Importantly, the presence of reasoning behaviors, rather than correctness of answers, proves to be the critical factor -- models primed with incorrect solutions containing proper reasoning patterns achieve comparable performance to those trained on correct solutions. Finally, leveraging continued pretraining with OpenWebMath data, filtered to amplify reasoning behaviors, enables the Llama model to match Qwen's self-improvement trajectory. Our findings establish a fundamental relationship between initial reasoning behaviors and the capacity for improvement, explaining why some language models effectively utilize additional computation while others plateau.
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representative citing papers
Online IL overcomes an information-theoretic bottleneck that offline IL faces in non-realizable settings even at horizon 1, under a new structural characterization of reward-relative misspecification.
StepCodeReasoner aligns code reasoning with verifiable stepwise execution traces via print anchors and bi-level GRPO reinforcement learning, reaching SOTA results on CRUXEval (91.1%) and LiveCodeBench (86.5%) for a 7B model.
Parallel thinking in LLMs suffers from overscaling where fixed global budgets waste samples; LanBo predicts per-sample budgets from latent states to raise utilization without hurting accuracy.
Prefix-RFT blends SFT and RFT via prefix sampling from demonstrations to outperform standalone SFT, RFT, and mixed-policy baselines on math reasoning problems.
One training example via RLVR boosts LLM math reasoning from 17.6% to 35.7% average across six benchmarks.
SFT supplies entangled compositional traces of atomic skills and routing modules; RL identifies those modules and enables recombination on novel compositions outside the SFT support.
HQRE entropy regularization makes multi-agent LLM coordination well-posed, yielding unique equilibria, linear mirror convergence, bounded Bayesian regret, and DICE gains of 4.3–8.5 pp on reasoning/planning tasks.
ReShift is a reasoning-level backdoor framework for VLMs that uses poisoned data construction and joint optimization to shift CoT trajectories on trigger while preserving surface coherence.
SEAR trains one LLM via adversarial process rewards to explore harmful reasoning paths but flip to safe outputs, reducing over-refusal while preserving safety.
On-policy self-distillation with sampled demonstrations reduces rollout diversity by amplifying existing probability gaps in the base model, unlike ideal RL which preserves ratios among correct outputs.
The L2 norm of LLM hidden states signals reasoning intensity, with a theoretical bound on SAE feature activations, enabling three new test-time scaling techniques that boost performance.
AnE combines Truth Anchor Expansion and Scaffold-Stripping to deliver 10.3% gains on eight multimodal reasoning benchmarks for MLLMs.
SSOPD converts intra-group correct-wrong contrast into process supervision by distilling a teacher distribution from the shortest correct completion into prefixes of the longest wrong completion, improving GRPO on AIME and HMMT benchmarks.
Reasoning gaps between base LLMs and LRMs concentrate on ~8% of early planning tokens; intervening with the reasoning model only at high-disagreement positions recovers performance.
STOP uses structured on-policy analysis to prune long reasoning traces to their earliest correct node, cutting token usage 19-42% with little accuracy loss on math benchmarks.
LLMs implement a second-order confidence architecture where the PANL activation encodes both error likelihood and the ability to correct it, beyond verbal confidence or log-probabilities.
A small set of sparse autoencoder features in LLMs drives shifts between generous and selfish allocations in dictator games, with causal patching and steering confirming their role and generalization to other social games.
RePro defines a surrogate objective with intensity and stability scores to generate process-level rewards that enhance LLM reasoning efficiency and accuracy within RLVR pipelines.
SPHINX generates synthetic visual puzzles for benchmarking LVLMs, where GPT-5 scores 51.1% and RLVR training improves both in-domain and external visual reasoning performance.
REVISOR adds multimodal visual-text reflection and a Dual Attribution Decoupled Reward to improve long-form video reasoning in MLLMs without extra supervised fine-tuning.
Archer introduces response-level entropy normalization and differentiated clipping/KL regularization in RLVR to encourage exploration on reasoning tokens while stabilizing knowledge tokens, yielding gains in pass@1 and pass@K on reasoning benchmarks.
High-entropy minority tokens drive RLVR gains, so restricting gradients to the top 20% maintains or improves performance over full updates on Qwen3 models, especially larger ones.
Prolonged RL training with KL control and reference policy resetting enables LLMs to develop novel reasoning strategies inaccessible to base models even under extensive sampling.
citing papers explorer
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DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning
DeepMath-103K is a new 103K-problem mathematical dataset with high difficulty, rigorous decontamination, and verifiable answers to support RL training of language-model reasoning.
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When Does Online Imitation Learning Help in LLM Post-Training? The Role of (Non-)Realizability Beyond Horizon
Online IL overcomes an information-theoretic bottleneck that offline IL faces in non-realizable settings even at horizon 1, under a new structural characterization of reward-relative misspecification.
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StepCodeReasoner: Aligning Code Reasoning with Stepwise Execution Traces via Reinforcement Learning
StepCodeReasoner aligns code reasoning with verifiable stepwise execution traces via print anchors and bi-level GRPO reinforcement learning, reaching SOTA results on CRUXEval (91.1%) and LiveCodeBench (86.5%) for a 7B model.
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On the Overscaling Curse of Parallel Thinking: System Efficacy Contradicts Sample Efficiency
Parallel thinking in LLMs suffers from overscaling where fixed global budgets waste samples; LanBo predicts per-sample budgets from latent states to raise utilization without hurting accuracy.
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Blending Supervised and Reinforcement Fine-Tuning with Prefix Sampling
Prefix-RFT blends SFT and RFT via prefix sampling from demonstrations to outperform standalone SFT, RFT, and mixed-policy baselines on math reasoning problems.
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Reinforcement Learning for Reasoning in Large Language Models with One Training Example
One training example via RLVR boosts LLM math reasoning from 17.6% to 35.7% average across six benchmarks.
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From Reasoning Traces to Reusable Modules: Understanding Compositional Generalization in Language Model Reasoning
SFT supplies entangled compositional traces of atomic skills and routing modules; RL identifies those modules and enables recombination on novel compositions outside the SFT support.
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DICE: Entropy-Regularized Equilibrium Selection for Stable Multi-Agent LLM Coordination
HQRE entropy regularization makes multi-agent LLM coordination well-posed, yielding unique equilibria, linear mirror convergence, bounded Bayesian regret, and DICE gains of 4.3–8.5 pp on reasoning/planning tasks.
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ReShift: Aha-Moment-Driven Reasoning-Level Backdoor Attacks on Vision-Language Models
ReShift is a reasoning-level backdoor framework for VLMs that uses poisoned data construction and joint optimization to shift CoT trajectories on trigger while preserving surface coherence.
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Addressing Over-Refusal in LLMs with Competing Rewards
SEAR trains one LLM via adversarial process rewards to explore harmful reasoning paths but flip to safe outputs, reducing over-refusal while preserving safety.
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On-Policy Self-Distillation with Sampled Demonstrations Reduces Output Diversity
On-policy self-distillation with sampled demonstrations reduces rollout diversity by amplifying existing probability gaps in the base model, unlike ideal RL which preserves ratios among correct outputs.
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The Tell-Tale Norm: $\ell_2$ Magnitude as a Signal for Reasoning Dynamics in Large Language Models
The L2 norm of LLM hidden states signals reasoning intensity, with a theoretical bound on SAE feature activations, enabling three new test-time scaling techniques that boost performance.
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AnE: Pushing the Reasoning Frontier of Multimodal LLMs via Anchor Evolution
AnE combines Truth Anchor Expansion and Scaffold-Stripping to deliver 10.3% gains on eight multimodal reasoning benchmarks for MLLMs.
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Self-Supervised On-Policy Distillation for Reasoning Language Models
SSOPD converts intra-group correct-wrong contrast into process supervision by distilling a teacher distribution from the shortest correct completion into prefixes of the longest wrong completion, improving GRPO on AIME and HMMT benchmarks.
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Reasoning Can Be Restored by Correcting a Few Decision Tokens
Reasoning gaps between base LLMs and LRMs concentrate on ~8% of early planning tokens; intervening with the reasoning model only at high-disagreement positions recovers performance.
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STOP: Structured On-Policy Pruning of Long-Form Reasoning in Low-Data Regimes
STOP uses structured on-policy analysis to prune long reasoning traces to their earliest correct node, cutting token usage 19-42% with little accuracy loss on math benchmarks.
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How LLMs Detect and Correct Their Own Errors: The Role of Internal Confidence Signals
LLMs implement a second-order confidence architecture where the PANL activation encodes both error likelihood and the ability to correct it, beyond verbal confidence or log-probabilities.
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Understanding the Mechanism of Altruism in Large Language Models
A small set of sparse autoencoder features in LLMs drives shifts between generous and selfish allocations in dictator games, with causal patching and steering confirming their role and generalization to other social games.
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Rectifying LLM Thought from Lens of Optimization
RePro defines a surrogate objective with intensity and stability scores to generate process-level rewards that enhance LLM reasoning efficiency and accuracy within RLVR pipelines.
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SPHINX: A Synthetic Environment for Visual Perception and Reasoning
SPHINX generates synthetic visual puzzles for benchmarking LVLMs, where GPT-5 scores 51.1% and RLVR training improves both in-domain and external visual reasoning performance.
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REVISOR: Beyond Textual Reflection, Towards Multimodal Introspective Reasoning in Long-Form Video Understanding
REVISOR adds multimodal visual-text reflection and a Dual Attribution Decoupled Reward to improve long-form video reasoning in MLLMs without extra supervised fine-tuning.
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Stabilizing Knowledge, Promoting Reasoning: Dual-Token Constraints for RLVR
Archer introduces response-level entropy normalization and differentiated clipping/KL regularization in RLVR to encourage exploration on reasoning tokens while stabilizing knowledge tokens, yielding gains in pass@1 and pass@K on reasoning benchmarks.
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Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning
High-entropy minority tokens drive RLVR gains, so restricting gradients to the top 20% maintains or improves performance over full updates on Qwen3 models, especially larger ones.
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ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models
Prolonged RL training with KL control and reference policy resetting enables LLMs to develop novel reasoning strategies inaccessible to base models even under extensive sampling.
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Grounded Reinforcement Learning for Visual Reasoning
ViGoRL introduces visually grounded RL that anchors reasoning steps to image coordinates and uses multi-turn zooming to outperform standard RL and supervised baselines on spatial and GUI reasoning benchmarks.
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The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning
Entropy minimization on self-generated outputs elicits strong reasoning in pretrained LLMs, matching or exceeding supervised RL methods on benchmarks.
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Search, Fail, Recover: A Training Framework for Correction-Aware Reasoning
Pyligent trains LLMs to search, detect failures via task validators, and backtrack to recoverable prefixes, improving solve rates by 13–73 points over gold-only SFT on hidden graphs, Sudoku, and Blocksworld.
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Data Selection Through Iterative Self-Filtering for Vision-Language Settings
An iterative bootstrapped self-filtering approach selects balanced clean and diverse subsets from noisy vision-language datasets to train improved CLIP models.
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Trust Region On-Policy Distillation
TrOPD stabilizes on-policy distillation for LLMs with trust-region learning, outlier estimation, and off-policy guidance, outperforming prior OPD methods on reasoning and code benchmarks.
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LANG: Reinforcement Learning for Multilingual Reasoning with Language-Adaptive Hint Guidance
LANG combines language-adaptive hint guidance, progressive decay, and difficulty-tailored learning horizons in RL to boost non-English reasoning performance while preserving language consistency.
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Evaluating the False Trust Engendered by LLM Explanations
LLM reasoning traces and post-hoc explanations increase false trust in incorrect predictions, whereas contrastive dual explanations enhance users' ability to distinguish correct from incorrect AI outputs.
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Mid-Training with Self-Generated Data Improves Reinforcement Learning in Language Models
Mid-training LLMs on self-generated diverse reasoning paths improves subsequent RL performance on mathematical benchmarks and OOD tasks.
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A Multi-Agent Framework for Automated Exploit Generation with Constraint-Guided Comprehension and Reflection
Vulnsage, a multi-agent framework, generates 34.64% more exploits than prior tools and verified 146 zero-day vulnerabilities in real-world open-source libraries.
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REFLEX: Self-Refining Explainable Fact-Checking via Verdict-Anchored Style Control
By steering activations along directions learned from base-vs-fine-tuned disagreements, REFLEX reports 64.99 macro-F1 on RAW-FC fact-checking with only ~465 self-refined contrastive samples and no retrieval.
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EEPO: Exploration-Enhanced Policy Optimization via Sample-Then-Forget
EEPO uses sample-then-forget rollouts with adaptive unlearning to boost exploration in RLVR, delivering relative gains of 24.3% on Qwen2.5-3B, 33.0% on Llama3.2-3B-Instruct, and 10.4% on Qwen3-8B-Base over GRPO across five reasoning benchmarks.
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Position: The Hidden Costs and Measurement Gaps of Reinforcement Learning with Verifiable Rewards
Budget-matched evaluations and partial-prompt contamination probes show several RLVR reasoning gaps shrink or vanish once budgets, prompts, and dataset versions are controlled.
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Self-Aligned Reward: Towards Effective and Efficient Reasoners
Self-aligned reward uses relative perplexity differences to encourage concise, query-specific reasoning in LLMs, yielding 4% accuracy gains and 30% lower inference cost when added to PPO or GRPO.
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Proximal Supervised Fine-Tuning
PSFT modifies supervised fine-tuning by incorporating trust-region ideas from RL to constrain policy changes, yielding better out-of-domain generalization in math and human-value tasks without entropy collapse.
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Emerging Properties in Unified Multimodal Pretraining
BAGEL is a unified decoder-only model that develops emerging complex multimodal reasoning abilities after pretraining on large-scale interleaved data and outperforms prior open-source unified models.
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Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models
The paper unifies perspectives on Long CoT in reasoning LLMs by introducing a taxonomy, detailing characteristics of deep reasoning and reflection, and discussing emergence phenomena and future directions.
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A Survey of Reinforcement Learning for Large Reasoning Models
A survey compiling RL methods, challenges, data resources, and applications for enhancing reasoning in large language models and large reasoning models since DeepSeek-R1.
- The Periodic Table of LLM Reasoning: A Structured Survey of Reasoning Paradigms, Methods, and Failure Modes