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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SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild
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abstract
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.
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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.
DistIL applies distributional DAgger with forward cross-entropy to achieve monotonic policy improvement and better Pass@N from rich feedback in RL for reasoning tasks.
ResMerge improves merging of RL expert LLMs via a stable residual consensus backbone plus gated head correction, outperforming task-vector and spectral baselines in capability preservation.
Mismatched wrong drafts from Qwen2.5-Math-1.5B improve Mathstral-7B GRPO training, reaching 71.98% greedy pass@1 on MATH-500 and lifting AIME 2025/2026 pass@k over baselines and other draft variants.
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.
BubbleSpec exploits long-tail bubbles in synchronous RL by using faster ranks' idle time to pre-generate rollout drafts for speculative decoding, reducing steps by 50% and raising throughput up to 1.8x while preserving exact synchrony.
The cancellation hypothesis shows how rollout-level rewards produce token-level credit assignment in critic-free RL through cancellation of opposing signals on shared tokens, with empirical support and batching interventions that enhance performance.
DUET improves RLVR by allocating tokens across both prompt selection and rollout length, outperforming full-budget baselines even when using only half the tokens.
HORA adaptively allocates rollouts using hit utility to improve Pass@K over compute-matched GRPO on math reasoning benchmarks while preserving Pass@1.
BoostLoRA grows effective adapter rank linearly via iterative boosting on hard examples with orthogonal low-rank updates, outperforming both single-shot ultra-low-rank adapters and full fine-tuning on math and code tasks with zero added inference overhead.
NExt accelerates RLVR training for LLMs by nonlinearly extrapolating low-rank parameter trajectories extracted from LoRA runs.
OPD for LLMs suffers length inflation and repetition collapse; StableOPD uses reference divergence and rollout mixing to prevent it and improve math reasoning performance by 7.2% on average.
GPS trains a small model on optimization history to predict prompt difficulty and select intermediate-difficulty diverse batches, yielding better training efficiency, final performance, and test-time allocation than baselines on reasoning benchmarks.
Large Reasoning Models override their own initial safety recognition during multi-step reasoning in a failure mode called Self-Jailbreak, which Chain-of-Guardrail mitigates through targeted trajectory-level step interventions.
One training example via RLVR boosts LLM math reasoning from 17.6% to 35.7% average across six benchmarks.
Introduces a hierarchical latent selection model showing SFT supplies raw module materials in compound traces while RL decomposes them to identify atomic modules and enable recombination for new reasoning configurations.
CPT is introduced as a pairwise reasoning-trace comparison stage that improves the reasoning-metacognition trade-off over standard SFT+RL pipelines across model scales.
ADR generates novel verifiable code tasks via atomic decomposition and recombination, outperforming heuristic baselines in originality, difficulty, and downstream RLVR gains across coding domains.
HASP upgrades textual skills into executable Program Functions that intervene in LLM agent loops at inference, post-training, or self-evolution, delivering 25% gains over ReAct and 30.4% over Search-R1 on reasoning benchmarks.
VideoRLVR uses SDE-GRPO optimization, dense decomposed rewards, and Early-Step Focus to train video diffusion models on verifiable reasoning tasks, outperforming supervised fine-tuning and other video generators on Maze, FlowFree, and Sokoban.
HölderPO unifies token-level aggregation in GRPO via the Hölder mean with a tunable p parameter and annealing schedule, delivering 54.9% average accuracy on math benchmarks and 93.8% success on ALFWorld.
HTPO introduces hierarchical token-level objective control in RLVR to balance exploration and exploitation by grouping tokens according to difficulty, correctness, and entropy, yielding up to 8.6% gains on AIME benchmarks over DAPO.
CASPO trains LLMs via iterative direct preference optimization so that token-level confidence tracks step-wise correctness, then applies Confidence-aware Thought pruning at inference to improve both reliability and speed on reasoning benchmarks.
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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Reinforcement Learning from Rich Feedback with Distributional DAgger
DistIL applies distributional DAgger with forward cross-entropy to achieve monotonic policy improvement and better Pass@N from rich feedback in RL for reasoning tasks.
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ResMerge: Residual-based Spectral Merging of Large Language Models
ResMerge improves merging of RL expert LLMs via a stable residual consensus backbone plus gated head correction, outperforming task-vector and spectral baselines in capability preservation.
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Weak-to-Strong Elicitation via Mismatched Wrong Drafts
Mismatched wrong drafts from Qwen2.5-Math-1.5B improve Mathstral-7B GRPO training, reaching 71.98% greedy pass@1 on MATH-500 and lifting AIME 2025/2026 pass@k over baselines and other draft variants.
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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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BubbleSpec: Turning Long-Tail Bubbles into Speculative Rollout Drafts for Synchronous Reinforcement Learning
BubbleSpec exploits long-tail bubbles in synchronous RL by using faster ranks' idle time to pre-generate rollout drafts for speculative decoding, reducing steps by 50% and raising throughput up to 1.8x while preserving exact synchrony.
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The Cancellation Hypothesis in Critic-Free RL: From Outcome Rewards to Token Credits
The cancellation hypothesis shows how rollout-level rewards produce token-level credit assignment in critic-free RL through cancellation of opposing signals on shared tokens, with empirical support and batching interventions that enhance performance.
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DUET: Optimize Token-Budget Allocation for Reinforcement Learning with Verifiable Rewards
DUET improves RLVR by allocating tokens across both prompt selection and rollout length, outperforming full-budget baselines even when using only half the tokens.
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Where to Spend Rollouts: Hit-Utility Optimal Rollout Allocation for Group-Based RLVR
HORA adaptively allocates rollouts using hit utility to improve Pass@K over compute-matched GRPO on math reasoning benchmarks while preserving Pass@1.
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BoostLoRA: Growing Effective Rank by Boosting Adapters
BoostLoRA grows effective adapter rank linearly via iterative boosting on hard examples with orthogonal low-rank updates, outperforming both single-shot ultra-low-rank adapters and full fine-tuning on math and code tasks with zero added inference overhead.
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Low-rank Optimization Trajectories Modeling for LLM RLVR Acceleration
NExt accelerates RLVR training for LLMs by nonlinearly extrapolating low-rank parameter trajectories extracted from LoRA runs.
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Demystifying OPD: Length Inflation and Stabilization Strategies for Large Language Models
OPD for LLMs suffers length inflation and repetition collapse; StableOPD uses reference divergence and rollout mixing to prevent it and improve math reasoning performance by 7.2% on average.
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Small Generalizable Prompt Predictive Models Can Steer Efficient RL Post-Training of Large Reasoning Models
GPS trains a small model on optimization history to predict prompt difficulty and select intermediate-difficulty diverse batches, yielding better training efficiency, final performance, and test-time allocation than baselines on reasoning benchmarks.
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When Models Outthink Their Safety: Unveiling and Mitigating Self-Jailbreak in Large Reasoning Models
Large Reasoning Models override their own initial safety recognition during multi-step reasoning in a failure mode called Self-Jailbreak, which Chain-of-Guardrail mitigates through targeted trajectory-level step interventions.
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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
Introduces a hierarchical latent selection model showing SFT supplies raw module materials in compound traces while RL decomposes them to identify atomic modules and enable recombination for new reasoning configurations.
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Enhancing LLM Metacognition via Cognitive Pairwise Training
CPT is introduced as a pairwise reasoning-trace comparison stage that improves the reasoning-metacognition trade-off over standard SFT+RL pipelines across model scales.
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Combinatorial Synthesis: Scaling Code RLVR via Atomic Decomposition and Recombination
ADR generates novel verifiable code tasks via atomic decomposition and recombination, outperforming heuristic baselines in originality, difficulty, and downstream RLVR gains across coding domains.
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Harnessing LLM Agents with Skill Programs
HASP upgrades textual skills into executable Program Functions that intervene in LLM agent loops at inference, post-training, or self-evolution, delivering 25% gains over ReAct and 30.4% over Search-R1 on reasoning benchmarks.
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Video Models Can Reason with Verifiable Rewards
VideoRLVR uses SDE-GRPO optimization, dense decomposed rewards, and Early-Step Focus to train video diffusion models on verifiable reasoning tasks, outperforming supervised fine-tuning and other video generators on Maze, FlowFree, and Sokoban.
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Holder Policy Optimisation
HölderPO unifies token-level aggregation in GRPO via the Hölder mean with a tunable p parameter and annealing schedule, delivering 54.9% average accuracy on math benchmarks and 93.8% success on ALFWorld.
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HTPO: Towards Exploration-Exploitation Balanced Policy Optimization via Hierarchical Token-level Objective Control
HTPO introduces hierarchical token-level objective control in RLVR to balance exploration and exploitation by grouping tokens according to difficulty, correctness, and entropy, yielding up to 8.6% gains on AIME benchmarks over DAPO.
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Confidence-Aware Alignment Makes Reasoning LLMs More Reliable
CASPO trains LLMs via iterative direct preference optimization so that token-level confidence tracks step-wise correctness, then applies Confidence-aware Thought pruning at inference to improve both reliability and speed on reasoning benchmarks.
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Teaching Thinking Models to Reason with Tools: A Full-Pipeline Recipe for Tool-Integrated Reasoning
A training recipe for tool-integrated reasoning models achieves state-of-the-art open-source results on math benchmarks such as 96.7% and 99.2% on AIME 2025 at 4B and 30B scales by balancing tool-use trajectories and optimizing for pass@k during SFT before stable RLVR.
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Rethinking RL for LLM Reasoning: It's Sparse Policy Selection, Not Capability Learning
RL for LLM reasoning acts as sparse policy selection at high-entropy tokens already present in the base model, enabling ReasonMaxxer—an efficient contrastive method that recovers most RL gains at three orders of magnitude lower cost.
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WebGen-R1: Incentivizing Large Language Models to Generate Functional and Aesthetic Websites with Reinforcement Learning
WebGen-R1 uses end-to-end RL with scaffold-driven generation and cascaded rewards for structure, function, and aesthetics to transform a 7B model into a generator of deployable multi-page websites that rivals much larger models.
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Too Correct to Learn: Reinforcement Learning on Saturated Reasoning Data
A parameter-free sampling strategy called CUTS combined with Mixed-CUTS training prevents mode collapse in RL for saturated LLM reasoning tasks and raises AIME25 Pass@1 accuracy by up to 15.1% over standard GRPO.
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HEALing Entropy Collapse: Enhancing Exploration in Few-Shot RLVR via Hybrid-Domain Entropy Dynamics Alignment
HEAL mitigates entropy collapse in few-shot RLVR by selectively adding general-domain data and aligning trajectory-level entropy dynamics, matching full-shot performance with 32 target samples.
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From $P(y|x)$ to $P(y)$: Investigating Reinforcement Learning in Pre-train Space
PreRL applies reward-driven updates to P(y) in pre-train space, uses Negative Sample Reinforcement to prune bad reasoning paths and boost reflection, and combines with standard RL in Dual Space RL to outperform baselines on reasoning tasks.
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When to Trust Tools? Adaptive Tool Trust Calibration For Tool-Integrated Math Reasoning
ATTC reduces 'Tool Ignored' errors in tool-integrated reasoning by adaptively trusting tool results according to generated code confidence, yielding 4.1-7.5% gains across models and datasets.
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Hindsight-Anchored Policy Optimization: Turning Failure into Feedback in Sparse Reward Settings
HAPO adds a hindsight-anchored SSI operator with Thompson gating to GRPO-style RLVR, achieving asymptotic consistency that recovers unbiased on-policy gradients as the policy improves.
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Flexible Entropy Control in RLVR with a Gradient-Preserving Perspective
Dynamic clipping strategies based on importance sampling regions enable precise entropy management in RLVR, mitigating collapse and improving benchmark performance.
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Sparse Reward Subsystem in Large Language Models
LLM hidden states contain a sparse reward subsystem consisting of value neurons that predict state value and dopamine neurons that encode step-level temporal difference errors.
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Unlocking Exploration in RLVR: Uncertainty-aware Advantage Shaping for Deeper Reasoning
UCAS refines RLVR advantage signals with a logit-space self-confidence proxy for response-level modulation and asymmetric token-level penalties based on raw logit certainty to boost exploration and reduce entropy collapse.
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When Importance Sampling Misallocates Credit: Asymmetric Ratios for Outcome-Supervised RL
The paper identifies that importance sampling ratios in outcome-supervised RL misallocate credit by creating unbalanced token updates, and introduces ASPO to correct the asymmetry for positive-advantage tokens.
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The Signal is in the Steps: Local Scoring for Reasoning Data Selection
LALP scores local reasoning steps rather than full trajectories to improve selection of training data from diverse teacher models for distilling long-form reasoning.
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Structured In-context Environment Scaling for Large Language Model Reasoning
SIE framework automatically constructs scalable, verifiable reasoning environments from structured data, improving in-domain performance and enabling generalization to out-of-domain math and logic tasks.
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EvoCoT: Overcoming the Exploration Bottleneck in Reinforcement Learning
EvoCoT uses self-generated and verified CoT trajectories in a two-stage curriculum to let LLMs learn from initially unsolved hard problems in RLVR settings.
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MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention
MiniMax-M1 is a 456B parameter hybrid-attention MoE model trained with CISPO RL that achieves performance comparable or superior to DeepSeek-R1 and Qwen3-235B on reasoning and software engineering tasks while training in three weeks on 512 GPUs.
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Tool-Aware Optimization with Entropy Guidance for Efficient Agentic Reinforcement Learning
TAO-RL improves agentic RL by filtering degenerate trajectories and reshaping advantages with tool-aware entropy bonuses, yielding better performance on reasoning benchmarks.
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RLVR without Ineffective Samples: Group Prioritized Off-Policy Optimization for LLM Reasoning
POPO uses recency-based prioritized group replay and decoupled off-policy optimization to avoid zero-variance ineffective samples in RLVR, accelerating LLM reasoning finetuning with fewer rollouts.
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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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Clipping Bottleneck: Stabilizing RLVR via Stochastic Recovery of Near-Boundary Signals
Proposes Near-boundary Stochastic Rescue (NSR) as a stochastic modification to clipping in RLVR that recovers near-boundary signals and yields gains over baselines like DAPO and GSPO.
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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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LamPO: A Lambda Style Policy Optimization for Reasoning Language Models
LamPO introduces a pairwise decomposed advantage with confidence-aware weighting to replace scalar group advantages in group-relative policy optimization for reasoning models.
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Rethinking Math Reasoning Evaluation: A Robust LLM-as-a-Judge Framework Beyond Symbolic Rigidity
An LLM-as-a-judge evaluation framework for math reasoning outperforms symbolic methods by accurately assessing diverse answer representations and formats.
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Learning to Pose Problems: Reasoning-Driven and Solver-Adaptive Data Synthesis
A reasoning-driven problem generator plans synthesis directions with CoT and uses solver performance feedback to adapt difficulty, producing complementary problems that yield a 3.4% average improvement across 10 reasoning benchmarks.
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A Model Can Help Itself: Reward-Free Self-Training for LLM Reasoning
SePT alternates self-generation of responses at controlled temperatures with training on the latest model outputs, yielding gains over a strong no-training baseline on six math reasoning benchmarks.
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Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective
Derives a token-level entropy change approximation revealing four factors, identifies limitations in prior entropy interventions, and proposes STEER which adaptively reweights tokens to mitigate collapse and improve performance on math and coding benchmarks.