The cumulative token IS ratio gives unbiased prefix correction and lower variance than full-sequence ratios for token-level gradients in LLM policy optimization, enabling CTPO to outperform GRPO and GSPO baselines on mathematical reasoning tasks.
Canonical reference
Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Exploration
Canonical reference. 80% of citing Pith papers cite this work as background.
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Pith papers citing it
Background
80% of classified citations
abstract
Reinforcement Learning with Verifiable Reward (RLVR) is a powerful method for enhancing the reasoning abilities of Large Language Models, but its full potential is limited by a lack of exploration in two key areas: Depth (the difficulty of problems) and Breadth (the number of training instances). Our analysis of the popular GRPO algorithm reveals a bias that down-weights difficult, low-accuracy problems, which are crucial for improving reasoning skills. To address this, we introduce Difficulty Adaptive Rollout Sampling (DARS), a method that re-weights difficult problems by using targeted, multi-stage rollouts. DARS increases the number of rollout outcomes for these harder problems according to our proposed re-balancing schedules and leads to consistent gains in Pass@K. We discovered that increasing rollout size alone does not improve performance and may actually impair it. In contrast, scaling the batch size to increase breadth via full-batch updates significantly boosted Pass@1 metrics. This improvement stems from higher token-level entropy, ensuring robust exploration and minimized gradient noise. We further present DARS-Breadth, a combined approach that uses DARS with a large breadth of training data. This method demonstrates simultaneous gains in both Pass@K and Pass@1, confirming that depth (adaptive exploration) and breadth (scaling iteration instances) are orthogonal and complementary dimensions for unlocking the full power of RLVR.
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roles
background 5representative citing papers
ResRL decouples shared semantics between positive and negative responses in LLM reinforcement learning via SVD-based projection residuals, outperforming baselines including NSR by up to 9.4% on math reasoning benchmarks.
NExt accelerates RLVR training for LLMs by nonlinearly extrapolating low-rank parameter trajectories extracted from LoRA runs.
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.
Survey that defines agentic RL for LLMs via POMDPs, introduces a taxonomy of planning/tool-use/memory/reasoning capabilities and domains, and compiles open environments from over 500 papers.
Survey mapping RL techniques onto LLM training and highlighting gaps in value-based, off-policy, and bootstrapping methods.
Sample difficulty in RLVR shows non-monotonic effects on LLM reasoning, with easy/medium problems strengthening computation and reasoning features while hard problems often yield weak or harmful signals.
citing papers explorer
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Rethinking Importance Sampling in LLM Policy Optimization: A Cumulative Token Perspective
The cumulative token IS ratio gives unbiased prefix correction and lower variance than full-sequence ratios for token-level gradients in LLM policy optimization, enabling CTPO to outperform GRPO and GSPO baselines on mathematical reasoning tasks.
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ResRL: Boosting LLM Reasoning via Negative Sample Projection Residual Reinforcement Learning
ResRL decouples shared semantics between positive and negative responses in LLM reinforcement learning via SVD-based projection residuals, outperforming baselines including NSR by up to 9.4% on math reasoning benchmarks.
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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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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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The Landscape of Agentic Reinforcement Learning for LLMs: A Survey
Survey that defines agentic RL for LLMs via POMDPs, introduces a taxonomy of planning/tool-use/memory/reasoning capabilities and domains, and compiles open environments from over 500 papers.
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Modularized Reinforcement Learning on LLMs: From MDP Creation to Exploration and Learning
Survey mapping RL techniques onto LLM training and highlighting gaps in value-based, off-policy, and bootstrapping methods.
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Mechanistically Interpreting the Role of Sample Difficulty in RLVR for LLMs
Sample difficulty in RLVR shows non-monotonic effects on LLM reasoning, with easy/medium problems strengthening computation and reasoning features while hard problems often yield weak or harmful signals.
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