mlsanityData to 7 Oct 2026

Where Hindsight Credit Can Reside: A Signed-Capacity View of Token Updates in RLVR

arXiv 2604.11056 ↗First posted 13 Apr 2026cs.LG cs.AIcited by 8

On the map: LLM reasoning → Reinforcement learning for reasoning

Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) improves the reasoning ability of Large Language Models (LLMs), but sparse outcome rewards make token-level credit assignment difficult. We study token-level credit as a reward-conditioned shift from the behavior policy to a hindsight posterior. In autoregressive RLVR, this shift can be expressed through Conditional Mutual Information (CMI), which shows that token entropy upper-bounds possible hindsight credit. Entropy, however, indicates capacity rather than update direction, so we introduce the Four Quadrant Decomposition to separate updates by reward polarity and token entropy. Controlled interventions show that these two factors jointly shape token updates. Sustained reasoning gains concentrate in signed high-entropy quadrants, whereas low-entropy updates saturate quickly. Based on this analysis, we propose Hindsight-Aware Policy Optimization (HAPO), a sign-preserving modification to GRPO that performs capacity-guided advantage reallocation. Experiments on mathematical reasoning benchmarks in two model settings show that HAPO achieves competitive performance among entropy-aware baselines.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 41 of its 62 references that are in the map. First posted on arXiv 13 Apr 2026.

Builds on

41 of 62 references.

Closest ancestors · 18

Same direction, newest first

  1. 2025Rethinking Sample Polarity in Reinforcement Learning with Verifiable Rewards25 Dec
  2. 2025Beyond High-Entropy Exploration: Correctness-Aware Low-Entropy Segment-Based Advantage Shaping for Reasoning LLMs30 Nov
  3. 2025Exploiting Tree Structure for Credit Assignment in RL Training of LLMs22 Sep
  4. 2025Stabilizing Knowledge, Promoting Reasoning: Dual-Token Constraints for RLVR21 Jul
  5. 2025Reasoning with Exploration: An Entropy Perspective17 Jun
  6. 2025KDRL: Post-Training Reasoning LLMs via Unified Knowledge Distillation and Reinforcement Learning2 Jun
  7. 2025Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning2 Jun
  8. 2025The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning2 Jun
  9. 2025On the Effect of Negative Gradient in Group Relative Deep Reinforcement Optimization24 May
  10. 2025The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning21 May
  11. 2025Do Not Let Low-Probability Tokens Over-Dominate in RL for LLMs19 May
  12. 2025GPG: A Simple and Strong Reinforcement Learning Baseline for Model Reasoning3 Apr
6 more
  1. 2025SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild24 Mar
  2. 2025Reinforcement Learning with Verifiable Rewards: GRPO's Effective Loss, Dynamics, and Success Amplification9 Mar
  3. 2025Process Reinforcement through Implicit Rewards3 Feb
  4. 2025The Lessons of Developing Process Reward Models in Mathematical Reasoning13 Jan
  5. 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations14 Dec
  6. 2022Solving math word problems with process- and outcome-based feedback25 Nov

Other references · 23

  1. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  2. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 8,851
  3. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,767
  4. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  5. 2017Deep reinforcement learning from human preferencescited by 3,846
  6. 2023SWE-bench: Can Language Models Resolve Real-World GitHub Issues?cited by 3,193
  7. 2024HybridFlow: A Flexible and Efficient RLHF Frameworkcited by 1,980
  8. 2022Solving Quantitative Reasoning Problems with Language Modelscited by 1,359
  9. 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,099
  10. 2017Hindsight Experience Replaycited by 1,096
  11. 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,057
  12. 2023Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMscited by 946
11 more
  1. 2017Counterfactual Multi-Agent Policy Gradientscited by 733
  2. 2025SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-trainingcited by 655
  3. 2019On Variational Bounds of Mutual Informationcited by 550
  4. 2025Demystifying Long Chain-of-Thought Reasoning in LLMscited by 323
  5. 2024VinePPO: Refining Credit Assignment in RL Training of LLMscited by 168
  6. 2025A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibilitycited by 89
  7. 2025Concise Reasoning via Reinforcement Learningcited by 78
  8. 2026Hindsight Credit Assignment for Long-Horizon LLM Agentscited by 51
  9. 2025Harnessing Uncertainty: Entropy-Modulated Policy Gradients for Long-Horizon LLM Agentscited by 43
  10. 2021An Information-Theoretic Perspective on Credit Assignment in Reinforcement Learningcited by 20
  11. 2024InstructPatentGPT: Training patent language models to follow instructions with human feedbackcited by 17

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 8.

8 papers.

  1. 2026Does On-Policy Distillation Really Distill? From Noisy Teacher to Self-Improvementcited by 8
  2. 2026Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoningcited by 7
  3. 2026Not All Tokens Learn Alike: Attention Entropy Reveals Heterogeneous Signals in RL Reasoningcited by 1
  4. 2026From Instance Selection to Fixed-Pool Data Recipe Search for Supervised Fine-Tuningcited by 1
  5. 2026Entropy Is Not Enough: Unlocking Effective Reinforcement Learning for Visual Reasoning via Vision-Anchored Token Selectioncited by 0
  6. 2026Surprising Success, Repeated Failure: Entropy-Guided Credit Assignment for Exploration in LLM Reasoningcited by 0
  7. 2026BoT-GRPO: Efficient Process-Reward RL for Reasoning via Bag-of-Token Aggregationcited by 0
  8. 2026GRPODropout: Less is More for Online Reinforcement Learning Rolloutscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Revisiting Entropy in Reinforcement Learning for Large Reasoning Models
  2. 2025Unlocking Exploration in RLVR: Uncertainty-aware Advantage Shaping for Deeper Reasoning
  3. 2026Which Tokens Matter? Adaptive Token Selection for RLVR with the Relative Surprisal Index
  4. 2026What are Key Factors for Updates in RL for LLM Reasoning?
  5. 2026On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation
  6. 2026A Gradient Perspective on RLVR Stability and Winner Advantage Policy Optimization
  7. 2025Exploration vs Exploitation: Rethinking RLVR through Clipping, Entropy, and Spurious Reward
  8. 2025Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward