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

arXiv: https://arxiv.org/abs/2604.11056 · HTML: https://mlsanity.com/paper/2604.11056/

## Key facts

- Cited by 8 papers in the map (data through 14 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.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 41)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [GPG: A Simple and Strong Reinforcement Learning Baseline for Model Reasoning](https://mlsanity.com/paper/2504.02546/) (2025)
- [Reinforcement Learning with Verifiable Rewards: GRPO's Effective Loss, Dynamics, and Success Amplification](https://mlsanity.com/paper/2503.06639/) (2025)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [Concise Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2504.05185/) (2025)

## Built on by (most cited first, 8 of 8)

- [Does On-Policy Distillation Really Distill? From Noisy Teacher to Self-Improvement](https://mlsanity.com/paper/2608.31046/) (2026)
- [Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2605.22263/) (2026)
- [Not All Tokens Learn Alike: Attention Entropy Reveals Heterogeneous Signals in RL Reasoning](https://mlsanity.com/paper/2605.07660/) (2026)
- [From Instance Selection to Fixed-Pool Data Recipe Search for Supervised Fine-Tuning](https://mlsanity.com/paper/2605.12944/) (2026)
- [Entropy Is Not Enough: Unlocking Effective Reinforcement Learning for Visual Reasoning via Vision-Anchored Token Selection](https://mlsanity.com/paper/2606.03937/) (2026)
- [Surprising Success, Repeated Failure: Entropy-Guided Credit Assignment for Exploration in LLM Reasoning](https://mlsanity.com/paper/2609.33781/) (2026)
- [BoT-GRPO: Efficient Process-Reward RL for Reasoning via Bag-of-Token Aggregation](https://mlsanity.com/paper/2610.09804/) (2026)
- [GRPODropout: Less is More for Online Reinforcement Learning Rollouts](https://mlsanity.com/paper/2610.11854/) (2026)

## 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.