# Where the Model Changes Its Mind: Hindsight-Divergence Localization for Efficient Reinforcement Learning with Verifiable Rewards

arXiv: https://arxiv.org/abs/2609.36864 · HTML: https://mlsanity.com/paper/2609.36864/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 33 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 26 of 26)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [ScienceWorld: Is your Agent Smarter than a 5th Grader?](https://mlsanity.com/paper/2203.07540/) (2022)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [TreeRL: LLM Reinforcement Learning with On-Policy Tree Search](https://mlsanity.com/paper/2506.11902/) (2025)
- [Unifying Group-Relative and Self-Distillation Policy Optimization via Sample Routing](https://mlsanity.com/paper/2604.02288/) (2026)
- [rStar-Coder: Scaling Competitive Code Reasoning with a Large-Scale Verified Dataset](https://mlsanity.com/paper/2505.21297/) (2025)
- [PivotRL: High Accuracy Agentic Post-Training at Low Compute Cost](https://mlsanity.com/paper/2603.21383/) (2026)
- [R3L: Reflect-then-Retry Reinforcement Learning with Language-Guided Exploration, Pivotal Credit, and Positive Amplification](https://mlsanity.com/paper/2601.03715/) (2026)
- [Branching Policy Optimization: Sandbox-Native Language Agent Reinforcement Learning](https://mlsanity.com/paper/2607.14171/) (2026)
- [HINT-SD: Targeted Hindsight Self-Distillation for Long-Horizon Agents](https://mlsanity.com/paper/2605.17873/) (2026)
- [Localizing Credit at the Divergence: Path-Conditioned Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2606.15576/) (2026)
- [SD-Search: On-Policy Hindsight Self-Distillation for Search-Augmented Reasoning](https://mlsanity.com/paper/2605.18299/) (2026)
- [Agent Reinforcement Learning via Pivotal-Aware Self-Feedback Retry](https://mlsanity.com/paper/2607.03702/) (2026)
- [Maximizing Rollout Informativeness under a Fixed Budget: A Submodular View of Tree Search for Tool-Use Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.05262/) (2026)

## Abstract (arXiv)

Group-relative methods for reinforcement learning with verifiable rewards (RLVR) learn from differences in rollout outcomes. Independently sampling complete trajectories is costly and does not explicitly explore the decision space at critical positions. Feedback on a completed trajectory can reveal which earlier choices the policy reconsiders, suggesting where to sample alternative continuations. We introduce Hindsight-Divergence Localization (HDL), which uses hindsight-induced changes in token log-likelihoods to select branch points. HDL generates a small number of complete root trajectories and fills each training group with continuations from the selected positions under the original task context. Each continuation reuses its root prefix and contributes policy updates only through its newly generated suffix, reducing generation cost while focusing additional exploration and learning on decisions after branching. Experiments with three models across math, code, and agent tasks show gains in both rollout efficiency and task performance. Compared with GRPO at matched group sizes and training steps, HDL yields up to a 2.5× reduction in generated tokens and a 1.8× speedup in rollout wall-clock time. Despite this reduced generation budget, HDL improves performance across all three domains, with gains of up to 12.5 points on agent tasks.