# Localizing Credit at the Divergence: Path-Conditioned Self-Distillation for LLM Reasoning

arXiv: https://arxiv.org/abs/2606.15576 · HTML: https://mlsanity.com/paper/2606.15576/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 23 references that are in the map.
- First posted on arXiv 14 Jun 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 22 of 22)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [What Makes a Reward Model a Good Teacher? An Optimization Perspective](https://mlsanity.com/paper/2503.15477/) (2025)
- [Nested Sequential Monte Carlo Methods](https://mlsanity.com/paper/1502.02536/) (2015)
- [MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration](https://mlsanity.com/paper/2603.28254/) (2026)
- [InSPO: Unlocking Intrinsic Self-Reflection for LLM Preference Optimization](https://mlsanity.com/paper/2512.23126/) (2025)
- [RC-GRPO: Reward-Conditioned Group Relative Policy Optimization for Multi-Turn Tool Calling Agents](https://mlsanity.com/paper/2602.03025/) (2026)
- [Learning to Substitute Words with Model-based Score Ranking](https://mlsanity.com/paper/2502.05933/) (2025)
- [When Right Meets Wrong: Bilateral Context Conditioning with Reward-Confidence Correction for GRPO](https://mlsanity.com/paper/2603.13134/) (2026)
- [MiCoTA: Bridging the Learnability Gap with Intermediate CoT and Teacher Assistants](https://mlsanity.com/paper/2507.01887/) (2025)
- [Towards A Unified View of Answer Calibration for Multi-Step Reasoning](https://mlsanity.com/paper/2311.09101/) (2023)
- [Calibrating and Rotating: A Unified Framework for Weight Conditioning in PEFT](https://mlsanity.com/paper/2511.00051/) (2025)
- [OPPO: Bayesian Value Recursion for Token-Level Credit Assignment in LLM Reasoning](https://mlsanity.com/paper/2605.21851/) (2026)
- [Calibrating Model-Based Evaluation Metrics for Summarization](https://mlsanity.com/paper/2604.17200/) (2026)

## Built on by (most cited first, 7 of 7)

- [LoongReflect: Boosting Long-Horizon Reflection in Search Agents via Global Perspective Distillation](https://mlsanity.com/paper/2608.11967/) (2026)
- [One Symptom, Three Levers: A Critical Review of On-Policy Self-Distillation](https://mlsanity.com/paper/2608.25936/) (2026)
- [Expected Reasoning-Step Return Unifies On-Policy Learning from Rewards and Teachers](https://mlsanity.com/paper/2609.32674/) (2026)
- [Where the Model Changes Its Mind: Hindsight-Divergence Localization for Efficient Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2609.36864/) (2026)
- [Diagnosing On-Policy Self-Distillation for Reasoning Language Models](https://mlsanity.com/paper/2609.39118/) (2026)
- [Privileged Context as Drift in On-Policy Self-Distillation](https://mlsanity.com/paper/2610.07842/) (2026)
- [A Privileged Teacher That Only Scores Cannot Search: Critique-Conditioned On-Policy Self-Distillation for Reasoning](https://mlsanity.com/paper/2610.13744/) (2026)

## Abstract (arXiv)

Reinforcement learning from verifiable rewards assigns a single scalar to each rollout, leaving token-level credit assignment underspecified in long reasoning traces. On-policy self-distillation addresses this by letting the same model act as a teacher conditioned on privileged information, producing a dense per-token signal. But the common choice of a ground-truth answer is only an endpoint cue: on terse-answer tasks, the teacher falls silent at the intermediate positions where path-level guidance matters most. We propose Hindsight Self-Distillation (HSD), which conditions the teacher on a successful peer rollout drawn from the current training group. Such a peer is an exact sample from the success-conditioned policy, requiring no additional sampled rollouts. By providing a full successful continuation rather than only the final answer, the resulting credit signal concentrates at the divergence position between a failed rollout and a successful peer. Across Qwen3-8B and Qwen3-32B on math and code benchmarks, HSD obtains the best result against GRPO variants and on-policy distillation baselines, with the largest gains on terse-answer tasks such as AIME.