# From Generic Correlation to Input-Specific Credit in On-Policy Self Distillation

arXiv: https://arxiv.org/abs/2605.11613 · HTML: https://mlsanity.com/paper/2605.11613/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 30 of its 34 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- 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, 30 of 30)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [ToolAlpaca: Generalized Tool Learning for Language Models with 3000 Simulated Cases](https://mlsanity.com/paper/2306.05301/) (2023)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Learning by Distilling Context](https://mlsanity.com/paper/2209.15189/) (2022)
- [RL with KL penalties is better viewed as Bayesian inference](https://mlsanity.com/paper/2205.11275/) (2022)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [CRISP: Compressed Reasoning via Iterative Self-Policy Distillation](https://mlsanity.com/paper/2603.05433/) (2026)

## Built on by (most cited first, 9 of 9)

- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [A Formula-Driven Survey and Research Agenda for On-Policy Distillation](https://mlsanity.com/paper/2606.22793/) (2026)
- [CROP: Task Relevance via Counterfactuals for Selective On-Policy Distillation](https://mlsanity.com/paper/2608.13387/) (2026)
- [Trust Is Not Enough: Influence Calibration for On-Policy Self-Distillation in Agentic RL](https://mlsanity.com/paper/2608.14945/) (2026)
- [Learning from Consensus and Disagreement: Unsupervised On-Policy Self-Distillation with Minority-Trajectory Contrast](https://mlsanity.com/paper/2608.08764/) (2026)
- [OptiAgent: End-to-End Optimization Modeling via Multi-Agent Iterative Refinement](https://mlsanity.com/paper/2607.05346/) (2026)
- [SMOPD: Selective Token-Entropy Masking for Dirty-History Multi-Turn On-Policy Self-Distillation](https://mlsanity.com/paper/2608.14647/) (2026)
- [Inductive Feedback for Mixed-Policy Distillation](https://mlsanity.com/paper/2609.35390/) (2026)
- [Composing What Each Teacher Learned: Multi-Teacher On-Policy Distillation through Teacher-Relative Shifts](https://mlsanity.com/paper/2610.10460/) (2026)

## Abstract (arXiv)

On-policy self-distillation has emerged as a promising paradigm for post-training language models, in which the model conditions on environment feedback to serve as its own teacher, providing dense token-level rewards without external teacher models or step-level annotations. Despite its empirical success, what this reward actually measures and what kind of credit it assigns remain unclear. Under a posterior-compatibility interpretation of feedback conditioning, standard in the implicit-reward literature, we show that the self-distillation token reward is a Bayesian filtering increment whose trajectory sum is exactly the pointwise mutual information between the response and the feedback given the input. This pMI can be raised by input-specific reasoning or by input-generic shortcuts, so we further decompose the teacher log-probability along the input axis. Based on this analysis, we propose CREDIT (Contrastive REward from DIsTillation), which isolates the input-specific component with a batch-contrastive baseline. At the sequence level, CREDIT is a teacher-side surrogate for a contrastive pMI objective that also penalizes responses remaining likely under unrelated inputs. Across coding, scientific reasoning, and tool-use benchmarks on two model families, CREDIT delivers the strongest aggregate performance at negligible additional compute.