# Inductive Feedback for Mixed-Policy Distillation

arXiv: https://arxiv.org/abs/2609.35390 · HTML: https://mlsanity.com/paper/2609.35390/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 31 of its 39 references that are in the map.
- First posted on arXiv 28 Sep 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 31)

- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [ToolAlpaca: Generalized Tool Learning for Language Models with 3000 Simulated Cases](https://mlsanity.com/paper/2306.05301/) (2023)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [TIP: Token Importance in On-Policy Distillation](https://mlsanity.com/paper/2604.14084/) (2026)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [DistiLLM-2: A Contrastive Approach Boosts the Distillation of LLMs](https://mlsanity.com/paper/2503.07067/) (2025)
- [Expanding the Capabilities of Reinforcement Learning via Text Feedback](https://mlsanity.com/paper/2602.02482/) (2026)
- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [On the Position Bias of On-Policy Distillation](https://mlsanity.com/paper/2606.22600/) (2026)
- [On-Policy Distillation with Curriculum Turn-level Guidance for Multi-turn Agents](https://mlsanity.com/paper/2606.15912/) (2026)
- [OGLS-SD: On-Policy Self-Distillation with Outcome-Guided Logit Steering for LLM Reasoning](https://mlsanity.com/paper/2605.12400/) (2026)
- [Formalizing Learning from Language Feedback with Provable Guarantees](https://mlsanity.com/paper/2506.10341/) (2025)
- [From Generic Correlation to Input-Specific Credit in On-Policy Self Distillation](https://mlsanity.com/paper/2605.11613/) (2026)
- [EDGE-OPD: Internalizing Privileged Context with Evidence Guided On-Policy Distillation](https://mlsanity.com/paper/2605.23493/) (2026)
- [Calibrating Teacher--Student Discrepancy for On-Policy Distillation](https://mlsanity.com/paper/2609.21619/) (2026)

## Abstract (arXiv)

Verbal feedback can identify errors and prescribe corrections, providing rich supervision for language-model post-training even when reliable programmatic verifiers are unavailable. Such feedback, often generated by a capable model, can be used to condition the teacher in on-policy distillation, which trains the student to match the teacher's predictions on student-generated rollouts. However, this approach can transfer teacher preferences that the feedback did not motivate, while leaving much of the feedback's guidance unused. We find that both problems come from the standard on-policy distillation objective, specifically the divergence it minimizes and the distribution it uses as its target. Our proposed method addresses both limitations. First, to isolate the information conveyed by the feedback from the teacher's inherent preferences, we treat verbal feedback as evidence for or against the hypothesis that a particular token comes next at a given prefix. We then adopt a probabilistic confirmation framework which uniquely determines an ordering over the vocabulary based on the teacher's predictions before and after it receives feedback. Using a confirmation score consistent with this ordering, we construct a target distribution within a trust region of the student. Second, to learn from guidance that student rollouts can leave unused, we derive a simple shared-rollout estimator of a symmetric divergence between the student and target distributions over rollouts, reusing student and feedback-conditioned teacher rollouts in both directions through importance weighting. Empirical evaluations show that our method outperforms the common on-policy distillation recipe and a recent contrastive variant on knowledge-based and agentic benchmarks.