# VISTA: Verifier-Informed Student-to-Teacher Adaptation for On-Policy Self-Distillation

arXiv: https://arxiv.org/abs/2608.28306 · HTML: https://mlsanity.com/paper/2608.28306/

## 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 21 of its 33 references that are in the map.
- First posted on arXiv 28 Aug 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, 21 of 21)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [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)
- [Deep Mutual Learning](https://mlsanity.com/paper/1706.00384/) (2017)
- [Be Your Own Teacher: Improve the Performance of Convolutional Neural Networks via Self Distillation](https://mlsanity.com/paper/1905.08094/) (2019)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Unifying distillation and privileged information](https://mlsanity.com/paper/1511.03643/) (2015)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [Large scale distributed neural network training through online distillation](https://mlsanity.com/paper/1804.03235/) (2018)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [Speculative Knowledge Distillation: Bridging the Teacher-Student Gap Through Interleaved Sampling](https://mlsanity.com/paper/2410.11325/) (2024)
- [Purified OPSD: On-Policy Self-Distillation Without Losing How to Think](https://mlsanity.com/paper/2607.02234/) (2026)
- [STEPS: Selective On-Policy Self-Distillation for Reasoning](https://mlsanity.com/paper/2605.10194/) (2026)
- [Anti-Self-Distillation for Reasoning RL via Pointwise Mutual Information](https://mlsanity.com/paper/2605.11609/) (2026)
- [DemoPSD: Disagreement-Modulated Policy Self-Distillation](https://mlsanity.com/paper/2607.02502/) (2026)
- [Diagnosing and Mitigating Thinking Collapse in On-Policy Self-Distillation](https://mlsanity.com/paper/2607.10805/) (2026)

## Abstract (arXiv)

On-policy self-distillation (OPSD) improves reasoning by training a problem-only student on its own rollouts using dense token-level supervision from a privileged teacher that also sees a reference solution. However, standard OPSD treats the teacher distribution as a fixed target along the student's rollout and updates only the student %, although -- even though privileged conditioning does not guarantee that the teacher always provides the most appropriate target for problem-only reasoning. This one-way supervision can therefore misdirect the student when the teacher distribution is misaligned with valid student reasoning. We therefore introduce Verifier-Informed Student-to-Teacher Adaptation (VISTA), which preserves the standard OPSD student update while using outcome-verified rollouts to adapt the teacher toward the student distribution. Within each verified rollout, VISTA further restricts this adaptation to the top-k positions with the largest teacher--student KL divergence. Notably, VISTA reuses the rollout and loss function from standard OPSD, introducing no additional sampling or separate reward objective. Across AIME24, AIME25, and HMMT25 with Qwen3 models at 1.7B, 4B, and 8B, VISTA achieves the highest Avg@12 at every scale, improving over OPSD by 0.6, 0.7, and 2.1 points, respectively. These results demonstrate the value of student supervision from outcome-verified rollouts and highlight student-to-teacher adaptation as a promising direction for OPSD.