# The Extrapolation Cliff in On-Policy Distillation of Near-Deterministic Structured Outputs

arXiv: https://arxiv.org/abs/2605.08737 · HTML: https://mlsanity.com/paper/2605.08737/

## Key facts

- Cited by 2 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 36 of its 41 references that are in the map.
- First posted on arXiv 9 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 36)

- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Document Ranking with a Pretrained Sequence-to-Sequence Model](https://mlsanity.com/paper/2003.06713/) (2020)
- [Is ChatGPT Good at Search? Investigating Large Language Models as Re-Ranking Agents](https://mlsanity.com/paper/2304.09542/) (2023)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [Overview of the TREC 2020 deep learning track](https://mlsanity.com/paper/2102.07662/) (2021)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [RankZephyr: Effective and Robust Zero-Shot Listwise Reranking is a Breeze!](https://mlsanity.com/paper/2312.02724/) (2023)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [RankT5: Fine-Tuning T5 for Text Ranking with Ranking Losses](https://mlsanity.com/paper/2210.10634/) (2022)
- [TIP: Token Importance in On-Policy Distillation](https://mlsanity.com/paper/2604.14084/) (2026)
- [Guiding LLMs The Right Way: Fast, Non-Invasive Constrained Generation](https://mlsanity.com/paper/2403.06988/) (2024)
- [DistiLLM-2: A Contrastive Approach Boosts the Distillation of LLMs](https://mlsanity.com/paper/2503.07067/) (2025)
- [Zero-Shot Listwise Document Reranking with a Large Language Model](https://mlsanity.com/paper/2305.02156/) (2023)
- [XGrammar: Flexible and Efficient Structured Generation Engine for Large Language Models](https://mlsanity.com/paper/2411.15100/) (2024)
- [JSONSchemaBench: A Rigorous Benchmark of Structured Outputs for Language Models](https://mlsanity.com/paper/2501.10868/) (2025)
- [FIRST: Faster Improved Listwise Reranking with Single Token Decoding](https://mlsanity.com/paper/2406.15657/) (2024)
- [Stable On-Policy Distillation through Adaptive Target Reformulation](https://mlsanity.com/paper/2601.07155/) (2026)
- [The Price of Format: Diversity Collapse in LLMs](https://mlsanity.com/paper/2505.18949/) (2025)
- [Learning to Generate Structured Output with Schema Reinforcement Learning](https://mlsanity.com/paper/2502.18878/) (2025)
- [When Importance Sampling Misallocates Credit: Asymmetric Ratios for Outcome-Supervised RL](https://mlsanity.com/paper/2510.06062/) (2025)
- [Think Inside the JSON: Reinforcement Strategy for Strict LLM Schema Adherence](https://mlsanity.com/paper/2502.14905/) (2025)

## Built on by (most cited first, 2 of 2)

- [The Teacher Is a Direction, Not a Destination: Extrapolating RL-Induced Representation Residuals in On-Policy Distillation](https://mlsanity.com/paper/2609.36484/) (2026)
- [Look Before You Select: Rethinking Vocabulary Sparsification in On-Policy Distillation](https://mlsanity.com/paper/2609.34386/) (2026)

## Abstract (arXiv)

A distilled student can copy its teacher's mistakes along with its skills. On-policy distillation (OPD), used in recent post-training recipes, has the teacher grade every token of the student's own outputs. Which teacher errors does it pass on? We build ErrOPD, a testbed whose teachers are fine-tuned to close a JSON list one item early, an error their students almost never make. The answer depends on the KL direction: across four model families, forward-KL OPD transmits the error within the training budget (+13-23 points), while reverse-KL OPD at our reference learning rate adds under 0.05 points. A duplicated ID and, where the decision arises, two SQL errors show the same split. The reverse-KL update scales with the student's own probability of a token, and an intervention tests this: giving reverse KL forward KL's gradient magnitude at the error decision alone makes it transmit on two model pairs. Reverse-KL OPD can delay such errors rather than block them: some runs adopt the error with longer training, and Qwen3 students that already make it, even rarely, adopt it within the budget. Because greedy evaluation on Qwen3 misses the inherited error, distilled students should also be audited on sampled outputs.