# Unbiased Top-k Estimation for On-Policy Distillation

arXiv: https://arxiv.org/abs/2609.34447 · HTML: https://mlsanity.com/paper/2609.34447/

## 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 24 of its 30 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, 24 of 24)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (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)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [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)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [Honeybee: Locality-enhanced Projector for Multimodal LLM](https://mlsanity.com/paper/2312.06742/) (2023)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [DistiLLM-2: A Contrastive Approach Boosts the Distillation of LLMs](https://mlsanity.com/paper/2503.07067/) (2025)
- [Not All Disagreement Is Learnable: Token Teachability in On-Policy Distillation](https://mlsanity.com/paper/2605.26844/) (2026)
- [Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe](https://mlsanity.com/paper/2605.03677/) (2026)
- [The Many Faces of On-Policy Distillation: Pitfalls, Mechanisms, and Fixes](https://mlsanity.com/paper/2605.11182/) (2026)
- [SCOPE: Signal-Calibrated On-Policy Distillation Enhancement with Dual-Path Adaptive Weighting](https://mlsanity.com/paper/2604.10688/) (2026)
- [Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation](https://mlsanity.com/paper/2604.13010/) (2026)
- [Bee: A High-Quality Corpus and Full-Stack Suite to Unlock Advanced Fully Open MLLMs](https://mlsanity.com/paper/2510.13795/) (2025)
- [KL for a KL: On-Policy Distillation with Control Variate Baseline](https://mlsanity.com/paper/2605.07865/) (2026)
- [On the Position Bias of On-Policy Distillation](https://mlsanity.com/paper/2606.22600/) (2026)
- [Learning to Focus: Causal Attention Distillation via Gradient-Guided Token Pruning](https://mlsanity.com/paper/2506.07851/) (2025)

## Abstract (arXiv)

On-policy distillation (OPD) is becoming an important component of large language model (LLM) post-training for transferring the reasoning capability of a strong teacher LLM to a weaker student LLM. OPD trains the student by minimizing the reverse KL divergence between the teacher and the student via rollouts generated by the student's policy. However, estimating the gradient of the reverse KL divergence in OPD remains a challenge. Using only the sampled token from the student-generated rollout is computationally cheap but provides limited distributional supervision, which will degrade accuracy. In addition, using the full vocabulary provides complete distributional supervision but is computationally expensive. Therefore, recent works propose Top-k OPD (TK-OPD) that use selected top-k tokens, which provides richer distributional supervision than sampled-token estimation at substantially lower computational cost than full-vocabulary estimation. Unfortunately, using only the selected top-k tokens induces bias, leading to accuracy degradation, as the probability mass outside the selected top-k tokens is discarded. To address the bias of TK-OPD, we propose Tail-Corrected Top-k On-Policy Distillation (TT-OPD). It preserves the advantages of TK-OPD, including rich distributional supervision and low computational cost, while providing an unbiased estimator of the gradient of the reverse KL divergence. The key insight of TT-OPD is to use not only the selected top-k tokens, but also the sampled token from the student-generated rollout, thereby recovering the discarded probability mass in expectation, avoiding the bias. Experimental results demonstrate that TT-OPD significantly outperforms other tested OPD variants.