# Cross-Tokenizer On-Policy Distillation via Byte-Prefix Marginalization

arXiv: https://arxiv.org/abs/2607.22334 · HTML: https://mlsanity.com/paper/2607.22334/

## Key facts

- Cited by 8 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 54 of its 60 references that are in the map.
- First posted on arXiv 24 Jul 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 54)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [ByT5: Towards a token-free future with pre-trained byte-to-byte models](https://mlsanity.com/paper/2105.13626/) (2021)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [How Good is Your Tokenizer? On the Monolingual Performance of Multilingual Language Models](https://mlsanity.com/paper/2012.15613/) (2020)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Teaching Small Language Models to Reason](https://mlsanity.com/paper/2212.08410/) (2022)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [CANINE: Pre-training an Efficient Tokenization-Free Encoder for Language Representation](https://mlsanity.com/paper/2103.06874/) (2021)
- [MEGABYTE: Predicting Million-byte Sequences with Multiscale Transformers](https://mlsanity.com/paper/2305.07185/) (2023)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [Byte Latent Transformer: Patches Scale Better Than Tokens](https://mlsanity.com/paper/2412.09871/) (2024)

## Built on by (most cited first, 8 of 8)

- [CompassOPD: Cross-Family On-Policy Distillation via Within-Family Likelihood Shifts](https://mlsanity.com/paper/2609.10154/) (2026)
- [Lightning Weave: Improving the Accuracy-Efficiency Frontier of Reasoning Models through Capability Composition](https://mlsanity.com/paper/2609.14708/) (2026)
- [CT-OPD: Counterfactual Trace On-Policy Distillation for Diffusion Vision-Language Models](https://mlsanity.com/paper/2609.32781/) (2026)
- [Dual-Vocabulary Language Model for Cross-Tokenizer Distillation](https://mlsanity.com/paper/2609.33816/) (2026)
- [Beyond Token Alignment: Event Completion for Cross-Tokenizer On-Policy Distillation](https://mlsanity.com/paper/2609.34738/) (2026)
- [Gains and Collapse in On-Policy Distillation:A Reinforcement Learning Perspective](https://mlsanity.com/paper/2610.03185/) (2026)
- [Rethinking Cross-Tokenizer On-Policy Distillation: From Alignment Coverage to Supervision Reliability](https://mlsanity.com/paper/2610.08448/) (2026)
- [ActionOPD: Distilling Decisions, Not Tokens](https://mlsanity.com/paper/2610.19820/) (2026)

## Abstract (arXiv)

Open-weight language models from different families exhibit complementary capabilities, motivating their consolidation into a compact student through on-policy distillation (OPD). However, full-vocabulary OPD typically assumes a shared tokenizer, while existing cross-tokenizer methods may discard teacher probability mass or assign it to student tokens with unrelated content. We introduce Byte-Prefix Marginalization (BPM), which re-expresses the teacher's next-token distribution over the student vocabulary in a shared byte space. Specifically, BPM assigns each teacher token's probability to the longest student token whose byte representation is a prefix of the teacher token's bytes, aggregates mass mapped to the same student token, and places otherwise unmatched mass in an explicit residual category. This produces a vocabulary-complete, byte-aligned, and mass-preserving target for dense OPD. The target exactly recovers the teacher-induced byte-prefix marginal when the relevant prefix does not span multiple teacher tokens (a condition satisfied at more than 99% of training positions) and uses a mass-preserving, chain-factorized lower bound otherwise. Across Qwen3-32B, GLM-Z1-9B-0414, and MiniMax-M2.7 as teachers, BPM consistently outperforms current cross-tokenizer methods on six mathematics and programming benchmarks, improving six-benchmark avg@8 by 3.7-6.6 points over the strongest baselines.