# CAST: Credit Alignment for Cross-Tokenizer On-Policy Distillation

arXiv: https://arxiv.org/abs/2610.13257 · HTML: https://mlsanity.com/paper/2610.13257/

## 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 23 references that are in the map.
- First posted on arXiv 9 Oct 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)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [Knowledge Fusion of Large Language Models](https://mlsanity.com/paper/2401.10491/) (2024)
- [DistiLLM-2: A Contrastive Approach Boosts the Distillation of LLMs](https://mlsanity.com/paper/2503.07067/) (2025)
- [Towards Cross-Tokenizer Distillation: the Universal Logit Distillation Loss for LLMs](https://mlsanity.com/paper/2402.12030/) (2024)
- [Stable On-Policy Distillation through Adaptive Target Reformulation](https://mlsanity.com/paper/2601.07155/) (2026)
- [Universal Cross-Tokenizer Distillation via Approximate Likelihood Matching](https://mlsanity.com/paper/2503.20083/) (2025)
- [KDRL: Post-Training Reasoning LLMs via Unified Knowledge Distillation and Reinforcement Learning](https://mlsanity.com/paper/2506.02208/) (2025)
- [Multi-Level Optimal Transport for Universal Cross-Tokenizer Knowledge Distillation on Language Models](https://mlsanity.com/paper/2412.14528/) (2024)
- [VOLD: Reasoning Transfer from LLMs to Vision-Language Models via On-Policy Distillation](https://mlsanity.com/paper/2510.23497/) (2025)
- [ToDi: Token-wise Distillation via Fine-Grained Divergence Control](https://mlsanity.com/paper/2505.16297/) (2025)
- [AlignDistil: Token-Level Language Model Alignment as Adaptive Policy Distillation](https://mlsanity.com/paper/2503.02832/) (2025)
- [Breaking the Tokenizer Barrier: On-Policy Distillation across Model Families](https://mlsanity.com/paper/2606.09456/) (2026)
- [Cross-Tokenizer LLM Distillation through a Byte-Level Interface](https://mlsanity.com/paper/2604.07466/) (2026)

## Abstract (arXiv)

Cross-tokenizer on-policy distillation (OPD) requires aligning teacher and student sequences before their scores can be compared. Decoded-text alignment provides such correspondence at the chunk level, but leaves a distinct problem unresolved: credit alignment. A chunk-level signal specifies how much a span should change, but not how that signal should be distributed across student tokens, while tokens without teacher correspondence remain unconstrained. We propose CAST (Chunk-aware credit Assignment with Selective Token Anchoring), a shift-or-stay framework that addresses both issues. For aligned chunks, CAST redistributes each chunk's advantage across student tokens using predictive uncertainty and local teacher-signal smoothness, emphasizing learning opportunities supported by locally consistent teacher feedback while preserving the chunk's total advantage. The resulting weights exactly solve a KL-regularized credit-allocation problem. For unaligned positions, CAST selectively anchors the student to its initial policy through a KL penalty, limiting drift where teacher supervision is unavailable. Because credit assignment is separated from chunk construction, CAST also applies to punctuation-defined or fixed-length chunks under shared tokenization. Across six mathematics, science, and code benchmarks, CAST improves the average over the strongest evaluated baseline by 2.45 and 1.32 points for cross-tokenizer transfer from Qwen3-8B to Mistral-7B and Llama-3.1-8B, respectively, and by 2.10 points for shared-tokenizer transfer to Qwen3-1.7B.