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

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.