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

• URL: http://arxiv.org/abs/2607.22334v1
• Date: Fri, 24 Jul 2026 14:12:54 GMT
• Title: Cross-Tokenizer On-Policy Distillation via Byte-Prefix Marginalization
• Abstract summary: Byte-Prefix Marginalization re-expresses the teacher's next-token distribution over the student vocabulary in a shared byte space.<n>BPM consistently outperforms current cross-tokenizer methods on six mathematics and programming benchmarks.
• Score: 15.613307729537096
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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