Cross-tokenizer knowledge distillation allows a student model to learn from teachers with incompatible vocabularies. Prior work operates on hidden states or logits; the latter is preferred as a drop-in replacement requiring no auxiliary components. Logit-based methods either use only the correct-token probability, missing the full 'dark knowledge' in the teacher's distribution, or operate on the full output distribution, relying on strict token partitioning and/or unprincipled heuristic ranking. We identify two key shortcomings of full-distribution, logit-based methods: (i) an uncommon-token failure, where critical tokens fall into the unmatched subset (e.g., Llama's 1100 multi-digit numerals under digit-splitting Qwen supervision) and are suppressed during training, reducing GSM8k from 12.89 to 2.56 compared to same-tokenizer KD from a weaker teacher; and (ii) over-conservative matching, where strict 1-to-1 matching excludes near-equivalent tokens across surface forms. These failures require distinct remedies: eliminating the partition when critical tokens are misaligned, and refining it when alignment is reliable. We propose X-Token, an approach with two complementary loss formulations targeting these issues. P-KL removes partitioning and aligns the student's distribution with the teacher's via a sparse projection matrix W (initialized from tokenizer-level string rules) to address the uncommon-token failure. H-KL retains the hybrid form while relaxing matching to align each student token with its top-ranked teacher mapping under W. Both objectives share W and extend naturally to multiple teachers. Empirically, on Llama-3.2-1B, X-Token outperforms the current state of the art GOLD by +3.82 average points with a Qwen3-4B teacher and by +0.5 with a Phi-4-Mini teacher. Further, a two-teacher setup (Phi-4-mini + Llama-3B) improves over single-teacher distillation by +1.3 points.
Knowledge distillation effectively transfers reasoning capabilities from large language models to lightweight student models. To enable knowledge transfer across disparate model families, researchers increasingly explore cross-tokenizer distillation. However, cross-tokenizer distillation remains challenging due to vocabulary and sequence misalignment, while approximate vocabulary alignment can introduce additional noise into distillation. To address these challenges, we propose Anchor-Based Cross-Tokenizer Distillation with Residual Regularization (ACTD). ACTD bridges structural heterogeneity through vocabulary and sequence alignment, while mitigating alignment noise via a novel anchor loss with residual regularization. We further extend this framework to a multi-teacher setting. Evaluated across five reasoning benchmarks with three distinct teacher models, ACTD achieves state-of-the-art performance. Moreover, its multi-teacher extension outperforms the strongest single-teacher and multi-teacher baselines, further demonstrating the robustness of our method.
On-Policy Distillation (OPD) has become a core technique in the post-training of Large Language Models (LLMs) for transferring knowledge from domain experts to student models. However, existing OPD distillation methods require teacher and student models to share the same tokenizer, restricting the applicability of OPD within the model series. Current mainstream practice typically employs Supervised Fine-Tuning (SFT) on teacher-generated responses for cross-tokenizer distillation, which fails to capture the rich knowledge embedded in the teacher's probability distribution. In this work, we enable the standard on-policy distillation method to operate across model families, ensuring that high-fidelity token-level signals can propagate across different tokenizers with a precise token-mapping algorithm. Extensive experiments show that cross-tokenizer OPD is significantly more compute-efficient than baselines on various benchmarks. Our results unlock a broader range of teacher-student pairs for OPD, opening up new avenues for adapting and enhancing interactions between LLMs.
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.