CSD: Common-Support Distillation for Cross-Tokenizer Knowledge Transfer

Cross-tokenizer logits distillation enables knowledge transfer across model families, allowing students to learn from stronger or more specialized teachers. However, differences in vocabulary and segmentation make teacher and student next-token distributions difficult to align. Existing logits-based methods are easy to integrate into standard distillation pipelines, but often rely on restrictive heuristics or tokenizer-pair-specific choices. They may restrict supervision to shared vocabulary subsets, require manually selecting different objectives for different tokenizer pairs, or match only the observed chunk and its complement rather than individual alternative continuations. We introduce Common-Support Distillation (CSD), a unified logits-based framework that constructs a shared support between the teacher and student at each aligned input chunk and matches the induced distributions with a single objective. For one-to-one alignments, CSD uses explicit common-token pairs as the shared support. For other alignments, it constructs a virtual support whose probabilities are computed using the autoregressive chain rule. A residual event captures probability mass outside the explicit support, ensuring that both induced distributions remain normalized. Across four teacher–student settings comprising Llama-3.2-1B and Gemma3-1B-PT students with Qwen and Phi teachers, CSD consistently achieves the highest average performance among the evaluated cross-tokenizer methods, outperforming the strongest alternative by up to $1.8$ points and surpassing both continued pretraining and same-tokenizer distillation. For Llama-3.1-8B, CSD improves average accuracy over the strongest evaluated baseline by up to $4.2$ points for the base student and $1.6$ points for the instruction-tuned student.