Beyond Token Alignment: Event Completion for Cross-Tokenizer On-Policy Distillation

On-policy distillation (OPD) transfers knowledge between language models through teacher supervision on student-generated trajectories. With different tokenizers, a single teacher token may require multiple student tokens to generate, creating intermediate states where the event is entered but not yet completed. Existing cross-tokenizer methods align tokens or text spans to construct comparable prediction targets. We study a complementary problem after partial generation: once the student produces a prefix of a teacher token, multiple next tokens may complete the same remaining bytes, but the teacher only specifies the required completion rather than how probability should be divided amon...

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