Distillation as Probability Transport: Routed On-Policy Distillation

Abstract:On-policy distillation (OPD) transfers teacher knowledge on student-generated trajectories, but efficient sampled objectives reduce the teacher distribution to scalar credit on individual tokens. Such credit indicates whether a token should gain or lose probability, yet leaves the corresponding redistribution unspecified. We recast OPD as teacher-guided probability transport and propose RouteOPD (Routed On-Policy Distillation), which decomposes local teacher--student disagreement into student-excess sources and teacher-deficit destinations and couples them into explicit transport pairs. RouteOPD optimizes pairwise log-odds toward jointly realizable targets obtained from a bounded teacher potential, while adapting the transport budget to the concentration of teacher demand. This formulation directs updates toward teacher-preferred destinations and controls their magnitude within a single transport operator. Experiments across four teacher--student settings and four mathematical-reasoning benchmarks demonstrate that RouteOPD consistently outperforms sampled reverse-KL OPD, with improvements accompanied by higher routing fidelity and lower background leakage. These results demonstrate the effectiveness of explicitly modeling probability transport in on-policy distillation.

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2609.08337 [cs.LG]

(or arXiv:2609.08337v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.08337 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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