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This paper is a machine learning method for training smaller language models from larger teacher models during on-policy distillation. It combines reverse and forward KL divergence signals through a shared descent direction and reports gains on math reasoning, with transfer to scientific QA and code. Readers should treat the results as benchmark-specific until independent replications appear, but the framing of KL objectives as complementary signals is a useful lens for distillation work.
OC-OPD: Observation-coordinated Supervision for On-Policy Distillation
arXiv:2611.01965v1 Announce Type: new Abstract: Reverse and forward Kullback--Leibler (KL) divergences provide complementary supervision in on-policy distillation: reverse KL refines the student's active token rankings, and forward KL allocates mass to teacher-supported candidates. At student-generated prefixes, we form a four-observation matrix by treating the student and teacher as both candidate sources and evaluators. The diagonal self-observations measure uncertainty, while source-centered cross-observations recover the two KL objectives. We establish an exact identity equating the Fisher inverse-metric coupling of their logit gradients with the sum of these contrasts, yielding a common local descent direction for distinct positive distributions. Observation-coordinated on-policy distillation (OC-OPD) uses observations to set preferences, closed-form bargaining to coordinate gradients, and distributional discrepancy to scale the update. Across three heterogeneous student settings (non-thinking generation, thinking generation, and base-model initialization), OC-OPD achieves strong gains in mathematical reasoning and transfers effectively to out-of-distribution scientific question answering and code generation. Our code is publicly available at: https://github.com/RuoranXu/OC-OPD.
Abstract:Reverse and forward Kullback--Leibler (KL) divergences provide complementary supervision in on-policy distillation: reverse KL refines the student's active token rankings, and forward KL allocates mass to teacher-supported candidates. At student-generated prefixes, we form a four-observation matrix by treating the student and teacher as both candidate sources and evaluators. The diagonal self-observations measure uncertainty, while source-centered cross-observations recover the two KL objectives. We establish an exact identity equating the Fisher inverse-metric coupling of their logit gradients with the sum of these contrasts, yielding a common local descent direction for distinct positive distributions. Observation-coordinated on-policy distillation (OC-OPD) uses observations to set preferences, closed-form bargaining to coordinate gradients, and distributional discrepancy to scale the update. Across three heterogeneous student settings (non-thinking generation, thinking generation, and base-model initialization), OC-OPD achieves strong gains in mathematical reasoning and transfers effectively to out-of-distribution scientific question answering and code generation. Our code is publicly available at: this https URL.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Optimization and Control (math.OC)
arXiv:2611.01965 [cs.LG]
(or arXiv:2611.01965v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2611.01965 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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