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This research introduces Flux-OPD, a novel on-policy distillation framework that addresses the challenge of supervising large language models in open-ended domains where explicit rewards are unavailable. By decomposing the reverse KL objective to manage conflicts between evolving context-conditioned teachers and a static anchor, the method effectively captures nuanced task preferences through dynamic supervision signals. The approach demonstrates improved performance over existing paradigms by stabilizing distillation targets without relying on verifiable reward functions.
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Flux-OPD: On-Policy Distillation with Evolving Contexts

arXiv2 min read

arXiv:2607.28022v1 Announce Type: new Abstract: Large language model training in open-ended domains lacks verifiable rewards, making task preferences difficult to formalize as effective supervision. Contexts can convey such preferences, yet provide little additional supervision once distilled into the student, motivating contexts that evolve with student performance. However, directly using evolving contexts as in-training supervision results in an unstable distillation target and conflicting distributions, requiring mechanisms to stabilize target and downweight conflicts. In this paper, we analyze the effect of contexts through a decomposition of the reverse KL objective, revealing two findings: the student is distilled toward the geometric mean of context-conditioned teachers, and the objective contains a conflict term that measures conflicts among these teachers. Based on this decomposition, we propose Flux-OPD, an OPD paradigm that uses evolving contexts as in-training supervision to capture task preferences in open-ended domains. Flux-OPD treats the differences between context-conditioned and context-free teachers as contextual difference signals, injects them as contextual corrections into the context-free teacher anchor, and weights their correction strength using the conflict term as an indicator. Experiments on open-ended tasks show that Flux-OPD outperforms existing OPD paradigms, highlighting the potential to combine teacher supervision with evolving contexts.

Abstract:Large language model training in open-ended domains lacks verifiable rewards, making task preferences difficult to formalize as effective supervision. Contexts can convey such preferences, yet provide little additional supervision once distilled into the student, motivating contexts that evolve with student performance. However, directly using evolving contexts as in-training supervision results in an unstable distillation target and conflicting distributions, requiring mechanisms to stabilize target and downweight conflicts. In this paper, we analyze the effect of contexts through a decomposition of the reverse KL objective, revealing two findings: the student is distilled toward the geometric mean of context-conditioned teachers, and the objective contains a conflict term that measures conflicts among these teachers. Based on this decomposition, we propose Flux-OPD, an OPD paradigm that uses evolving contexts as in-training supervision to capture task preferences in open-ended domains. Flux-OPD treats the differences between context-conditioned and context-free teachers as contextual difference signals, injects them as contextual corrections into the context-free teacher anchor, and weights their correction strength using the conflict term as an indicator. Experiments on open-ended tasks show that Flux-OPD outperforms existing OPD paradigms, highlighting the potential to combine teacher supervision with evolving contexts.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2607.28022 [cs.LG]

(or arXiv:2607.28022v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.28022 arXiv-issued DOI via DataCite (pending registration)

Full text under the publisher's open licence · 211 words

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