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We studies top-$k$-truncated, temperature-scaled off-policy distillation by decomposing this problem into two questions: an \\emph{objective-to-capability} analysis of how the training objective shapes token-level supervision and downstream performance, and a \\emph{data-to-objective} analysis of how data heterogeneity should inform objective routing. We first show that the language-modeling objective ($L_{\\mathrm{LM}}$) and the knowledge-distillation objective ($L_{\\mathrm{KD}}$) induce systematically different capability profiles, and trace this divergence to a gradient-level tension between \\emph{direct observed-token reinforcement} and \\emph{teacher-supported alternative supervision}. To quantify this tension, we introduce diagnostic metrics -- su","title":"Let the Data Decide: Supervision Analysis, Capability Trade-offs, and Adaptive Objective Routing in Continued Pre-Training via Off-Policy Distillation","url":"https://arxiv.org/abs/2607.16246","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.16246v1 Announce Type: cross \nAbstract: Off-policy distillation is now central to large language model pre-training, yet how training data, objective parameterization, and model capabilities interact remains poorly characterized. We studies top-$k$-truncated, temperature-scaled off-policy distillation by decomposing this problem into two questions: an \\emph{objective-to-capability} analysis of how the training objective shapes token-level supervision and downstream performance, and a \\emph{data-to-objective} analysis of how data heterogeneity should inform objective routing. 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