Supervised fine-tuning (SFT) is a key component of language model post-training, enabling effective task adaptation and serving as an important foundation for subsequent reinforcement learning. Recent methods seek to improve SFT by introducing token-level weights into the training objective, where these weights are typically derived from a model's output distribution at each token position. To better understand how such weighting schemes affect SFT, we analyze their optimization objectives and theoretically characterize the target distributions they induce. Our analysis shows that dynamic weighting methods, such as Dynamic Fine-Tuning (DFT), induce a heavily sharpened distribution, whereas static weighting methods fit a target distribution proportional to the product of the data distribution and a frozen prior. These findings suggest that static weighting provides a more stable training target, while its effectiveness critically depends on the quality of the prior distribution. Building on this observation, we propose Self-Privileged Fine-Tuning (SPFT), which uses a frozen copy of the initial model conditioned on privileged information (such as ground truth for mathematical questions) as a prior to provide guidance for token-level weighting during fine-tuning. Through a Bayesian decomposition, we further show that SPFT reweights the standard static prior according to how informative each target token is for predicting the ground-truth outcome, thereby assigning larger weights to more predictive tokens. Experiments on mathematical reasoning and code generation show that SPFT improves over standard SFT and other baselines across the main settings.

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