A Unifying Lens on Supervised Fine-Tuning Through Target Distribution Design

Supervised fine-tuning (SFT) is an efficient approach for downstream task adaptation and often serves as the initialization stage for reinforcement learning (RL), but it can show weaker generalization than RL. A key limitation is its off-policy objective: SFT fits fixed demonstrations token by token, including targets poorly aligned with the model's pretrained distribution, which can lead to overfitting. A recent line of work addresses this issue by assigning larger training weights to tokens better aligned with the current model's predictive distribution, with the intuition that fitting these tokens are less distortive to the model's pretrained knowledge and representations. However, computing the token weights from the model that is currently fine-tuned entangles token weights with the optimization trajectory, inducing a self-reinforcing dynamics as the distribution rapidly departs from the pretrained model. To address this, we propose PriFT (Prior-support guided Fine-Tuning), which derives token weights from a frozen pretrained reference to obtain a stable reweighting signal unaffected by fine-tuning. This signal estimates prior support: the extent to which each target token is supported by the pretrained distribution. Across multiple existing token-reweighting rules, replacing the reweighting signal from the online model to pretrained model consistently improves performance. We introduce two instantiations: PriFT-prob uses pretrained token probability, while PriFT-mass selects tokens by cumulative probability mass under the pretrained distribution. Extensive experiments on mathematical reasoning, code generation, and medical question answering show that PriFT achieves state-of-the-art results among SFT baselines and provides a better initialization for subsequent RL training.

Supervised fine-tuning (SFT) is the standard approach for adapting pretrained language models to downstream domains, yet it often improves target-domain behavior at the cost of degrading pre-existing capabilities. Standard cross-entropy fine-tuning promotes only the observed label token and leaves unconstrained how probability mass is redistributed over other plausible alternatives, potentially distorting the rich local preference structure learned during pretraining. We first analyze next-token predictions using Shannon and Renyi entropies, revealing that pretrained models exhibit a regular multimodal entropy structure. These entropy peaks correspond to varying numbers of plausible alternatives, indicating that the base model intrinsically encodes rich distributional knowledge beyond the single supervised token. Motivated by this observation, we propose LP-SFT, a Local-Preserving Supervised Fine-Tuning objective designed to explicitly protect this inherent entropy structure. At each step, LP-SFT constructs an adaptive support of alternative tokens and applies a locally normalized preservation loss to maintain the base model's relative structure among them, while standard cross-entropy independently optimizes the supervised token. Across mixed-domain and single-domain fine-tuning experiments, LP-SFT improves overall performance over vanilla SFT and recent SFT-enhancement baselines, achieving the best balance between pass@1 accuracy and pass@k performance. These results suggest that local preservation helps mitigate capability degradation without collapsing sampling-accessible diversity.

Supervised fine-tuning (SFT) applies a uniform cross-entropy loss to all target tokens, even though different tokens provide unequal learning signals for mathematical reasoning. This uniform treatment can over-sharpen already mastered tokens while amplifying learning pressure on uncertain, low-confidence tokens, leading to suboptimal training dynamics. We propose Trimmed Logit-Gap SFT (TrimSFT), a simple token-level reweighting method that scales the SFT loss according to the logit gap between the gold token and its strongest competitor. TrimSFT trims supervision away from both extremes: tokens already mastered (large logit gap) and tokens weakly supported by the current model (small or negative logit gap), concentrating learning within an intermediate logit-gap region between them. We instantiate this principle with a Gaussian weight centered at margin m with bandwidth τ, requiring no reference model or additional forward pass. We evaluate TrimSFT on six base models from the Llama, Qwen, and DeepMath families across five mathematical reasoning benchmarks. TrimSFT consistently improves over standard SFT, achieving the best average performance on five out of six models, with gains of up to +26.9 points over SFT on MATH500. Further analyses show that the bandwidth τ matters more than the exact margin location, and that half-trim variants that remove supervision pressure from only one side yield inferior trade-offs. A token-level logit-gap distribution analysis suggests that TrimSFT reshapes model confidence in a more balanced way than uniform SFT or monotonic reweighting methods. These results suggest that reasoning SFT can benefit from trimming both extremes rather than treating all tokens uniformly.