InfoSFT: Learn More and Forget Less with Information-Aware Token Weighting

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) 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.

Supervised fine-tuning (SFT) is a standard approach for adapting LLMs to a target distribution, but in settings such as personalization, where each author requires separate weight access, optimization, storage, and retraining, its costs become prohibitive. We propose Weightless Fine-Tuning (WFT), a training-free decoding-time method that approximates the distributional effect of SFT without weight updates. WFT computes supervised residuals on an author's training sequence and transports them to the current prompt through a cross-prefix transport operator estimated from dropout-induced cross-covariance. The operator captures how a perturbation at one context propagates to predictions at another, replacing gradient-based parameter updates with logit-space corrections. On three LaMP personalization benchmarks, WFT achieves the best average performance across datasets, matches or exceeds SFT on individual tasks, and outperforms other lightweight baselines on average. In a budget-controlled comparison, WFT approaches SFT performance using less than 7% of the effective computation. Logit-level analysis shows a cosine similarity of 0.875 between the logit shifts induced by WFT and SFT over 95% of the next-token probability mass, suggesting that WFT captures the distributional effect of supervised adaptation without modifying model weights.