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) typically maximizes the likelihood of every token in a demonstrated trajectory. However, an observed token can be non-unique, noisy, or misaligned with the model prior. Strictly fitting toward this one-hot target may be suboptimal, especially when the pretrained model encodes a rich knowledge prior. In this work, we reinterpret SFT as target distribution design: instead of studying only the loss objective, we analyze the token-level target that the loss drives the model to match. We introduce the Q-target framework, which decomposes SFT supervision into two explicit choices: (1) how strongly to rely on the observed token, and (2) how to allocate the remaining probability mass over alternatives. This perspective unifies many existing SFT variants as implicit choices of the target distribution Q. Building on this view, we propose Target-SFT which constructs the training objective directly from the desired target distribution. This method consistently outperforms across the ten reasoning dataset-model settings evaluated, showing the effectiveness of this target-based approach. Overall, our formulation reveals a more fundamental design principle for SFT training and opens a broader search space for SFT objectives.
Supervised fine-tuning (SFT) is the de facto standard for adapting large language models (LLMs) to target domains, but it often degrades the model's general capabilities, a phenomenon known as catastrophic forgetting. Existing approaches typically modify the SFT loss to mitigate forgetting, but they inevitably operate along a domain-generality trade-off. In this work, we step outside this trade-off by decoupling the two capabilities at the model level: we keep the original base model for general capability, and selectively invoke the SFT expert only when domain-specific knowledge is required. Specifically, we propose CPR (Critical-Point Routing), a token-level routing framework between a base model and its expert derivative, based on critical tokens where the base model fails but the expert succeeds. We train a lightweight hierarchical router that estimates the expert-call probability per token, and pair it with a tailored inference procedure that combines momentum smoothing and threshold gating. Across diverse model-domain configurations, CPR achieves state-of-the-art across all settings, surpassing SFT expert by 1.4-5.5% in domain performance while recovering its general-capability drop from 3.4-14.5% to at most 0.5%, with minimal overhead from invoking the expert on only one-third of tokens.
Supervised fine-tuning (SFT) provides the standard approach for teaching LLMs new behaviors from offline expert demonstrations. However, standard SFT uniformly fits all samples -- including those with low likelihood under the base model -- which can disproportionately drive training updates toward overfitting specific samples rather than learning the target behavior. Moreover, adapting to these unlikely samples induces substantial policy shifts that degrade prior capabilities. Existing methods mitigate this by filtering, regenerating, or down-weighting low-likelihood data. In doing so, they often suppress precisely the novel behaviors the base model has yet to learn. We propose InfoSFT, a principled weighting scheme for the SFT objective that concentrates learning signals on maximally informative, medium-confidence tokens -- those neither overly familiar to the base model nor too unlikely to cause instability. Requiring only a one-line modification to the standard token-wise loss, InfoSFT demonstrably improves generalization over vanilla SFT and likelihood-weighted baselines across math, code, and chain-of-thought tasks with diverse model families, while better preserving pre-existing capabilities.