Title: Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum
Primary area: foundation or frontier models, including LLMs
Keywords: Post-Training, SFT, training objectives

Abstract: Supervised fine-tuning (SFT) is the standard approach for post-training large language models (LLMs), yet it often shows limited generalization. We trace this limitation to its default training objective: negative log likelihood (NLL).  While NLL is classically optimal when training from scratch, post-training operates in a different paradigm and could violate its optimality assumptions, where models already encode task-relevant priors and supervision can be long and noisy. To this end, we study a general family of probability-based objectives and characterize their effectiveness under different conditions. Through comprehensive experiments and extensive ablation studies across 7 model backbones, 14 benchmarks, and 3 domains, we uncover a critical dimension that governs objective behavior: the *model-capability continuum*. Near the *model-strong* end, prior-leaning objectives that downweight low-probability tokens (*e.g.,* $-p$, $-p^{10}$, thresholded variants) consistently outperform NLL; toward the *model-weak* end, NLL dominates; in between, no single objective prevails. Our theoretical analysis further elucidates how objectives trade places across the continuum, providing a principled foundation for adapting objectives to model capability.

TL;DR: We revisit supervised fine-tuning (SFT) for large language models, introducing a model-capability continuum that shows negative log-likelihood is not universally optimal and characterizes when alternative objectives succeed or fail.