Geometric Calibration of Supervised Fine-Tuning

Recent studies investigate the weight geometry through its spectral structure, which characterizes how the weights transform different input directions. Within this view, supervised fine-tuning (SFT) is shown to induce dense updates that perturb the spectral geometry of pre-SFT weights along their principal directions, potentially disrupting the model's prior knowledge. These observations motivate using the geometry of pre-SFT weights as a reference for refining learned SFT updates. We study this perspective as Geometric Calibration and develop SPACE Subspace Projection for Adapted Checkpoint Enhancement), a lightweight post-hoc method that selectively reverts SFT update components within the principal subspace of the pre-SFT weights while preserving those in its orthogonal complement. SPACE is a data-free, training-free method that requires only the pre- and post-SFT checkpoints. We evaluate SPACE on Qwen2.5, Qwen3, Qwen3.5, Llama-3.1, and Olmo-3 models ranging from 2B to 14B, across mathematical, coding, and medical SFT, as well as several SFT variants. Overall, SPACE mitigates out-of-domain (OOD) capability regression while further improving in-domain (ID) performance over the uncalibrated SFT checkpoints. For math SFT, SPACE yields average ID/OOD gains of 2.85/2.26 points on Qwen2.5-7B, and 2.41/1.52 points on Qwen3-14B-Base, respectively. These results highlight how the geometric relationship between SFT updates and pre-SFT weights shapes the adapted model's capabilities and, more broadly, motivate geometry-aware parameter updates for continual model improvement.