arXiv:2610.08061v1 Announce Type: new Abstract: Supervised fine-tuning can substantially improve the downstream utility of large language models (LLMs) but may compromise their safety. Existing safety-preserving methods constrain downstream updates using safety-related parameters or subspaces, but mainly focus on safety preservation rather than joint safety and utility enhancement, lack a theoretical characterization of the optimal safety-related subspace and safety-preserving task update, and typically rely on a static safety subspace that may become outdated during fine-tuning. To address these limitations, we propose ASCENT, a downstream fine-tuning framework for safety--utility co-enhancement through first-order optimal safety-aware periodic calibration and task optimization. We model safety as a function of LLM parameters $S(\theta)$ and use its first-order approximation to characterize safety changes under parameter updates. Under a fixed rank and Frobenius-norm budget, we prove that the update constructed from the top-$r$ singular components of the safety-function gradient maximizes the estimated safety change, and use it for periodic calibration to preserve and improve safety. We further derive a unique safety-preserving task update that stays close to the original task update while penalizing negative effects on the estimated safety change. ASCENT alternates these optimal task and calibration updates to jointly enhance safety and utility. Experiments across multiple LLM families and downstream tasks show that ASCENT improves downstream utility by up to 20.3\% and reduces attack success rate by up to 35.5\%, achieving state-of-the-art safety and utility across all evaluated settings. Our code is available at https://github.com/ZJU-LLM-Safety/ASCENT.