Title: Harnessing Optimization Dynamics for Curvature-Informed Model Merging
Primary area: transfer learning, meta learning, and lifelong learning
Keywords: Large Language Models (LLMs), Model Merging, Pruning, Post-training

Abstract: Model merging is an effective strategy for composing capabilities in large language models without the need for costly joint retraining. We study this process in the supervised fine-tuning (SFT) stage, consolidating multiple checkpoints specialized for distinct capabilities (e.g., math, coding, and precise instruction following) into a single model. First, we introduce Optimization Trajectory Aware (OTA) Merging, a curvature-aware method for mitigating task interference that uses optimizer second-moment statistics as a diagonal curvature proxy to first prune the task vector with our Fast Fisher Grafting (FFG) technique and then reweight the pruned vector. When merging diverse, capability-based checkpoints, OTA improves the merged model's performance over strong baseline methods, as evaluated on unseen capability-based benchmarks. Second, we conduct a comprehensive, theoretically-inspired empirical analysis to explain the effectiveness of OTA. Our analysis surprisingly reveals that FFG implicitly induces a layer- and role-wise aware pruning mechanism that is capable of maintaining fine-tuning performance at much more aggressive pruning ratios compared to magnitude pruning and that exhibits interpretable task localization properties. Third, an extensive comparison of our curvature proxy across capability checkpoints shows that experts converge to a basin with substantial curvature similarity, offering a novel lens on why simple linear merging can be effective in practice. This result further strengthens our ablation study, showing that FFG is critical for merging performance. Finally, we develop a memory-light variant of OTA that efficiently compresses the second moments, mitigating the additional storage requirements of our method and improving scalability. We make all code, training and evaluation scripts, visualization artifacts, and capability-specific SFT checkpoints accessible through an anonymized repository at \url{https://github.com/anon123ota-dotcom/ota-ffg}.