Bridging Training and Merging Through Momentum-Aware Optimization

• URL: http://arxiv.org/abs/2512.17109v1
• Date: Thu, 18 Dec 2025 22:37:33 GMT
• Title: Bridging Training and Merging Through Momentum-Aware Optimization
• Authors: Alireza Moayedikia, Alicia Troncoso,
• Abstract summary: Training large neural networks and task-specific computation models require parameter importance estimation.<n>Current compute curvature information during training, discard it, then recompute similar information for merging.<n>We introduce a unified framework that factorized momentum and curvature statistics during training, then recompute similar information for merging.
• Score: 8.035521056416242
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Training large neural networks and merging task-specific models both exploit low-rank structure and require parameter importance estimation, yet these challenges have been pursued in isolation. Current workflows compute curvature information during training, discard it, then recompute similar information for merging -- wasting computation and discarding valuable trajectory data. We introduce a unified framework that maintains factorized momentum and curvature statistics during training, then reuses this information for geometry-aware model composition. The proposed method achieves memory efficiency comparable to state-of-the-art approaches while accumulating task saliency scores that enable curvature-aware merging without post-hoc Fisher computation. We establish convergence guarantees for non-convex objectives with approximation error bounded by gradient singular value decay. On natural language understanding benchmarks, curvature-aware parameter selection outperforms magnitude-only baselines across all sparsity levels, with multi-task merging improving over strong baselines. The proposed framework exhibits rank-invariant convergence and superior hyperparameter robustness compared to existing low-rank optimizers. By treating the optimization trajectory as a reusable asset rather than discarding it, our approach eliminates redundant computation while enabling more principled model composition.

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