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SAM-on-the-Curve: Sharpness-Aware Mode Connectivity for Robust Weight-Space Interpolation

arXiv · AI, language, vision and robotics · article · Sep 15, 2026 · UTC

Deep neural networks that are independently trained to similar performance can be connected by low-loss parametric curves in weight space, a phenomenon known as Mode Connectivity (MC). This geometric property underpins practical techniques such as weight averaging, model ensembling, and model merging. We argue that low-loss connectivity is an incomplete geometric criterion: it controls loss only along a one-dimensional trajectory while leaving the surrounding weight-space neighborhood unconstrained, so the optimized curve may traverse sharp ridges that become fragile under distribution shift.

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