Geodesic Mode Connectivity

Charlie Tan, Theodore Long, Sarah Zhao, Rudolf Laine

Keywords: geometry, information geometry, mode connectivity, geodesic, generalization

TL;DR: We explore mode connectivity, the phenomenon of trained models being connected by a path of low loss, in the context of geodesics in distribution space.

Abstract: Mode connectivity is a phenomenon where trained models are connected by a path of low loss. We reframe this in the context of Information Geometry, where neural networks are studied as spaces of parameterized distributions with curved geometry. We hypothesize that shortest paths in these spaces, known as geodesics, correspond to mode-connecting paths in the loss landscape. We propose an algorithm to approximate geodesics and demonstrate that they achieve mode connectivity.