Connectedness of loss landscapes via the lens of Morse theory

Danil Akhtiamov, Matt Thomson

Keywords: Mode connectivity, Morse Theory, Loss Landscapes, Saddle Points, Non-Convex Optimization

TL;DR: We explore mode connectivity via the lens of Morse theory

Abstract: Mode connectivity is a recently discovered property of neural networks stating that two weight configurations of small loss can usually be connected by a path of small loss. The mode connectivity property is interesting practically as it has applications to design of optimizers with better generalization properties and various other applied topics as well as theoretically as it suggests that loss landscapes of deep networks have very nice properties even though they are known to be highly non-convex. The goal of this work is to study connectedness of loss landscapes via the lens of Morse theory. A brief introduction to Morse theory is provided.