Connectedness of loss landscapes via the lens of Morse theory
Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations, PMLR 197:171-181, 2023.
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.