A Note on Connectivity of Sublevel Sets in Deep Learning

Abstract

It is shown that for deep neural networks, a single wide layer of width $N+1$ ($N$ being the number of training samples) suffices to prove the connectivity of sublevel sets of the training loss function. In the two-layer setting, the same property may not hold even if one has just one neuron less (i.e. width $N$ can lead to disconnected sublevel sets).

References in corpus (1)

• The Loss Surfaces of Multilayer Networks

Cited by in corpus (1)

• On the Theory of Implicit Deep Learning: Global Convergence with Implicit Layers