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).

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