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arXiv · 2101.08576

A Note on Connectivity of Sublevel Sets in Deep Learning

Quynh Nguyen
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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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Quynh Nguyen. 2021-01-21. A Note on Connectivity of Sublevel Sets in Deep Learning. https://arxiv.org/abs/2101.08576

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