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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 connectivityof sublevel sets of the training loss function. In the two-layer setting, thesame property may not hold even if one has just one neuron less (i.e. width $N$can lead to disconnected sublevel sets).

A Note on Connectivity of Sublevel Sets in Deep Learning