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For one-hidden-layer ReLU networks, we prove that all differentiable localminima are global inside differentiable regions. We give the locations andlosses of differentiable local minima, and show that these local minima can beisolated points or continuous hyperplanes, depending on an interplay betweendata, activation pattern of hidden neurons and network size. Furthermore, wegive necessary and sufficient conditions for the existence of saddle points aswell as non-differentiable local minima, and their locations if they exist.

Understanding Global Loss Landscape of One-hidden-layer ReLU Networks, Part 1: Theory