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