  Mode connectivity is a surprising phenomenon in the loss landscape of deep
nets. Optima -- at least those discovered by gradient-based optimization --
turn out to be connected by simple paths on which the loss function is almost
constant. Often, these paths can be chosen to be piece-wise linear, with as few
as two segments. We give mathematical explanations for this phenomenon,
assuming generic properties (such as dropout stability and noise stability) of
well-trained deep nets, which have previously been identified as part of
understanding the generalization properties of deep nets. Our explanation holds
for realistic multilayer nets, and experiments are presented to verify the
theory.
