**Abstract:** Many modern neural networks rely solely on ReLU activation functions for nonlinearity, motivated by factors including both the computational simplicity of ReLUs and their role in helping prevent vanishing gradients. These networks are consequently piecewise linear functions and this opens the door to studying their behavior using combinatorial and geometric techniques without direct analog for networks employing smooth nonlinearities such as sigmoid activations. In this talk, we will discuss metrics that take advantage of this linear geometry and can be used to classify in and out-of-distribution inputs for ReLU networks.

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