Abstract
A Piece-wise Linear Neural Network (PLNN) is a deep neural network composed of only Rectified Linear Units (ReLU) activation function. Interestingly, even though PLNNs are a nonlinear system in general, we show that PLNNs can be expressed in terms of linear constraints because ReLU function is a piece-wise linear function. We suggested that the robustness of Neural Networks (NNs) can be verified by investigating the feasible region of these constraints. Intuitively, suggested robustness represents the minimum Euclidean distance from the input needed to change its predicted class. Moreover, the run-time of calculating robustness is as fast as a feed forward neural network.
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