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We present a technique for neural network verification using mixed-integerprogramming (MIP) formulations. We derive a \emph{strong formulation} for eachneuron in a network using piecewise linear activation functions. Additionally,as in general, these formulations may require an exponential number ofinequalities, we also derive a separation procedure that runs in super-lineartime in the input dimension. We first introduce and develop our technique onthe class of \emph{staircase} functions, which generalizes the ReLU, binarized,and quantized activation functions. We then use results for staircaseactivation functions to obtain a separation method for general piecewise linearactivation functions. Empirically, using our strong formulation and separationtechnique, we can reduce the computational time in exact verification settingsbased on MIP and improve the false negative rate for inexact verifiers relyingon the relaxation of the MIP formulation.

Neural Network Verification as Piecewise Linear Optimization: Formulations for the Composition of Staircase Functions