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Verifying that input-output relationships of a neural network conform toprescribed operational specifications is a key enabler towards deploying thesenetworks in safety-critical applications. Semidefinite programming (SDP)-basedapproaches to Rectified Linear Unit (ReLU) network verification transcribe thisproblem into an optimization problem, where the accuracy of any suchformulation reflects the level of fidelity in how the neural networkcomputation is represented, as well as the relaxations of intractableconstraints. While the literature contains much progress on improving thetightness of SDP formulations while maintaining tractability, comparativelylittle work has been devoted to the other extreme, i.e., how to most accuratelycapture the original verification problem before SDP relaxation. In this work,we develop an exact, convex formulation of verification as a completelypositive program (CPP), and provide analysis showing that our formulation isminimal -- the removal of any constraint fundamentally misrepresents the neuralnetwork computation. We leverage our formulation to provide a unifying view ofexisting approaches, and give insight into the source of large relaxation gapsobserved in some cases.

A Unified View of SDP-based Neural Network Verification through Completely Positive Programming