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In this work, we develop a novel input feature selection framework forReLU-based deep neural networks (DNNs), which builds upon a mixed-integeroptimization approach. While the method is generally applicable to variousclassification tasks, we focus on finding input features for imageclassification for clarity of presentation. The idea is to use a trained DNN,or an ensemble of trained DNNs, to identify the salient input features. Theinput feature selection is formulated as a sequence of mixed-integer linearprogramming (MILP) problems that find sets of sparse inputs that maximize theclassification confidence of each category. These ''inverse'' problems areregularized by the number of inputs selected for each category and bydistribution constraints. Numerical results on the well-known MNIST andFashionMNIST datasets show that the proposed input feature selection allows usto drastically reduce the size of the input to $\sim$15\% while maintaining agood classification accuracy. This allows us to design DNNs with significantlyfewer connections, reducing computational effort and producing DNNs that aremore robust towards adversarial attacks.

Model-based feature selection for neural networks: A mixed-integer programming approach