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Bridging logical and algorithmic reasoning with modern machine learningtechniques is a fundamental challenge with potentially transformative impact.On the algorithmic side, many NP-hard problems can be expressed as integerprograms, in which the constraints play the role of their "combinatorialspecification." In this work, we aim to integrate integer programming solversinto neural network architectures as layers capable of learning both the costterms and the constraints. The resulting end-to-end trainable architecturesjointly extract features from raw data and solve a suitable (learned)combinatorial problem with state-of-the-art integer programming solvers. Wedemonstrate the potential of such layers with an extensive performance analysison synthetic data and with a demonstration on a competitive computer visionkeypoint matching benchmark.

CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints