Strong mixed-integer programming formulations for trained neural networks

• Published in: Mathematical programming Vol. 183; no. 1-2; pp. 3 - 39
• Main Authors: Anderson, Ross, Huchette, Joey, Ma, Will, Tjandraatmadja, Christian, Vielma, Juan Pablo
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2020; Springer Nature B.V
• Subjects: Calculus of Variations and Optimal Control; Optimization; Combinatorics; Full Length Paper; Image classification; Integer programming; Linear functions; Linear programming; Machine learning; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Mathematics of Computing; Mixed integer; Neural networks; Numerical Analysis; Theoretical; Formulations; Deep learning; Mixed-integer programming; 90C11

We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying that an image classification network is robust to adversarial i...