Strong mixed-integer programming formulations for trained neural networks

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...

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Vydáno v:Mathematical programming Ročník 183; číslo 1-2; s. 3 - 39
Hlavní autoři: Anderson, Ross, Huchette, Joey, Ma, Will, Tjandraatmadja, Christian, Vielma, Juan Pablo
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2020
Springer Nature B.V
Témata:
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
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí: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 inputs, or solving decision problems where the objective function is a machine learning model. We present a generic framework, which may be of independent interest, that provides a way to construct sharp or ideal formulations for the maximum of d affine functions over arbitrary polyhedral input domains. We apply this result to derive MIP formulations for a number of the most popular nonlinear operations (e.g. ReLU and max pooling) that are strictly stronger than other approaches from the literature. We corroborate this computationally, showing that our formulations are able to offer substantial improvements in solve time on verification tasks for image classification networks.
Bibliografie:ObjectType-Article-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-020-01474-5