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Alternating minimization for regression with tropical rational functions

Alex Dunbar and Lars Ruthotto

Vol. 15 (2024), No. 1, 85–111
Abstract

We propose an alternating minimization heuristic for regression over the space of tropical rational functions with fixed exponents. The method alternates between fitting the numerator and denominator terms via tropical polynomial regression, which is known to admit a closed form solution. We demonstrate the behavior of the alternating minimization method experimentally. Experiments demonstrate that the heuristic provides a reasonable approximation of the input data. Our work is motivated by applications to ReLU neural networks, a popular class of network architectures in the machine learning community which are closely related to tropical rational functions.

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Keywords
tropical algebra, regression, ReLU neural networks, tropical geometry, machine learning
Mathematical Subject Classification
Primary: 14T90, 62J02, 90C24
Milestones
Received: 1 June 2023
Revised: 29 February 2024
Accepted: 1 May 2024
Published: 17 July 2024
Authors
Alex Dunbar
Department of Mathematics
Emory University
Atlanta, GA
United States
Lars Ruthotto
Departments of Mathematics and Computer Science
Emory University
Atlanta, GA
United States