# Alternating Minimization for Regression with Tropical Rational Functions

arXiv: https://arxiv.org/abs/2305.20072 · HTML: https://mlsanity.com/paper/2305.20072/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Understanding Deep Neural Networks with Rectified Linear Units](https://mlsanity.com/paper/1611.01491/) (2016)
- [Tropical Geometry of Deep Neural Networks](https://mlsanity.com/paper/1805.07091/) (2018)
- [Nonlinear Approximation and (Deep) ReLU Networks](https://mlsanity.com/paper/1905.02199/) (2019)
- [A Tropical Approach to Neural Networks with Piecewise Linear Activations](https://mlsanity.com/paper/1805.08749/) (2018)
- [Tropical Polynomial Division and Neural Networks](https://mlsanity.com/paper/1911.12922/) (2019)
- [Tropical Geometry and Piecewise-Linear Approximation of Curves and Surfaces on Weighted Lattices](https://mlsanity.com/paper/1912.03891/) (2019)
- [Tropical Support Vector Machine and its Applications to Phylogenomics](https://mlsanity.com/paper/2003.00677/) (2020)
- [Tropical Support Vector Machines: Evaluations and Extension to Function Spaces](https://mlsanity.com/paper/2101.11531/) (2021)
- [Sparsity in Max-Plus Algebra and Systems](https://mlsanity.com/paper/1801.09850/) (2018)
- [Monomial tropical cones for multicriteria optimization](https://mlsanity.com/paper/1707.09305/) (2017)

## Abstract (arXiv)

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.