Computing Linear Regions in Neural Networks with Skip Connections
Machine Learning
2025-09-22 v1 Symbolic Computation
Abstract
Neural networks are important tools in machine learning. Representing piecewise linear activation functions with tropical arithmetic enables the application of tropical geometry. Algorithms are presented to compute regions where the neural networks are linear maps. Through computational experiments, we provide insights on the difficulty to train neural networks, in particular on the problems of overfitting and on the benefits of skip connections.
Cite
@article{arxiv.2509.15441,
title = {Computing Linear Regions in Neural Networks with Skip Connections},
author = {Johnny Joyce and Jan Verschelde},
journal= {arXiv preprint arXiv:2509.15441},
year = {2025}
}
Comments
Accepted for publication in the proceedings in Computer Algebra in Scientific Computing 2025