Computing Linear Regions in Neural Networks with Skip Connections

Johnny Joyce, Jan Verschelde
9/18/2025
cs.LGcs.SC

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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.

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Cite this paper

@article{joyce2025computing,
  title  = {Computing Linear Regions in Neural Networks with Skip Connections},
  author = {Johnny Joyce and Jan Verschelde},
  year   = {2025},
  eprint = {2509.15441},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2509.15441v1}
}

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