arXiv Machine Learning September 18, 2026 By Paul Lezeau, Thomas Walker, Yueqi Cao, Shiv Bhatia, Anthea Monod

A Computational Tropical Geometry Framework for Neural Networks

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The paper introduces a computational tropical geometry framework for symbolically analyzing neural networks with tropical activations. It presents an algorithm that computes the network’s linear regions as explicit unions of polyhedra, proves its correctness, and connects the number of linear regions to the monomials in the tropical expression. The authors also define the Hoffman constant to bound distances to the farthest linear region and release the open‑source Julia library TropicalNN.jl to implement these tools, demonstrating their use on proof‑of‑concept examples.

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