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arXiv · 2510.14068

On the expressivity of sparse maxout networks

Moritz Grillo·Tobias Hofmann
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Abstract

We study the expressivity of sparse maxout networks, where each neuron takes a fixed number of inputs from the previous layer and employs a, possibly multi-argument, maxout activation. This setting captures key characteristics of convolutional or graph neural networks. We establish a duality between functions computable by such networks and a class of virtual polytopes, linking their geometry to questions of network expressivity. In particular, we derive a tight bound on the dimension of the associated polytopes, which serves as the central tool for our analysis. Building on this, we construct a sequence of depth hierarchies. While sufficiently deep sparse maxout networks are universal, we prove that if the required depth is not reached, width alone cannot compensate for the sparsity of a fixed indegree constraint.

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Moritz Grillo, Tobias Hofmann. 2025-10-15. On the expressivity of sparse maxout networks. https://arxiv.org/abs/2510.14068

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