On the expressivity of sparse maxout networks
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909849618481152 |
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| author | Grillo, Moritz Hofmann, Tobias |
| author_facet | Grillo, Moritz Hofmann, Tobias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the expressivity of sparse maxout networks Grillo, Moritz Hofmann, Tobias Machine Learning Artificial Intelligence Combinatorics 68T07, 52B05, 14T99 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. |
| title | On the expressivity of sparse maxout networks |
| topic | Machine Learning Artificial Intelligence Combinatorics 68T07, 52B05, 14T99 |
| url | https://arxiv.org/abs/2510.14068 |