Neural Polytopes

Koji Hashimoto; Tomoya Naito; Hisashi Naito

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arXiv · 2307.00721

Neural Polytopes

Koji Hashimoto·Tomoya Naito·Hisashi Naito

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Abstract

We find that simple neural networks with ReLU activation generate polytopes as an approximation of a unit sphere in various dimensions. The species of polytopes are regulated by the network architecture, such as the number of units and layers. For a variety of activation functions, generalization of polytopes is obtained, which we call neural polytopes. They are a smooth analogue of polytopes, exhibiting geometric duality. This finding initiates research of generative discrete geometry to approximate surfaces by machine learning.

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cs.LG cs.GR hep-th math.GT

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Koji Hashimoto, Tomoya Naito, Hisashi Naito. 2023-07-03. Neural Polytopes. https://arxiv.org/abs/2307.00721

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