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Poster
in
Workshop: The Synergy of Scientific and Machine Learning Modelling (SynS & ML) Workshop

Neural Polytopes

Koji Hashimoto · Tomoya Naito · Hisashi Naito

Keywords: [ linear activation ] [ discrete geometry ] [ polytopes ]


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 discrete geome- try via machine learning and also a visualization of trained networks.

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