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arXiv · 2212.13713

Global universality of the two-layer neural network with the $k$-rectified linear unit

N. Hatano·M. Ikeda·I. Ishikawa·Y. Sawano
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Abstract

This paper concerns the universality of the two-layer neural network with the $k$-rectified linear unit activation function with $k=1,2,\ldots$ with a suitable norm without any restriction on the shape of the domain. This type of result is called global universality, which extends the previous result for $k=1$ by the present authors. This paper covers $k$-sigmoidal functions as an application of the fundamental result on $k$-rectified linear unit functions.

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N. Hatano, M. Ikeda, I. Ishikawa, Y. Sawano. 2022-12-28. Global universality of the two-layer neural network with the $k$-rectified linear unit. https://arxiv.org/abs/2212.13713

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