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arXiv · 2504.14476

Some density theorems in neural network with variable exponent

Mitsuo Izuki·Takahiro Noi·Yoshihiro Sawano·Hirokazu Tanaka
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Abstract

In this paper, we extend several approximation theorems, originally formulated in the context of the standard $L^p$ norm, to the more general framework of variable exponent spaces. Our study is motivated by applications in neural networks, where function approximation plays a crucial role. In addition to these generalizations, we provide alternative proofs for certain well-known results concerning the universal approximation property. In particular, we highlight spaces with variable exponents as illustrative examples, demonstrating the broader applicability of our approach.

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Mitsuo Izuki, Takahiro Noi, Yoshihiro Sawano, Hirokazu Tanaka. 2025-04-20. Some density theorems in neural network with variable exponent. https://arxiv.org/abs/2504.14476

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