Some density theorems in neural network with variable exponent
Functional Analysis
2025-04-22 v1
Abstract
In this paper, we extend several approximation theorems, originally formulated in the context of the standard 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.
Cite
@article{arxiv.2504.14476,
title = {Some density theorems in neural network with variable exponent},
author = {Mitsuo Izuki and Takahiro Noi and Yoshihiro Sawano and Hirokazu Tanaka},
journal= {arXiv preprint arXiv:2504.14476},
year = {2025}
}