English

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 LpL^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.

Keywords

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}
}
R2 v1 2026-06-28T23:04:32.200Z