Universal approximation theorem for neural networks with inputs from a topological vector space

Vugar Ismailov
9/19/2024
cs.LGcs.NEstat.ML

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Abstract

We study feedforward neural networks with inputs from a topological vector space (TVS-FNNs). Unlike traditional feedforward neural networks, TVS-FNNs can process a broader range of inputs, including sequences, matrices, functions and more. We prove a universal approximation theorem for TVS-FNNs, which demonstrates their capacity to approximate any continuous function defined on this expanded input space.

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Cite this paper

@article{ismailov2024universal,
  title  = {Universal approximation theorem for neural networks with inputs from a topological vector space},
  author = {Vugar Ismailov},
  year   = {2024},
  eprint = {2409.12913},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2409.12913v1}
}

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