mlsanityData to 7 Oct 2026

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

arXiv 2409.12913 ↗First posted 19 Sep 2024cs.LG cs.NE stat.MLcited by 4

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Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 5 of its 24 references that are in the map. First posted on arXiv 19 Sep 2024.

Builds on

5 of 24 references.

References · 5

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  2. 2021Two-layer neural networks with values in a Banach spacecited by 26
  3. 2021Approximation capability of two hidden layer feedforward neural networks with fixed weightscited by 24
  4. 2017On the approximation by single hidden layer feedforward neural networks with fixed weightscited by 19
  5. 2024Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networkscited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 2.

4 papers.

  1. 2024Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEscited by 2
  2. 2025SVarM: Linear Support Varifold Machines for Classification and Regression on Geometric Datacited by 1
  3. 2026Topological DeepONets and a generalization of the Chen-Chen operator approximation theoremcited by 1
  4. 2026Universality of shallow and deep neural networks on non-Euclidean spacescited by 0