On shallow feedforward neural networks with inputs from a topological space
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Abstract (arXiv)
We study feedforward neural networks with inputs from a topological space (TFNNs). We prove a universal approximation theorem for shallow TFNNs, which demonstrates their capacity to approximate any continuous function defined on this topological space. As an application, we obtain an approximative version of Kolmogorov's superposition theorem for compact metric spaces.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 12 of its 33 references that are in the map. First posted on arXiv 3 Apr 2025.
Builds on
12 of 33 references.
References · 12
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
- 2020Non-Euclidean Universal Approximationcited by 29
- 2021Two-layer neural networks with values in a Banach spacecited by 26
- 2021Approximation capability of two hidden layer feedforward neural networks with fixed weightscited by 24
- 2022Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformercited by 22
- 2017On the approximation by single hidden layer feedforward neural networks with fixed weightscited by 19
- 2023Global universal approximation of functional input maps on weighted spacescited by 19
- 2023On the Kolmogorov neural networkscited by 19
- 2024Mixtures of Neural Operators Reduce Active Complexity in Operator Learningcited by 16
- 2024Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networkscited by 11
- 2023An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learningcited by 7
- 2024Neural networks in non-metric spacescited by 3
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Citing papers per year: 2026: 2.
2 papers.