On shallow feedforward neural networks with inputs from a topological space

• URL: http://arxiv.org/abs/2504.02321v1
• Date: Thu, 03 Apr 2025 06:48:46 GMT
• Title: On shallow feedforward neural networks with inputs from a topological space
• Authors: Vugar Ismailov,
• Abstract summary: We study feedforward neural networks with inputs from a topological space (TFNNs)<n>We prove a universal approximation theorem for shallow TFNNs, which demonstrates their capacity to approximate any continuous function defined on this topological space.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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