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<p>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.</p>

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On shallow feedforward neural networks with inputs from a topological space

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Vugar E. Ismailov

摘要

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.