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

2024/09/19 by Vugar E. Ismailov, Ismailov, Vugar
Computer Science · Engineering · #Neural Networks and Applications #Advanced Numerical Analysis Techniques #Fuzzy Logic and Control Systems

paper · pdf · doi:10.48550/arxiv.2409.12913

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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