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

• URL: http://arxiv.org/abs/2409.12913v1
• Date: Thu, 19 Sep 2024 17:10:14 GMT
• Title: Universal approximation theorem for neural networks with inputs from a topological vector space
• Authors: Vugar Ismailov,
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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