Universal approximation theorem for neural networks with inputs from a topological vector space
<|reference_start|>Universal approximation theorem for neural networks with inputs from a topological vector space: 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.<|reference_end|>
@article{ismailov2024universal,
    title={Universal approximation theorem for neural networks with inputs from a
  topological vector space},
    author={Vugar Ismailov},
    journal={arXiv preprint arXiv:2409.12913},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.12913},
    primaryClass={cs.LG cs.NE stat.ML}
}