A systematic approach maps any-dimensional invariant functions to a unique function on an infinite-dimensional limit space admitting a topology with compact sets where universality holds, with examples of non-universal architectures and fixes.
Universal approximation results for neural networks with non-polynomialactivationfunctionovernon-compactdomains.arXiv preprint arXiv:2410.14759, 2024
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Banach-valued random feature models, including random single-hidden-layer networks, universally approximate elements of Bochner spaces over non-compact domains with explicit approximation rates.
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Any-Dimensional Invariant Universality
A systematic approach maps any-dimensional invariant functions to a unique function on an infinite-dimensional limit space admitting a topology with compact sets where universality holds, with examples of non-universal architectures and fixes.
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Universal approximation property of Banach space-valued random feature models including random neural networks
Banach-valued random feature models, including random single-hidden-layer networks, universally approximate elements of Bochner spaces over non-compact domains with explicit approximation rates.