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The learning speed of feed-forward neural networks is notoriously slow, and researchers have tried introducing randomness to reduce the learning requirement. One such approach is the Random Vector Functional Link (RVFL) network, which is a single-layer feed-forward neural network with randomly selected input-to-hidden layer weights and biases.
The authors provide a corrected version of the original theorem by Igelnik and Pao, which shows that RVFL networks can universally approximate continuous functions on compact domains, with the approximation error decaying at a rate proportional to the inverse of the number of nodes in the network.
The authors further provide a non-asymptotic version of the theorem, which gives an error guarantee with high probability when the number of network nodes is sufficiently large, albeit with an additional Lipschitz requirement on the activation function.
The authors generalize their results to the case of approximating continuous functions defined on smooth, compact submanifolds of Euclidean space, providing theoretical guarantees in both the asymptotic and non-asymptotic forms.
The authors illustrate their results on manifolds with numerical experiments.
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by Deanna Neede... at arxiv.org 03-29-2024
https://arxiv.org/pdf/2007.15776.pdfDeeper Inquiries