Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications

arXiv:2402.11397v1 Announce Type: new
Abstract: We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal weights and biases, offering computational efficiency. We demonstrate that there exists a choice of external weights, for any family of such RPNNs, with non-polynomial infinitely differentiable activation functions, that exhibit an exponential convergence rate when approximating any infinitely differentiable function. For …

abstract applications approximation arxiv biases computational concept convergence cs.lg cs.na efficiency explore math.na networks neural networks practical projection random theory through type weights and biases