Abstract
We provide a constructive proof of the theorem of function approximation by perceptrons (cf Leshno et al. [1], Hornik [2]) when the activation function ψ isC∞ with all its derivatives non 0 at 0. We deal with uniform approximation on compact sets of continuous functions on ℜd,d≥1. This approach is elementary and provides some approximation results for the derivatives along with some bounds for the hidden layer.
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Attali, JG., Pagès, G. Approximation of functions by perceptrons: a new approach. Neural Process Lett 2, 19–22 (1995). https://doi.org/10.1007/BF02332161
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DOI: https://doi.org/10.1007/BF02332161