Approximation of functions by neural networks

01/29/2019

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by   Andreas Thom, et al.

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We study the approximation of measurable functions on the hypercube by functions arising from affine neural networks. Our main achievement is an approximation of any measurable function f W_n → [-1,1] up to a prescribed precision ε>0 by a bounded number of neurons, depending only on ε and not on the function f or n ∈ N.