Robustness of representations in multilayer feedforward neural networks

Recent research has shown that multilayer feedforward networks with sigmoidal activation functions are universal approximators, and that this holds for more general activations as well. The mathematical underpinning for these results has been various: Kolmogorov's resolution of Hilbert's thirteenth problem; the Stone-Weierstrass theorem; approximation of Fourier and Radon integral representations; and convergence of probability measures. This paper

	Rigorously establishes the robustness of feedforward network realizations.
	Uses a theorem of Wiener and ideas of translation invariant subspaces to provide conditions for universal approximations toL 1 andL 2 functions by networks, for quite general activation functions.

The second result extends and simplifies some of the recent results of Stinchcombe and White, at least for the special cases ofL ₁ andL ₂ functions.