This is one of the theoretical results most frequently cited to justify the use of sigmoidal neural networks in applications. By this statement one refers to the fact that sigmoidal neural networks have been shown to be able to approximate any continuous function arbitrarily well. Numerous results in the literature have established variants of this universal approximation property by considering distinct function classes to be approximated by network architectures using different types of neural activation functions with respect to various approximation criteria, see for instance [1, 2, 3, 5, 6, 11, 12, 14, 15].

This is one of the theoretical results most frequently cited to justify the use of sigmoidal neural networks in applications. By this statement one refers to the fact that sigmoidal neural networks have been shown to be able to approximate any continuous function arbitrarily well. Numerous results in the literature have established variants of this universal approximation property by considering distinct function classes to be approximated by network architectures using different types of neural activation functions with respect to various approximation criteria, see for instance [1, 2, 3, 5, 6, 11, 12, 14, 15].

This is one of the theoretical results most frequently cited to justify the use of sigmoidal neural networks in applications. By this statement one refers to the fact that sigmoidal neural networks have been shown to be able to approximate any continuous function arbitrarily well. Numerous results in the literature have established variants of this universal approximation property by considering distinct function classes to be approximated by network architectures using different types of neural activation functions with respect to various approximation criteria, see for instance [1, 2, 3, 5, 6, 11, 12, 14, 15].

Furthermore it is shown that networks of noisy spiking neurons with temporal coding have a strictly larger computational power than sigmoidal neural nets with the same number of units. 1 Introduction and Definitions We consider a formal model SNN for a §piking neuron network that is basically a reformulation of the spike response model (and of the leaky integrate and fire model) without using 6-functions (see [Maass, 1996a] or [Maass, 1996b] for further backgrou nd).

Abstract: There exist a number of negative results ([J), [BR), [KV]) about learning on neural nets in Valiant's model [V) for probably approximately correct learning ("PAClearning"). These negative results are based on an asymptotic analysis where one lets the number of nodes in the neural net go to infinit.y. Hence this analysis is less adequate for the investigation of learning on a small fixed neural net.

Abstract: There exist a number of negative results ([J), [BR), [KV]) about learning on neural nets in Valiant's model [V) for probably approximately correct learning ("PAClearning"). These negative results are based on an asymptotic analysis where one lets the number of nodes in the neural net go to infinit.y. Hence this analysis is less adequate for the investigation of learning on a small fixed neural net.

Abstract: There exist a number of negative results ([J), [BR), [KV]) about learning on neural nets in Valiant's model [V) for probably approximately correctlearning ("PAClearning"). These negative results are based on an asymptotic analysis where one lets the number of nodes in the neural net go to infinit.y. Hence this analysis is less adequate forthe investigation of learning on a small fixed neural net.