| Turing Universality of Neural Nets (Revisited) (2007) | |||||||||||||||||
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| . We show how to use recursive function theory to prove Turing universality of finite analog recurrent neural nets, with a piecewise linear sigmoid function as activation function. We emphasize the modular construction of nets within nets, a relevant issue from the software engineering point of view. Keywords. Neural computation, recursive function theory, modularity. 1 Introduction In this paper we work with analog recurrent neural nets (ARNN's) as in [Siegelmann and Sontag 95]. In each instant t each neuron i updates its activity x i in the following non-linear way: x (t+1) = s( j=1 N a ij x j (t) + j=1 M b ij u (t) + c i ) where a ij , b ij and c are rational weights (and therefore Turing computable); N is the number of neurons, M the number of input streams u ; and s is the piecewise linear sigmoid function, s(x) = 0, x<0 x, 0x1 1, x>1 which is a continuous function as opposed to the Heaviside function. The latter, when used in the context of analog neural nets all... | |||||||||||||||||
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