The Dynamic Universality of Sigmoidal Neural Networks

The Dynamic Universality of Sigmoidal Neural Networks

We investigate the computational power of recurrent neural networks that apply the sigmoid activation function _(x)=[2 (1+e)]&1. These networks are extensively used in automatic learning of non-linear dynamical behavior. We show that in the noiseless model, there exists a universal architecture that can be used to compute any recursive (Turing) function. This is the first result of its kind for...

Ridge Functions, Sigmoidal Functions and Neural Networks

This paper considers mainly approximation by ridge functions. Fix a point a 2 IR n and a function g : IR ! IR. Then the function f : IR n ! IR deened by f (x) = g(ax), x 2 IR n , is a ridge or plane wave function. A sigmoidal function is a particular example of the function g which closely resembles 1 at 1 and 0 at ?1. This paper discusses approximation problems involving general ridge function...

Multi-sigmoidal units and neural networks

Finiteness Results for Sigmoidal "Neural" Networks

1 1+x 2. This shows that arbitrary (not exp-ra denable) analytic functions may result in architectures with in-nite VC dimension. (Moreover, the architecture used is the simplest one that appears in neural nets practice.) Note that if we wish the x i 's to be bounded, for instance to be restricted to the interval [01; 1], one may replace the above x i 's and w j 's by xi c and cw j , where c = ...

Dynamic Sliding Mode Control of Nonlinear Systems Using Neural Networks

Dynamic sliding mode control (DSMC) of nonlinear systems using neural networks is proposed. In DSMC the chattering is removed due to the integrator which is placed before the input control signal of the plant. However, in DSMC the augmented system is one dimension bigger than the actual system i.e. the states number of augmented system is more than the actual system and then to control of such ...