Stability and convergence properties of a novel, multi-zero, artificial neural network

Abstract

Summary form only given. If the signal function f(x) of an N-dimensional neural network is a nonlinear multi-zero function in x such as sin( pi x), the stability and convergence properties of this network are mainly controlled by the connection matrix, of the network. If the connection matrix is programmed correctly, the system will have many global and asymptotic stable states. In the N-dimensional state space, each stable state (or final state) is surrounded by a domain of attraction such that whenever the initial state (or the input state) falls within this domain, the system will converge to the final state at the center of the domain. For a system possessing sin( pi ,x) signal functions, it is proved theoretically that the components of all final states are composed of integer numbers. Therefore, for any N-dimensional arbitrary analog input, the output will always be an N-bit, quantized M-nary (as against binary) digital output. The mapping relation between the N-dimensional analog input and the N-bit, M-ary digital output can be adjusted by adjusting the connection matrix. That is, the circuit can be trained to learn certain input-output mapping rules.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>