Dynamic bidirectional associative memory using chaotic neural network

Abstract

The proposed chaotic neuron has an internal dynamics, which is represented by the form of linear self-feedback and nonlinear self-feedback. Nonlinear self-feedback, as a product of a switching function and Gaussian function, has an effective value near the origin. Judging by externals, a neuron with negative nonlinear self-feedback is denoted as M1, while a neuron with positive one is denoted as M2. The ouput of M1 has a continuous value using sigmoid function, where as the output of M2 has 1 or 1 using sign function. Chaos is only evoked near the origin and its functional role is to divide the input space into two regions of positive and negative with an ambiguous intersection. Local minima problem, posed in gradient-based search, is solved using M1. For an unstructured search space the proposed local minima free search algorithm using M1 activates the search agent to jump from current configuration when the gradient-based algorithm get stuck in a local minimum. To accommodate the amount of chaotic jump to the search space an adaptation scheme, which increases the expectation value of the chaotic jump, is proposed by investigating the order statistics of multiple trials numerically. Bidirectional associative memory (BAM) is an important neural network model, which can be employed to model human thinking and machine intelligence by association. Owing to its lowest connection complexity, guaranteed convergence and stronger error-correction capability, BAM has attracted particular attention in neural network research. However, BAMs suffer from low storage capacity. Furthermore, all the bidirectional associative memories with neurons of Hopfield type are internally static at the neuron-level, so that an input pattern in X-layer cannot be learned with multiple output patterns in Y-layer. Learning process itself is impossible because multiple access with a key pattern cannot be represented by any function. Chaotic neural network as a BAM consists of two layers with ...