Training of a feedforward multiple-valued neural network by error backpropagation with a multilevel threshold function

A technique for the training of multiple-valued neural networks based on a backpropagation learning algorithm employing a multilevel threshold function is proposed. The optimum threshold width of the multilevel function and the range of the learning parameter to be chosen for convergence are derived. Trials performed on a benchmark problem demonstrate the convergence of the network within the specified range of parameters.

I. Introduction

The binary model of the artificial neurons does not describe the complexity of biological neurons fully since the neurons actually handle continuous data. However, analog neurons implemented in an integrated chip require high-precision resistors and are easily affected by electrical noise. Because of the problems associated with the binary and analog neurons, research on multilevel neural networks for modeling the biological neurons has attracted great attention [1]– [3]. Multiple-valued logic establishes a balance between the quantized integrity of binary and the information density of analog signaling. Multiple-valued logic neuron has robust separation ability and a very fast operation speed in pattern recognition when compared to an ordinary linear neuron. Tang et al. introduced multiple-valued algebraic system of learning incorporating a weighted sum and piecewise linear functions [4]. An ARTMAP based multiple-valued neural network for the recognition and prediction of multiple-valued patterns is presented in [5]. A self-organizing neural network for the recognition of multiple-valued patterns is explained in [6].