STUDY OF THE KOHONEN NETWORK WITH A DISCRETE STATE-SPACE

Digital (or mixed mode) circuit implementations of neural networks bring one major modification to their ideal, defectless models: quantization of the weights dynamics. Would this modification completely perturb the behavior of the network, it will never be possible to implement it on a digital (or mixed mode) VLSI chip. Clearly, the analysis of quantization effects is crucial for practical applications. It has been mainly studied for Hopfield networks and multi-layer networks. We study this issue in the Kohonen network, since it has received little attention so far. A Kohonen net is a self-organising map preserving the topology of the input space (Kohonen, 1989). The first part of the paper is devoted to the mathematical treatment of the self-organisation property of a one-dimensional array with discrete weights. This property has been already established for continuous-valued weights, we will see that we need additional hypothesis to ensure a correct result when the weights are discrete-valued. The second part presents a qualitative extension of this analysis to more general cases.