STUDY OF THE KOHONEN NETWORK WITH A DISCRETE STATE-SPACE

Digital (or mixed mode) circuit implementations of neural networks bri ng one major modification to their ideal, defectless models: quantizat ion of the weights dynamics. Would this modification completely pertur b 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 qu antization effects is crucial for practical applications. It has been mainly studied for Hopfield networks and multi-layer networks. We stud y this issue in the Kohonen network, since it has received little atte ntion so far. A Kohonen net is a self-organising map preserving the to pology of the input space (Kohonen, 1989). The first part of the paper is devoted to the mathematical treatment of the self-organisation pro perty of a one-dimensional array with discrete weights. This property has been already established for continuous-valued weights, we will se e that we need additional hypothesis to ensure a correct result when t he weights are discrete-valued. The second part presents a qualitative extension of this analysis to more general cases.