An associative network with cross inhibitory connections

Abstract

Kohonen's optimal associative mapping is well known as a fundamental paradigm of associative memory. The mapping can be embodied by a two-layered network consisting of neuron-like elements which are linked by forward connections. The weights of the connections can be determined by pseudoinverse calculation of a pattern matrix. As will be shown in this paper, however, the optimal associative mapping can also be embodied by a mathematically equivalent network consisting of three layers, some neurons of the middle layer of which are linked with cross inhibitory connections. The connection weights can be determined by correlation calculation of pattern vectors, requiring no pseudoinverse calculation. In addition, the associative power of the network can considerably be enhanced by incorporating a familiar nonlinear characteristic into the constituent neurons. Central points of this paper are: to give a mathematically precise description as to how to determine the connection weights of the cross-inhibition type of optimal associative networks; to mention some advantageous points of the network in comparison with the forward connection type of networks; to give a geometrical interpretation on the role of a nonlinear characteristic of individual neurons.