Emergence of Topographic Cortical Maps in a Parameterless Local Competition Network

Abstract

A major research problem in the area of unsupervised learning is the understanding of neuronal selectivity, and its role in the formation of cortical maps. Kohonen devised a self-organizing map algorithm to investigate this problem, which achieved partial success in replicating biological observations. However, a problem in using Kohonen’s approach is that it does not address the stability-plasticity dilemma, as the learning rate decreases monotonically.

In this paper, we propose a solution to cortical map formation which tackles the stability-plasticity problem, where the map maintains stability while enabling plasticity in the presence of changing input statistics. We adapt the parameterless SOM (Berglund and Sitte 2006) and also modify Kohonen’s original approach to allow local competition in a larger cortex, where multiple winners can exist.

The learning rate and neighborhood size of the modified Kohonen’s method are set automatically based on the error between the local winner’s weight vector and its input. We used input images consisting of lines of random orientation to train the system in an unsupervised manner. Our model shows large scale topographic organization of orientation across the cortex, which compares favorably with cortical maps measured in visual area V1 in primates. Furthermore, we demonstrate the plasticity of this map by showing that the map reorganizes when the input statistics are chanaged.