The Role of Weight Normalization in Competitive Learning

The effect of different kinds of weight normalization on the outcome of a simple competitive learning rule is analyzed. It is shown that there are important differences in the representation formed depending on whether the constraint is enforced by dividing each weight by the same amount (“divisive enforcement”) or subtracting a fixed amount from each weight (“subtractive enforcement”). For the divisive cases weight vectors spread out over the space so as to evenly represent “typical” inputs, whereas for the subtractive cases the weight vectors tend to the axes of the space, so as to represent “extreme” inputs. The consequences of these differences are examined.

Topography and ocular dominance: a model exploring positive correlations

The map from eye to brain in vertebrates is topographic, i.e., neighbouring points in the eye map to neighbouring points in the brain. In addition, when two eyes innervate the same target structure, the two sets of fibres segregate to form ocular dominance stripes. Experimental evidence from the frog and goldfish suggests that these two phenomena may be subserved by the same mechanisms. We present a computational model that addresses the formation of both topography and ocular dominance. The model is based on a form of competitive learning with subtractive enforcement of a weight normalization rule. Inputs to the model are distributed patterns of activity presented simultaneously in both eyes. An important aspect of this model is that ocular dominance segregation can occur when the two eyes are positively correlated, whereas previous models have tended to assume zero or negative correlations between the eyes. This allows investigation of the dependence of the pattern of stripes on the degree of correlation between the eyes: we find that increasing correlation leads to narrower stripes. Experiments are suggested to test this prediction.