Analysis of the elastic net model applied to the formation of ocular dominance and orientation columns

The development and structure of orientation (OR) and ocular dominance (OD) maps in the primary visual cortex of cats and monkeys can be modelled using the elastic net algorithm, which attempts to find an 'optimal' cortical representation of the input features. Here we analyse this behaviour in terms of parameters of the feature space. We derive expressions for the OR periodicity, and the first bifurcation point as a function of the annealing parameter using the methods of Durbin et al (Durbin R, Szeliski R and Yuille A 1989 Neural Computation 1 348-58). We also investigate the effect of the relative order of OR and OD development on overall map structure. This analysis suggests that developmental order can be predicted from the final OR and OD periodicities. In conjunction with experimentally measured values for these periodicities, the model predicts that (i) in normal macaques OD develops first, (ii) in normal cats OR develops first and (iii) in strabismic cats OD develops first.