Learning recurrent neural models with minimal complexity from neural tuning data

Abstract

A learning algorithm for the estimation of the structure of nonlinear recurrent neural models from neural tuning data is presented. The proposed method combines support vector regression with additional constraints that result from a stability analysis of the dynamics of the fitted network model. The optimal solution can be determined from a single convex optimization problem that can be solved with semidefinite programming techniques. The method successfully estimates the feed-forward and the recurrent connectivity structure of neural field models using as data only examples of stable stationary solutions of the neural dynamics. The class of neural models that can be learned is quite general. The only a priori assumptions are the translation invariance and the smoothness of the feed-forward and recurrent spatial connectivity profile. The efficiency of the method is illustrated by comparing it with estimates based on radial basis function networks and support vector regression.