Optimal pruning in neural networks

We study pruning strategies in simple perceptrons subjected to supervised learning. Our analytical results, obtained through the statistical mechanics approach to learning theory, are independent of the learning algorithm used in the training process. We calculate the post-training distribution P(J) of synaptic weights, which depends only on the overlap rho(0) achieved by the learning algorithm before pruning and the fraction kappa of relevant weights in the teacher network. From this distribution, we calculate the optimal pruning strategy for deleting small weights. The optimal pruning threshold grows from zero as straight theta(opt)(rho(0), kappa) approximately [rho(0)-rho(c)(kappa)](1/2) above some critical value rho(c)(kappa). Thus, the elimination of weak synapses enhances the network performance only after a critical learning period. Possible implications for biological pruning phenomena are discussed.