On-line learning of unrealizable tasks

The dynamics of on-line learning is investigated for structurally unrealizable tasks in the context of two-layer neural networks with an arbitrary number of hidden neurons. Within a statistical mechanics framework, a closed set of differential equations describing the learning dynamics can be derived, for the general case of unrealizable isotropic tasks. In the asymptotic regime one can solve the dynamics analytically in the limit of a large number of hidden neurons, providing an analytical expression for the residual generalization error, the optimal and critical asymptotic training parameters, and the corresponding prefactor of the generalization error decay.