Dynamics of online Hebbian learning with structurally unrealizable restricted training sets

We present an exact solution for the dynamics of online Hebbian learning in neural networks, with restricted and unrealizable training sets. In contra st to other studies on learning with restricted training sets, unrealizabil ity is here caused by structural mismatch, rather than data noise: the teac her machine is a perceptron with a reversed-wedge-type transfer function, w hile the student machine is a perceptron with a sigmoidal transfer function . We calculate the glassy dynamics of the macroscopic performance measures, training error and generalization error, and the (non-Gaussian) student fi eld distribution. Our results, which find excellent confirmation in numeric al simulations, provide a new benchmark test for general formalisms with wh ich to study unrealizable learning processes with restricted training sets.