Learning and generalization theories of large committee--machines

The study of the distribution of volumes associated to the internal representations of learning examples allows us to derive the critical learning capacity ($\alpha_c=\frac{16}{\pi} \sqrt{\ln K}$) of large committee machines, to verify the stability of the solution in the limit of a large number $K$ of hidden units and to find a Bayesian generalization cross--over at $\alpha=K$.