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 $\left( {\alpha _c = \frac{{16}}{\pi }\sqrt {\ln \,k} } \right)$ 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 a=K.