CONSTRUCTION ALGORITHM FOR THE PARITY-MACHINE

An algorithm for the training of a special multilayered feed-forward neural network is presented. The strategy is very similar to the well-known tiling algorithm, yet the resulting architecture is completely different. Neurons are added in one layer only. The output of the network is given by the product of its k many hidden neurons, which is for +/- 1 units the result of the parity-operation. The capacity alpha(c) of a network trained according to the algorithm is estimated for the storage of randomly defined classifications. The asymptotic dependence is found to be alpha(c) approximately k ln k for k --> infinity. This is in agreement with recent analytic results for the algorithm-independent storage capacity of a parity-machine.