Learning of higher-order perceptrons with tunable complexities

We study learning from examples by higher-order perceptrons, which realize polynomially separable rules. The model complexities of the networks are made 'tunable' by varying the relative orders of different monomial terms. We analyse the learning curves of higher-order perceptrons when the Gibbs algorithm is used for training. It is found that learning occurs in a stepwise manner. This is because the number of examples needed to constrain the corresponding phase-space component scales differently.