Learning capability assessment and feature space optimization for higher-order neural networks

A technique for evaluating the learning capability and optimizing the feature space of a class of higher-order neural networks is presented. It is shown that supervised learning can be posed as an optimization problem in which inequality constraints are used to code the information contained in the training patterns and to specify the degree of accuracy expected from the neural network. The approach establishes: (a) whether the structure of the network can effectively learn the training patterns and, if it can, a connectivity which corresponds to satisfactorily learning; (b) those features which can be suppressed from the definition of the feature space without deteriorating performance; and (c) if the structure is not appropriate for learning the training patterns, the minimum set of patterns which cannot be learned. The technique is tested with two examples and results are discussed