Set-valued functional neural mapping and inverse system approximation

This work explores set-valued functional neural mapping and inverse system approximation by learning state-regulated multilayer neural networks. Multilayer neural organization is extended to recruit a discrete regulating state in addition to predictive attributes in the input layer. The network mapping regulated over a set of finite discrete states translates a predictor to many targets. Stimuli and responses clamped at visible units are assumed as mixtures of paired predictors and targets sampled from many joined elementary mappings. Unknown regulating states are related to missing exclusive memberships of paired training data to distinct sources. Learning a state-regulated neural network for set-valued mapping approximation involves retrieving unknown exclusive memberships and refining network interconnections. The learning process is realized by a hybrid of mean field annealing and Levenberg-Marquardt methods that simultaneously track expectations of unknown regulating states and optimal interconnections among consecutive layers along a physical-like annealing process. Numerical simulations show the presented learning process well reconstructing many joined elementary functions for set-valued functional mapping and inverse system approximation.