Least MSE reconstruction by self-organization. I. Multi-layer neural-nets

A self-organizing net based on the least mean square error reconstruction (LMSER) principles is proposed, which produces a local learning rule. The author introduces the architecture of this multilayer net, proves the stability of its dynamic process in the perception phase, and derives the local learning rule which performs gradient descent of the least MSE of the reconstruction. It is shown that this net has a number of potential functions, such as associative memory, feature extraction, data compression, unsupervised pattern clustering and recognition, attentional recognition, and, for interpreting the development of orientation cells in the cortical field, the emergence of an imaginary image in the brain. The possibilities are considered of extending the net to the supervised learning mode and to a generalized associative memory which may increase the capacity considerably