Abstract: A neural network system includes means for accomplishing artificial intelligence functions in three formerly divergent implementations. These functions include: supervised learning, unsupervised learning, and associative memory storage and retrieval. The subject neural network is created by addition of a non-linear layer to a more standard neural network architecture. The non-linear layer functions to expand a functional input space to a signal set including orthonormal elements, when the input signal is visualized as a vector representation. An input signal is selectively passed to a non-linear transform circuit, which outputs a transform signal therefrom. Both the input signal and the transform signal are placed in communication with a first layer of a plurality of processing nodes. An improved hardware implementation of the subject system includes a highly parallel, hybrid analog/digital circuitry.