Learning and memory properties in fully connected networks

This paper summarises recent results of theoretical analysis and numerical simulation, in fully connected networks of the Little-Hopfield class. The theoretical analysis is based on methods of statistical mechanics as applied to spin-glass problems, and the numerical work involves massively parallel simulations on the ICL Distributed Array Processor (DAP). Specific applications include: (i) exact results for the fraction of nominal vectors which are perfectly stored by the usual Hebbian rule; (ii) a numerical estimate of the position of the second phase transition in the Hopfield model, at which there is effectively total loss of memory capacity; (iii) a numerical study of the nature of the spurious states in the model; (iv) an exploration of the performance of a learning algorithm, including the exact storage of up to 512 (random) nominal vectors in a 512 node model; (v) a theoretical study of the phase transitions in generalizations where the energy function is a monomial in the state vectors.