Dynamics and optimal storage capacity of neural networks

The study of neural networks by physicists started as an extension of the theory of spin glasses. For this approach to be valid, one had to assume symmetric interactions between the neurons. The true interactions between neurons are non symmetric. In order to treat this asymmetry, new techniques have been developed which should be useful in the study of systems far from equilibrium. One can construct a class of models (diluted asymmetric networks), the dynamical properties of which can be calculated analytically. These networks have many properties in common with symmetric networks: Retrieval of stored patterns, maximum storage capacity, mixed states. They also have several properties specific to the asymmetry: Chaotic behaviour and continuous distribution of activities