Partially connected models of neural networks
Andrew Canning, E. Gardner · Journal of Physics A Mathematical and General · 1988
A partially connected Hopfield neural network model is studied under the restriction that w, the ratio of connections per site to the size of the system, remains finite as the size N to infinity with the connection structure at each site being the same. The replica symmetric mean field theory equations for the order parameters are derived. The zero-temperature forms of these equations are then solved numerically for a few different 'local' connectivity architectures showing phase transitions at different critical storage ratios, alpha c , where the states which the authors are trying to store in the network become discontinuously unstable. They show that the information capacity per connection improves for partially connected systems.