Phase transitions in dilute, locally connected neural networks

We report numerical studies of the memory-loss phase transition in Hopfield-like symmetric neural networks in which the neurons are connected to all other neurons within a local neighborhood (dense, short-range connectivity). The number of connections per neuron K scales as the number of neurons N raised to a power less than 1 (i.e., KN, <1). We use the recently developed Lee-Kosterlitz finite-size scaling technique to determine the critical value of below which the first-order phase transition disappears.