Retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks

Abstract

The retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks are derived and studied in replica-symmetric mean-field theory generalizing earlier works on either the fully connected or the symmetrical extremely diluted network. Capacity-gain parameter phase diagrams are obtained for the Q=3, Q=4 and $Q=\infty$ state networks with uniformly distributed patterns of low activity in order to search for the effects of a gradual dilution of the synapses. It is shown that enlarged regions of continuous changeover into a region of optimal performance are obtained for finite stochastic noise and small but finite connectivity. The de Almeida-Thouless lines of stability are obtained for arbitrary connectivity, and the resulting phase diagrams are used to draw conclusions on the behavior of symmetrically diluted networks with other pattern distributions of either high or low activity.

21 pages, revtex

Cited by in corpus (6)

• The Little-Hopfield model on a Random Graph
• Mean-field dynamics of sequence processing neural networks with finite connectivity
• Synchronous versus sequential updating in the three-state Ising neural network with variable dilution
• Feed-forward chains of recurrent attractor neural networks with finite dilution near saturation
• The three-state layered neural network with finite dilution
• Multiplicative versus additive noise in multi-state neural networks