Synchronous versus sequential updating in the three-state Ising neural network with variable dilution

Abstract

The three-state Ising neural network with synchronous updating and variable dilution is discussed starting from the appropriate Hamiltonians. The thermodynamic and retrieval properties are examined using replica mean-field theory. Capacitytemperature phase diagrams are derived for several values of the pattern activity and different gradations of dilution, and the information content is calculated. The results are compared with those for sequential updating. The effect of self-coupling is established. Also the dynamics is studied using the generating function technique for both synchronous and sequential updating. Typical flow diagrams for the overlap order parameter are presented. The differences with the signal-to-noise approach are outlined.

Instability of frozen-in states in synchronous Hebbian neural networks

“…These models can be thought as extensions of Little's model with generalized synaptic interactions and multi-state units [6]. Only a small fraction of neurons that change sign appear to be involved in the stationary states [7,8], and the work in those studies was mainly devoted to fixed-point solutions for the macroscopic parameters. On the other hand, stationary period-two solutions for the macroscopic parameters, that arise from a fraction of units changing sign at each time step, have been found in the recent work on the synchronous dynamics of symmetric sequence processing without a self-interaction [9].…”

Symmetric sequence processing in a recurrent neural network model with a synchronous dynamics

“…The presence of self-interactions of the units, which is consistent with detailed balance in the synchronous dynamics of a network with a symmetric interaction matrix, has not been considered so far except in Little's model which has a simple Hebbian learning rule [20][21][22][23][24][25]. The role of self-interactions, which may be either excitatory or inhibitory, is to control the fraction of spin flips in the dynamics.…”

Instability of frozen-in states in synchronous Hebbian neural networks

“…These models can be thought as extensions of Little's model with generalized synaptic interactions and multi-state units [6]. Only a small fraction of neurons that change sign appear to be involved in the stationary states [7,8], and the work in those studies was mainly devoted to fixed-point solutions for the macroscopic parameters. On the other hand, stationary period-two solutions for the macroscopic parameters, that arise from a fraction of units changing sign at each time step, have been found in recent work on the synchronous dynamics of symmetric sequence processing without a self-interaction [9].…”