Parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network

Abstract

Abstract. The parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network is studied using signal-to-noise analysis techniques. Evolution equations for the order parameters are derived, both at zero and finite temperature. The retrieval properties of the network are discussed in terms of the four-spin coupling strength and the temperature. It is shown that the presence of a four-spin coupling enhances the retrieval quality.PACS. 64.60.Cn Order-disorder transformations; statistical mechanics of model systems -75.10.Hk Classical spin models -87.10.+e General, theoretical, and mathematical biophysics -02.50.-r Probability theory, stochastic processes and statistics

Signal-to-noise analysis of Hopfield neural networks with a formulation of the dynamics in terms of transition probabilities

“…The critical capacity is greater than that of the Little-Hopfield model. These results contrast with what was found in the asymmetric extremely diluted model where the critical capacity at low temperatures decreases with increasing J and where the model without four-spin coupling has a greater critical capacity [23]. The lines of Fig.…”

“…We introduce an analysis of the path probability of one neuron in order to obtain the contribution of all feedback correlations to the dynamics of this neuron. The results of this analysis are included in the expansion of the average over paths (23). In Ref.…”

“…In Ref. [23] a possible biological justification of this network appears. Statics and dynamics of the fully connected model with finite loading were studied in Ref.…”

“…On the other hand, statics and dynamics of the asymmetric extremely diluted model and infinite loading were studied in Ref. [23] with the SNA method.…”

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

“…As mentioned in the introduction it is known that synchronous updating can lead to two-cycles as stationary solutions. Results for the Hopfield model [28,29] and the Blume-Emery-Griffiths model [30,31] show that such cycles do not appear in the retrieval region of the corresponding phase diagrams. Therefore, cycles have been neglected in the replica calculation of the retrieval properties of these models.…”