Phase transitions of an oscillator neural network with a standard Hebb learning rule

Abstract

Studies have been carried out on the phase transition phenomena of an oscillator network model based on a standard Hebb learning rule such as the Hopfield model. The relative phase informations, the in phase and antiphase, can be embedded in the network. By self-consistent signal-to-noise analysis, it was found that the storage capacity is given by ␣ c ϭ0.042, which is better than that of Cook's model. However, the retrieval quality is worse. In addition, an investigation was made into an acceleration effect caused by asymmetry of the phase dynamics. Finally, it was numerically shown that the storage capacity can be improved by modifying the shape of the coupling function.

Statistical mechanics of stochastic neural networks: Relationship between the self-consistent signal-to-noise analysis, Thouless-Anderson-Palmer equation, and replica symmetric calculation approaches

“…Variants of the above analog networks such as oscillator networks based on phase oscillator models have also been studied using the SCSNA to show that memory recall accompanied by synchronization of oscillators is of relevance in associative memory physiological neuronal systems [22,23,24,25,26]. The SCSNA becomes readily applicable to stochastic networks such as Ising spin networks of the Hopfield model, if they can be transformed into equivalent deterministic analog netwiorks.…”

“…Use of nonmontonic transfer functions in associative memory neural networks has been shown to improve the network performances in such a way that the storage capacity is increased beyond the well known value of 0.138 of the AGS under the correlation type learning rule [19,20,21,22,29].…”

“…where ξ Effects of the output proportional term are pronounced in the case of deterministic analog networks with a nonmontonic transfer function [19,20,21,22,29] for which the existence of energy functions is not ensured. Use of nonmontonic transfer functions in associative memory neural networks has been shown to improve the network performances in such a way that the storage capacity is increased beyond the well known value of 0.138 of the AGS under the correlation type learning rule [19,20,21,22,29].…”

Multibranch Entrainment and Slow Evolution among Branches in Coupled Oscillators

“…when g(ω) = δ(ω)], detailed balance holds, since the coupling function is an odd function [5,7]. Thus, in the limit σ → 0, this model can be mapped to the equilibrium system.…”

Controlling the synchronization properties of two dipolarly coupled vortex based spin-torque nano-oscillators by the intermediate of a third one

“…Thanks to these features they are excellent candidates for building computing systems inspired from neural synchronization in the brain [12][13][14][15] . Indeed bio-inspired computing with oscillators requires to be able to fabricate very large arrays of interacting oscillators, and to be able to control the degree of coupling between the oscillators 16,17 . If several physical phenomena can be used to couple spin-torque oscillators, such as spin waves 5,6,18 or electric currents 7,19 , one of the most appealing towards the realization of dense arrays is the dipolar coupling.…”