The Blume-Emery-Griffiths neural network with synchronous updating and variable dilution

Bollé, Désiré; Blanco, J. Busquets

doi:10.1140/epjb/e2005-00328-7

Cited by 10 publications

(14 citation statements)

References 24 publications

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“…These are solutions in which oscillations of the correlation function persist, so that the oscillation amplitude c 1 = 1 − c 0 is strictly positive. Setting ω = π in (21,22) gives…”

Section: Time-translation Invariant Ergodic Statesmentioning

confidence: 99%

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Stationary states of a spherical Minority Game with ergodicity breaking

Galla

Sherrington²

2005

J. Stat. Mech.

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Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in [1] displays a phase with broken ergodicity and dependence of the macroscopic stationary state on initial conditions. The model thus bears more similarity with the original MG. Still, all order parameters including the volatility can computed in the ergodic phases without making any approximations. We also study the effects of market impact correction on the phase diagram. Finally we discuss a continuous-time version of the model as well as the differences between on-line and batch update rules. Our analytical results are confirmed convincingly by comparison with numerical simulations. In an appendix we extend the analysis of [1] to a model with general time-step, and compare the dynamics and statics of the two spherical models.

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“…These are solutions in which oscillations of the correlation function persist, so that the oscillation amplitude c 1 = 1 − c 0 is strictly positive. Setting ω = π in (21,22) gives…”

Section: Time-translation Invariant Ergodic Statesmentioning

confidence: 99%

“…Furthermore, one realises that in the derivation of (31) only the case ω = π in Eqs. (21,22) is used, so that χ ′ and λ 0 can be computed independently of c 0 and χ. We may hence conjecture that (31) still holds in the non-ergodic regime (at least in approximation).…”

Section: The Non-ergodic Phasementioning

confidence: 99%

Stationary states of a spherical Minority Game with ergodicity breaking

Galla

Sherrington²

2005

J. Stat. Mech.

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“…Here the stationary states depend on the combination of both types of dynamical processes. Also the phase diagrams of the Hopfield neural network [2] and the Blume-Emery-Griffiths model [3] depend on the updating mode, while those of the Q-state Ising model [3,4] and the Sherrington-Kirkpatrick spin glass [5] are independent of the used scheme. Recently, there was a controversial discussion about the number of attractors that increases exponentially with the system size for synchronous update [6], and with a power for critical Boolean networks [7] for asynchronous update.…”

Section: Introductionmentioning

confidence: 99%

Impact of the updating scheme on stationary states of networks

Radicchi¹,

Ahn²,

Meyer‐Ortmanns³

2008

J. Phys. A: Math. Theor.

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From Boolean networks it is well known that the number of attractors as a function of the system size depends on the updating scheme which is chosen either synchronously or asynchronously. In this contribution, we report on a systematic interpolation between synchronous and asynchronous updating in a one-dimensional chain of Ising spins. The stationary state for fully synchronous updating is antiferromagnetic. The interpolation allows us to locate a phase transition between phases with an absorbing and a fluctuating stationary state. The associated universality class is that of parity conservation. We also report on a more recent study of asynchronous updates applied to the yeast cell-cycle network. Compared to the synchronous update, the basin of attraction of the largest attractor considerably shrinks and the convergence to the biological pathway slows down and is less dominant. Both examples illustrate how sensitively the stationary states and the properties of attractors can depend on the updating mode of the algorithm.

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“…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].…”

Section: Introductionmentioning

confidence: 99%

Instability of frozen-in states in synchronous Hebbian neural networks

Metz,

Theumann

2008

Preprint

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The full dynamics of a synchronous recurrent neural network model with Ising binary units and a Hebbian learning rule with a finite self-interaction is studied in order to determine the stability to synaptic and stochastic noise of frozen-in states that appear in the absence of both kinds of noise. Both, the numerical simulation procedure of Eissfeller and Opper and a new alternative procedure that allows to follow the dynamics over larger time scales have been used in this work. It is shown that synaptic noise destabilizes the frozen-in states and yields either retrieval or paramagnetic states for not too large stochastic noise. The indications are that the same results may follow in the absence of synaptic noise, for low stochastic noise.

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The Blume-Emery-Griffiths neural network with synchronous updating and variable dilution

Cited by 10 publications

References 24 publications

Stationary states of a spherical Minority Game with ergodicity breaking

Stationary states of a spherical Minority Game with ergodicity breaking

Impact of the updating scheme on stationary states of networks

Instability of frozen-in states in synchronous Hebbian neural networks

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