2 research outputs found
The Blume-Emery-Griffiths neural network: dynamics for arbitrary temperature
The parallel dynamics of the fully connected Blume-Emery-Griffiths neural
network model is studied for arbitrary temperature. By employing a
probabilistic signal-to-noise approach, a recursive scheme is found determining
the time evolution of the distribution of the local fields and, hence, the
evolution of the order parameters. A comparison of this approach is made with
the generating functional method, allowing to calculate any physical relevant
quantity as a function of time. Explicit analytic formula are given in both
methods for the first few time steps of the dynamics. Up to the third time step
the results are identical. Some arguments are presented why beyond the third
time step the results differ for certain values of the model parameters.
Furthermore, fixed-point equations are derived in the stationary limit.
Numerical simulations confirm our theoretical findings.Comment: 26 pages in Latex, 8 eps figure
Parallel dynamics of the fully connected Blume-Emery-Griffiths neural network
The parallel dynamics of the fully connected Blume-Emery-Griffiths neural
network model is studied at zero temperature for arbitrary using a
probabilistic approach. A recursive scheme is found determining the complete
time evolution of the order parameters, taking into account all feedback
correlations. It is based upon the evolution of the distribution of the local
field, the structure of which is determined in detail. As an illustrative
example, explicit analytic formula are given for the first few time steps of
the dynamics. Furthermore, equilibrium fixed-point equations are derived and
compared with the thermodynamic approach. The analytic results find excellent
confirmation in extensive numerical simulations.Comment: 22 pages, 12 figure