137 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
On the equivalence of the Ashkin-Teller and the four-state Potts-glass models of neural networks
We show that for a particular choice of the coupling parameters the
Ashkin-Teller spin-glass neural network model with the Hebb learning rule and
one condensed pattern yields the same thermodynamic properties as the
four-state anisotropic Potts-glass neural network model. This equivalence is
not seen at the level of the Hamiltonians.Comment: 3 pages, revtex, additional arguments presente
A layered neural network with three-state neurons optimizing the mutual information
The time evolution of an exactly solvable layered feedforward neural network
with three-state neurons and optimizing the mutual information is studied for
arbitrary synaptic noise (temperature). Detailed stationary
temperature-capacity and capacity-activity phase diagrams are obtained. The
model exhibits pattern retrieval, pattern-fluctuation retrieval and spin-glass
phases. It is found that there is an improved performance in the form of both a
larger critical capacity and information content compared with three-state
Ising-type layered network models. Flow diagrams reveal that saddle-point
solutions associated with fluctuation overlaps slow down considerably the flow
of the network states towards the stable fixed-points.Comment: 17 pages Latex including 6 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
Synchronous versus sequential updating in the three-state Ising neural network with variable dilution
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. Capacity-temperature 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.Comment: 21 pages Latex, 12 eps figures and 1 ps figur
Optimal coloured perceptrons
Ashkin-Teller type perceptron models are introduced. Their maximal capacity
per number of couplings is calculated within a first-step
replica-symmetry-breaking Gardner approach. The results are compared with
extensive numerical simulations using several algorithms.Comment: 8 pages in Latex with 2 eps figures, RSB1 calculations has been adde
Mutual information and self-control of a fully-connected low-activity neural network
A self-control mechanism for the dynamics of a three-state fully-connected
neural network is studied through the introduction of a time-dependent
threshold. The self-adapting threshold is a function of both the neural and the
pattern activity in the network. The time evolution of the order parameters is
obtained on the basis of a recently developed dynamical recursive scheme. In
the limit of low activity the mutual information is shown to be the relevant
parameter in order to determine the retrieval quality. Due to self-control an
improvement of this mutual information content as well as an increase of the
storage capacity and an enlargement of the basins of attraction are found.
These results are compared with numerical simulations.Comment: 8 pages, 8 ps.figure
Correlated patterns in non-monotonic graded-response perceptrons
The optimal capacity of graded-response perceptrons storing biased and
spatially correlated patterns with non-monotonic input-output relations is
studied. It is shown that only the structure of the output patterns is
important for the overall performance of the perceptrons.Comment: 4 pages, 4 figure
An optimal Q-state neural network using mutual information
Starting from the mutual information we present a method in order to find a
hamiltonian for a fully connected neural network model with an arbitrary,
finite number of neuron states, Q. For small initial correlations between the
neurons and the patterns it leads to optimal retrieval performance. For binary
neurons, Q=2, and biased patterns we recover the Hopfield model. For
three-state neurons, Q=3, we find back the recently introduced
Blume-Emery-Griffiths network hamiltonian. We derive its phase diagram and
compare it with those of related three-state models. We find that the retrieval
region is the largest.Comment: 8 pages, 1 figur
Gardner optimal capacity of the diluted Blume-Emery-Griffiths neural network
The optimal capacity of a diluted Blume-Emery-Griffiths neural network is
studied as a function of the pattern activity and the embedding stability using
the Gardner entropy approach. Annealed dilution is considered, cutting some of
the couplings referring to the ternary patterns themselves and some of the
couplings related to the active patterns, both simultaneously (synchronous
dilution) or independently (asynchronous dilution). Through the de
Almeida-Thouless criterion it is found that the replica-symmetric solution is
locally unstable as soon as there is dilution. The distribution of the
couplings shows the typical gap with a width depending on the amount of
dilution, but this gap persists even in cases where a particular type of
coupling plays no role in the learning process.Comment: 9 pages Latex, 2 eps figure
- …