985 research outputs found
Thermodynamic properties of extremely diluted symmetric Q-Ising neural networks
Using the replica-symmetric mean-field theory approach the thermodynamic and
retrieval properties of extremely diluted {\it symmetric} -Ising neural
networks are studied. In particular, capacity-gain parameter and
capacity-temperature phase diagrams are derived for and .
The zero-temperature results are compared with those obtained from a study of
the dynamics of the model. Furthermore, the de Almeida-Thouless line is
determined. Where appropriate, the difference with other -Ising
architectures is outlined.Comment: 16 pages Latex including 6 eps-figures. Corrections, also in most of
the figures have been mad
On-Line AdaTron Learning of Unlearnable Rules
We study the on-line AdaTron learning of linearly non-separable rules by a
simple perceptron. Training examples are provided by a perceptron with a
non-monotonic transfer function which reduces to the usual monotonic relation
in a certain limit. We find that, although the on-line AdaTron learning is a
powerful algorithm for the learnable rule, it does not give the best possible
generalization error for unlearnable problems. Optimization of the learning
rate is shown to greatly improve the performance of the AdaTron algorithm,
leading to the best possible generalization error for a wide range of the
parameter which controls the shape of the transfer function.)Comment: RevTeX 17 pages, 8 figures, to appear in Phys.Rev.
Statistical Mechanics of Learning in the Presence of Outliers
Using methods of statistical mechanics, we analyse the effect of outliers on
the supervised learning of a classification problem. The learning strategy aims
at selecting informative examples and discarding outliers. We compare two
algorithms which perform the selection either in a soft or a hard way. When the
fraction of outliers grows large, the estimation errors undergo a first order
phase transition.Comment: 24 pages, 7 figures (minor extensions added
Effects of Water Stress on Seed Production in Ruzi Grass \u3ci\u3e(Brachiaria ruziziensis Germain and Everard)\u3c/i\u3e
Water stress at different stages of reproductive development influenced seed yield in Ruzi grass differently. Under mild water stress, the earlier in the reproductive developmental stage the stress was applied (before ear emergence) the faster the plants recovered and the less the ultimate damage to inflorescence structure and seed set compared with the situation where water stress occurred during the later stages after inflorescences had emerged. Conversely, severe water stress before ear emergence had a severe effect in damaging both inflorescence numbers and seed quality. Permanent damage to the reproductive structures resulted in deformed inflorescences. Moreover, basal vegetative tillers were stunted and were capable of only limited regrowth after re-watering
The Little-Hopfield model on a Random Graph
We study the Hopfield model on a random graph in scaling regimes where the
average number of connections per neuron is a finite number and where the spin
dynamics is governed by a synchronous execution of the microscopic update rule
(Little-Hopfield model).We solve this model within replica symmetry and by
using bifurcation analysis we prove that the spin-glass/paramagnetic and the
retrieval/paramagnetictransition lines of our phase diagram are identical to
those of sequential dynamics.The first-order retrieval/spin-glass transition
line follows by direct evaluation of our observables using population dynamics.
Within the accuracy of numerical precision and for sufficiently small values of
the connectivity parameter we find that this line coincides with the
corresponding sequential one. Comparison with simulation experiments shows
excellent agreement.Comment: 14 pages, 4 figure
Multi-Choice Minority Game
The generalization of the problem of adaptive competition, known as the
minority game, to the case of possible choices for each player is
addressed, and applied to a system of interacting perceptrons with input and
output units of the type of -states Potts-spins. An optimal solution of this
minority game as well as the dynamic evolution of the adaptive strategies of
the players are solved analytically for a general and compared with
numerical simulations.Comment: 5 pages, 2 figures, reorganized and clarifie
Fixed Points of Hopfield Type Neural Networks
The set of the fixed points of the Hopfield type network is under
investigation. The connection matrix of the network is constructed according to
the Hebb rule from the set of memorized patterns which are treated as distorted
copies of the standard-vector. It is found that the dependence of the set of
the fixed points on the value of the distortion parameter can be described
analytically. The obtained results are interpreted in the terms of neural
networks and the Ising model.Comment: RevTEX, 19 pages, 2 Postscript figures, the full version of the
earler brief report (cond-mat/9901251
A Hebbian approach to complex network generation
Through a redefinition of patterns in an Hopfield-like model, we introduce
and develop an approach to model discrete systems made up of many, interacting
components with inner degrees of freedom. Our approach clarifies the intrinsic
connection between the kind of interactions among components and the emergent
topology describing the system itself; also, it allows to effectively address
the statistical mechanics on the resulting networks. Indeed, a wide class of
analytically treatable, weighted random graphs with a tunable level of
correlation can be recovered and controlled. We especially focus on the case of
imitative couplings among components endowed with similar patterns (i.e.
attributes), which, as we show, naturally and without any a-priori assumption,
gives rise to small-world effects. We also solve the thermodynamics (at a
replica symmetric level) by extending the double stochastic stability
technique: free energy, self consistency relations and fluctuation analysis for
a picture of criticality are obtained
- âŠ