824 research outputs found
Online Learning with Ensembles
Supervised online learning with an ensemble of students randomized by the
choice of initial conditions is analyzed. For the case of the perceptron
learning rule, asymptotically the same improvement in the generalization error
of the ensemble compared to the performance of a single student is found as in
Gibbs learning. For more optimized learning rules, however, using an ensemble
yields no improvement. This is explained by showing that for any learning rule
a transform exists, such that a single student using
has the same generalization behaviour as an ensemble of
-students.Comment: 8 pages, 1 figure. Submitted to J.Phys.
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
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.
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
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
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
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
(S)-3-Dimethylamino-2-{(4S,5R)-5-[(R)-2,2-dimethyl-1,3-dioxolan-4-yl]-2,2-dimethyl-1,3-dioxolan-4-yl}-2-hydroxypropanoic acid
The Kiliani reaction on 1-deoxy-(N,N-dimethylamino)-d-fructose, itself readily available from reaction of dimethylamine and d-glucose, proceeded to give access to the title β-sugar amino acid, C15H27NO7. X-ray crystallography determined the stereochemistry at the newly formed chiral center. There are two molecules in the asymmetric unit; they are related by a pseudo-twofold rotation axis and have very similar geometries, differing only in the conformation of one of the acetonide rings. All the acetonide rings adopt envelope conformations; the flap atom is oxygen in three of the rings, but carbon in one of them. There are two strong hydrogen bonds between the two independent molecules, and further weak hydrogen bonds link the molecules to form infinite chains running parallel to the a axis
Statistical Mechanics of Support Vector Networks
Using methods of Statistical Physics, we investigate the generalization
performance of support vector machines (SVMs), which have been recently
introduced as a general alternative to neural networks. For nonlinear
classification rules, the generalization error saturates on a plateau, when the
number of examples is too small to properly estimate the coefficients of the
nonlinear part. When trained on simple rules, we find that SVMs overfit only
weakly. The performance of SVMs is strongly enhanced, when the distribution of
the inputs has a gap in feature space.Comment: REVTeX, 4 pages, 2 figures, accepted by Phys. Rev. Lett (typos
corrected
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