258 research outputs found
Learning a spin glass: determining Hamiltonians from metastable states
We study the problem of determining the Hamiltonian of a fully connected
Ising Spin Glass of units from a set of measurements, whose sizes needs to
be bits. The student-teacher scenario, used to study learning
in feed-forward neural networks, is here extended to spin systems with
arbitrary couplings. The set of measurements consists of data about the local
minima of the rugged energy landscape. We compare simulations and analytical
approximations for the resulting learning curves obtained by using different
algorithms.Comment: 5 pages, 1 figure, to appear in Physica
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.
Dynamical transitions in the evolution of learning algorithms by selection
We study the evolution of artificial learning systems by means of selection.
Genetic programming is used to generate a sequence of populations of algorithms
which can be used by neural networks for supervised learning of a rule that
generates examples. In opposition to concentrating on final results, which
would be the natural aim while designing good learning algorithms, we study the
evolution process and pay particular attention to the temporal order of
appearance of functional structures responsible for the improvements in the
learning process, as measured by the generalization capabilities of the
resulting algorithms. The effect of such appearances can be described as
dynamical phase transitions. The concepts of phenotypic and genotypic
entropies, which serve to describe the distribution of fitness in the
population and the distribution of symbols respectively, are used to monitor
the dynamics. In different runs the phase transitions might be present or not,
with the system finding out good solutions, or staying in poor regions of
algorithm space. Whenever phase transitions occur, the sequence of appearances
are the same. We identify combinations of variables and operators which are
useful in measuring experience or performance in rule extraction and can thus
implement useful annealing of the learning schedule.Comment: 11 pages, 11 figures, 2 table
Stability diagrams for bursting neurons modeled by three-variable maps
We study a simple map as a minimal model of excitable cells. The map has two
fast variables which mimic the behavior of class I neurons, undergoing a
sub-critical Hopf bifurcation. Adding a third slow variable allows the system
to present bursts and other interesting biological behaviors. Bifurcation lines
which locate the excitability region are obtained for different planes in
parameter space.Comment: 7 pages, 3 figures, accepted for publicatio
Gradient descent learning in and out of equilibrium
Relations between the off thermal equilibrium dynamical process of on-line
learning and the thermally equilibrated off-line learning are studied for
potential gradient descent learning. The approach of Opper to study on-line
Bayesian algorithms is extended to potential based or maximum likelihood
learning. We look at the on-line learning algorithm that best approximates the
off-line algorithm in the sense of least Kullback-Leibler information loss. It
works by updating the weights along the gradient of an effective potential
different from the parent off-line potential. The interpretation of this off
equilibrium dynamics holds some similarities to the cavity approach of
Griniasty. We are able to analyze networks with non-smooth transfer functions
and transfer the smoothness requirement to the potential.Comment: 08 pages, submitted to the Journal of Physics
Functional Optimisation of Online Algorithms in Multilayer Neural Networks
We study the online dynamics of learning in fully connected soft committee
machines in the student-teacher scenario. The locally optimal modulation
function, which determines the learning algorithm, is obtained from a
variational argument in such a manner as to maximise the average generalisation
error decay per example. Simulations results for the resulting algorithm are
presented for a few cases. The symmetric phase plateaux are found to be vastly
reduced in comparison to those found when online backpropagation algorithms are
used. A discussion of the implementation of these ideas as practical algorithms
is given
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