85 research outputs found
Comment on "Consistency, amplitudes, and probabilities in quantum theory"
In a recent article [Phys. Rev. A 57, 1572 (1998)] Caticha has concluded that
``nonlinear variants of quantum mechanics are inconsistent.'' In this note we
identify what it is that nonlinear quantum theories have been shown to be
inconsistent with.Comment: LaTeX, 5 pages, no figure
Opinion Dynamics of Learning Agents: Does Seeking Consensus Lead to Disagreement?
We study opinion dynamics in a population of interacting adaptive agents
voting on a set of complex multidimensional issues. We consider agents which
can classify issues into for or against. The agents arrive at the opinions
about each issue in question using an adaptive algorithm. Adaptation comes from
learning and the information for the learning process comes from interacting
with other neighboring agents and trying to change the internal state in order
to concur with their opinions. The change in the internal state is driven by
the information contained in the issue and in the opinion of the other agent.
We present results in a simple yet rich context where each agent uses a Boolean
Perceptron to state its opinion. If there is no internal clock, so the update
occurs with asynchronously exchanged information among pairs of agents, then
the typical case, if the number of issues is kept small, is the evolution into
a society thorn by the emergence of factions with extreme opposite beliefs.
This occurs even when seeking consensus with agents with opposite opinions. The
curious result is that it is learning from those that hold the same opinions
that drives the emergence of factions. This results follows from the fact that
factions are prevented by not learning at all from those agents that hold the
same opinion. If the number of issues is large, the dynamics becomes trapped
and the society does not evolve into factions and a distribution of moderate
opinions is observed. We also study the less realistic, but technically simpler
synchronous case showing that global consensus is a fixed point. However, the
approach to this consensus is glassy in the limit of large societies if agents
adapt even in the case of agreement.Comment: 16 pages, 10 figures, revised versio
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
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
Maximum Entropy and Bayesian Data Analysis: Entropic Priors
The problem of assigning probability distributions which objectively reflect
the prior information available about experiments is one of the major stumbling
blocks in the use of Bayesian methods of data analysis. In this paper the
method of Maximum (relative) Entropy (ME) is used to translate the information
contained in the known form of the likelihood into a prior distribution for
Bayesian inference. The argument is inspired and guided by intuition gained
from the successful use of ME methods in statistical mechanics. For experiments
that cannot be repeated the resulting "entropic prior" is formally identical
with the Einstein fluctuation formula. For repeatable experiments, however, the
expected value of the entropy of the likelihood turns out to be relevant
information that must be included in the analysis. The important case of a
Gaussian likelihood is treated in detail.Comment: 23 pages, 2 figure
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
Entropy Distance: New Quantum Phenomena
We study a curve of Gibbsian families of complex 3x3-matrices and point out
new features, absent in commutative finite-dimensional algebras: a
discontinuous maximum-entropy inference, a discontinuous entropy distance and
non-exposed faces of the mean value set. We analyze these problems from various
aspects including convex geometry, topology and information geometry. This
research is motivated by a theory of info-max principles, where we contribute
by computing first order optimality conditions of the entropy distance.Comment: 34 pages, 5 figure
The XY Spin-Glass with Slow Dynamic Couplings
We investigate an XY spin-glass model in which both spins and couplings
evolve in time: the spins change rapidly according to Glauber-type rules,
whereas the couplings evolve slowly with a dynamics involving spin correlations
and Gaussian disorder. For large times the model can be solved using replica
theory. In contrast to the XY-model with static disordered couplings, solving
the present model requires two levels of replicas, one for the spins and one
for the couplings. Relevant order parameters are defined and a phase diagram is
obtained upon making the replica-symmetric Ansatz. The system exhibits two
different spin-glass phases, with distinct de Almeida-Thouless lines, marking
continuous replica-symmetry breaking: one describing freezing of the spins
only, and one describing freezing of both spins and couplings.Comment: 7 pages, Latex, 3 eps figure
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