1,194 research outputs found
On-Line Learning Theory of Soft Committee Machines with Correlated Hidden Units - Steepest Gradient Descent and Natural Gradient Descent -
The permutation symmetry of the hidden units in multilayer perceptrons causes
the saddle structure and plateaus of the learning dynamics in gradient learning
methods. The correlation of the weight vectors of hidden units in a teacher
network is thought to affect this saddle structure, resulting in a prolonged
learning time, but this mechanism is still unclear. In this paper, we discuss
it with regard to soft committee machines and on-line learning using
statistical mechanics. Conventional gradient descent needs more time to break
the symmetry as the correlation of the teacher weight vectors rises. On the
other hand, no plateaus occur with natural gradient descent regardless of the
correlation for the limit of a low learning rate. Analytical results support
these dynamics around the saddle point.Comment: 7 pages, 6 figure
A Neural Network model with Bidirectional Whitening
We present here a new model and algorithm which performs an efficient Natural
gradient descent for Multilayer Perceptrons. Natural gradient descent was
originally proposed from a point of view of information geometry, and it
performs the steepest descent updates on manifolds in a Riemannian space. In
particular, we extend an approach taken by the "Whitened neural networks"
model. We make the whitening process not only in feed-forward direction as in
the original model, but also in the back-propagation phase. Its efficacy is
shown by an application of this "Bidirectional whitened neural networks" model
to a handwritten character recognition data (MNIST data).Comment: 16page
Fluctuation Theorems on Nishimori Line
The distribution of the performed work for spin glasses with gauge symmetry
is considered. With the aid of the gauge symmetry, which leads to the
exact/rigorous results in spin glasses, we find a fascinating relation of the
performed work as the fluctuation theorem. The integral form of the resultant
relation reproduces the Jarzynski-type equation for spin glasses we have
obtained. We show that similar relations can be established not only for the
distribution of the performed work but also that of the free energy of spin
glasses with gauge symmetry, which provides another interpretation of the phase
transition in spin glasses.Comment: 10 pages, and 1 figur
Parametric Fokker-Planck equation
We derive the Fokker-Planck equation on the parametric space. It is the
Wasserstein gradient flow of relative entropy on the statistical manifold. We
pull back the PDE to a finite dimensional ODE on parameter space. Some
analytical example and numerical examples are presented
Bifurcation analysis in an associative memory model
We previously reported the chaos induced by the frustration of interaction in
a non-monotonic sequential associative memory model, and showed the chaotic
behaviors at absolute zero. We have now analyzed bifurcation in a stochastic
system, namely a finite-temperature model of the non-monotonic sequential
associative memory model. We derived order-parameter equations from the
stochastic microscopic equations. Two-parameter bifurcation diagrams obtained
from those equations show the coexistence of attractors, which do not appear at
absolute zero, and the disappearance of chaos due to the temperature effect.Comment: 19 page
Field Theoretical Analysis of On-line Learning of Probability Distributions
On-line learning of probability distributions is analyzed from the field
theoretical point of view. We can obtain an optimal on-line learning algorithm,
since renormalization group enables us to control the number of degrees of
freedom of a system according to the number of examples. We do not learn
parameters of a model, but probability distributions themselves. Therefore, the
algorithm requires no a priori knowledge of a model.Comment: 4 pages, 1 figure, RevTe
The core structure of presolar graphite onions
Of the ``presolar particles'' extracted from carbonaceous chondrite
dissolution residues, i.e. of those particles which show isotopic evidence of
solidification in the neighborhood of other stars prior to the origin of our
solar system, one subset has an interesting concentric
graphite-rim/graphene-core structure. We show here that single graphene sheet
defects in the onion cores (e.g. cyclopentane loops) may be observable edge-on
by HREM. This could allow a closer look at models for their formation, and in
particular strengthen the possibility that growth of these assemblages proceeds
atom-by-atom with the aid of such in-plane defects, under conditions of growth
(e.g. radiation fluxes or grain temperature) which discourage the graphite
layering that dominates subsequent formation of the rim.Comment: 4 pages, 7 figures, 11 refs, see also
http://www.umsl.edu/~fraundor/isocore.htm
Nonparametric Information Geometry
The differential-geometric structure of the set of positive densities on a
given measure space has raised the interest of many mathematicians after the
discovery by C.R. Rao of the geometric meaning of the Fisher information. Most
of the research is focused on parametric statistical models. In series of
papers by author and coworkers a particular version of the nonparametric case
has been discussed. It consists of a minimalistic structure modeled according
the theory of exponential families: given a reference density other densities
are represented by the centered log likelihood which is an element of an Orlicz
space. This mappings give a system of charts of a Banach manifold. It has been
observed that, while the construction is natural, the practical applicability
is limited by the technical difficulty to deal with such a class of Banach
spaces. It has been suggested recently to replace the exponential function with
other functions with similar behavior but polynomial growth at infinity in
order to obtain more tractable Banach spaces, e.g. Hilbert spaces. We give
first a review of our theory with special emphasis on the specific issues of
the infinite dimensional setting. In a second part we discuss two specific
topics, differential equations and the metric connection. The position of this
line of research with respect to other approaches is briefly discussed.Comment: Submitted for publication in the Proceedings od GSI2013 Aug 28-30
2013 Pari
The volume of Gaussian states by information geometry
We formulate the problem of determining the volume of the set of Gaussian
physical states in the framework of information geometry. That is, by
considering phase space probability distributions parametrized by the
covariances and supplying this resulting statistical manifold with the
Fisher-Rao metric. We then evaluate the volume of classical, quantum and
quantum entangled states for two-mode systems showing chains of strict
inclusion
Recommended from our members
Selective deposition of silver and copper films by condensation coefficient modulation
Whilst copper and silver are the conductors of choice for myriad current and emerging applications, patterning these metals is a slow and costly process. We report the remarkable finding that an extremely thin (âź10 nm) printed layer of specific organofluorine compounds enables selective deposition of copper and silver vapour, with metal condensing only where the organofluorine layer is not. This unconventional approach is fast, inexpensive, avoids metal waste and the use of harmful chemical etchants, and leaves the metal surface uncontaminated. We have used this approach to fabricate thin films of these metals with 6 million apertures cmâ2 and grids of âź1 Îźm lines, through to 10 cm diameter apertures. We have also fabricated semi-transparent organic solar cells in which the top silver electrode is patterned with a dense array of 2 Îźm diameter apertures, which cannot be achieved by any other scalable means directly on an organic electronic device
- âŚ