3,849 research outputs found
Noisy regression and classification with continuous multilayer networks
We investigate zero temperature Gibbs learning for two classes of
unrealizable rules which play an important role in practical applications of
multilayer neural networks with differentiable activation functions:
classification problems and noisy regression problems. Considering one step of
replica symmetry breaking, we surprisingly find that for sufficiently large
training sets the stable state is replica symmetric even though the target rule
is unrealizable. Further, the classification problem is shown to be formally
equivalent to the noisy regression problem.Comment: 7 pages, including 2 figure
Field-free two-direction alignment alternation of linear molecules by elliptic laser pulses
We show that a linear molecule subjected to a short specific elliptically
polarized laser field yields postpulse revivals exhibiting alignment
alternatively located along the orthogonal axis and the major axis of the
ellipse. The effect is experimentally demonstrated by measuring the optical
Kerr effect along two different axes. The conditions ensuring an optimal
field-free alternation of high alignments along both directions are derived.Comment: 5 pages, 4 color figure
Ionisation by quantised electromagnetic fields: The photoelectric effect
In this paper we explain the photoelectric effect in a variant of the
standard model of non relativistic quantum electrodynamics, which is in some
aspects more closely related to the physical picture, than the one studied in
[BKZ]: Now we can apply our results to an electron with more than one bound
state and to a larger class of electron-photon interactions. We will specify a
situation, where ionisation probability in second order is a weighted sum of
single photon terms. Furthermore we will see, that Einstein's equality
for the maximal kinetic energy of
the electron, energy of the photon and ionisation gap
is the crucial condition for these single photon terms to be nonzero.Comment: 59 pages, LATEX2
Asymptotic Level Density of the Elastic Net Self-Organizing Feature Map
Whileas the Kohonen Self Organizing Map shows an asymptotic level density
following a power law with a magnification exponent 2/3, it would be desired to
have an exponent 1 in order to provide optimal mapping in the sense of
information theory. In this paper, we study analytically and numerically the
magnification behaviour of the Elastic Net algorithm as a model for
self-organizing feature maps. In contrast to the Kohonen map the Elastic Net
shows no power law, but for onedimensional maps nevertheless the density
follows an universal magnification law, i.e. depends on the local stimulus
density only and is independent on position and decouples from the stimulus
density at other positions.Comment: 8 pages, 10 figures. Link to publisher under
http://link.springer.de/link/service/series/0558/bibs/2415/24150939.ht
Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation
We calculate exactly both the microcanonical and canonical thermodynamic
functions (TDFs) for a one-dimensional model system with piecewise constant
Lennard-Jones type pair interactions. In the case of an isolated -particle
system, the microcanonical TDFs exhibit (N-1) singular (non-analytic)
microscopic phase transitions of the formal order N/2, separating N
energetically different evaporation (dissociation) states. In a suitably
designed evaporation experiment, these types of phase transitions should
manifest themselves in the form of pressure and temperature oscillations,
indicating cooling by evaporation. In the presence of a heat bath (thermostat),
such oscillations are absent, but the canonical heat capacity shows a
characteristic peak, indicating the temperature-induced dissociation of the
one-dimensional chain. The distribution of complex zeros (DOZ) of the canonical
partition may be used to identify different degrees of dissociation in the
canonical ensemble.Comment: version accepted for publication in PRE, minor additions in the text,
references adde
Collision of One-Dimensional Nonlinear Chains
We investigate one-dimensional collisions of unharmonic chains and a rigid
wall. We find that the coefficient of restitution (COR) is strongly dependent
on the velocity of colliding chains and has a minimum value at a certain
velocity. The relationship between COR and collision velocity is derived for
low-velocity collisions using perturbation methods. We found that the velocity
dependence is characterized by the exponent of the lowest unharmonic term of
interparticle potential energy
Scaling properties of granular materials
Given an assembly of viscoelastic spheres with certain material properties,
we raise the question how the macroscopic properties of the assembly will
change if all lengths of the system, i.e. radii, container size etc., are
scaled by a constant. The result leads to a method to scale down experiments to
lab-size.Comment: 4 pages, 2 figure
Phase transitions in soft-committee machines
Equilibrium statistical physics is applied to layered neural networks with
differentiable activation functions. A first analysis of off-line learning in
soft-committee machines with a finite number (K) of hidden units learning a
perfectly matching rule is performed. Our results are exact in the limit of
high training temperatures. For K=2 we find a second order phase transition
from unspecialized to specialized student configurations at a critical size P
of the training set, whereas for K > 2 the transition is first order. Monte
Carlo simulations indicate that our results are also valid for moderately low
temperatures qualitatively. The limit K to infinity can be performed
analytically, the transition occurs after presenting on the order of N K
examples. However, an unspecialized metastable state persists up to P= O (N
K^2).Comment: 8 pages, 4 figure
Statistical mechanics of mutual information maximization
An unsupervised learning procedure based on maximizing the mutual information between the outputs of two networks receiving different but statistically dependent inputs is analyzed (Becker S. and Hinton G., Nature, 355 (1992) 161). By exploiting a formal analogy to supervised learning in parity machines, the theory of zero-temperature Gibbs learning for the unsupervised procedure is presented for the case that the networks are perceptrons and for the case of fully connected committees
Microcanonical quantum fluctuation theorems
Previously derived expressions for the characteristic function of work
performed on a quantum system by a classical external force are generalized to
arbitrary initial states of the considered system and to Hamiltonians with
degenerate spectra. In the particular case of microcanonical initial states
explicit expressions for the characteristic function and the corresponding
probability density of work are formulated. Their classical limit as well as
their relations to the respective canonical expressions are discussed. A
fluctuation theorem is derived that expresses the ratio of probabilities of
work for a process and its time reversal to the ratio of densities of states of
the microcanonical equilibrium systems with corresponding initial and final
Hamiltonians.From this Crooks-type fluctuation theorem a relation between
entropies of different systems can be derived which does not involve the time
reversed process. This entropy-from-work theorem provides an experimentally
accessible way to measure entropies.Comment: revised and extended versio
- âŠ