29 research outputs found
A perturbative approach to non-linearities in the information carried by a two layer neural network
We evaluate the mutual information between the input and the output of a two
layer network in the case of a noisy and non-linear analogue channel. In the
case where the non-linearity is small with respect to the variability in the
noise, we derive an exact expression for the contribution to the mutual
information given by the non-linear term in first order of perturbation theory.
Finally we show how the calculation can be simplified by means of a
diagrammatic expansion. Our results suggest that the use of perturbation
theories applied to neural systems might give an insight on the contribution of
non-linearities to the information transmission and in general to the neuronal
dynamics.Comment: Accepted as a preprint of ICTP, Triest
Time evolution of the extremely diluted Blume-Emery-Griffiths neural network
The time evolution of the extremely diluted Blume-Emery-Griffiths neural
network model is studied, and a detailed equilibrium phase diagram is obtained
exhibiting pattern retrieval, fluctuation retrieval and self-sustained activity
phases. It is shown that saddle-point solutions associated with fluctuation
overlaps slow down considerably the flow of the network states towards the
retrieval fixed points. A comparison of the performance with other three-state
networks is also presented.Comment: 8 pages, 5 figure
Statistical mechanics of the multi-constraint continuous knapsack problem
We apply the replica analysis established by Gardner to the multi-constraint
continuous knapsack problem,which is one of the linear programming problems and
a most fundamental problem in the field of operations research (OR). For a
large problem size, we analyse the space of solution and its volume, and
estimate the optimal number of items to go into the knapsack as a function of
the number of constraints. We study the stability of the replica symmetric (RS)
solution and find that the RS calculation cannot estimate the optimal number of
items in knapsack correctly if many constraints are required.In order to obtain
a consistent solution in the RS region,we try the zero entropy approximation
for this continuous solution space and get a stable solution within the RS
ansatz.On the other hand, in replica symmetry breaking (RSB) region, the one
step RSB solution is found by Parisi's scheme. It turns out that this problem
is closely related to the problem of optimal storage capacity and of
generalization by maximum stability rule of a spherical perceptron.Comment: Latex 13 pages using IOP style file, 5 figure
Bump formation in a binary attractor neural network
This paper investigates the conditions for the formation of local bumps in
the activity of binary attractor neural networks with spatially dependent
connectivity. We show that these formations are observed when asymmetry between
the activity during the retrieval and learning is imposed. Analytical
approximation for the order parameters is derived. The corresponding phase
diagram shows a relatively large and stable region, where this effect is
observed, although the critical storage and the information capacities
drastically decrease inside that region. We demonstrate that the stability of
the network, when starting from the bump formation, is larger than the
stability when starting even from the whole pattern. Finally, we show a very
good agreement between the analytical results and the simulations performed for
different topologies of the network.Comment: about 14 page
The mutual information of a stochastic binary channel: validity of the Replica Symmetry Ansatz
We calculate the mutual information (MI) of a two-layered neural network with
noiseless, continuous inputs and binary, stochastic outputs under several
assumptions on the synaptic efficiencies. The interesting regime corresponds to
the limit where the number of both input and output units is large but their
ratio is kept fixed at a value . We first present a solution for the MI
using the replica technique with a replica symmetric (RS) ansatz. Then we find
an exact solution for this quantity valid in a neighborhood of . An
analysis of this solution shows that the system must have a phase transition at
some finite value of . This transition shows a singularity in the third
derivative of the MI. As the RS solution turns out to be infinitely
differentiable, it could be regarded as a smooth approximation to the MI. This
is checked numerically in the validity domain of the exact solution.Comment: Latex, 29 pages, 2 Encapsulated Post Script figures. To appear in
Journal of Physics
Power spectra of self-organized critical sandpiles
We analyze the power spectra of avalanches in two classes of self-organized
critical sandpile models, the Bak-Tang-Wiesenfeld model and the Manna model. We
show that these decay with a power law, where the exponent value
is significantly smaller than 2 and equals the scaling exponent
relating the avalanche size to its duration. We discuss the basic ingredients
behind this result, such as the scaling of the average avalanche shape.Comment: 7 pages, 3 figures, submitted to JSTA
System size resonance in an attractor neural network
We study the response of an attractor neural network, in the ferromagnetic
phase, to an external, time-dependent stimulus, which drives the system
periodically two different attractors. We demonstrate a non-trivial dependance
of the system via a system size resonance, by showing a signal amplification
maximum at a certain finite size.Comment: 7 pages, 9 figures, submitted to Europhys. Let
Explicit Renormalization Group for D=2 random bond Ising model with long-range correlated disorder
We investigate the explicit renormalization group for fermionic field
theoretic representation of two-dimensional random bond Ising model with
long-range correlated disorder. We show that a new fixed point appears by
introducing a long-range correlated disorder. Such as the one has been observed
in previous works for the bosonic () description. We have calculated
the correlation length exponent and the anomalous scaling dimension of
fermionic fields at this fixed point. Our results are in agreement with the
extended Harris criterion derived by Weinrib and Halperin.Comment: 5 page