114 research outputs found
Disappearance of Spurious States in Analog Associative Memories
We show that symmetric n-mixture states, when they exist, are almost never
stable in autoassociative networks with threshold-linear units. Only with a
binary coding scheme we could find a limited region of the parameter space in
which either 2-mixtures or 3-mixtures are stable attractors of the dynamics.Comment: 5 pages, 3 figures, accepted for publication in Phys Rev
Localized activity profiles and storage capacity of rate-based autoassociative networks
We study analytically the effect of metrically structured connectivity on the
behavior of autoassociative networks. We focus on three simple rate-based model
neurons: threshold-linear, binary or smoothly saturating units. For a
connectivity which is short range enough the threshold-linear network shows
localized retrieval states. The saturating and binary models also exhibit
spatially modulated retrieval states if the highest activity level that they
can achieve is above the maximum activity of the units in the stored patterns.
In the zero quenched noise limit, we derive an analytical formula for the
critical value of the connectivity width below which one observes spatially
non-uniform retrieval states. Localization reduces storage capacity, but only
by a factor of 2~3. The approach that we present here is generic in the sense
that there are no specific assumptions on the single unit input-output function
nor on the exact connectivity structure.Comment: 4 pages, 4 figure
Mean Field Theory For Non-Equilibrium Network Reconstruction
There has been recent progress on the problem of inferring the structure of
interactions in complex networks when they are in stationary states satisfying
detailed balance, but little has been done for non-equilibrium systems. Here we
introduce an approach to this problem, considering, as an example, the question
of recovering the interactions in an asymmetrically-coupled,
synchronously-updated Sherrington-Kirkpatrick model. We derive an exact
iterative inversion algorithm and develop efficient approximations based on
dynamical mean-field and Thouless-Anderson-Palmer equations that express the
interactions in terms of equal-time and one time step-delayed correlation
functions.Comment: new version, accepted in PRL. For the Supp. Mat. (ref. 11), please
contact the author
Dynamics and Performance of Susceptibility Propagation on Synthetic Data
We study the performance and convergence properties of the Susceptibility
Propagation (SusP) algorithm for solving the Inverse Ising problem. We first
study how the temperature parameter (T) in a Sherrington-Kirkpatrick model
generating the data influences the performance and convergence of the
algorithm. We find that at the high temperature regime (T>4), the algorithm
performs well and its quality is only limited by the quality of the supplied
data. In the low temperature regime (T<4), we find that the algorithm typically
does not converge, yielding diverging values for the couplings. However, we
show that by stopping the algorithm at the right time before divergence becomes
serious, good reconstruction can be achieved down to T~2. We then show that
dense connectivity, loopiness of the connectivity, and high absolute
magnetization all have deteriorating effects on the performance of the
algorithm. When absolute magnetization is high, we show that other methods can
be work better than SusP. Finally, we show that for neural data with high
absolute magnetization, SusP performs less well than TAP inversion.Comment: 9 pages, 7 figure
Ising Models for Inferring Network Structure From Spike Data
Now that spike trains from many neurons can be recorded simultaneously, there
is a need for methods to decode these data to learn about the networks that
these neurons are part of. One approach to this problem is to adjust the
parameters of a simple model network to make its spike trains resemble the data
as much as possible. The connections in the model network can then give us an
idea of how the real neurons that generated the data are connected and how they
influence each other. In this chapter we describe how to do this for the
simplest kind of model: an Ising network. We derive algorithms for finding the
best model connection strengths for fitting a given data set, as well as faster
approximate algorithms based on mean field theory. We test the performance of
these algorithms on data from model networks and experiments.Comment: To appear in "Principles of Neural Coding", edited by Stefano Panzeri
and Rodrigo Quian Quirog
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