505 research outputs found
Neural Distributed Autoassociative Memories: A Survey
Introduction. Neural network models of autoassociative, distributed memory
allow storage and retrieval of many items (vectors) where the number of stored
items can exceed the vector dimension (the number of neurons in the network).
This opens the possibility of a sublinear time search (in the number of stored
items) for approximate nearest neighbors among vectors of high dimension. The
purpose of this paper is to review models of autoassociative, distributed
memory that can be naturally implemented by neural networks (mainly with local
learning rules and iterative dynamics based on information locally available to
neurons). Scope. The survey is focused mainly on the networks of Hopfield,
Willshaw and Potts, that have connections between pairs of neurons and operate
on sparse binary vectors. We discuss not only autoassociative memory, but also
the generalization properties of these networks. We also consider neural
networks with higher-order connections and networks with a bipartite graph
structure for non-binary data with linear constraints. Conclusions. In
conclusion we discuss the relations to similarity search, advantages and
drawbacks of these techniques, and topics for further research. An interesting
and still not completely resolved question is whether neural autoassociative
memories can search for approximate nearest neighbors faster than other index
structures for similarity search, in particular for the case of very high
dimensional vectors.Comment: 31 page
Transient dynamics for sequence processing neural networks
An exact solution of the transient dynamics for a sequential associative
memory model is discussed through both the path-integral method and the
statistical neurodynamics. Although the path-integral method has the ability to
give an exact solution of the transient dynamics, only stationary properties
have been discussed for the sequential associative memory. We have succeeded in
deriving an exact macroscopic description of the transient dynamics by
analyzing the correlation of crosstalk noise. Surprisingly, the order parameter
equations of this exact solution are completely equivalent to those of the
statistical neurodynamics, which is an approximation theory that assumes
crosstalk noise to obey the Gaussian distribution. In order to examine our
theoretical findings, we numerically obtain cumulants of the crosstalk noise.
We verify that the third- and fourth-order cumulants are equal to zero, and
that the crosstalk noise is normally distributed even in the non-retrieval
case. We show that the results obtained by our theory agree with those obtained
by computer simulations. We have also found that the macroscopic unstable state
completely coincides with the separatrix.Comment: 21 pages, 4 figure
An associative network with spatially organized connectivity
We investigate the properties of an autoassociative network of
threshold-linear units whose synaptic connectivity is spatially structured and
asymmetric. Since the methods of equilibrium statistical mechanics cannot be
applied to such a network due to the lack of a Hamiltonian, we approach the
problem through a signal-to-noise analysis, that we adapt to spatially
organized networks. The conditions are analyzed for the appearance of stable,
spatially non-uniform profiles of activity with large overlaps with one of the
stored patterns. It is also shown, with simulations and analytic results, that
the storage capacity does not decrease much when the connectivity of the
network becomes short range. In addition, the method used here enables us to
calculate exactly the storage capacity of a randomly connected network with
arbitrary degree of dilution.Comment: 27 pages, 6 figures; Accepted for publication in JSTA
Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines
In the past three decades, many theoretical measures of complexity have been
proposed to help understand complex systems. In this work, for the first time,
we place these measures on a level playing field, to explore the qualitative
similarities and differences between them, and their shortcomings.
Specifically, using the Boltzmann machine architecture (a fully connected
recurrent neural network) with uniformly distributed weights as our model of
study, we numerically measure how complexity changes as a function of network
dynamics and network parameters. We apply an extension of one such
information-theoretic measure of complexity to understand incremental Hebbian
learning in Hopfield networks, a fully recurrent architecture model of
autoassociative memory. In the course of Hebbian learning, the total
information flow reflects a natural upward trend in complexity as the network
attempts to learn more and more patterns.Comment: 16 pages, 7 figures; Appears in Entropy, Special Issue "Information
Geometry II
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
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