8,121 research outputs found
Maximum Likelihood Associative Memories
Associative memories are structures that store data in such a way that it can
later be retrieved given only a part of its content -- a sort-of
error/erasure-resilience property. They are used in applications ranging from
caches and memory management in CPUs to database engines. In this work we study
associative memories built on the maximum likelihood principle. We derive
minimum residual error rates when the data stored comes from a uniform binary
source. Second, we determine the minimum amount of memory required to store the
same data. Finally, we bound the computational complexity for message
retrieval. We then compare these bounds with two existing associative memory
architectures: the celebrated Hopfield neural networks and a neural network
architecture introduced more recently by Gripon and Berrou
Comment on "Probabilistic Quantum Memories"
This is a comment on two wrong Phys. Rev. Letters papers by C.A.
Trugenberger. Trugenberger claimed that quantum registers could be used as
exponentially large "associative" memories. We show that his scheme is no
better than one where the quantum register is replaced with a classical one of
equal size.
We also point out that the Holevo bound and more recent bounds on "quantum
random access codes" pretty much rule out powerful memories (for classical
information) based on quantum states.Comment: REVTeX4, 1 page, published versio
A Comparative Study of Sparse Associative Memories
We study various models of associative memories with sparse information, i.e.
a pattern to be stored is a random string of s and s with about
s, only. We compare different synaptic weights, architectures and retrieval
mechanisms to shed light on the influence of the various parameters on the
storage capacity.Comment: 28 pages, 2 figure
Adiabatic Quantum Optimization for Associative Memory Recall
Hopfield networks are a variant of associative memory that recall information
stored in the couplings of an Ising model. Stored memories are fixed points for
the network dynamics that correspond to energetic minima of the spin state. We
formulate the recall of memories stored in a Hopfield network using energy
minimization by adiabatic quantum optimization (AQO). Numerical simulations of
the quantum dynamics allow us to quantify the AQO recall accuracy with respect
to the number of stored memories and the noise in the input key. We also
investigate AQO performance with respect to how memories are stored in the
Ising model using different learning rules. Our results indicate that AQO
performance varies strongly with learning rule due to the changes in the energy
landscape. Consequently, learning rules offer indirect methods for
investigating change to the computational complexity of the recall task and the
computational efficiency of AQO.Comment: 22 pages, 11 figures. Updated for clarity and figures, to appear in
Frontiers of Physic
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
The sparse Blume-Emery-Griffiths model of associative memories
We analyze the Blume-Emery-Griffiths (BEG) associative memory with sparse
patterns and at zero temperature. We give bounds on its storage capacity
provided that we want the stored patterns to be fixed points of the retrieval
dynamics. We compare our results to that of other models of sparse neural
networks and show that the BEG model has a superior performance compared to
them.Comment: 23 p
Harmonic analysis of neural networks
Neural networks models have attracted a lot of
interest in recent years mainly because there
were perceived as a new idea for computing.
These models can be described as a network in
which every node computes a linear threshold
function. One of the main difficulties in analyzing
the properties of these networks is the fact
that they consist of nonlinear elements. I will
present a novel approach, based on harmonic
analysis of Boolean functions, to analyze neural
networks. In particular I will show how this
technique can be applied to answer the following
two fundamental questions (i) what is the computational
power of a polynomial threshold element
with respect to linear threshold elements?
(ii) Is it possible to get exponentially many spurious
memories when we use the outer-product
method for programming the Hopfield model
Storage capacity of holographic associative memories
The storage capacity of holographic associative memories is estimated. An argument based on the available degrees of freedom shows that the number of patterns that can be stored is limited by the space-bandwidth product of the hologram divided by the number of pixels in each pattern. A statistical calculation shows that if we attempt to store associations by multiply exposing the hologram, the cross talk among the stored items severely degrades the output fidelity. This confirms the storage capacity predicted by the degrees-of-freedom argument
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