Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Non-Binary Associative Memory with Exponential Pattern Retrieval
  Capacity and Iterative Learning: Extended Results   We consider the problem of neural association for a network of non-binary
neurons. Here, the task is to first memorize a set of patterns using a network
of neurons whose states assume values from a finite number of integer levels.
Later, the same network should be able to recall previously memorized patterns
from their noisy versions. Prior work in this area consider storing a finite
number of purely random patterns, and have shown that the pattern retrieval
capacities (maximum number of patterns that can be memorized) scale only
linearly with the number of neurons in the network.
  In our formulation of the problem, we concentrate on exploiting redundancy
and internal structure of the patterns in order to improve the pattern
retrieval capacity. Our first result shows that if the given patterns have a
suitable linear-algebraic structure, i.e. comprise a sub-space of the set of
all possible patterns, then the pattern retrieval capacity is in fact
exponential in terms of the number of neurons. The second result extends the
previous finding to cases where the patterns have weak minor components, i.e.
the smallest eigenvalues of the correlation matrix tend toward zero. We will
use these minor components (or the basis vectors of the pattern null space) to
both increase the pattern retrieval capacity and error correction capabilities.
  An iterative algorithm is proposed for the learning phase, and two simple
neural update algorithms are presented for the recall phase. Using analytical
results and simulations, we show that the proposed methods can tolerate a fair
amount of errors in the input while being able to memorize an exponentially
large number of patterns.

16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess