**7. Associative Neural
Memories**

**7.0 Introduction**

This chapter is concerned with associative learning
and retrieval of information (vector patterns) in neural-like
networks. These networks are usually referred to as associative
neural memories (or associative memories) and they represent one
of the most extensively analyzed class of artificial neural networks.
Various associative memory architectures are presented with emphasis
on dynamic (recurrent) associative memory architectures. These
memories are treated as nonlinear dynamical systems where information
retrieval is realized as an evolution of the system's state in
a high-dimensional state space. Dynamic associative memories
(DAM's) are a class of recurrent artificial neural networks which
utilize a learning/recording algorithm to store vector patterns
(usually binary patterns) as stable memory states. The retrieval
of these stored "memories" is accomplished by first
initializing the DAM with a noisy or partial input pattern (key)
and then allowing the DAM to perform a collective relaxation search
to arrive at the stored memory which is best associated with the
input pattern.

The chapter starts by presenting some simple networks
which are capable of functioning as associative memories and derives
the necessary conditions for perfect storage and retrieval of
a given set of memories. The chapter continues by presenting
additional associative memory models with particular attention
given to DAM's. The characteristics of high-performance DAM's
are defined, and stability, capacity, and retrieval dynamics of
various DAM's are analyzed. Finally, the application of a DAM
to the solution of combinatorial optimization problems is described.

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