**
Associative Neural Memories: Theory and Implementation
by Mohamad H. Hassoun**

(Oxford Press, 1993)

This edited volume brings together significant works on
associative neural memory theory (architecture, learning, analysis, and
design) and hardware implementation (VLSI and optoelectronic) by leading
international researchers. The purpose of this book is to integrate recent
fundamental and significant research results on associative neural memories
into a single volume, and present the material in a clear and organized
format which makes it accessible to researchers and students.

Associative neural memories are a class of artificial neural
networks (connectionist nets) which have gained substantial attention relative
to other neural net paradigms. Associative memories have been the subject of
research since the early seventies. Recent interest in these memories has been
spurred by the seminal work of Hopfield in the early eighties, who has shown
how a simple discrete nonlinear dynamical system can exhibit associative
recall of stored binary patterns through collective computing. Since then, a
number of important contributions have appeared in conference proceedings
and technical journals addressing various issues of associative neural
memories, including multiple-layer architectures, recording/storage
algorithms, capacity, retrieval dynamics, fault-tolerance, and hardware
implementation. Currently, associative neural memories are among the most
extensively studied and understood neural paradigms. They have been studied as
possible models of biological associative phenomena, as models of cognition
and categorical perception, as high-dimensional nonlinear dynamical systems,
as collective computing nets, as error-correcting nets, and as fault-
tolerant content addressable computer memories.

This book is organized into an introductory chapter and four
parts: Biological and Psychological Connections, Artificial Associative Neural
Memory Models, Analysis of Memory Dynamics and Capacity, and
Implementation. The group of chapters in the first part deals with
associative neural models which have close connections to biological and/or
psychological aspects of memory. This group consists of three chapters by D.
Alkon et al., P. Kanerva, and J. Anderson. The second part of this book
consists of three chapters by Y.-F. Wang et al., A. Dembo, and B. Baird
and F. Eeckman. These chapters present more complex extensions of the
simple associative memory models covered in the introductory chapter, and
study their recall capabilities.The analysis of artificial associative
neural memory dynamics, capacity, and error-correction capabilities are
addressed in part three, which comprises the seven chapters by S.-I. Amari and
H.-F. Yanai, R. Paturi, F. Waugh et al., S. Hui et al., G. Pancha and S.
Venkatesh, S. Yoshizawa et al., and P.-C. Chung and T. Krile. The last part
of the book deals with hardware implementation of associative neural memories
(some of these memories and/or their associated recording algorithms
constitute variations and/or extensions to those discussed in earlier
chapters). Here, three chapters by A. G. Andreou and K. A. Boahen, M.
Verleysen et al., and T.-D. Chiueh and R. Goodman address electronic VLSI
implementations. Two additional chapters, one by F. T. S. Yu and the other by
K. Kyuma et al., present optoelectronic implementations.

Chapter 1 is an introduction to basic dynamic associative
memory (DAM) architectures and their associated learning/recording
algorithms. DAMs are treated as collective nonlinear dynamical systems in
which information retrieval is accomplished through an evolution of the
system's state in a high dimensional (binary) state space. This chapter
reviews some basic supervised learning/recording algorithms and derives the
necessary conditions for perfect storage and retrieval of memories in a simple
DAM. The characteristics of high-performance DAMs are outlined and such
general issues as stability, capacity, and retrieval dynamics are
discussed. Also, references to other chapters of the book are made so as to
point out architecture extensions, additional learning algorithms, formal
analysis, and other associative neural memory issues which are briefly
described in this introductory chapter.

Chapter 2 demonstrates the important contributions that
neurobiology can make to the design of artificial neural networks in general
and associative learning nets in particular. It describes some results of
biochemical and biophysical experiments that elucidate the properties of the
Hermissenda visual-vestibular network, followed by descriptions of two
computer models, each representing a different level of aggregation of the
essential features of learning and memory. A biologically-based computer model
called Dystal is presented. The model demonstrates efficient associative
learning and is applied to problems in face recognition and optical character
recognition applications.

Chapter 3 describes and analyzes a class of associative memories
known as "sparse distributed memory" and relates it to associative memory
models of the cerebellum, digital random access memory, and other sparse
memory models reported in the literature. The chapter presents a unified
formulation of a broad class of two-layer feedforward associative memory
architectures, and advances the concept of "pattern computing" as a new
computing model, as contrasted to numeric computing and symbolic computing.

Chapter 4 focuses on the brain-state-in-a-box (BSB) associative
memory as a low-order approximation to a broad range of human cognitive
operations. The chapter presents the theory of the BSB model and informally
describes some of its mathematical properties. Simulations are presented
that show how BSB can model psychological response time.

Chapters 5-7 present more complex models of artificial associative
neural memories as compared to those reviewed in chapter 1. Chapter 5
addresses bidirectional associative memory (BAM), originally proposed
independently by B. Kosko and Okajima et al. in 1987, and proposes several
alternative recording schemes for improved recall. In chapter 6, a class of
high-density associative memory models with such desirable properties as high
capacity, controllable basins of attraction, and fast convergence speed is
proposed and analyzed. In chapter 7, the "projection algorithm"-based
network and its extensions are proposed for the guaranteed associative memory
storage of analog patterns, continuous sequences, and chaotic attractors in
the same network, with no spurious attractors. In this chapter, the authors
concentrate on mathematical analysis and engineering-oriented applications
of the projection algorithm-based memory. The chapter also attempts to
relate the emergent dynamical behavior of interconnected modules of the
proposed network to those of cortical computations by taking the view that
oscillatory and possibly chaotic network modules form the actual cortical
substrate of diverse sensory, motor, and cognitive operations.

The next group of seven chapters, chapters 8-14, deals with the
analysis of various aspects of associative memory, such as capacity,
convergence dynamics, shaping basin of attractions, effects of non-monotonic
activation functions on retrieval dynamics, and fault tolerance. Chapter 8
formulates and presents a unified approach to the analysis of various
architectures of associative memories based on a statistical neurodynamical
method which allows for the analysis of associative recall dynamics and
storage capacity. The method is applied to cross-correlation, cascaded,
cyclic, autocorrelation, and associative sequence generator associative
memories. Chapter 9 presents a detailed, rigorous mathematical analysis of
convergence in the synchronous and asynchronous updated Hopfield associative
memory. Theorems are presented, along with their proofs, on the amount of
error-correction and the rate of convergence as a function of the number of
fundamental memories. The stability and dynamics of analog parallel updated
associative memories are studied in chapter 10. The operation of these dynamic
analog nets as associative memories is explained in terms of phase diagrams,
relating memory loading to neuron activation function slopes, for
correlation and generalized inverse recording. Chapter 11 examines the
stability of the generalized BSB associative memory. It characterizes the
stability and location of all fixed points of the BSB model for different
weight matrices. In chapter 12, a family of algorithms is discussed for DAM
recording in terms of memory capacity and algorithm complexity. The chapter
also emphasizes recording schemes for controlling the basins of attraction of
selected memories and/or controling the basins of attraction of selected
memory vector/pattern components. Chapter 13 adopts a piecewise linear non-
monotonic neuron activation function in a dynamic autocorrelation
associative memory and investigates the existence and stability of equilibrium
states. This chapter also gives theoretical estimates on the capacity of
such memories. Chapter 14 analyzes the effects of the faults characteristic
of optical and electronic implementation technologies on implemented
associative memory retrieval characteristics.

Chapters 15-19 cover hardware implementations of associative
neural memories. In chapter 15, some basic building blocks for VLSI
implementation of neural circuitry are described. The basic principles of
analog VLSI architectures are discussed in connection with precision
limitations encountered with such technology. The chapter describes how to
overcome some of these limitations by appropriate designs of artificial
neurons and adaptation of basic associative learning algorithms. Chapter 16
describes a hybrid analog/digital CMOS chip implementation of a high-
capacity exponential correlation associative memory (ECAM), along with
simulations and experimental validation. The chapter also analyzes the storage
capacity and error-correction characteristics of ECAMs, and the effect of
hardware-limited exponentiation dynamic range on capacity. In chapter 17, a
scalable, efficient, and fault-tolerant chip design of a novel bidirectional
associative memory architecture, based on subthreshold current mode MOS
transistors, is described and validated through simulations. The design
techniques employed in this chapter allow for compact implementation which can
potentially lead to associative memory chips with densities approaching that
of static random access memory (RAM). An optical implementation of a dynamic
single-layer associative memory based on a liquid crystal television (LQTV)
spatial light modulator (SLM) is described in chapter 18. Robust associative
retrieval is demonstrated in this optical memory for several recording
algorithms. This chapter also describes how a high-dimensional set of memories
can be handled by employing a space-time sharing architecture. Finally,
chapter 19 considers the implementation of neural network architectures
employing 3-D optical neurochips with on-chip analog memory capabilities based
on integrated LED and variable sensitivity photodetector (VSPD) arrays.
Experimental results are reported for a two-layer winner-takes-all-based
associative memory for stamp classification and a two-layer perceptron net
employing back error propagation learning.

In putting this book together, an effort was made to include those
researchers who are in many cases the originators of significant ideas on
associative neural memories. However, as in any book like this, it would be
impossible to include all significant work on this topic. Therefore, my
strategy was to invite contributions byleading researchers who are able to
relate their ideas to others in the literature, and who, in some cases,
present a unifying framework for the study of associative neural memories.

I would like to take this opportunity to thank those who have
contributed in various ways to the completion of this book. This project would
not have been successful without the enthusiasm and professional cooperation
of the contributing authors and their high-quality chapter contributions. I
would like to thank the National Science Foundation for support of my work
on associative neural memories through a Presidential Young Investigator Award
(Grant ECE-9057896). In particular, my thanks go to Dr. Paul Werbos of NSF for
his support of my research ideas since 1988. Also, thanks go to Ford Motor
Company, Sun Microsystems, Unisys Corporation, and Zenith Data Systems for
their valuable support, which has contributed directly or indirectly to the
success of this project. Special thanks to Donald C. Jackson of Oxford
University Press for his interest and help in publishing this book. I also
take this opportunity to thank my wife Amal for her understanding and support,
and thank my daughter Lamees for her patience.

Mohamad H. Hassoun

Detroit, June 1992

Click here to return to the CNNL homepage