Associative Memory: A System-Theoretical Approach

ISBN-13: 9783642963865 / Angielski / Miękka / 2012 / 178 str.

T. Kohonen

Opis

About the Scope of This Text This book contains two types of material ~ first, the many divergent and often diffuse meanings given to the concepts of association, associative memory, and associative recaZZ are expounded. A review of this kind was felt necessary because there apparently does not exist any single monograph which could serve as a reference to these topics. But the presentation of the main body of this text is motivated by quite other reasons: in recent years, plenty of interesting mathematical and system-theoretical material has been published which makes it possible to gain a view of associative memory which is different from the conventional abstract and computationally oriented approaches. It seems that the basic operation of associative memory, the storage of information together with the relations or links between the data items, and the selective recall of stored information relative to a piece of key or cue information presented, is not restricted to certain computer-technological implementations but can also be reflected in more general mathematically describable processes in certain physical or other systems, especially in their adaptive state changes. It further seems that some generally known forms of associative memory, namely, certain computer technological artifacts, or abstract systems of concepts or data, are in fact special representations of a class of processes characterized as associative memory.

Spis treści

1. Introduction.- 1.1 On the Physical Embodiment of Associative Information Structures.- 1.1.1 A System-Model Approach to the Associative Memory.- 1.1.2 Relational Structures of Knowledge.- 1.1.3 Acquisition and Retrieval of Knowledge as Structured Sequences.- 1.2 Implementations of Associative Recall.- 1.2.1 Basic Characteristics of Associative Memories.- 1.2.2 The Content-Addressable Memory (CAM).- 1.2.3 Hash-Coding.- 1.2.4 Holographic Associative Memories.- 1.2.5 Nonholographic, Distributed Associative Memories.- 1.3 Mathematical Notations and Methods.- 1.3.1 Vector Space Concepts.- 1.3.2 Matrix Notations.- 1.3.3 Further Properti es of Matrices.- 1.3.4 Matrix Equations.- 1.3.5 Projection Operators.- 1.3.6 Matrix Differential Calculus.- 2. Associative Search Methods.- 2.1 Addressing by the Contents.- 2.1.1 Hash-Coding Principles.- 2.1.2 An Example of Hash-Coding: Multiple-Keyword Search.- 2.1.3 A Processing Language for Associative Data Structures.- 2.2 Content-Addressable Memories.- 2.2.1 Associative Recall by the Partial Match Operation.- 2.2.2 Hardware Implementation of the CAM Structure.- 2.2.3 Parallel Comparison of Magnitudes.- 2.3 Optimal Associative Mappings.- 2.3.1 System Model for an Analog Associative Memory.- 2.3.2 Autoassociative Recall as an Orthogonal Projection.- 2.3.3 The Novelty Filter.- 2.3.4 Autoassociative Encoding.- 2.3.5 Optimal Linear Associative Mappings.- 2.3.6 Optimal Nonlinear Associative Mappings.- 2.3.7 The Problem of Invariant Recognition.- 2.3.8 Relationship Between Associative Mapping, Linear Regression, and Linear Estimation.- 2.4 Relationship of Associative Mappings to Pattern Classification.- 2.4.1 Discriminant Functions.- 2.4.2 Comparison Methods.- 2.4.3 Statistical Formulation of Pattern Classification.- 3. Adaptive Formation of Optimal Associative Mappings.- 3.1 On the Implementation of Conditioned Responses in Simple Physical Systems.- 3.1.1 A Simple Adaptive Linear System.- 3.1.2 On the Physical Realizability of Adaptive Elements.- 3.2 Adaptive Filters Which Compute Orthogonal Projections.- 3.2.1 The Novelty Detector Paradigm.- 3.2.2 Analysis of the Adaptive Linear Unit by Means of Matrix Products.- 3.2.3 An Extremely Fast Adaptive Process Which Generates the Novel ty Filter.- 3.2.4 Adaptation With Forgetting.- 3.3 Recursive Generation of the Optimal Associative Mapping.- 3.3.1 Linear Corrective Algorithms.- 3.3.2 The General Setting for the Computation of M = YX+.- 3.3.3 Recursive Evaluation of the Best Exact Solution (Gradient Projection Method).- 3.3.4 Recursive Evaluation of the Best Approximate Solution (Regression Solution).- 3.3.5 Recursive Solution in the General Case.- 4. On Biological Associative Memory.- 4.1 Physiological Foundations of Memory.- 4.1.1 On the Mechanisms of Memory in Biological Systems.- 4.1.2 Structural Features of Some Neural Networks.- 4.1.3 Functional Features of Neurons.- 4.1.4 Modelling of the Synaptic Plasticity.- 4.1.5 Can the Memory Capacity Ensue from Synaptic Changes?.- 4.2 Computerized Models of Associative Memory in Neural Networks.- 4.2.1 The Associative Network Paradigm.- 4.2.2 The Novelty Filter Paradigm.- 4.2.3 Review of Related Approaches.- References.- Author Index.