Analysis of Bidirectional Associative Memory using SCSNA and Statistical Neurodynamics

Bidirectional associative memory (BAM) is a kind of an artificial neural network used to memorize and retrieve heterogeneous pattern pairs. Many efforts have been made to improve BAM from the the viewpoint of computer application, and few theoretical studies have been done. We investigated the theoretical characteristics of BAM using a framework of statistical-mechanical analysis. To investigate the equilibrium state of BAM, we applied self-consistent signal to noise analysis (SCSNA) and obtained a macroscopic parameter equations and relative capacity. Moreover, to investigate not only the equilibrium state but also the retrieval process of reaching the equilibrium state, we applied statistical neurodynamics to the update rule of BAM and obtained evolution equations for the macroscopic parameters. These evolution equations are consistent with the results of SCSNA in the equilibrium state.Comment: 13 pages, 4 figure

The stability and attractivity of neural associative memories.

Han-bing Ji.Thesis (Ph.D.)--Chinese University of Hong Kong, 1996.Includes bibliographical references (p. 160-163).Microfiche. Ann Arbor, Mich.: UMI, 1998. 2 microfiches ; 11 x 15 cm

Associative neural networks: properties, learning, and applications.

by Chi-sing Leung.Thesis (Ph.D.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 236-244).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Background of Associative Neural Networks --- p.1Chapter 1.2 --- A Distributed Encoding Model: Bidirectional Associative Memory --- p.3Chapter 1.3 --- A Direct Encoding Model: Kohonen Map --- p.6Chapter 1.4 --- Scope and Organization --- p.9Chapter 1.5 --- Summary of Publications --- p.13Chapter I --- Bidirectional Associative Memory: Statistical Proper- ties and Learning --- p.17Chapter 2 --- Introduction to Bidirectional Associative Memory --- p.18Chapter 2.1 --- Bidirectional Associative Memory and its Encoding Method --- p.18Chapter 2.2 --- Recall Process of BAM --- p.20Chapter 2.3 --- Stability of BAM --- p.22Chapter 2.4 --- Memory Capacity of BAM --- p.24Chapter 2.5 --- Error Correction Capability of BAM --- p.28Chapter 2.6 --- Chapter Summary --- p.29Chapter 3 --- Memory Capacity and Statistical Dynamics of First Order BAM --- p.31Chapter 3.1 --- Introduction --- p.31Chapter 3.2 --- Existence of Energy Barrier --- p.34Chapter 3.3 --- Memory Capacity from Energy Barrier --- p.44Chapter 3.4 --- Confidence Dynamics --- p.49Chapter 3.5 --- Numerical Results from the Dynamics --- p.63Chapter 3.6 --- Chapter Summary --- p.68Chapter 4 --- Stability and Statistical Dynamics of Second order BAM --- p.70Chapter 4.1 --- Introduction --- p.70Chapter 4.2 --- Second order BAM and its Stability --- p.71Chapter 4.3 --- Confidence Dynamics of Second Order BAM --- p.75Chapter 4.4 --- Numerical Results --- p.82Chapter 4.5 --- Extension to higher order BAM --- p.90Chapter 4.6 --- Verification of the conditions of Newman's Lemma --- p.94Chapter 4.7 --- Chapter Summary --- p.95Chapter 5 --- Enhancement of BAM --- p.97Chapter 5.1 --- Background --- p.97Chapter 5.2 --- Review on Modifications of BAM --- p.101Chapter 5.2.1 --- Change of the encoding method --- p.101Chapter 5.2.2 --- Change of the topology --- p.105Chapter 5.3 --- Householder Encoding Algorithm --- p.107Chapter 5.3.1 --- Construction from Householder Transforms --- p.107Chapter 5.3.2 --- Construction from iterative method --- p.109Chapter 5.3.3 --- Remarks on HCA --- p.111Chapter 5.4 --- Enhanced Householder Encoding Algorithm --- p.112Chapter 5.4.1 --- Construction of EHCA --- p.112Chapter 5.4.2 --- Remarks on EHCA --- p.114Chapter 5.5 --- Bidirectional Learning --- p.115Chapter 5.5.1 --- Construction of BL --- p.115Chapter 5.5.2 --- The Convergence of BL and the memory capacity of BL --- p.116Chapter 5.5.3 --- Remarks on BL --- p.120Chapter 5.6 --- Adaptive Ho-Kashyap Bidirectional Learning --- p.121Chapter 5.6.1 --- Construction of AHKBL --- p.121Chapter 5.6.2 --- Convergent Conditions for AHKBL --- p.124Chapter 5.6.3 --- Remarks on AHKBL --- p.125Chapter 5.7 --- Computer Simulations --- p.126Chapter 5.7.1 --- Memory Capacity --- p.126Chapter 5.7.2 --- Error Correction Capability --- p.130Chapter 5.7.3 --- Learning Speed --- p.157Chapter 5.8 --- Chapter Summary --- p.158Chapter 6 --- BAM under Forgetting Learning --- p.160Chapter 6.1 --- Introduction --- p.160Chapter 6.2 --- Properties of Forgetting Learning --- p.162Chapter 6.3 --- Computer Simulations --- p.168Chapter 6.4 --- Chapter Summary --- p.168Chapter II --- Kohonen Map: Applications in Data compression and Communications --- p.170Chapter 7 --- Introduction to Vector Quantization and Kohonen Map --- p.171Chapter 7.1 --- Background on Vector quantization --- p.171Chapter 7.2 --- Introduction to LBG algorithm --- p.173Chapter 7.3 --- Introduction to Kohonen Map --- p.174Chapter 7.4 --- Chapter Summary --- p.179Chapter 8 --- Applications of Kohonen Map in Data Compression and Communi- cations --- p.181Chapter 8.1 --- Use Kohonen Map to design Trellis Coded Vector Quantizer --- p.182Chapter 8.1.1 --- Trellis Coded Vector Quantizer --- p.182Chapter 8.1.2 --- Trellis Coded Kohonen Map --- p.188Chapter 8.1.3 --- Computer Simulations --- p.191Chapter 8.2 --- Kohonen MapiCombined Vector Quantization and Modulation --- p.195Chapter 8.2.1 --- Impulsive Noise in the received data --- p.195Chapter 8.2.2 --- Combined Kohonen Map and Modulation --- p.198Chapter 8.2.3 --- Computer Simulations --- p.200Chapter 8.3 --- Error Control Scheme for the Transmission of Vector Quantized Data --- p.213Chapter 8.3.1 --- Motivation and Background --- p.214Chapter 8.3.2 --- Trellis Coded Modulation --- p.216Chapter 8.3.3 --- "Combined Vector Quantization, Error Control, and Modulation" --- p.220Chapter 8.3.4 --- Computer Simulations --- p.223Chapter 8.4 --- Chapter Summary --- p.226Chapter 9 --- Conclusion --- p.232Bibliography --- p.23