Mathematics of Neural Networks: Models, Algorithms and Applications

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Stephen W. Ellacott, John C. Mason, Iain J. Anderson
Springer Science & Business Media, May 31, 1997 - Computers - 403 pages
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This volume of research papers comprises the proceedings of the first International Conference on Mathematics of Neural Networks and Applications (MANNA), which was held at Lady Margaret Hall, Oxford from July 3rd to 7th, 1995 and attended by 116 people. The meeting was strongly supported and, in addition to a stimulating academic programme, it featured a delightful venue, excellent food and accommo dation, a full social programme and fine weather - all of which made for a very enjoyable week. This was the first meeting with this title and it was run under the auspices of the Universities of Huddersfield and Brighton, with sponsorship from the US Air Force (European Office of Aerospace Research and Development) and the London Math ematical Society. This enabled a very interesting and wide-ranging conference pro gramme to be offered. We sincerely thank all these organisations, USAF-EOARD, LMS, and Universities of Huddersfield and Brighton for their invaluable support. The conference organisers were John Mason (Huddersfield) and Steve Ellacott (Brighton), supported by a programme committee consisting of Nigel Allinson (UMIST), Norman Biggs (London School of Economics), Chris Bishop (Aston), David Lowe (Aston), Patrick Parks (Oxford), John Taylor (King's College, Lon don) and Kevin Warwick (Reading). The local organiser from Huddersfield was Ros Hawkins, who took responsibility for much of the administration with great efficiency and energy. The Lady Margaret Hall organisation was led by their bursar, Jeanette Griffiths, who ensured that the week was very smoothly run.
 

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Contents

NTUPLE NEURAL NETWORKS
3
INFORMATION GEOMETRY OF NEURAL NETWORKS AN OVERVIEW
15
A TUTORIAL AND EXTENSIONS
24
ARE THERE UNIVERSAL PRINCIPLES OF BRAIN COMPUTATION?
34
ONLINE TRAINING OF MEMORYDRIVEN ATTRACTOR NETWORKS
41
MATHEMATICAL PROBLEMS ARISING FROM CONSTRUCTING AN ARTIFICIAL BRAIN
47
SUBMITTED PAPERS
59
THE SUCCESSFUL USE OF PROBABILITY DATA IN CONNECTIONIST MODELS
61
CONVERGENCE IN NOISY TRAINING
220
NONLINEAR LEARNING DYNAMICS WITH A DIFFUSING MESSENGER
225
A VARIATIONAL APPROACH TO ASSOCIATIVE MEMORY
230
TRANSFORMATION OF NONLINEAR PROGRAMMING PROBLEMS INTO SEPARABLE ONES USING MULTILAYER NEURAL NETWORKS
235
A THEORY OF SELFORGANISING NEURAL NETWORKS
240
NEURAL NETWORK SUPERVISED TRAINING BASED ON A DIMENSION REDUCING METHOD
245
A TRAINING METHOD FOR DISCRETE MULTILAYER NEURAL NETWORKS
250
LOCAL MINIMAL REALISATIONS OF TRAINED HOPFIELD NETWORKS
255

WEIGHTED MIXTURE OF MODELS FOR ONLINE LEARNING
67
LOCAL MODIFICATIONS TO RADIAL BASIS NETWORKS
73
A STATISTICAL ANALYSIS OF THE MODIFIED NLMS RULES
78
FINITE SIZE EFFECTS IN ONLINE LEARNING OF MULTILAYER NEURAL NETWORKS
84
CONSTANT FANIN DIGITAL NEURAL NETWORKS ARE VLSIOPTIMAL
89
THE APPLICATION OF BINARY ENCODED 2ND DIFFERENTIAL SPECTROMETRY IN PREPROCESSING OF UVVIS ABSORPTION SPECTR...
95
A NONEQUIDISTANT ELASTIC NET ALGORITHM
101
UNIMODAL LOADING PROBLEMS
107
ON THE USE OF SIMPLE CLASSIFIERS FOR THE INITIALISATION OF ONEHIDDENLAYER NEURAL NETS
113
MODELLING CONDITIONAL PROBABILITY DISTRIBUTIONS FOR PERIODIC VARIABLES
118
INTEGRODIFFERENTIAL EQUATIONS IN COMPARTMENTAL MODEL NEURODYNAMICS
123
NONLINEAR MODELS FOR NEURAL NETWORKS
129
A NEURAL NETWORK FOR THE TRAVELLING SALESMAN PROBLEM WITH A WELL BEHAVED ENERGY FUNCTION
134
SEMIPARAMETRIC ARTIFICIAL NEURAL NETWORKS
140
AN EVENTSPACE FEEDFORWARD NETWORK USING MAXIMUM ENTROPY PARTITIONING WITH APPLICATION TO LOW LEVEL SPE...
146
APPROXIMATING THE BAYESIAN DECISION BOUNDARY FOR CHANNEL EQUALISATION USING SUBSET RADIAL BASIS FUNCTION ...
151
APPLICATIONS OF GRAPH THEORY TO THE DESIGN OF NEURAL NETWORKS FOR AUTOMATED FINGERPRINT IDENTIFICATION
156
ZERO DYNAMICS AND RELATIVE DEGREE OF DYNAMIC RECURRENT NEURAL NETWORKS
161
THE BANDAND SPACELIMITED FUNCTIONS QUESTIONS
166
UNSUPERVISED LEARNING OF TEMPORAL CONSTANCIES BY PYRAMIDALTYPE NEURONS
171
NUMERICAL ASPECTS OF MACHINE LEARNING IN ARTIFICIAL NEURAL NETWORKS
176
LEARNING ALGORITHMS FOR RAMBASED NEURAL NETWORKS
181
ANALYSIS OF CORRELATION MATRIX MEMORY AND PARTIAL MATCHIMPLICATIONS FOR COGNITIVE PSYCHOLOGY
186
REGULARIZATION AND REALIZABILITY IN RADIAL BASIS FUNCTION NETWORKS
192
A UNIVERSAL APPROXIMATOR NETWORK FOR LEARNING CONDITIONAL PROBABILITY DENSITIES
198
CONVERGENCE OF A CLASS OF NEURAL NETWORKS
204
APPLICATIONS OF THE COMPARTMENTAL MODEL NEURON TO TIME SERIES ANALYSIS
209
INFORMATION THEORETIC NEURAL NETWORKS FOR CONTEXTUALLY GUIDED UNSUPERVISED LEARNING
215
DATA DEPENDENT HYPERPARAMETER ASSIGNMENT
259
TRAINING RADIAL BASIS FUNCTION NETWORKS BY USING SEPARABLE AND ORTHOGONALIZED GAUSSIANS
265
ERROR BOUNDS FOR DENSITY ESTIMATION BY MIXTURES
270
ON SMOOTH ACTIVATION FUNCTIONS
275
GENERALISATION AND REGULARISATION BY GAUSSIAN FILTER CONVOLUTION OF RADIAL BASIS FUNCTION NETWORKS
280
A LIE ALGEBRAIC APPROACH FOR A NOVEL NEURAL ARCHITECTURE
285
STOCHASTIC NEURODYNAMICS AND THE SYSTEM SIZE EXPANSION
290
AN UPPER BOUND ON THE BAYESIAN ERROR BARS FOR GENERALIZED LINEAR REGRESSION
295
CAPACITY BOUNDS FOR STRUCTURED NEURAL NETWORK ARCHITECTURES
300
ONLINE LEARNING IN MULTILAYER NEURAL NETWORKS
306
SPONTANEOUS DYNAMICS AND ASSOCIATIVE LEARNING IN AN ASSYMETRIC RECURRENT RANDOM NEURAL NETWORK
312
A STATISTICAL MECHANICS ANALYSIS OF GENETIC ALGORITHMS FOR SEARCH AND LEARNING
318
VOLUMES OF ATTRACTION BASINS IN RANDOMLY CONNECTED BOOLEAN NETWORKS
323
EVIDENTIAL REJECTION STRATEGY FOR NEURAL NETWORK CLASSIFIERS
328
DYNAMICS APPROXIMATION AND CHANGE POINT RETRIEVAL FROM A NEURAL NETWORK MODEL
333
QUERY LEARNING FOR MAXIMUM INFORMATION GAIN IN A MULTILAYER NEURAL NETWORK
339
SHIFT ROTATION AND SCALE INVARIANT SIGNATURES FOR TWODIMENSIONAL CONTOURS IN A NEURAL NETWORK ARCHITECT...
344
FUNCTION APPROXIMATION BY THREELAYER ARTIFICIAL NEURAL NETWORKS
349
A PILOT STUDY IN A PHONEME RECOGNITION TASK
355
MULTISPECTRAL IMAGE ANALYSIS USING PULSED COUPLED NEURAL NETWORKS
361
REASONING NEURAL NETWORKS
366
CAPACITY OF THE UPSTART ALGORITHM
372
REGRESSION WITH GAUSSIAN PROCESSES
378
STOCHASTIC FORWARDPERTURBATION ERROR SURFACE AND PROGRESSIVE LEARNING IN NEURAL NETWORKS
383
DYNAMICAL STABILITY OF A HIGHDIMENSIONAL SELFORGANIZING MAP
389
MEASUREMENTS OF GENERALISATION BASED ON INFORMATION GEOMETRY
394
SEQUENTIAL COMPOSITION
399
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