Mathematics of Neural Networks

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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This book examines the mathematics, probability, statistics, and computational theory underlying neural networks and their applications. In addition to the theoretical work, the book covers a considerable range of neural network topics such as learning and training, neural network classifiers, memory-based networks, self-organizing maps and unsupervised learning, Hopfeld networks, radial basis function networks, and general network modelling and theory. Added to the book's mathematical and neural network topics are applications in chemistry, speech recognition, automatic control, nonlinear programming, medicine, image processing, finance, time series, and dynamics. As a result, the book surveys a wide range of recent research on the theoretical foundations of creating neural network models in a variety of application areas.

Contenu
I Invited Papers.- 1 N-Tuple Neural Networks.- 2 Information Geometry Of Neural Networks An Overview.- 3 Q-Learning: A Tutorial and Extensions.- 4 Are There Universal Principles of Brain Computation?.- 5 On-Line Training of Memory-Driven Attractor Networks.- 6 Mathematical Problems Arising From Constructing An Artificial Brain.- II Submitted Papers.- 7 The Successful Use of Probability Data in Connectionist Models.- 8 Weighted Mixture Of Models For On-Line Learning.- 9 Local Modifications to Radial Basis Networks.- 10 A Statistical Analysis of the Modified Nlms Rules.- 11 Finite Size Effects in on-Line Learning of Multi-Layer Neural Networks.- 12 Constant Fan-In Digital Neural Networks are Vlsi-Optimal.- 13 The Application Of Binary Encoded 2nd Differential Spectrometry in Preprocessing of Uv-Vis Absorption Spectral Data.- 14 A Non-Equidistant Elastic Net Algorithm.- 15 Unimodal Loading Problems.- 16 On The Use of Simple Classifiers for the Initialisation of One-Hidden-Layer Neural Nets.- 17 Modelling Conditional Probability Distributions for Periodic Variables.- 18 Integro-Differential Equations in Compartmental Model Neurodynamics.- 19 Nonlinear Models For Neural Networks.- 20 A Neural Network for The Travelling Salesman Problem with a Well Behaved Energy function.- 21 Semiparametric Artificial Neural Networks.- 22 An Event-Space Feedforward Network Using Maximum Entropy Partitioning with Application to Low Level Speech Data.- 23 Approximating the Bayesian Decision Boundary for Channel Equalisation Using Subset Radial Basis Function Network.- 24 Applications of Graph Theory to the Design of Neural Networks for Automated Fingerprint Identification.- 25 Zero Dynamics And Relative Degree Of Dynamic Recurrent Neural Networks.- 26 Irregular Sampling Approach toNeurocontrol: The Band-And Space-Limited Functions Questions.- 27 Unsupervised Learning of Temporal Constancies by Pyramidal-Type Neurons.- 28 Numerical Aspects of Machine Learning in Artificial Neural Networks.- 29 Learning Algorithms for Ram-Based Neural Networks.- 30 Analysis Of Correlation Matrix Memory and Partial Match-Implications for Cognitive Psychology.- 31 Regularization and Realizability in Radial Basis Function Networks.- 32 A Universal Approximator Network for Learning Conditional Probability Densities.- 33 Convergence af a Class of Neural Networks.- 34 Applications of the Compartmental Model Neuron to Time Series Analysis.- 35 Information Theoretic Neural Networks For Contextually Guided Unsupervised Learning.- 36 Convergence in Noisy Training.- 37 Non-Linear Learning Dynamics with a Diffusing Messenger.- 38 A Variational Approach to Associative Memory.- 39 Transformation of Nonlinear Programming Problems Into Separable Ones Using Multilayer Neural Networks.- 40 A Theory of Self-Organising Neural Networks.- 41 Neural Network Supervised Training Based on a Dimension Reducing Method.- 42 A Training Method for Discrete Multilayer Neural Networks.- 43 Local Minimal Realisations of Trained Hopfield Networks.- 44 Data Dependent Hyperparameter Assignment.- 45 Training Radial Basis Function Networks by Using Separable and Orthogonalized Gaussians.- 46 Error Bounds for Density Estimation by Mixtures.- 47 On Smooth Activation Functions.- 48 Generalisation and Regularisation by Gaussian Filter Convolution of Radial Basis Function Networks.- 49 Dynamical System Prediction: A Lie Algebraic Approach for a Novel Neural Architecture.- 50 Stochastic Neurodynamics and the System Size Expansion.- 51 An Upper Bound on the Bayesian Error Bars for Generalized Linear Regression.- 52 Capacity Bounds for Structured Neural Network Architectures.- 53 On-Line Learning In Multilayer Neural Networks.- 54 Spontaneous Dynamics and Associative Learning in an Assymetric Recurrent Random Neural Network.- 55 A Statistical Mechanics Analysis of Genetic Algorithms for Search and Learning.- 56 Volumes of Attraction Basins in Randomly Connected Boolean Networks.- 57 Evidential Rejection Strategy for Neural Network Classifiers.- 58 Dynamics Approximation and Change Point Retrieval from a Neural Network Model.- 59 Query Learning for Maximum Information Gain in a Multi-Layer Neural Network.- 60 Shift, Rotation and Scale Invariant Signatures for Two-Dimensional Contours, in a Neural Network Architecture.- 61 Function Approximation by Three-Layer Artificial Neural Networks.- 62 Neural Network Versus Statistical Clustering Techniques: A Pilot Study in a Phoneme Recognition Task.- 63 Multispectral Image Analysis Using Pulsed Coupled Neural Networks.- 64 Reasoning Neural Networks.- 65 Capacity of the Upstart Algorithm.- 66 Regression with Gaussian Processes.- 67 Stochastic Forward-Perturbation, Error Surface and Progressive Learning in Neural Networks.- 68 Dynamical Stability of a High-Dimensional Self-Organizing Map.- 69 Measurements of Generalisation Based on Information Geometry.- 70 Towards an Algebraic Theory of Neural Networks: Sequential Composition.