Mathematics of Neural Networks: Models, Algorithms and Applications

Front Matter....Pages i-xxii
Front Matter....Pages 1-1
N-Tuple Neural Networks....Pages 3-14
Information Geometry of Neural Networks — An Overview —....Pages 15-23
Q-Learning: A Tutorial and Extensions....Pages 24-33
Are There Universal Principles of Brain Computation?....Pages 34-40
On-Line Training of Memory-Driven Attractor Networks....Pages 41-46
Mathematical Problems Arising from Constructing an Artificial Brain....Pages 47-57
Front Matter....Pages 59-59
The Successful Use of Probability Data in Connectionist Models....Pages 61-66
Weighted Mixture of Models For On-Line Learning....Pages 67-72
Local Modifications to Radial Basis Networks....Pages 73-77
A Statistical Analysis of the Modified NLMS Rules....Pages 78-83
Finite Size Effects in On-Line Learning of Multi-Layer Neural Networks....Pages 84-88
Constant Fan-in Digital Neural Networks are VLSI-Optimal....Pages 89-94
The Application of Binary Encoded 2nd Differential Spectrometry in Preprocessing of UV-Vis Absorption Spectral Data....Pages 95-100
A Non-Equidistant Elastic Net Algorithm....Pages 101-106
Unimodal Loading Problems....Pages 107-112
On the Use of Simple Classifiers for the Initialisation of One-Hidden-Layer Neural Nets....Pages 113-117
Modelling Conditional Probability Distributions for Periodic Variables....Pages 118-122
Integro-Differential Equations in Compartmental Model Neurodynamics....Pages 123-128
Nonlinear Models for Neural Networks....Pages 129-133
A Neural Network for the Travelling Salesman Problem with a Well Behaved Energy Function....Pages 134-139
Front Matter....Pages 59-59
Semiparametric Artificial Neural Networks....Pages 140-145
An Event-Space Feedforward Network Using Maximum Entropy Partitioning with Application to Low Level Speech Data....Pages 146-150
Approximating the Bayesian Decision Boundary for Channel Equalisation Using Subset Radial Basis Function Network....Pages 151-155
Applications of Graph Theory to the Design of Neural Networks for Automated Fingerprint Identification....Pages 156-160
Zero Dynamics and Relative Degree of Dynamic Recurrent Neural Networks....Pages 161-165
Irregular Sampling Approach to Neurocontrol: The Band-And Space-Limited Functions Questions....Pages 166-170
Unsupervised Learning of Temporal Constancies by Pyramidal-Type Neurons.....Pages 171-175
Numerical Aspects of Machine Learning in Artificial Neural Networks....Pages 176-180
Learning Algorithms for Ram-Based Neural Networks....Pages 181-185
Analysis of Correlation Matrix Memory and Partial Match-Implications for Cognitive Psychology....Pages 186-191
Regularization and Realizability in Radial Basis Function Networks....Pages 192-197
A Universal Approximator Network for Learning Conditional Probability Densities....Pages 198-203
Convergence of a Class of Neural Networks....Pages 204-208
Applications of the Compartmental Model Neuron to Time Series Analysis....Pages 209-214
Information Theoretic Neural Networks for Contextually Guided Unsupervised Learning....Pages 215-219
Convergence in Noisy Training....Pages 220-224
Non-Linear Learning Dynamics with a Diffusing Messenger....Pages 225-229
A Variational Approach to Associative Memory....Pages 230-234
Transformation of Nonlinear Programming Problems into Separable ones Using Multilayer Neural Networks....Pages 235-239
A Theory of Self-Organising Neural Networks....Pages 240-244
Front Matter....Pages 59-59
Neural Network Supervised Training Based on a Dimension Reducing Method....Pages 245-249
A Training Method for Discrete Multilayer Neural Networks....Pages 250-254
Local Minimal Realisations of Trained Hopfield Networks....Pages 255-258
Data Dependent Hyperparameter Assignment....Pages 259-264
Training Radial Basis Function Networks by Using Separable and Orthogonalized Gaussians....Pages 265-269
Error Bounds for Density Estimation by Mixtures....Pages 270-274
On Smooth Activation Functions....Pages 275-279
Generalisation and Regularisation by Gaussian Filter Convolution of Radial Basis Function Networks....Pages 280-284
Dynamical System Prediction: A Lie Algebraic Approach for a Novel Neural Architecture....Pages 285-289
Stochastic Neurodynamics and the System Size Expansion....Pages 290-294
An Upper Bound on the Bayesian Error Bars for Generalized Linear Regression....Pages 295-299
Capacity Bounds for Structured Neural Network Architectures....Pages 300-305
On-Line Learning in Multilayer Neural Networks....Pages 306-311
Spontaneous Dynamics and Associative Learning in an Assymetric Recurrent Random Neural Network....Pages 312-317
A Statistical Mechanics Analysis of Genetic Algorithms for Search and Learning....Pages 318-322
Volumes of Attraction Basins in Randomly Connected Boolean Networks....Pages 323-327
Evidential Rejection Strategy for Neural Network Classifiers....Pages 328-332
Dynamics Approximation and Change Point Retrieval from a Neural Network Model....Pages 333-338
Query Learning for Maximum Information Gain in a Multi-Layer Neural Network....Pages 339-343
Shift, Rotation and Scale Invariant Signatures for Two-Dimensional Contours, in a Neural Network Architecture....Pages 344-348
Front Matter....Pages 59-59
Function Approximation by Three-Layer Artificial Neural Networks....Pages 349-354
Neural Network Versus Statistical Clustering Techniques: A Pilot Study in a Phoneme Recognition Task....Pages 355-360
Multispectral Image Analysis Using Pulsed Coupled Neural Networks....Pages 361-365
Reasoning Neural Networks....Pages 366-371
Capacity of the Upstart Algorithm....Pages 372-377
Regression with Gaussian Processes....Pages 378-382
Stochastic Forward-Perturbation, Error Surface and Progressive Learning in Neural Networks....Pages 383-388
Dynamical Stability of a High-Dimensional Self-Organizing Map....Pages 389-393
Measurements of Generalisation Based on Information Geometry....Pages 394-398
Towards an Algebraic Theory of Neural Networks: Sequential Composition....Pages 399-403