Dealing with Complexity

1 Recurrent Neural Networks: Some Systems-Theoretic Aspects.- 1 Introduction.- 2 System-Theory Results: Statements.- 3 System-Theory Results: Discussion.- 4 Computational Power.- 5 Some Remarks.- 2 The Use of State Space Control Theory for Analysing Feedforward Neural Networks.- 1 Introduction.- 2 State Space Theory.- 3 State Space Representation of Feedforward Neural Networks.- 4 Observability of Feedforward Neural Networks.- 5 Controllability.- 6 Stability.- 7 Discussion.- 8 Appendix: Linear Systems of Equations [7].- 3 Statistical Decision Making and Neural Networks.- 1 Introduction.- 2 Statistical Decision Making.- 3 Bayesian Learning.- 4 On Ingredients of Bayesian Learning.- 5 Interlude on Gaussian Linear Regression Model.- 6 Approximate On-Line Estimation.- 7 Conclusions.- 4 A Tutorial on the EM Algorithm and its Applications to Neural Network Learning.- 1 Introduction.- 2 The EM Algorithm.- 3 Practical Applications.- 4 Convergence Properties.- 5 Concluding Remarks.- 5 On the Effectiveness of Memory-Based Methods inMachine Learning.- 1 Introduction.- 2 Background.- 3 The Curse of Dimensionality.- 4 The Barron-Jones Theory.- 5 Experimental Results.- 6 Analysis of Memory-Based Methods.- 7 Discussion.- 6 A Study of Non Mean Square Error Criteria for the Training of Neural Networks.- 1 Introduction.- 2 Statement of the Problem.- 3 Cost Function Minimisation for ? = E(y/x).- 4 Cost Function Minimisation for the Median of p(y/x).- 5 Simulation Results.- 6 Conclusion.- 7 A Priori Information in Network Design.- 1 Introduction.- 2 Preliminaries.- 3 Recurrent Networks and Relative Order.- 4 Simulations.- 5 Conclusions.- 8 Neurofuzzy Systems Modelling: A Transparent Approach.- 1 Empirical Data Modelling.- 2 Neurofuzzy Construction Algorithms.- 3 Modelling Case Studies.- 4Conclusions.- 9 Feature Selection and Classification by a Modified Model with Latent Structure.- 1 Introduction.- 2 Modified Model with Latent Structure.- 3 Optimizing Model Parameters.- 4 Approach to Feature Selection.- 5 Pseudo-Bayes Decision Rule.- 6 Experiments.- 7 Summary and Conclusion.- 10 Geometric Algebra Based Neural Networks.- 1 Introduction.- 2 Complex-Valued Neural Networks.- 3 Comments on the Applicability of CVNNs to n-Dimensional Signals.- 4 Generalisations of CVNNs Within a GA Framework.- 5 Summary.- 11 Discrete Event Complex Systems: Scheduling with Neural Networks.- 1 Introduction.- 2 The DNN Architecture.- 3 Continuous Time Control Law.- 4 Real-Time Scheduling.- 5 Simulation Results.- 6 Summary.- 12 Incremental Approximation by Neural Networks.- 1 Introduction.- 2 Approximation of Functions by One-Hidden-Layer Networks.- 3 Rates of Approximation of Incremental Approximants.- 4 Variation with Respect to a Set of Functions.- 5 Incremental Approximation by Perceptron and RBF Networks.- 6 Discussion.- 13 Approximation of Smooth Functions by Neural Networks.- 1 Introduction.- 2 Preliminaries.- 3 Complexity Theorems.- 4 Local Approximation.- 5 Some Open Problems.- 14 Rates of Approximation in a Feedforward Network Depend on the Type of Computational Unit.- 1 Introduction.- 2 Feedforward Networks with Various Computational Units.- 3 Discussion.- 15 Recent Results and Mathematical Methods for Functional Approximation by Neural Networks.- 1 Introduction.- 2 Individual vs Variable Context.- 3 Nonlinear Approximation.- 4 Feedforward Architectures.- 5 Lower Bounds on Rate of Approximation.- 6 Uniqueness of Approximation by Neural Networks.- 7 Other Approaches.- 16 Differential Neurocontrol of Multidimensional Systems.- 1 Introduction.- 2 Neurophysiological Basis.- 3 Scheme of the Differential Neurocontroller.- 4 Multiplicative Units.- 5 Feedback Block.- 6 Feedforward Block.- 7 Convergence of Learning.- 8 Computer Simulations.- 9 Conclusions.- 17 The Psychological Limits of Neural Computation.- 1 Neural Networks and Turing Machines.- 2 Function Approximation.- 3 Representation of Logical Functions Using Neural Networks.- 4 The Complexity of Learning in Neural Networks.- 5 Learning Logical Functions.- 6 The Optimization of Circuits.- 7 Final Remarks.- 18 A Brain-Like Design to Learn Optimal Decision Strategies in Complex Environments.- 1 Introduction.- 2 Time-Chunked Approximate Dynamic Programming.- 3 Temporal Chunking with Neural Networks.- 4 Spatial Chunking and Critical Subsystems.- 5 Adding the Third Brain.- Research Acknowledgements.