Models of Neural Networks III: Association, Generalization, and Representation - Softcover

Inhaltsangabe

1. Global Analysis of Recurrent Neural Networks.- 1.1 Global Analysis-Why?.- 1.2 A Framework for Neural Dynamics.- 1.2.1 Description of Single Neurons.- 1.2.2 Discrete-Time Dynamics.- 1.2.3 Continuous-Time Dynamics.- 1.2.4 Hebbian Learning.- 1.3 Fixed Points.- 1.3.1 Sequential Dynamics: Hopfield Model.- 1.3.2 Parallel Dynamics: Little Model.- 1.3.3 Continuous Time: Graded-Response Neurons.- 1.3.4 Iterated-Map Networks.- 1.3.5 Distributed Dynamics.- 1.3.6 Network Performance.- 1.3.7 Intermezzo: Delayed Graded-Response Neurons.- 1.4 Periodic Limit Cycles and Beyond.- 1.4.1 Discrete-Time Dynamics.- 1.4.2 Continuous-Time Dynamics.- 1.5 Synchronization of Action Potentials.- 1.5.1 Phase Locking.- 1.5.2 Rapid Convergence.- 1.6 Conclusions.- References.- 2. Receptive Fields and Maps in the Visual Cortex: Models of Ocular Dominance and Orientation Columns.- 2.1 Introduction.- 2.2 Correlation-Based Models.- 2.2.1 The Von der Malsburg Model of V1 Development.- 2.2.2 Mathematical Formulation.- 2.2.3 Semilinear Models.- 2.2.4 How Semilinear Models Behave.- 2.2.5 Understanding Ocular Dominance and Orientation Columns with Semilinear Models.- 2.2.6 Related Semilinear Models.- 2.3 The Problem of Map Structure.- 2.4 The Computational Significance of Correlatin-Based Rules.- 2.4.1 Efficient Representation of Information.- 2.4.2 Self-Organizing Maps and Associative Memories.- 2.5 Open Questions.- References.- 3. Associative Data Storage and Retrieval in Neural Networks.- 3.1 Introduction and Overview.- 3.1.1 Memory and Representation.- 3.1.2 Retrieval from the Memory.- 3.1.3 Fault Tolerance in Addressing.- 3.1.4 Various Memory Tasks.- 3.1.5 Retrieval Errors.- 3.2 Neural Associatve Memory Models.- 3.2.1 Retrieval Process.- 3.2.2 Storage Process.- 3.2.3 Distributed Storage.- 3.3 Analysis of the Retrieval Process.- 3.3.1 Random Pattern Generation.- 3.3.2 Site Averaging and Threshold Setting.- 3.3.3 Binary Storage Procedure.- 3.3.4 Incremental Storage Procedure.- 3.4 Information Theory of the Memory Process.- 3.4.1 Mean Information Content of Data.- 3.4.2 Association Capacity.- 3.4.3 Including the Addressing Process.- 3.4.4 Asymptotic Memory Capacities.- 3.5 Model Performance.- 3.5.1 Binary Storage.- 3.5.2 Incremental Storage.- 3.6 Discussion.- 3.6.1 Heteroassociation.- 3.6.2 Autoassociation.- 3.6.3 Relations to Other Approaches.- 3.6.4 Summary.- Appendix 3.1.- Appendix 3.2.- References.- 4. Inferences Modeled with Neural Networks.- 4.1 Introduction.- 4.1.1 Useful Definitions.- 4.1.2 Proposed Framework.- 4.1.3 How Far Can We Go with the Formal-Logic Approach?.- 4.2 Model for Cognitive Systems and for Experiences.- 4.2.1 Cognitive Systems.- 4.2.2 Experience.- 4.2.3 From the Hebb Rule to the Postulate?.- 4.3 Inductive Inference.- 4.3.1 Optimal Inductive Inference.- 4.3.2 Unique Inductive Inference.- 4.3.3 Practicability of the Postulate.- 4.3.4 Biological Example.- 4.3.5 Limitation of Inductive Inference in Terms of Complexity.- 4.3.6 Summary for Inductive Inference.- 4.4 External Memory.- 4.4.1 Counting.- 4.5 Limited Use of External Memory.- 4.5.1 Counting.- 4.5.2 On Wittgenstein's Paradox.- 4.6 Deductive Inference.- 4.6.1 Biological Example.- 4.6.2 Mathematical Examples.- 4.6.3 Relevant Signal Flow.- 4.6.4 Mathematical Examples Revisited.- 4.6.5 Further Ansatz.- 4.6.6 Proofs by Complete Induction.- 4.6.7 On Sieves.- 4.7 Conclusion.- References.- 5. Statistical Mechanics of Generalization.- 5.1 Introduction.- 5.2 General Results.- 5.2.1 Phase Space of Neural Networks.- 5.2.2 VC Dimension and Worst-Case Results.- 5.2.3 Bayesian Approach and Statistical Mechanics.- 5.2.4 Information-Theoretic Results.- 5.2.5 Smooth Networks.- 5.3 The Perceptron.- 5.3.1 Some General Properties.- 5.3.2 Replica Theory.- 5.3.3 Results for Bayes and Gibbs Algorithms.- 5.4 Geometry in Phase Space and Asymptotic Scaling.- 5.5 Applications to Perceptrons.- 5.5.1 Simple Learning: Hebb Rule.- 5.5.2 Overfitting.- 5.5.3 Maximal Stability.- 5.5.4 Queries.- 5.5.5 Discontinuous Lea

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