1. The biological paradigm (PDF)
- 1.1 Neural computation
- 1.1.1 Natural and artificial neural networks
- 1.1.2 Models of computation
- 1.1.3 Elements of a computing model
- 1.2 Networks of neurons
- 1.2.1 Structure of the neurons
- 1.2.2 Transmission of information
- 1.2.3 Information processing at the neurons and synapses
- 1.2.4 Storage of information - Learning
- 1.2.5 The neuron - a self-organizing system
- 1.3 Artificial neural networks
- 1.3.1 Networks of primitive functions
- 1.3.2 Approximation of functions
- 1.3.3 Caveat
- 1.4 Historical and bibliographical remarks
- 2.1 Networks of functions
- 2.1.1 Feed-forward and recurrent networks
- 2.1.2 The computing units
- 2.2 Synthesis of Boolean functions
- 2.2.1 Conjunction, disjunction, negation
- 2.2.2 Geometric interpretation
- 2.2.3 Constructive synthesis
- 2.3 Equivalent networks
- 2.3.1 Weighted and unweighted networks
- 2.3.2 Absolute and relative inhibition
- 2.3.3 Binary signals and pulse coding
- 2.4 Recurrent networks
- 2.4.1 Stored state networks
- 2.4.2 Finite automata
- 2.4.3 Finite automata and recurrent networks
- 2.4.4 A first classification of neural networks
- 2.5 Harmonic analysis of logical function
- 2.5.1 General expression
- 2.5.2 The Hadamard-Walsh transform
- 2.5.3 Applications of threshold logic
- 2.6 Historical and bibliographical remarks
3. Weighted Networks - The Perceptron (PDF)
- 3.1 Perceptrons and parallel processing
- 3.1.1 Perceptrons as weighted threshold elements
- 3.1.2 Computational limits of the perceptron model
- 3.2 Implementation of logical functions
- 3.2.1 Geometric interpretation
- 3.2.2 The XOR problem
- 3.3 Linearly separable functions
- 3.3.1 Linear separability
- 3.3.2 Duality of input space and weight space
- 3.3.3 The error function in weight space
- 3.3.4 General decision curves
- 3.4 Applications and biological analogy
- 3.4.1 Edge detection with perceptrons
- 3.4.2 The structure of the retina
- 3.4.3 Pyramidal networks and the neocognitron
- 3.4.4 The silicon retina
- 3.5 Historical and bibliographical remarks
4. Perceptron learning (PDF)
- 4.1 Learning algorithms for neural networks
- 4.1.1 Classes of learning algorithms
- 4.1.2 Vector notation
- 4.1.3 Absolute linear separability
- 4.1.4 The error surface and the search method
- 4.2 Algorithmic learning
- 4.2.1 Geometric visualization
- 4.2.2 Convergence of the algorithm
- 4.2.3 Accelerating convergence
- 4.2.4 The pocket algorithm
- 4.2.5 Complexity of perceptron learning
- 4.3 Linear programming
- 4.3.1 Inner points of polytopes
- 4.3.2 Linear separability as linear optimization
- 4.3.3 Karmarkar´s Algorithm
- 4.4 Historical and bibliographical remarks
5. Unsupervised learning and clustering algorithms (PDF)
- 5.1 Competitive learning
- 5.1.1 Generalization of the perceptron problem
- 5.1.2 Unsupervised learning through competition
- 5.2 Convergence analysis
- 5.2.1 The one-dimensional case - Energy function
- 5.2.2 Multidimensional case - The classical methods
- 5.2.3 Unsupervised learning as minimization problem
- 5.2.4 Stability of the solutions
- 5.3 Principal component analysis
- 5.3.1 Unsupervised reinforcement learning
- 5.3.2 Convergence of the learning algorithm
- 5.3.3 Multiple principal components
- 5.4 Examples
- 5.4.1 Pattern recognition
- 5.4.2 Image compression
- 5.5 Historical and bibliographical remarks
6. One and two layered networks (PDF)
- 6.1 Structure and geometric visualization
- 6.1.1 Network architecture
- 6.1.2 The XOR problem revisited
- 6.1.3 Geometric visualization
- 6.2 Counting regions in input and weight space
- 6.2.1 Weight space regions for the XOR problem
- 6.2.2 Bipolar vectors
- 6.2.3 Projection of the solution regions
- 6.2.4 Geometric interpretation
- 6.3 Regions for two layered networks
- 6.3.1 Regions in weight space for the XOR problem
- 6.3.2 Number of regions in general
- 6.3.3 Consequences
- 6.3.4 The Vapnik-Chervonenkis dimension
- 6.3.5 The problem of local minima
- 6.4 Historical and bibliographical remarks
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7. The backpropagation algorithm (PDF)
- 7.1 Learning as gradient descent
- 7.1.1 Differentiable activation functions
- 7.1.2 Regions in input space
- 7.1.3 Local minima of the error function
- 7.2 General feed-forward networks
- 7.2.1 The learning problem
- 7.2.2 Derivatives of network functions
- 7.2.3 Steps of the backpropagation algorithm
- 7.2.4 Learning with Backpropagation
- 7.3 The case of layered networks
- 7.3.1 Extended network
- 7.3.2 Steps of the algorithm
- 7.3.3 Backpropagation in matrix form
- 7.3.4 The locality of backpropagation
- 7.3.5 An Example
- 7.4 Recurrent networks
- 7.4.1 Backpropagation through time
- 7.4.2 Hidden Markov Models
- 7.4.3 Variational problems
- 7.5 Historical and bibliographical remarks
8. Fast learning algorithms (PDF)
- 8.1 Introduction - Classical backpropagation
- 8.1.1 Backpropagation with momentum
- 8.1.2 The fractal geometry of backpropagation
- 8.2 Some simple improvements to backpropagation
- 8.2.1 Initial weight selection
- 8.2.2 Clipped derivatives and offset term
- 8.2.3 Reducing the number of floating-point operations
- 8.2.4 Data decorrelation
- 8.3 Adaptive step algorithms
- 8.3.1 Silva and Almeida´s algorithm
- 8.3.2 Delta-bar-delta
- 8.3.3 RPROP
- 8.3.4 The Dynamic Adaption Algorithm
- 8.4 Second-order algorithms
- 8.4.1 Quickprop
- 8.4.2 Second-order backpropagation
- 8.5 Relaxation methods
- 8.5.1 Weight and node perturbation
- 8.5.2 Symmetric and asymmetric relaxation
- 8.5.3 A final thought on taxonomy
- 8.6 Historical and bibliographical remarks
9. Statistics and Neural Networks (PDF)
- 9.1 Linear and nonlinear regression
- 9.1.1 The problem of good generalization
- 9.1.2 Linear regression
- 9.1.3 Nonlinear units
- 9.1.4 Computing the prediction error
- 9.1.5 The jackknife and cross-validation
- 9.1.6 Committees of networks
- 9.2 Multiple regression
- 9.2.1 Visualization of the solution regions
- 9.2.2 Linear equations and the pseudoinverse
- 9.2.3 The bidden layer
- 9.2.4 Computation of the pseudoinverse
- 9.3 Classification networks
- 9.3.1 An application: NETtalk
- 9.3.2 The Bayes property of classifier networks
- 9.3.3 Connectionist speech recognition
- 9.3.4 Autoregressive models for time series analysis
- 9.4 Historical and bibliographical remarks
10. The complexity of learning (PDF)
- 10.1 Network functions
- 10.1.1 Learning algorithms for multilayer networks
- 10.1.2 Hilbert´s problem and computability
- 10.1.3 Kolmogorov´s theorem
- 10.2 Function approximation
- 10.2.1 The one-dimensional case
- 10.2.2 The multidimensional case
- 10.3 Complexity of learning problems
- 10.3.1 Complexity classes
- 10.3.2 NP-complete learning problems
- 10.3.3 Complexity of learning with AND-OR networks
- 10.3.4 Simplifications of the network architecture
- 10.3.5 Learning with hints
- 10.4 Historical and bibliographical remarks
- 11.1 Fuzzy sets and fuzzy logic
- 11.1.1 Imprecise data and imprecise rules
- 11.1.2 The fuzzy set concept
- 11.1.3 Geometric representation of fuzzy sets
- 11.1.4 Set theory, logic operators and geometry
- 11.1.5 Families of fuzzy operators
- 11.2 Fuzzy inferences
- 11.2.1 Inferences from imprecise data
- 11.2.2 Fuzzy numbers and inverse operation
- 11.3 Control with fuzzy logic
- 11.3.1 Fuzzy controllers
- 11.3.2 Fuzzy networks
- 11.3.3 Function approximation with fuzzy methods
- 11.3.4 The eye as a fuzzy system - color vision
- 11.4 Historical and bibliographical remarks
12. Associative Networks (PDF)
- 12.1 Associative pattern recognition
- 12.1.1 Recurrent networks and types of associative memories
- 12.1.2 Structure of an associative memory
- 12.1.3 The eigenvector automaton
- 12.2 Associative learning
- 12.2.1 Hebbian Learning - The correlation matrix
- 12.2.2 Geometric interpretation of Hebbian learning
- 12.2.3 Networks as dynamical systems - Some experiments
- 12.2.4 Another visualization
- 12.3 The capacity problem
- 12.4 The pseudoinverse
- 12.4.1 Definition and properties of the pseudoinverse
- 12.4.2 Orthogonal projections
- 12.4.3 Holographic memories
- 12.4.4 Translation invariant pattern recognition
- 12.5 Historical and bibliographical remarks
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13. The Hopfield Model (PDF)
- 13.1 Synchronous and asynchronous networks
- 13.1.1 Recursive networks with stochastic dynamics
- 13.1.2 The bidirectional associative memory
- 13.1.3 The energy function
- 13.2 Definition of Hopfield networks
- 13.2.1 Asynchronous networks
- 13.2.2 Examples of the model
- 13.2.3 Isomorphism between the Hopfield and Ising models
- 13.3 Converge to stable states
- 13.3.1 Dynamics of Hopfield networks
- 13.3.2 Convergence proof
- 13.3.3 Hebbian learning
- 13.4 Equivalence of Hopfield and perceptron learning
- 13.4.1 Perceptron learning in Hopfield networks
- 13.4.2 Complexity of learning in Hopfield models
- 13.5 Parallel combinatorics
- 13.5.1 NP-complete problems and massive parallelism
- 13.5.2 The multiflop problem
- 13.5.3 The eight rooks problem
- 13.5.4 The eight queens problem
- 13.5.5 The traveling salesman
- 13.5.6 The limits of Hopfield networks
- 13.6 Implementation of Hopfield networks
- 13.6.1 Electrical implementation
- 13.6.2 Optical implementation
- 13.7 Historical and bibliographical remarks
14. Stochastic networks (PDF)
- 14.1 Variations of the Hopfield model
- 14.1.1 The continuous model
- 14.2 Stochastic systems
- 14.2.1 Simulated annealing
- 14.2.2 Stochastic neural networks
- 14.2.3 Markov chains
- 14.2.4 The Boltzmann distribution
- 14.2.5 Physical meaning of the Boltzmann distribution
- 14.3 Learning algorithms and applications
- 14.3.1 Boltzmann learning
- 14.3.2 Combinatorial optimization
- 14.4 Historical and bibliographical remarks
15. Kohonen networks (PDF)
- 15.1 Self-organization
- 15.1.1 Charting input space
- 15.1.2 Topology preserving maps in the brain
- 15.2 Kohonen´s model
- 15.2.1 Learning algorithm
- 15.2.2 Mapping low dimensional spaces with high-dimensional grids
- 15.3 Analysis of convergence
- 15.3.1 Potential function - the one-dimensional case
- 15.3.2 The two-dimensional case
- 15.3.3 Effect of a unit´s neighborhood
- 15.3.4 Metastable states
- 15.3.5 What dimension for Kohonen networks?
- 15.4 Applications
- 15.4.1 Approximation of functions
- 15.4.2 Inverse kinematics
- 15.5 Historical and bibliographical remarks
16. Modular Neural Network (PDF)
- 16.1 Constructive algorithms for modular networks
- 16.1.1 Cascade correlation
- 16.1.2 Optimal modules and mixtures of experts
- 16.2 Hybrid networks
- 16.2.1 The ART architecures
- 16.2.2 Maximum entropy
- 16.2.3 Counterpropagation networks
- 16.2.4 Spline networks
- 16.2.5 Radial basis functions
- 16.3 Historical and bibliographical remarks
17. Genetic Algorithms (PDF)
- 17.1 Coding and operators
- 17.1.1 Optimization problems
- 17.1.2 Methods of stochastic optimization
- 17.1.3 Genetic coding
- 17.1.4 Information exchange with genetic operators
- 17.2 Properties of genetic algorithms
- 17.2.1 Convergence analysis
- 17.2.2 Deceptive problems
- 17.2.3 Genetic drift
- 17.2.4 Gradient methods versus genetic algorithms
- 17.3 Neural networks and genetic algorithms
- 17.3.1 The problem of symmetries
- 17.3.2 A numerical experiment
- 17.3.3 Other applications of Gas
- 17.4 Historical and bibliographical remarks
18. Hardware for neural networks (PDF)
- 18.1 Taxonomy of neural hardware
- 18.1.1 Performance requirements
- 18.1.2 Types of neurocomputers
- 18.2 Analog neural networks
- 18.2.1 Coding
- 18.2.2 VLSI transistor circuits
- 18.2.3 Transistors with stored charge
- 18.2.4 CCD components
- 18.3 Digital networks
- 18.3.1 Numerical representation of weights and signals
- 18.3.2 Vector and signal processors
- 18.3.3 Systolic arrays
- 18.3.4 One-dimensional structures
- 18.4 Innovative computer architectures
- 18.4.1 VLSI microprocessors for neural networks
- 18.4.2 Optical computers
- 18.4.3 Pulse coded networks
- 18.5 Historical and bibliographical remarks
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