It is now clear that the brain is unlikely to be understood without recourse to computational theories. The theme of An Introduction to Natural Computation is that ideas from diverse areas such as neuroscience, information theory, and optimization theory have recently been extended in ways that make them useful for describing the brains programs. This book provides a comprehensive introduction to the computational material that forms the underpinnings of the currently evolving set of brain models. It stresses the broad spectrum of learning models--ranging from neural network learning through reinforcement learning to genetic learning--and situates the various models in their appropriate neural context. To write about models of the brain before the brain is fully understood is a delicate matter. Very detailed models of the neural circuitry risk losing track of the task the brain is trying to solve. At the other extreme, models that represent cognitive constructs can be so abstract that they lose all relationship to neurobiology. An Introduction to Natural Computation takes the middle ground and stresses the computational task while staying near the neurobiology.

Natural Computation 1.1 Introduction 1.2 The Brain 1.2.1 Subsystems 1.2.2 Maps 1.2.3 Neurons 1.3 Computational Theory 1.4 Elements Of Natural Computation 1.4.1 Minimum Description Length Example 1: A Program That Prints 10,000 Ones Example 2: A Neuron's Receptive Field 1.4.2 Learning 1.4.3 Architectures Constraints of Time and Space Cognitive Hierarchies 1.5 Overview 1.5.1 Core Concepts 1.5.2 Learning to React: Memories 1.5.3 Learning During a Lifetime: Programs 1.5.4 Learning Across Generations: Architectures 1.6 The Grand Challenge Notes Exercises I CORE CONCEPTS Fitness 2.1 Introduction 2.2 Bayes' Rule Example: Vision Test 2.3 Probability Distributions 2.3.1 Discrete Distributions Binomial Distribution Poisson Distribution 2.3.2 Continuous Distributions Normal Distribution Gaussian Approximation to a Binomial Distribution Example 2.4 Information Theory 2.4.1 Information Content and Channel Capacity 2.4.2 Entropy 2.4.3 Reversible Codes Irreversible Codes 2.5 Classification 2.6 Minimum Description Length Example: Image Coding Appendix: Laws of Probability Example Notes Exercises Programs 3.1 Introduction 3.2 Heuristic Search 3.2.1 The Eight-Puzzle 3.3 Two-Person Games 3.3.1 Minimax 3.3.2 Alpha and Beta Cutoffs 3.4 Biological State Spaces Notes Exercises Data 4.1 Data Compression 4.2 Coordinate Systems 4.3 Eigenvalues And Eigenvectors 4.3.1 Eigenvalues of Positive Matrices 4.4 Random Vectors 4.4.1 Normal Distribution 4.4.2 Eigenvalues and Eigenvectors of the Covariance Matrix 4.5 High-Dimensional Spaces 4.6 Clustering Appendix: Linear Algebra Review Notes Exercises Dynamics 5.1 Overview 5.2 Linear Systems 5.2.1 The General Case 5.2.2 Intuitive Meaning of Eigenvalues and Eigenvectors 5.3 Nonlinear Systems 5.3.1 Linearizing a Nonlinear System 5.3.2 Lyapunov Stability Appendix: Taylor Series Notes Exercises Optimization 6.1 Introduction 6.2 Minimization Algorithms 6.3 The Method of Lagrange Multipliers 6.4 Optimal Control 6.4.1 The Euler-Lagrange Method 6.4.2 Dynamic Programming Notes Exercises II MEMORIES The Cortex As A Hierarchical Memory Neural Network Models Content-Addressable Memory Supervised Learning Unsupervised Learning Notes Content-Addressable Memory 7.1 Introduction 7.2 Hopfield Memories 7.2.1 Stability 7.2.2 Lyapunov Stability 7.3 Kanerva Memories 7.3.1 Implementation 7.3.2 Performance of Kanerva Memories 7.3.3 Implementations of Kanerva Memories 7.4 Radial Basis Functions 7.5 Kalman Filtering Notes Exercises Supervised Learning 8.1 Introduction 8.2 Perceptrons 8.3 Continuous Activation Functions 8.3.1 Unpacking the Notation 8.3.2 Generating the Solution 8.4 Recurrent Networks 8.5 Minimum Description Length 8.6 The Activation Function 8.6.1 Maximum Likelihood with Gaussian Errors 8.6.2 Error Functions Notes Exercises Unsupervised Learning 9.1 Introduction 9.2 Principal Components 9.3 Competitive Learning 9.4 Topological Constraints 9.4.1 The Traveling Salesman Example 9.4.2 Natural Topologies 9.5 Supervised Competitive Learning 9.6 Multimodal Data 9.6.1 Initial Labeling Algorithm 9.6.2 Minimizing Disagreement 9.7 Independent Components Notes Exercises III PROGRAMS Brain Subsystems That Use Chemical Rewards The Role of Rewards System Integration Learning Models Markov Systems Reinforcement Learning Notes Markov Models 10.1 Introduction 10.2 Markov Models 10.2.1 Regular Chains 10.2.2 Nonregular Chains 10.3 Hidden Markov Models 10.3.1 Formal Definitions 10.3.2 Three Principal Problems 10.3.3 The Probability of an Observation Sequence 10.3.4 Most Probable States 10.3.5 Improving the Model Note Exercises Reinforcement Learning 11.1 Introduction 11.2 Markov Decision Process 11.3 The Core Idea: Policy Improvement 11.4 Q-Learning 11.5 Temporal-Difference-Learning 11.6 Learning With A Teacher 11.7 Partially Observable MDPs 11.7.1 Avoiding Bad States 11.7.2 Learning State Information from Temporal Sequences 11.7.3 Distiguishing the Value of States 11.8 Summary Notes Exercises IV SYSTEMS Gene Primer Learning Across Generations: Systems Standard Genetic Algorithms Genetic Programming Notes Genetic Algorithms 12.1 Introduction 12.1.1 Genetic Operators 12.1.2 An Example 12.2 Schemata 12.2.1 Schemata Theorem 12.2.2 The Bandit Problem 12.3 Determining Fitness 12.3.1 Racing for Fitness 12.3.2 Coevolution of Parasites Notes Exercises Genetic Programming 13.1 Introduction 13.2 Genetic Operators For Programs 13.3 Genetic Programming 13.4 Analysis 13.5 Modules 13.5.1 Testing for a Module Function 13.5.2 When to Diversify 13.6 Summary Notes Exercises Summary 14.1 Learning To React: Memories 14.2 Learning During A Lifetime: Programs 14.3 Learning Across Generations: Systems 14.4 The Grand Challenge Revisited Note Index

Dana H. Ballard is Professor of Computer Science at the University of Texas at Austin.

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