An Introduction to Natural Computation

By: Dana H. Ballard

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Paperback | 22 January 1999

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Paperback
332 Pages

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18+

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0.1 x 0.1 x 0.1

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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 brain's 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.

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Figures
Tables
Preface
Natural Computation
Introduction
The Brain
Subsystems
Maps
Neurons
Computational Theory
Elements Of Natural Computation
Minimum Description Length
Example 1: A Program That Prints 10,000 Ones
Example 2: A Neuron's Receptive Field
Learning
Architectures
Constraints of Time and Space
Cognitive Hierarchies
Overview
Core Concepts
Learning to React: Memories
Learning During a Lifetime: Programs
Learning Across Generations: Architectures
The Grand Challenge
Notes
Exercises
Core Concepts
Fitness
Introduction
Bayes' Rule
Example: Vision Test
Probability Distributions
Discrete Distributions
Binomial Distribution
Poisson Distribution
Continuous Distributions
Normal Distribution
Gaussian Approximation to a Binomial Distribution
Example
Information Theory
Information Content and Channel Capacity
Entropy
Reversible Codes
Irreversible Codes
Classification
Minimum Description Length
Example: Image Coding
Appendix: Laws of Probability
Example
Notes
Exercises
Programs
Introduction
Heuristic Search
The Eight-Puzzle
Two-Person Games
Minimax
Alpha and Beta Cutoffs
Biological State Spaces
Notes
Exercises
Data
Data Compression
Coordinate Systems
Eigenvalues And Eigenvectors
Eigenvalues of Positive Matrices
Random Vectors
Normal Distribution
Eigenvalues and Eigenvectors of the Covariance Matrix
High-Dimensional Spaces
Clustering
Appendix: Linear Algebra Review
Notes
Exercises
Dynamics
Overview
Linear Systems
The General Case
Intuitive Meaning of Eigenvalues and Eigenvectors
Nonlinear Systems
Linearizing a Nonlinear System
Lyapunov Stability
Appendix: Taylor Series
Notes
Exercises
Optimization
Introduction
Minimization Algorithms
The Method of Lagrange Multipliers
Optimal Control
The Euler-Lagrange Method
Dynamic Programming
Notes
Exercises
Memories
The Cortex As A Hierarchical Memory
Neural Network Models
Content-Addressable Memory
Supervised Learning
Unsupervised Learning
Notes
Content-Addressable Memory
Introduction
Hopfield Memories
Stability
Lyapunov Stability
Kanerva Memories
Implementation
Performance of Kanerva Memories
Implementations of Kanerva Memories
Radial Basis Functions
Kalman Filtering
Notes
Exercises
Supervised Learning
Introduction
Perceptrons
Continuous Activation Functions
Unpacking the Notation
Generating the Solution
Recurrent Networks
Minimum Description Length
The Activation Function
Maximum Likelihood with Gaussian Errors
Error Functions
Notes
Exercises
Unsupervised Learning
Introduction
Principal Components
Competitive Learning
Topological Constraints
The Traveling Salesman Example
Natural Topologies
Supervised Competitive Learning
Multimodal Data
Initial Labeling Algorithm
Minimizing Disagreement
Independent Components
Notes
Exercises
Programs
Brain Subsystems That Use Chemical Rewards
The Role of Rewards
System Integration
Learning Models
Markov Systems
Reinforcement Learning
Notes
Markov Models
Introduction
Markov Models
Regular Chains
Nonregular Chains
Hidden Markov Models
Formal Definitions
Three Principal Problems
The Probability of an Observation Sequence
Most Probable States
Improving the Model
Note
Exercises
Reinforcement Learning
Introduction
Markov Decision Process
The Core Idea: Policy Improvement
Q-Learning
Temporal-Difference-Learning
Learning With A Teacher
Partially Observable MDPs
Avoiding Bad States
Learning State Information from Temporal Sequences
Distiguishing the Value of States
Summary
Notes
Exercises
Systems
Gene Primer
Learning Across Generations: Systems
Standard Genetic Algorithms
Genetic Programming
Notes
Genetic Algorithms
Introduction
Genetic Operators
An Example
Schemata
Schemata Theorem
The Bandit Problem
Determining Fitness
Racing for Fitness
Coevolution of Parasites
Notes
Exercises
Genetic Programming
Introduction
Genetic Operators For Programs
Genetic Programming
Analysis
Modules
Testing for a Module Function
When to Diversify
Summary
Notes
Exercises
Summary
Learning To React: Memories
Learning During A Lifetime: Programs
Learning Across Generations: Systems
The Grand Challenge Revisited
Note
Index
Table of Contents provided by Publisher. All Rights Reserved.

An Introduction to Natural Computation

At a Glance

Paperback

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