Stone J. Principles of Neural Information Theory.Computational Neuroscience 2018
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Stone J. Principles of Neural Information Theory.Computational Neuroscience 2018
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The brain is the most complex computational machine known to science, even though its components (neurons) are slow and unreliable compared to a laptop computer. In this richly illustrated book, Shannon's mathematical theory of information is used to explore the computational efficiency of neurons, with special reference to visual perception and the efficient coding hypothesis. Evidence from a diverse range of research papers is used to show how information theory defines absolute limits on neural processing; limits which ultimately determine the neuroanatomical microstructure of the eye and brain. Written in an informal style, with a comprehensive glossary, tutorial appendices, and a list of annotated Further Readings, this book is an ideal introduction to the principles of neural information theory.
In the Light of Evolution
Introduction
All That We See
In the Light of Evolution
In Search of General Principles
Information Theory and Biology
An Overview of Chapters
Information Theory
Introduction
Finding a Route, Bit by Bit
Information and Entropy
Maximum Entropy Distributions
Channel Capacity
Mutual Information
The Gaussian Channel
Fourier Analysis
Summary
Measuring Neural Information
Introduction
The Neuron
Why Spikes?
Neural Information
Gaussian Firing Rates
Information About What?
Does Timing Precision Matter?
Rate Codes and Timing Codes
Summary
Pricing Neural Information
Introduction
The Efficiency-Rate Trade-Off
Paying with Spikes
Paying with Hardware
Paying with Power
Optimal Axon Diameter
Optimal Distribution of Axon Diameters
Axon Diameter and Spike Speed
Optimal Mean Firing Rate
Optimal Distribution of Firing Rates
Optimal Synaptic Conductance
Summary
Encoding Colour
Introduction
The Eye
How Aftereffects Occur
The Problem with Colour
A Neural Encoding Strategy
Encoding Colour
Why Aftereffects Occur
Measuring Mutual Information
Maximising Mutual Information
Principal Component Analysis
PCA and Mutual Information
Evidence for Efficiency
Summary
Encoding Time
Introduction
Linear Models
Neurons and Wine Glasses
The LNP Model
Estimating LNP Parameters
The Predictive Coding Model
Estimating Predictive Coding Parameters
Evidence for Predictive Coding
Summary
Encoding Space
Introduction
Spatial Frequency
Do Ganglion Cells Decorrelate Images?
Optimal Receptive Fields: Overview
Receptive Fields and Information
Measuring Mutual Information
Maximising Mutual Information
van Hateren’s Model
Predictive Coding of Images
Evidence for Predictive Coding
Is Receptive Field Spacing Optimal?
Summary
Encoding Visual Contrast
Introduction
The Compound Eye
Not Wasting Capacity
Measuring the Eye’s Response
Maximum Entropy Encoding
Evidence for Maximum Entropy Coding
Summary
The Neural Rubicon
Introduction
The Darwinian Cost of Efficiency
Crossing the Neural Rubicon
Further Reading
Appendices
Glossary
Mathematical Symbols
Correlation and Independence
A Vector Matrix Tutorial
Neural Information Methods
Key Equations
References
Index