Principles of Neural Information Theory: Computational Neuroscience and Metabolic Efficiency

by James V Stone

Overview

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 metabolic efficiency of neurons, with special reference to visual perception. Evidence from a diverse range of research papers is used to show how information theory defines absolute limits on neural efficiency; limits which ultimately determine the neuroanatomical microstructure of the eye and brain. Written in an informal style, with a comprehensive glossary, tutorial appendices, explainer boxes, and a list of annotated Further Readings, this book is an ideal introduction to cutting-edge research in neural information theory.

Product Details

ISBN-13:	9780993367922
Publisher:	Tutorial Introductions
Publication date:	05/15/2018
Series:	Tutorial Introductions
Pages:	214
Product dimensions:	6.00(w) x 9.00(h) x 0.45(d)

About the Author

Dr James Stone is an Honorary Reader in Vision and Computational Neuroscience at the University of Sheffield, England.

Table of Contents

Principles of Neural Information Theory

1. In the Light of Evolution

1.1. Introduction

1.2. All That We See

1.3. In the Light of Evolution

1.4. In Search of General Principles

1.5. Information Theory and Biology

1.6. An Overview of Chapters

2. Information Theory

2.1. Introduction.

2.2. Finding a Route, Bit by Bit

2.3. Information and Entropy

2.4. Maximum Entropy Distributions

2.5. Channel Capacity

2.6. Mutual Information

2.7. The Gaussian Channel

2.8. Fourier Analysis

2.9. Summary

3. Measuring Neural Information

3.1. Introduction

3.2. The Neuron

3.3. Why Spikes?

3.4. Neural Information

3.5. Gaussian Firing Rates

3.6. Information About What?

3.7. DoesTiming Precision Matter?

3.8. Rate Codes and Timing Codes

3.9. Summary

4. Pricing Neural Information

4.1. Introduction

4.2. The Efficiency-Rate Trade Off

4.3. Paying With Spikes

4.4. Paying With Hardware

4.5. Paying With Power

4.6. Optimal Axon Diameter

4.7. Optimal Distribution of Axon Diameters

4.8. Axon Diameter and Spike Speed

4.9. Optimal Mean Firing Rate

4.10.Optimal Distribution of Firing Rates

4.11.Optimal Synaptic Conductance

4.12. Summary

5. Encoding Colour

5.1. Introduction

5.2. The Eye

5.3. How Aftereffects Occur

5.4. The Problem With Colour

5.5. A Neural Encoding Strategy

5.6. Encoding Colour

5.7. Why Aftereffects Occur

5.8. Measuring Mutual Information

5.9. Maximising Mutual Information

5.10. Principal Component Analysis

5.11. PCA and Mutual Information

5.12.Evidence for Efficiency

5.13. Summary

6. Encoding Time

6.1. Introduction

6.2. Linear Models

6.3. Neurons and Wine Glasses

6.4. The LNP Model

6.5. Estimating LNP Parameters

6.6. The Predictive Coding Model

6.7. Estimating Predictive Coding Parameters

6.8. Evidence for Predictive Coding

6.9. Summary

7. Encoding Space

7.1. Introduction

7.2. SpatialFrequency

7.3. Do Ganglion Cells Decorrelate Images?

7.4. Optimal Receptive Fields: Overview

7.5. Receptive Fields and Information

7.6. Measuring Mutual Information

7.7. Maximising Mutual Information

7.8. van Hateren’s Model

7.9. Predictive Coding of Images

7.10. Evidence For Predictive Coding

7.11. Is Receptive Field Spacing Optimal?

7.12. Summary

8. Encoding Visual Contrast

8.1. Introduction

8.2. The Compound Eye

8.3. Not Wasting Capacity

8.4. Measuring the Eye’s Response.

8.5. Maximum Entropy Encoding

8.6. Evidence For Maximum Entropy Coding

8.7. Summary

9. The Neural Rubicon

9.1. Introduction.

9.2. The Darwinian Cost of Efficiency

9.3. Crossing the Neural Rubicon Further Reading

Appendices

A. Glossary

B. Mathematical Symbols

C. Correlation and Independence

D. A Vector Matrix Tutorial

E. Neural Information Methods

F. Key Equations

References

Index

Editorial Reviews

“This is a terrific book, which cannot fail to help any student who wants to understand precisely how energy and information constrain neural design. The tutorial approach adopted makes it more like a novel than a textbook. Consequently, both mathematically sophisticated readers and readers who prefer verbal explanations should be able to understand the material. Overall, Stone has managed to weave the disparate strands of neuroscience, psychophysics, and Shannon’s theory of communication into a coherent account of neural information theory. I only wish I'd had this text as a student!”

Peter Sterling, Professor of Neuroscience, University of Pennsylvania, USA.

"Essential reading for any student of the why of neural coding: why do neurons send signals they way they do? Stone's insightful, clear, and eminently readable synthesis of classic studies is a gateway to a rich, glorious literature on the brain. Student and professor alike will find much to spark their minds within. I shall be keeping this wonderful book close by, as a sterling reminder to ask not just how brains work, but why."

Professor Mark Humphries, School of Psychology, University of Nottingham, UK.

"This excellent book provides an accessible introduction to an information theoretic perspective on how the brain works, and (more importantly) why it works that way. Using a wide range of examples, including both structural and functional aspects of brain organisation, Stone describes how simple optimisation principles derived from Shannon's information theory predict physiological parameters (e.g. axon diameter) with remarkable accuracy. These principles are distilled from original research papers, and the informal presentation style means that the book can be appreciated as an overview; but full mathematical details are also provided for dedicated readers. Stone has integrated results from a diverse range of experiments, and in so doing has produced an invaluable introduction to the nascent field of neural information theory. "

Dr Robin Ince, Centre for Cognitive Neuroimaging, Institute of Neuroscience and Psychology, University of Glasgow, UK.

From the Publisher