Neural engineering: computation, representation, and dynamics in neurobiological systems

377 Pages·2003·4.857 MB·English

by  Chris Eliasmith, C. H. Anderson

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Neural Engineering
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ComputationalNeuroscience
TerrenceJ.SejnowskiandTomasoA.Poggio,editors
NeuralNetsinElectricFish,WalterHeiligenberg,1991
TheComputationalBrain,PatriciaS.ChurchlandandTerrenceJ.Sejnowski,1992
DynamicBiologicalNetworks:TheStomatogastricNervousSystem,editedbyRonaldM.
Harris-Warrick,EveMarder,AllenI.Selverston,andMauriceMoulins,1992
TheNeurobiologyofNeuralNetworks,editedbyDanielGardner,1993
Large-ScaleNeuronalTheories of the Brain, edited by Christof Koch and Joel L. Davis,
1994
The TheoreticalFoundationsofDendritic Function:SelectedPapers ofWilfrid Rallwith
Commentaries,editedbyIdanSegev,JohnRinzel,andGordonM.Shepherd,1995
ModelsofInformationProcessingintheBasalGanglia,editedbyJamesC.Houk,JoelL.
Davis,andDavidG.Beiser,1995
Spikes: Exploring the Neural Code, Fred Rieke, David Warland, Rob de Ruyter van
Steveninck,andWilliamBialek,1997
Neurons, Networks, and Motor Behavior, edited by Paul S. Stein, Sten Grillner, Allen I.
Selverston,andDouglasG.Stuart,1997
MethodsinNeuronalModeling:FromIonstoNetworks,secondedition,editedbyChristof
KochandIdanSegev,1998
Fundamentals of Neural Network Modeling: Neuropsychology and Cognitive Neuro-
science,editedbyRandolphW.Parks,DanielS.Levine,andDebraL.Long,1998
Neural Codes and Distributed Representations: Foundations of Neural Computation,
editedbyLaurenceAbbottandTerrenceJ.Sejnowski,1999
UnsupervisedLearning:FoundationsofNeuralComputation,edited byGeoffreyHinton
andTerrenceJ.Sejnowski,1999
FastOscillationsinCorticalCircuits,RogerD.Traub,JohnG.R.Jefferys,andMilesA.
Whittington,1999
ComputationalVision:InformationProcessinginPerceptionandVisualBehavior,Hanspeter
A.Mallot,2000
GraphicalModels:FoundationsofNeuralComputation,editedbyMichaelI.Jordanand
TerrenceJ.Sejnowski,2001
Self-Organizing Map Formation: Foundations of Neural Computation, edited by Klaus
ObermayerandTerrenceJ.Sejnowski,2001
NeuralEngineering:Computation,Representation,andDynamicsinNeurobiologicalSys-
tems,ChrisEliasmithandCharlesH.Anderson,2003
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Neural Engineering
Computation,Representation,andDynamicsinNeurobiologicalSystems
ChrisEliasmithandCharlesH.Anderson
ABradfordBook
TheMITPress
Cambridge,Massachusetts
London,England
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c 2003MassachusettsInstituteofTechnology
A(cid:1)ll rights reserved. No part of this book may be reproduced in any form by any electronic or
mechanicalmeans(includingphotocopying,recording,orinformationstorageandretrieval)without
permissioninwritingfromthepublisher.
ThisbookwastypesetinTimesbytheauthorsusingLYXandLATEXandwasprintedandboundin
theUnitedStatesofAmerica.
LibraryofCongressCataloging-in-PublicationData
Eliasmith,Chris.
Neural engineering : computation, representation, and dynamics
in neurobiological systems / Chris Eliasmith and Charles H.
Anderson.
p.cm.–(Computationalneuroscience)
“ABradfordbook.”
Includesbibliographicalreferencesandindex.
ISBN0-262-05071-4(hc.)
1.Neuralnetworks(Neurobiology)2.Neuralnetworks(Computer
science) 3. Computational neuroscience. I. Anderson, Charles H.
II.Title.III.Series.
QP363.3.E4542002
573.8’5–dc21
2002070166
10987654321
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ToJen,Alana,Alex,andCharlie
and
ToDavidVanEssen
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This page intentionally left blank
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Contents
Preface xiii
Usingthisbookasacoursetext xvii
Acknowledgments xix
1 Ofneuronsandengineers 1
1.1 Explainingneuralsystems 3
1.2 Neuralrepresentation 5
1.2.1 Thesingleneuron. . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Beyondthesingleneuron. . . . . . . . . . . . . . . . . 11
1.3 Neuraltransformation 13
1.4 Threeprinciplesofneuralengineering 15
1.4.1 Principle1 . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4.2 Principle2 . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4.3 Principle3 . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4.4 Addendum . . . . . . . . . . . . . . . . . . . . . . . . 18
1.5 Methodology 19
1.5.1 Systemdescription . . . . . . . . . . . . . . . . . . . . 19
1.5.2 Designspecification . . . . . . . . . . . . . . . . . . . 21
1.5.3 Implementation . . . . . . . . . . . . . . . . . . . . . . 21
1.5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 22
1.6 Apossibletheoryofneurobiologicalsystems 23
I REPRESENTATION
2 Representationinpopulationsofneurons 29
2.1 Representingscalarmagnitudes 30
2.1.1 Engineeredrepresentation . . . . . . . . . . . . . . . . 30
2.1.2 Biologicalrepresentation . . . . . . . . . . . . . . . . . 33
2.2 Noiseandprecision 40
2.2.1 Noisyneurons . . . . . . . . . . . . . . . . . . . . . . 40
2.2.2 Biologicalrepresentationandnoise . . . . . . . . . . . 42
2.3 Anexample:Horizontaleyeposition 44
2.3.1 Systemdescription . . . . . . . . . . . . . . . . . . . . 44
2.3.2 Designspecification . . . . . . . . . . . . . . . . . . . 46
2.3.3 Implementation . . . . . . . . . . . . . . . . . . . . . . 47
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2.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4 Representingvectors 49
2.5 Anexample:Armmovements 52
2.5.1 Systemdescription . . . . . . . . . . . . . . . . . . . . 53
2.5.2 Designspecification . . . . . . . . . . . . . . . . . . . 54
2.5.3 Implementation . . . . . . . . . . . . . . . . . . . . . . 55
2.5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 55
2.6 Anexample:Semicircularcanals 57
2.6.1 Systemdescription . . . . . . . . . . . . . . . . . . . . 57
2.6.2 Implementation . . . . . . . . . . . . . . . . . . . . . . 58
2.7 Summary 59
3 Extendingpopulationrepresentation 61
3.1 Arepresentationalhierarchy 61
3.2 Functionrepresentation 63
3.3 Functionspacesandvectorspaces 69
3.4 Anexample:Workingmemory 72
3.4.1 Systemdescription . . . . . . . . . . . . . . . . . . . . 73
3.4.2 Designspecification . . . . . . . . . . . . . . . . . . . 74
3.4.3 Implementation . . . . . . . . . . . . . . . . . . . . . . 77
3.4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 78
3.5 Summary 79
4 Temporalrepresentationinspikingneurons 81
4.1 Theleakyintegrate-and-fire(LIF)neuron 81
4.1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . 81
4.1.2 CharacterizingtheLIFneuron . . . . . . . . . . . . . . 83
4.1.3 StrengthsandweaknessesoftheLIFneuronmodel . . . 88
4.2 Temporalcodesinneurons 89
4.3 Decodingneuralspikes 92
4.3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . 92
4.3.2 Neuronpairs . . . . . . . . . . . . . . . . . . . . . . . 94
4.3.3 Representingtimedependentsignalswithspikes . . . . 96
4.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 103
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4.4 InformationtransmissioninLIFneurons 105
4.4.1 FindingoptimaldecodersinLIFneurons . . . . . . . . 105
4.4.2 Informationtransmission . . . . . . . . . . . . . . . . . 109
4.4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 114
4.5 Morecomplexsingleneuronmodels 115
4.5.1 AdaptingLIFneuron . . . . . . . . . . . . . . . . . . . 116
4.5.2 -neuron . . . . . . . . . . . . . . . . . . . . . . . . . 118
(cid:1)
4.5.3 Adapting,conductance-basedneuron . . . . . . . . . . 123
4.5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 126
4.6 Summary 127
5 Population-temporalrepresentation 129
5.1 Puttingtimeandpopulationstogetheragain 129
5.2 Noiseandprecision:Dealingwithdistortions 132
5.3 Anexample:Eyepositionrevisited 136
5.3.1 Implementation . . . . . . . . . . . . . . . . . . . . . . 136
5.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 137
5.4 Summary 139
II TRANSFORMATION
6 Feed-forwardtransformations 143
6.1 Lineartransformationsofscalars 143
6.1.1 Acommunicationchannel . . . . . . . . . . . . . . . . 143
6.1.2 Addingtwovariables . . . . . . . . . . . . . . . . . . . 148
6.2 Lineartransformationsofvectors 151
6.3 Nonlineartransformations 153
6.3.1 Multiplyingtwovariables . . . . . . . . . . . . . . . . 154
6.4 Negativeweightsandneuralinhibition 160
6.4.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 166
6.5 Anexample:Thevestibularsystem 168
6.5.1 Systemdescription . . . . . . . . . . . . . . . . . . . . 169
6.5.2 Designspecification . . . . . . . . . . . . . . . . . . . 174
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