The Noisy Brain: Stochastic Dynamics as a Principle of Brain Function

397 Pages·2010·4.03 MB·English

by  Edmund T. Rolls, Gustavo Deco

The Noisy Brain:
Stochastic Dynamics as a Principle of
Brain Function
Edmund T. Rolls
OxfordCentreforComputationalNeuroscience
Oxford
England
Gustavo Deco
InstitucioCatalanadeRecercaiEstudisAvancats(ICREA)
UniversitatPompeuFabra
Barcelona
Spain
.
OXFORD UNIVERSITY PRESS OXFORD 2010
Title Pages
Stochastic Dynamics as a Principle of Brain Function (p.ii)
The Noisy Brain The Noisy Brain
(p.iv)
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Preface
The relatively random spiking times of individual neurons produce a source of noise in the
brain. The aim of this book is to consider the effects of this and other noise on brain pro-
cessing. We show that in cortical networks this noise can be an advantage, for it leads to
probabilisticbehaviourthatisadvantageousindecision-making,bypreventingdeadlock,and
is important in signal detectability. We show how computations can be performed through
stochastic dynamical effects, including the role of noise in enabling probabilistic jumping
acrossbarriersintheenergylandscapedescribingtheflowofthedynamicsinattractornet-
works.Theresultsobtainedinneurophysiologicalstudiesofdecision-makingandsignalde-
tectabilityaremodelledbythestochasticalneurodynamicsofintegrate-and-firenetworksof
neuronswithprobabilisticneuronalspiking.Wedescribehowthesestochasticneurodynami-
caleffectscanbeanalyzed,andtheirimportanceinmanyaspectsofbrainfunction,including
decision-making, perception, memory recall, short-term memory, and attention. We show
howinstabilitiesinthesebraindynamicsmaycontributetothecognitivesymptomsinaging
andinpsychiatricstatessuchasschizophrenia,andhowoverstabilitymaycontributetothe
symptomsinobsessive-compulsivedisorder.
This is a new approach to the dynamics of neural processing, in which we show that
noise breaks deterministic computations, and has many advantages. These principles need
to be analyzed in order to understand brain function and behaviour, and it is an aim of this
book to elucidate the stochastic, that is probabilistic, dynamics of brain processing, and its
advantages. The book describes approaches that provide a foundation for this understand-
ing,includingintegrate-and-firemodelsofbrainandcognitivefunctionthatincorporatethe
stochasticspiking-relateddynamics,andmean-fieldanalysesthatareconsistentintermsof
theparameterswiththese,butallowformalanalysisofthenetworks.Afeatureofthetreat-
mentofthemean-fieldapproachisthatweintroducenewwaysinwhichitcanbeextended
to include some of the effects of noise on the operation of the system. The book thus de-
scribestheunderpinningsinphysicsofthisnewapproachtotheprobabilisticfunctioningof
thebrain.However,atthesametime,mostoftheconceptsofthebookandtheprinciplesof
the stochastic operation of the brain described in the book, can be understood by neurosci-
entists and others interested in brain function who do not have expertise in mathematics or
theoreticalphysics,andthebookhasbeenwrittenwiththisinmind.
We believe that the principles of the stochastic dynamics of brain function described in
thisbookareimportant,forbrainfunctioncannotbeunderstoodasadeterministicnoiseless
system.
Tounderstandhowthebrainworks,includinghowitfunctionsinmemory,attention,and
decision-making,itisnecessarytocombinedifferentapproaches,includingneuralcomput-
ation.Neurophysiologyatthesingleneuronlevelisneededbecausethisisthelevelatwhich
information is exchanged between the computing elements of the brain, the neurons. Evi-
dence from the effects of brain damage, including that available from neuropsychology, is
neededtohelpunderstandwhatdifferentpartsofthesystemdo,andindeedwhateachpart
is necessary for. Functional neuroimaging is useful to indicate where in the human brain
different processes take place, and to show which functions can be dissociated from each
other.Knowledgeofthebiophysicalandsynapticpropertiesofneuronsisessentialtounder-
standhowthecomputingelementsofthebrainwork,andthereforewhatthebuildingblocks
vi | Preface
ofbiologicallyrealisticcomputationalmodelsshouldbe.Knowledgeoftheanatomicaland
functional architecture of the cortex is needed to show what types of neuronal network ac-
tuallyperformthecomputation.Theapproachofneuralcomputationisalsoneeded,asthis
is required to link together all the empirical evidence to produce an understanding of how
thesystemactuallyworks.Butanunderstandingoftheroleofnoiseinbraincomputationis
alsocrucial,asweshowinthisbook.Thisbookutilizesevidencefromalltheseapproaches
to develop an understanding of how different types of memory, perception, attention, and
decision-making are implemented by processing in the brain, and are influenced by the ef-
fectsofnoise.
Weemphasizethattounderstandmemory,perception,attention,anddecision-makingin
the brain, we are dealing with large-scale computational systems with interactions between
theparts,andthatthisunderstandingrequiresanalysisatthecomputationalandgloballevel
of the operation of many neurons to perform together a useful function. Understanding at
the molecular level is important for helping to understand how these large-scale computa-
tionalprocessesareimplementedinthebrain,butwillnotbyitselfgiveanyaccountofwhat
computationsareperformedtoimplementthesecognitivefunctions.Instead,understanding
cognitive functions such as memory recall, attention, and decision-making requires single
neuron data to be closely linked to computational models of how the interactions between
largenumbersofneuronsandmanynetworksofneuronsallowthesecognitiveproblemsto
be solved. The single neuron level is important in this approach, for the single neurons can
bethoughtofasthecomputationalunitsofthesystem,andisthelevelatwhichtheinform-
ationisexchangedbythespikingactivitybetweenthecomputationalelementsofthebrain.
Thesingleneuronlevelistherefore,becauseitisthelevelatwhichinformationiscommu-
nicated between the computing elements of the brain, the fundamental level of information
processing,andthelevelatwhichtheinformationcanbereadout(byrecordingthespiking
activity)inordertounderstandwhatinformationisbeingrepresentedandprocessedineach
brainarea.Moreover,theprobabilisticspikingofindividualneuronsisanimportantsource
ofnoiseinthebrain,andmustbetakenintoaccounttounderstandbrainfunction.
Atestofwhetherone’sunderstandingiscorrectistosimulatetheprocessingonacom-
puter, and to show whether the simulation can perform the tasks of memory systems in the
brain, and whether the simulation has similar properties to the real brain. The approach of
neural computation leads to a precise definition of how the computation is performed, and
topreciseandquantitativetestsofthetheoriesproduced.Howmemorysystemsinthebrain
work is a paradigm example of this approach, because memory-like operations which in-
volve altered functionality as a result of synaptic modification are at the heart of how all
computationsinthebrainareperformed.Ithappensthatattentionanddecision-makingcan
beunderstoodintermsofinteractionsbetweenandfundamentaloperationsofnetworksthat
implementcomputationsthatimplementmemoryoperationsinthebrain,andthereforeitis
natural to treat these areas of cognitive neuroscience as well as memory in this book. The
samefundamentalconceptsbasedontheoperationofneuronalcircuitrycanbeappliedtoall
thesefunctions,asisshowninthisbook.
One of the distinctive properties of this book is that it links the neural computation ap-
proach not only firmly to neuronal neurophysiology, which provides much of the primary
dataabouthowthebrainoperates,butalsotopsychophysicalstudies(forexampleofatten-
tion); to psychiatric studies of patients; to functional magnetic resonance imaging (fMRI)
(and other neuroimaging) approaches; and to approaches influenced by theoretical physics
about how the operation of large scale systems can be understood as a result of statistical
effectsinitscomponents,inthiscasetheneurons.Theempiricalevidencethatisbroughtto
bearislargelyfromnon-humanprimatesandfromhumans,becauseoftheconsiderablesim-
ilarityoftheirmemoryandrelatedsystems,andtheoverallaimstounderstandhowmemory,
Preface| vii
attention, decision-making and related functions are implemented in the human brain, and
thedisordersthatcanarise.
Theoverallaimsofthebookaredevelopedfurther,andtheplanofthebookisdescribed,
inChapter1,Section1.1.
Partofthematerialdescribedinthebookreflectsworkperformedincollaborationwith
many colleagues, whose tremendous contributions are warmly appreciated. The contribu-
tions of many will be evident from the references cited in the text. Especial appreciation is
duetoAlessandroTreves,MarcoLoh,andSimonM.Stringer,whohavecontributedgreatly
inanalwaysinterestingandfruitfulresearchcollaborationoncomputationalaspectsofbrain
function, and to many neurophysiology and functional neuroimaging colleagues who have
contributed to the empirical discoveries that provide the foundation to which the computa-
tional neuroscience must always be closely linked, and whose names are cited throughout
thetext.Muchoftheworkdescribedwouldnothavebeenpossiblewithoutfinancialsupport
fromanumberofsources,particularlytheMedicalResearchCounciloftheUK,theHuman
Frontier Science Program, the Wellcome Trust, and the James S. McDonnell Foundation.
The book was typeset by the Edmund Rolls using LaTex and WinEdt, and Gustavo Deco
tookprimaryresponsibilityfortheAppendix.
The covers show part of the picture Ulysses and the Sirens painted in 1909 by Herbert
James Draper.The version on the back cover has noise added, and might be called Ulysses
and the Noisy Sirens. The metaphors are of noise: sirens, and stormy, irregular, water; of
waves and basins of attraction: the waves on the horizon; of decision-making: the rational
consciousinUlyssesresistingthegene-basedemotion-relatedattractors;andofUlyssesthe
explorer(theGreekOdysseusofHomer),alwaysandindefatigably(liketheauthors)seeking
newdiscoveriesabouttheworld(andhowitworks).
Updatestosomeofthepublicationscitedinthisbookareavailableathttp://www.oxcns.org.
Wededicatethisworktotheoverlappinggroup:ourfamilies,friends,andmanycolleagues
whosecontributionsaregreatlyappreciated–insalutempraesentium,inmemoriamabsen-
tium.Inaddition,GustavoDecothanksanddedicatesthisbooktohisfamily,MariaEugenia,
Nikolas,Sebastian,Martin,andMatthias.Weremembertooaclosecolleagueandfriend,the
theoreticalphysicistDanielAmit,whocontributedmuchtotheanalysisofattractornetworks
(Amit1989,BrunelandAmit1997).
Contents
1 Introduction:Neuronal,Cortical,andNetworkfoundations 1
1.1 Introductionandoverview 1
1.2 Neurons 3
1.3 Synapticmodification 4
1.4 Long-termpotentiationandlong-termdepression 5
1.5 Neuronalbiophysics 10
1.6 Actionpotentialdynamics 11
1.7 Systems-levelanalysisofbrainfunction 12
1.8 Thefinestructureofthecerebralneocortex 17
1.8.1 Thefinestructureandconnectivityoftheneocortex 17
1.8.2 Excitatorycellsandconnections 17
1.8.3 Inhibitorycellsandconnections 19
1.8.4 Quantitativeaspectsofcorticalarchitecture 21
1.8.5 Functionalpathwaysthroughthecorticallayers 23
1.8.6 Thescaleoflateralexcitatoryandinhibitoryeffects,andtheconceptofmodules 25
1.9 Backprojectionsinthecortex 26
1.9.1 Architecture 26
1.9.2 Recall 28
1.9.3 Attention 29
1.9.4 Backprojections,attractornetworks,andconstraintsatisfaction 30
1.10 Autoassociationorattractormemory 30
1.10.1 Architectureandoperation 32
1.10.2 Introductiontotheanalysisoftheoperationofautoassociationnetworks 33
1.10.3 Properties 35
1.10.4 Useofautoassociationnetworksinthebrain 39
1.11 Noise,andthesparsedistributedrepresentationsfoundinthebrain 40
1.11.1 Definitions 41
1.11.2 Advantagesofdifferenttypesofcoding 42
1.11.3 Firingratedistributionsandsparseness 43
1.11.4 Informationtheoreticunderstandingofneuronalrepresentations 57
2 Stochasticneurodynamics 65
2.1 Introduction 65
2.2 Networkdynamics:theintegrate-and-fireapproach 65
2.2.1 Fromdiscretetocontinuoustime 66
2.2.2 Continuousdynamicswithdiscontinuities:integrate-and-fireneuronalnetworks 67
x | Contents
2.2.3 Anintegrate-and-fireimplementationwithNMDAreceptorsanddynamicalsyn-
apses 71
2.3 Attractornetworks,energylandscapes,andstochasticdynamics 73
2.4 Reasonswhythebrainisinherentlynoisyandstochastic 78
2.5 Braindynamicswithandwithoutstochasticity:anintroductiontomean-fieldtheory 80
2.6 Networkdynamics:themean-fieldapproach 81
2.7 Mean-fieldbasedtheory 82
2.7.1 Populationactivity 83
2.7.2 Themean-fieldapproachusedinthemodelofdecision-making 85
2.7.3 Themodelparametersusedinthemean-fieldanalysesofdecision-making 87
2.7.4 Mean-fieldneurodynamicsusedtoanalyzecompetitionandcooperationbetween
networks 88
2.7.5 Aconsistentmean-fieldandintegrate-and-fireapproach 88
3 Short-termmemoryandstochasticdynamics 91
3.1 Introduction 91
3.2 Corticalshort-termmemorysystemsandattractornetworks 91
3.3 Prefrontalcortexshort-termmemorynetworks,andtheirrelationtoperceptualnetworks 94
3.4 Computationalnecessityforaseparate,prefrontalcortex,short-termmemorysystem 98
3.5 Synapticmodificationisneededtosetupbutnottoreuseshort-termmemorysystems 98
3.6 What,where,andobject–placecombinationshort-termmemoryintheprefrontalcortex 99
3.7 Hierarchicallyorganizedseriesofattractornetworks 100
3.8 Stochasticdynamicsandthestabilityofshort-termmemory 102
3.8.1 Analysisofthestabilityofshort-termmemory 103
3.8.2 Stabilityandnoiseinthemodelofshort-termmemory 104
3.8.3 Alterationsofstability 106
3.9 Memoryfortheorderofitemsinshort-termmemory 114
3.10 Stochasticdynamicsandlong-termmemory 120
4 Attentionandstochasticdynamics 121
4.1 Introduction 121
4.2 Biasedcompetition—singleneuronstudies 121
4.3 Abasiccomputationalmoduleforbiasedcompetition 126
4.4 Theneuronalandbiophysicalmechanismsofattention 128
4.5 Stochasticdynamicsandattention 132
4.6 Disengagementofattention,andneglect 135
4.7 Decreasedstabilityofattentionproducedbyalterationsinsynapticallyactivatedionchan-
nels 135
4.8 Increasedstabilityofattentionproducedbyalterationsinsynapticallyactivatedionchan-
nels 137
5 Probabilisticdecision-making 139
5.1 Introduction 139
5.2 Decision-makinginanattractornetwork 140