Bridging Neural and Computational Viewpoints on Perceptual Decision Making

Review

Bridging

Neural

and

Computational

Viewpoints

on

Perceptual

Decision-Making

Redmond

G.

O

’

Connell,

* Michael

N.

Shadlen,

KongFatt

Wong-Lin,

and

Simon

P.

Kelly

*

Sequentialsamplingmodelshaveprovidedadominanttheoreticalframework

guiding computational and neurophysiological investigations of perceptual

decision-making.Whilethesemodelssharethebasicprinciplethatdecisions

areformedbyaccumulatingsensoryevidencetoabound,theycomeinmany

formsthatcanmakesimilarpredictionsofchoicebehaviourdespiteinvoking

fundamentallydifferentmechanisms. Theidentificationofneuralsignals that

reflectsomeofthecorecomputationsunderpinningdecisionformationoffers

newavenuesforempiricallytestingandrefiningkeymodelassumptions.Here,

wehighlightrecenteffortstoexploretheseavenuesand,insodoing,consider

theconceptualandmethodologicalchallengesthatarisewhenseekingtoinfer

decisioncomputationsfromcomplexneuraldata.

Decision-MakingasaCoreComponentofCognition

Theterm ‘decision-making’often calls to mindscenarios such as votingin anelection or selectingacourseofstudy.Yet,evensimplyperceivingoursensoryenvironmentreliesona continuousstreamofelementaryjudgments,knownas‘perceptualdecisions’.Insomecases, perceptualdecisionscanbeasconsequentialasthoserequiringmoreabstractjudgements(e. g.,isthetrafficlightredorgreen?).Inthehighlycomplexanddynamicenvironmentthatwe inhabit,makingaccurateandtimelydecisionsisaconsiderablechallengeforthebrain,since theinformationitreceivesisalmostalwaystosomedegreeunreliable.Understandinghowthe brain overcomes the challenges associated with perceptual decision-making could also illuminatebroaderprinciplesofcomputationthatextendtoarangeofcognitiveoperations[1].

Thetheoreticalfoundationsformodernresearchonperceptualdecision-makingwerelaidwithin mathematicalpsychology,withthedevelopmentof‘sequentialsampling’orevidence

accumu-lation(seeGlossary)models[2–6].Thesemodelshavealonghistoryofsuccessfullyaccounting

for choice behaviour in arange of contexts and, in addition, thecore computations that they specify appeartobemirroredincertaincomponentsofneuralactivityintherodent[7],monkey[8,9],and humanbrain [10]. Consequently,recent years havewitnessed agrowth and confluence in researcheffortstoidentifythecomputationsthroughwhichperceptualdecisionsareformed, aswellastomap,measure,andmanipulatetheneuralstructuresandprocessesthroughwhich theyareimplemented,allanchoredtotheframeworkofsequentialsampling.Thesecontinuing advanceshave given rise to an expandingrepertoireof approaches combiningneural and computationalviewpoints[11].Inthisreview,weshineaspotlightonrecenttrendsinusing onesuchapproach,whereneuralsignalsreflectingkeyaspectsofboundedevidence accumu-lationareusedtoinformabstractdecisionmodels.Wediscussthepotentialofthisapproachin providingstronggroundsformodeladjudicationincaseswherebehaviouralmodellingalonefalls shortand,thus,foradvancingimportanttheoreticaldebatesaboutdecisioncomputations.We alsohighlighttheconceptualandmethodologicalchallengesinvolved.

Highlights

Sequentialsamplingmodelshavebeen widelyembracedincontemporary deci-sionneuroscience.Themodelscomein many forms that, despitecontaining fundamentallydifferentalgorithmic ele-ments,canmakehighlysimilar predic-tionsforbehaviour.Consequently, it can be difficult to definitively adjudicate between alternative models based solelyonquantitativefitstobehaviour.

The discovery of brain signals that reflectkeyneuralcomputations under-pinning decision-making is opening new avenues for empirically testing andrefiningmodelpredictions.

Neurophysiologicalresearchis highlight-ingthemultilayeredneuralarchitecture forimplementingeventhemost elemen-tarysensorimotordecisions.Wedonot yetknowhowmanyprocessinglayers arerequirednorwhatdistinct computa-tionsareperformedateachlayer.

1

TrinityCollegeInstituteof NeuroscienceandSchoolof Psychology,TrinityCollegeDublin, Ireland

2

HowardHughesMedicalInstitute andDepartmentofNeuroscience, ColumbiaUniversity,NewYork,NY 10032,USA

3

ZuckermanMindBrainBehaviour InstituteandKavliInstituteforBrain Science,ColumbiaUniversity,New York,NY10032,USA

4

IntelligentSystemsResearchCentre, UniversityofUlster,MageeCampus, NorthlandRoad,Derry,BT487JL,UK

5

SchoolofElectricalandElectronic Engineering,UniversityCollege Dublin,Dublin,Ireland

*Correspondence:

[email protected](R.G.O’Connell)and

[email protected](S.P.Kelly).

AbstractDecisionModelsandChallengesinModelSelection

Sequentialsamplingmodelswereoriginallybasedonnormativemodelsforminimisingthetime takentoachieveacertainlevelofquality-controlaccuracy[12].Sequentialsamplingmodels providequantitativelyaccurateaccountsofbehaviouronarangeoftasks,includingperceptual detections and discriminations, lexical memory, response inhibition, and even social and value-based decisions (comprehensively reviewed in [13,14]). This powerful class of psychological process models can explain both random and systematic variations in performance.Furthermore,thesemodelscandecomposechoicereactiontimesandaccuracy intomeaningfullatentparameters,suchasthestrengthoftheevidenceenteringthedecision process(‘driftrate’;i.e.,theexpectationoftheevidencedistributionbeingsampled)andthe cumulative quantity required to trigger commitment (‘decision bound’). Ongoing research basedonthesebehaviouralmodelscontinuestofruitfullyexaminehowdecisionsareshaped byfactorssuchasspeedpressure,value,priorknowledge,anddistractinginformation,aswell ashowperceptualdecisionsareaffectedbybraindisorders[14].

Manymodelvariantsexistbecausetherearemanyalternativeimplementationsofadecision process basedonsequentialsampling (Box1).In manycases,competingmodel variants basedonfundamentallydifferentmechanismscanproducethesamebehaviouralsignature. This problem of model mimicry significantly hampers adjudication between competing accounts,andhasgivenrisetoseverallongstandingdebates.Totakeaninstructiveexample, thereisongoingdisagreementaboutwhetherthecriterionamountofevidencethatwerequire toreachcommitmentcandynamicallychangeduringthecourseofadecision.

Inthemostwidelysubscribedmodels[13](Box1),althoughtheboundscanbeadjustedacross differentcontextsto emphasisespeedversus accuracy, inany given trial the boundsare

Glossary

Evidenceaccumulation:according tosequentialsamplingmodels, accurateperceptualdecisionscan beachievedinthefaceofsensory noisebyrepeatedlysamplingand integratingindependentsamplesof evidenceandwithholding commitmentuntilapredefined quantityhasaccruedinfavourofone ofthedecisionalternatives.Thereare multiplepossiblewaysthatthis generalprocesscanbeimplemented bothmathematicallyand

neurophysiologically.

Modelparsimony:mathematical decisionmodelshavetraditionally beenevaluatedusingstatistical methodsthatbalancetheabilityofa modeltoaccountforobserved behaviouragainstitscomplexity. Evaluationmethodsthatconsiderfits toneuralaswellasbehaviouraldata areneededtofacilitatethe developmentofmoredetailed modelsthatcanaccountforthe neuralimplementationofthedecision process.

Neuraldecisionsignal:aneural signalthattracestheprocessof decisionformation.Typically,the termisusedtodistinguishneural computationsthataretiedsolelyto thechoiceoutcomefromsensory responsesthatexhibittrial-to-trial correlationswithchoicebehaviour (see‘SensoryEvidenceSignal’

below).Here,weusetheterm primarilytorefertoneural representationofaccumulated evidencesupportingdecision formation.Single-unitand non-invasiveelectrophysiological recordingstudieshaveisolated signalsexhibitingevidence accumulationdynamicsthataccount forthetimingandaccuracyofthe observer’sperceptualreports.The abilitytodirectlyobserveand measuresuchsignalsopensnew avenuesforadjudicatingbetween alternativedecisionmodelsand developingnewmodelsthatreflect theneuralimplementationofthe decisionprocessaswellasits output.

Neurallyinformedmodelling:the practiceofbasingmodel constructionorconstrainingmodel parametersusingqualitativeand/or quantitativeobservationsfrom empiricalneuraldata.Thisapproach

Box1.SequentialSamplingModels:DifferentFlavoursforDifferentResearchObjectives

Overtheyears,severaldecisionmodelvariantshavebeendevelopedbasedonthecoreprinciplesofsequential samplingandboundedevidenceaccumulation.Instandard,1Ddiffusionmodels,forexample,asequenceofsamples fromaGaussiandistributionrepresentingnoisysensoryevidencewith,say,meanmΔt(‘driftrate’)andvarianceDt,is accumulateduntilthecumulantreachesanupperorlowerbound.Thedriftratescaleswithstimulusstrengthandthe boundsaresettoachieveabalancebetweenspeedandaccuracydemands.Thesubject’soverallresponsetimeis modelledasasumofthetimeittakesthisdiffusionprocesstoreachthebound,anda‘nondecision’timeaccountingfor additionaldelaysassociatedwithencoding,routing[100]and/ormotorexecutionprocesses.Inapopular,versatile versionofthismodel,threeoftheparameters(thestartingpoint,driftrateandnondecisiontime)arenotfixedbutrather canvaryrandomlyfromtrialtotrial,whichprovidessignificantflexibilitytocapturerelativelyfastorslowerrorsand specificRTdistributionshapes[64].

Bothsimplerandmorecomplexversionsofthismodelhavebeendeveloped,andthechoiceamongthesedependson researchgoals.Ingeneral,cognitivemodellingisprimarilyconcernedwithforgingabstractmathematicalaccountsof behaviour,theparametersofwhichserveasmechanisticallyinterpretablemetricsoftaskperformance.Unlikeneuralor biophysicalmodelling,cognitivemodelsdonotgenerallystrivetorepresentdetailsofneurophysiological

implementa-tion[101].Severalreducedmodelshavebeendevelopedtoachievethiswithcomputationalease,forexampleby

excludingtrial-to-trialvariabilityparameters,wheretherelativespeedoferrorresponsesisnotcritical[102],orby excludingthewithin-trialnoiseparameter(‘ballistic,’racingaccumulators[103,104]).

contrastswithmodel-informed neuroscienceapproaches,inwhich anexistingmodelisleveragedto furnishmechanisticallydefined behaviouralmetricsforcorrelation withneuraldata.Fora

comprehensivereviewofthedistinct approachestointegrating

mathematicalandneurophysiological characterisationsofdecision-making,

see[11,66].

Sensoryevidencesignal:asignal thatreflectsthesensoryinputtoa perceptualdecision.Anystimuluswill elicitarangeofsensorysignals, manyofwhichmaybeirrelevantto thetaskathand.Thekey distinguishingcharacteristicsofa sensoryevidencesignalarethatits momentarylevelshouldco-varywith adecision-relevantstimulusvariable anditsactivityshouldpredictchoice behaviourinastimulus-independent manner(alsoknownas‘choice probability’).

Urgencysignal:an evidence-independentcomponentofneural decisionsignalactivitythatexpedites choicecommitment.Suchsignals canbeaccommodatedin mathematicalmodelsasadynamic adjustmenttothequantityof evidencerequiredtotrigger commitment(i.e.,acollapsing decisionbound).Therecent identificationofurgencysignalsthat growasafunctionofdeliberation timechallengesthedominantviewin themathematicalmodellingliterature that,onceadjusted,decisionbounds remainfixedforthedurationofa decision.

assumedtobeconstantovertime.Yet,‘collapsing’bounds(i.e.,onesthatdecreaseovertime within atrial) providean optimal policy accordingto normativetheory under the common situationwhereevidencestrengthvariesunpredictablyacrosstrialsandissometimesweak [15,16],orwhereresponsesmustbemadewithinastrictdeadline[15,17].Oneofthemain reasonswhycollapsingboundshavenotbeenincorporatedinthedominantmodelsisbecause keybehaviouralconsequencesofdoingso,suchasdecreasedaccuracyfortrialswithlonger reactiontimes,canbealsoproducedwithinadriftdiffusionmodelwithconstantbounds,viaan alternativemechanisminvolvingtrial-to-trialvariabilityindriftrate[13](Figure1).

Establishingtherelativeprominenceofthesealternativemechanismsinchoicebehaviourhas consequencesbeyondmattersofpreferenceinmodel-fittingapproaches.Thesealternative accounts reflect fundamentally different algorithmic elements and, therefore, adjudicating between them has important implications for our understanding of normal and abnormal decision-making.Forexample,therehasbeenanincreasingapplicationofsequentialsampling

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modelsinstudiesseekingtobetterunderstanddecision-makingdeficitsobservedin psychi-atricpopulations[18,19]orimpairmentsassociatedwithneurodegenerativedisease[20,21].If relativelyslowresponsetimeswereobservedforerrorresponsesinagivenclinicalpopulation (e.g.,[21]),anexplanationbasedonafasterboundcollapse(e.g.,duetoamoreimpulsive decisionpolicy oraversiontomisseddeadlines) wouldhave differentimplicationsthan one basedongreaterdriftratevariability(e.g.,duetofluctuationsinattentionalengagement,see belowforfurtherdiscussion),withrespecttobothexplanatoryaccountsofthedisorderand effortsto treat it. Similarly, anincreasing trendin humanneuroimaging research is to use decisionmodelparameterestimatesfrombehaviouraldatafitsinstatisticalanalysestolocalise decision-relevantbrainregions[11,22].Here,again,theparticularchoiceofmodelcouldhave majorconsequencesbothfortheparticularareasidentifiedandtheinterpretationoftherole theymightactuallyhaveindecisionformation[23].

Inbehaviouralmodelcomparisonsbetweentwomechanismsthatproducethesame qualita-tivebehaviouralpattern,theoutcome cangreatly dependonthenumberandnatureofthe parametersusedtoimplementthosemechanisms.Totakeanexamplerelevanttotheabove debate,Hawkinsetal.[24]recentlyconductedformalmodelcomparisonswithseveralhuman andmonkeydatasetstoadjudicatebetweencollapsingboundsanddriftratevariability.The comparisonswereconductedusingBayesInformationCriterion(BIC),whichbalances

good-ness of fit with model parsimony. The authors found that most data sets were better

explained by a constant bound model with drift rate variability. Of note, however, in this comparison,collapsingboundmodelsalsoincludeddriftratevariabilityinadditiontoseveral parametersdescribingthe collapse(nonlinearfunctionsoftime).Asaresult,the collapsing boundmodelswereatadisadvantage,sinceBICmetricspenaliseforcomplexity.Inanattempt toaddressthis,asecondmaincomparisonwasmadewithacollapsingboundmodelcontrived to have the same number of parameters as the constant bound model. Again, the data favouredconstantbounds,butagainquestionsremain,sincetheparametersthatwereomitted fromthecollapsingboundmodelwereonesthataccountforqualitativelydistinctandoften significantaspectsofbehaviouraldata(e.g.,fasterrorsanddistributionshape).Thesimplest waytoimplementacollapsingbound(i.e.,alinearfunctionoftime)wasnotconsidered.By contrast,amorerecentstudythatdidusesuchalinearimplementationshowedanimproved BICforamodelthatincludedcollapsingboundsalongsidedriftratevariability[25].

NeurallyInformedDecisionModels

provide critical guidance in constructing, constraining, and adjudicating between abstract, cognitiveprocessmodels.Returningtoourexampleabove,collapsingboundsanddriftrate variabilityeachmake,infact,specificpredictionsforneuralsignalsrelevanttodecisionformation, andmanydataalreadyexisttoexaminesuchpredictions.

Severalrecentneurophysiologicalstudiesinhumansandmonkeyshavefurnishedevidencethat decisionboundsare,atleastincertaincontexts,adjusteddynamicallyduringdecisionformation [25,42–45].Forexample,studyingmotiondirectiondecisions,Hanksetal.[43]demonstratedthat thespikingactivityofneuronsinareaLIP,inadditiontoitsdependenceondirectionandevidence strength,alsoexhibitedanevidence-independentcomponentofbuild-upforbothchoice alter-natives,andthisurgency signalrose moresteeply underspeedpressure (Figure1D).By imposingaprogressivereductioninthequantityofevidenceneededtotriggercommitmentto anyofthechoicealternatives,urgencysignalsprovideaneuralmechanismforimplementingthe collapsingboundsproposedinmathematicalmodels.Inadditiontothisdynamiccomponent, Hanksetal.alsoobservedthatLIPactivitywaselevatedattheoutsetofthedecisionunderspeed pressure,consistent with anadditionalstatic componentof theboundadjustment,andthe findingsofotherhumanneuroimaging[46–48]andmonkey[49]studies.Despitethesestarting pointand time-dependent variations, LIPactivity convergedto acommon level before the perceptualreport.Basedontheseobservations,amodelthatallowedforbothstaticanddynamic adjustmentstothedecisionboundwasconstructed.Crucially,theadditionalparameters describ-ingtheseboundadjustmentswerenotfittothebehaviouraldatabut measureddirectlyfromneural activity,andtheonlyparametersthatwerefreetovarywereonesthatdidnotdifferbetweenthe

Box2.ProbingDecision-RelatedNeuralActivityinNon-InvasiveRecordings

Significantadvancesinisolatingdecisionsignalsfromnon-invasivehumanbrainrecordingsopenpossibilitiesfor translatingthedetailedcharacterisationsofdecisionmechanismswroughtfromnonhumanneurophysiologytothe humanbraininbothhealthanddisease.Moreover,globalbrainrecordingtechniques,suchaselectro-and/or magneto-encephalography(EEG/MEG)andfMRIcancomplementintracranialinvestigationsbyofferingawidersystems-level viewofdecision-relatedprocesses.However,achallengeisthatnon-invasiveassayssufferfromlimitedspatialor temporalresolution.InEEG/MEG,signalsatthescalpreflectthesumofconcurrentlyactivecomponentsofneural activity.Severalapproacheshavebeenusedtodisentanglethecomponentsspecificallywitharoleindecision-making. Oneapproachistodesignparadigmsthat,bytheirnature,producesignalsrelatedtothecoreingredientsofadecision (e.g.,sensoryevidence,itsaccumulationovertime,andemergentmotorpreparation)whileminimising decision-irrelevantneuralactivitycomponents.Forexample,decisionsbasedongradualchangesintheintensityofflickering visualorauditorystimulireadilyfurnishsensoryevidencesignalsthroughsteady-stateflicker-responseamplitudesand eliminateirrelevantearlysensory-evokedpotentialsnormallyevokedbysuddenintensitytransients[37].Thisallows observationofdecisionformationdynamicsrelativelydirectlywithoutimposinganyconstraintsontheformtheyshould take.Thedownsideisthattheapproachworksbestforveryelementarydecisions.

Otherapproacheshaveusedsignal-analyticmethodstoextractdecision-relevantsignalsduringmorecomplextasks involvinghigher-ordercategorisations.Forexample,usingataskrequiringaccumulationoforientationinformation varyingstochasticallyoverdiscretesequentialsamples,sample-by-sampleregressionanalysescanfurnishdistinct signalcomponentsrelatedtodecision-irrelevantsensorychangesandrelevantdecision-updateprocesses[108,109]. AnotherapproachusesmultivariateclassificationalgorithmstoderivefunctionallydefinedEEGcomponentsthat,similar totheobserversthemselves,discriminatebetweenblurredimagesofhigh-levelobjects,suchascarsandfaces[38]. Significantpromiseliesincombiningtheaboveparadigm-designandanalyticapproaches.

Fortheabovementionednon-invasiveneurophysiologyapproaches,theabilitytotakemeasurementsofdynamic decisionsignalsatmultiplehierarchicallevelsinthedecisionarchitecturehasbeendemonstrated,yetthepotentialto usesuchmeasurementsinneurallyinformed,orevenneurallyconstrained,modellingisonlybeginningtoberealised

[25,61].Jointneural–behaviouralmodelfittingcanalsobedoneinamoredata-drivenmanner,withoutnecessarily

twospeedpressureconditions.Nevertheless,theresultantmodelprovidedacompellingfittothe behaviouraldata,includingtheextentoftheimpactofspeedpressure.Althoughithasbeen suggestedthatsuchurgencyeffectsarepeculiartomonkeys[13],andspeciesdifferencesofthis naturelikelydoexist,consistenteffects haverecentlybeenreported inhumanelectrophysiological indicesofmotorpreparation [25],suggestingthatthe effectisgeneralisableatleastacross primates. Alongside the growingnumber of empirical demonstrations ofurgency and their increased incorporationinto abstract models,new lines of researchare seekingto identify plausiblebiophysicalmechanismsfortheirgeneration.Neuralnetworkmodellingstudieshave demonstratedthepotentialroleofdynamicmodulationsofneuralgain[50–52],inparticularthose mediatedby neuromodulatory arousal systems [53], the dynamic activity of which can be empiricallyexaminedviachangestopupildiameter[25].

Drift rate variability is an undeniably convenient feature of abstract decision models for quantitativefittingofbehaviour[54],butit isseldom scrutinisedintermsofpossible neuro-physiologicalunderpinnings.Themostobviouscandidateunderlyingcauseistherandom trial-to-trialfluctuationinthemeanfiringratesofneuronsencodingsensoryevidencesignals.In thecontext of two-alternativedecisions, suchfluctuations wouldhave to take theform of randombiasestowardsonealternativeortheother,ratherthannonselectivevariationsrelated togeneralarousalortaskengagement,sincedriftrateisdrivenbydifferentialevidence.Such fluctuationswould also have to occuron theslow timescale oftypical trialdurations and, therefore, should give rise to significant and broad autocorrelation in evidence-encoding neurons.Thishasbeenexaminedinseveralareas,includingmonkeymiddletemporalvisual area(MT)formotiondecisions,whereautocorrelationlevelsare,infact,lowandhaveshort(on theorderof<100ms)timescales[55,56],atleastcomparedwithhigherbrainareas[57].This does not preclude variability in the weighting of such evidence signals as inputs to the accumulationprocess,anditispossiblethatbroadfluctuationsaremoreprominentinother sensoryareas,otherspecies,and/orothertasks.Forexample,duringcontinuousmonitoring for sensory targets occurring at highly unpredictable times, one could speculate that the absenceoftimeconstraintsmayminimisetheinfluenceofurgencysignals,whiletheincreased demandsonsustainedattentionmay yieldtrial-to-trialfluctuationsinsensoryevidencethat impactthetimingandprobabilityoftargetdetections[58].

Ingeneral,therearemanydifferentwaysinwhichobservationsofdecision-relatedneuralsignal dynamics caninform psychological process modellingandthereby help to convergeona computationalaccountofthebrain’sdecisionmechanisms[11,30].Thequestionofwhichis themosteffectiveuseofneuraldatadependsonthenatureofthedataavailable,theparadigm used,andtheparticular mechanismsbeingexamined.Inthe caseofHankset al.[43],for instance,theparticularsetofstimulusconditionsthatwasrunenabledthetimecourseofthe urgencysignaltobederiveddirectlyfromtheneuraldataandappliedasaconstraintinthe model[59].Moregenerally,thecorrespondencebetweendiscretemeasuresofneuralsignal dynamics(e.g.,onsettimeorrateofbuild-upofadecisionsignal)andmodelparameters(e.g., nondecisiontimeordriftrate)maybemoreindirect,orlackthetypeof‘one-to-one’mapping thatcanprovidedefinitiveconstraintsformodelparameters.Insuchcases,empiricalneural dynamicscan becomparedwithsimulatedmodeldynamics [30],whichcan bedoneina coupleofalternativeways.

closer to the neural reality. Alternatively, in cases where behavioural data alone provide sufficientconstraintsforareasonablefit,a‘two-step’approachcanbetaken,where behav-iouralfitsareusedtosimulatedynamicsforcomparisonwithneuraldynamicsinaseparate step.Forexample,inarecentstudyofrapid,value-biasedsensorimotordecisionsinhumans [61],severalcandidatemodelsinvokingstarting-pointversusdriftratebiaseswerefirstfitto behaviour.Asfoundinmostpreviousstudies(e.g.,[62,63]),astarting-pointbiasproducedthe betterfitundertheassumptionofstationary(nontime-varying)driftrate.Bycontrast,adriftrate biasprovidedabetterfitwhendriftratewasinsteadassumedtoincreaseovertimewithinatrial, totakeaccountofthegradualnatureofearlysensoryencodingprocesseswhenviewedonthe timescaleofveryfastdecisions.Whenevidenceaccumulationdynamicsweresimulatedforall models,thisvalue-biased,temporallyincreasingdriftratemodelmadetheuniqueprediction thatneuralsignaturesofdecisionformationshouldexhibita‘turnaround’patternonlow-value sensory cues, where differentialevidence is initially accumulated towards the wrong (but higher-value) alternative and is then dynamically rerouted towards the correct alternative. Theseverydynamicswereobservedinelectrophysiologicaldecisionsignalsatboththelevel ofmotor preparationand motor-independentevidenceaccumulation.This studyillustrates howqualitativemodelcomparisonsfacilitatedbyelectrophysiologicalsignalstracingdecision formationcanbolstertheoutcomesofquantitative,behaviouralmodelcomparisons.

Neuralsignalanalysescouldsimilarlyhaveacriticalroleintheapplicationofmodelsinresearch involving group comparisons. For example, consider the choice of ‘scaling parameter’, a parameterwhosevalueisfixed,toanchorthemodelfitandtosetthearbitraryscaleonwhich allotherparametersaremeasured(hencethename).Acommonchoiceinabstractdecision models(e.g.,thedriftdiffusionmodel,DDM)istosetwithin-trialnoisetoafixedvalue[64]. However,iswithin-trialnoiseuniformacrossindividualsorgroupsofindividualsinreality?Itis conceivable,forinstance,thatindividualswithacertainclinicaldisorderwouldhave greater within-trialnoisecompared withhealthy individuals[65]. Differencessuch as this could in principle beobserved directly through neural recordings, and help identify deficits among distinctmechanisticelementsofthedecisionprocess.

Anobviouscaveatshouldbenotedinrelationtoanyoftheaboveapproaches:itmustbetaken intoaccounthowconfidentwearethatthesignalsinquestionareindeedtracingthecoreneural computationsthatgiverisetodecisions[66].Sincemanybrainsignals(e.g.,sensoryandmotor) arelikelytobecorrelatedinsomewaywiththeobserver’schoices,examiningsignaldynamics during the period of deliberation and establishing a temporal relationship between those dynamics and choice commitment (e.g., reaction time) is an essential step to avoid an erroneousattributionoffunction.Thus,aswithfittingofbehaviouralone,immediate-response paradigms that pinpoint the timeof decision commitment provide critical constraintsthat enablemoredefinitivemodelcomparison[9,36].Inaddition,itisimportanttotakeaccountof thefact thatthe rolesofdistinct brainareasandsignalsindecision-makingare likelytask dependent(seebelowandBox3).

AccountingforaMultitieredNeuralArchitecture

computations.Insomecases,behaviouraleffectsemanatingfromdifferentprocessinglevels canbedisentangledthroughexperimentaldesign.Forexample,arecentbehaviouralstudy examinedchoicebiasesarisingfromdifferencesintheenergeticcostassociatedwithreporting eachalternative.Theauthorsfoundthatthesechoicebiasesdidnotoriginateatthemotorlevel, as one might perhaps expect, but at an upstream level of decision formation that was independentfrommotoreffectors[69].

Inmanycases,however,thereareclearlimitstotheabilitytolocaliseeffectsamonghierarchical processinglevelsusingbehaviouralanalysisalone.Severalkeyparametersofsequentialsampling modelsarelikelysubjecttoinfluencesatmultipleprocessinglevels,andtheseinfluencesoften cannot bedisentangled. Forexample, changes inthe ‘nondecision time’parameter (which accountsfordelaysduetoprocessesnotdirectlyassociatedwithevidenceaccumulation)could stemfromaltereddelaysattheoutsetofthedecisionprocess(e.g.,sensoryencoding)and/orat theendofit(e.g.,motorexecution).Thereisalsoambiguityinthedependenceofaparameteron changesatasingleprocessinglevelversusinthetransmissionofinformationbetweenlevels;for example,driftrateisdependentnotonlyonthestrengthandreliabilityofsensoryrepresentations themselves,butalsoontheweightingorreferencevaluesusedincastingthoserepresentationsas aninputtotheaccumulationprocess(e.g.,‘driftcriterion’setting[64]).

Thus,thereismuchtobegainedfromexaminingdecision-relevantneuraldynamicsateachof thekeyprocessinglevelsunderpinningdecisionformation.Akeychallengeinthisendeavouris that,eveninthecaseofelementarysensorimotordecisions,wedonotyetknowhowmany levelsofprocessingtheretrulyare inthecomputationalsense.Multiregionrecordingshave revealedthatchoice-selectivesignalsarerapidlytransmittedacrossmanyareas[70,71]and,as oneproceedstoward themotor endof thehierarchy, neuralactivity is progressively more closelyassociatedwiththesubject’sactionchoiceratherthanthestimulusfeatures[67,72]. However,beyondthisgeneralprinciple,thedistinctroleofeachstepofthepathwayandits individualcontributiontoimplementingthealgorithmusedbythebraintomakeagivendecision are difficult to establish. In monkeys, for example, decision-related build-up activity with comparablelatencies has been observed inLIP [73], medial intraparietal area [74] frontal

Box3.CausalInference

MuchresearcheffortindecisionneurosciencehasfocusedonrecordingsfromareaLIP,andthisworkhasyielded insightsintothecomputationalmechanismsbywhichthebrainaccommodatesspeed–accuracydemands[43],prior biases[111],multiplealternatives[42],switchingbetweenalternateevidencedimensions[112],andotherproblems regularlyfacedbyrealdecision-makers.Astheseinsightshaveamassed,soalsohasthemisconceptionthatsuch findingsimplythatthecentralfunctionofLIPistoaccumulateevidencefordecisions.Thisisofcoursemisguided.LIP simplycontainsneuronsthepropertiesofwhich,characterisedoverdecadesofcarefulresearchintosaccadictarget selection[113,114],makeitpossibletorigorouslystudycertaintransformationscommontomanydecisions.Tostudy thesetransformations,experimentalconditionsneedtobecarefullycontrivedsoastorenderLIPneuronsinformativein thiscontext,forinstance,bydesigningdecisionparadigmsbasedonsimplefeaturediscriminationsandonchoicesthat arereportedviasaccadestowardsorawayfromtargetsplacedwithinthereceptivefieldoftherecordedneuron. Moreover,thesestudiestypicallyrecordfromasubsetofLIPneuronsthatexhibitsustainedfiringduringdelayperiods beforesaccadeexecution,onthegroundsthattheseneuronsarelikelybestequippedtotracetemporallyextended decisionprocesses.Whenonestepsoutsideofthesespecificconditions,thechoice-relevantdynamicsobservedinLIP canchangesubstantially.Forexample,inthecontextofvisualsearch,neuralsignaturesofevidenceaccumulationare observedintheFEF[49,75],whereasLIPactivityhasbeenlinkedmoretotherepresentationofsalienceasthecore

eyefield(FEF)[75,76],prefrontalcortex[77,78],superiorcolliculus[79],basalganglia[80,81], dorsal[82]andventralpremotorcortex[83],andprimarymotorcortex[44].Notsurprisingly, manyresearcheffortshaveturnedtoidentifyingthedistinctcontributionsthattheseareasmake (Box3,Figure2).

Non-invasive human recording techniques can provide a more global view over several processinglevelsintandem,althoughtheirlowerresolutionnecessitatestheuseofparadigm designsand/oranalysismethodsthataimtodisentangletheirmeasurement(Box2).Human electrophysiology studies have isolatedtwo functionally distinct classesof decision signal reflectingaccumulate-to-thresholddynamics:effector-selectivesignalsthat,similartosignals

Lateral intraparietal area (LIP)

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Frontal orienƟng fields (FEF) Centroparietal posiƟvity (CPP)

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0.2 0.2 0.5 0.8

0.5 Strong Weak Strong Weak Time (S) Time (S) Time (S)

Fixed S-R mapping Variable S-R mapping Ignore moƟon

Choose leŌ

Choose right

Time (S) Accumulator value

T_in Preferred

Preferred Null Null Tin T_in T_out T_out Tout μ V/ m 2 μ V/ m 2 μ V/ m 2

inareassuchasLIP,representthetranslationofsensoryevidenceintoaspecificmotorplan [25,39,84],anda domain-generalsignalthat buildswithcumulativeevidenceregardlessof whetherresponsesareimmediate,delayed,ornotrequiredatall,orofthesensoryfeatureor modalitybeingdecidedupon[37,85](Figure2C).Thelattersupramodal,motor-independent signal, termed the ‘centroparietal positivity’ (CPP), was also found to precede evidence-selective motor preparation signals [58], further suggesting that it operates at a level of processingintermediatingbetweensensoryencodingandmotorpreparation.

Thisdiscoverynotonlybuildsonlongstandingassertionsthatthebrainmusthouseabstract-level mechanismstoaffordflexibilityinmappingsensationstoappropriateactions[86–90],butalso refinesthispicturebysuggestingthatsuchintermediateprocessescanoperatethewaymore dedicatedcircuitsdo;thatis,byapproximatinganaccumulationofsampledevidencetowardsa criterionordecisionbound.Theintracranialoriginsofthissignalareasyetunknown.Giventhe similarityinboundedaccumulationdynamics,itistemptingtolinktheCPPwithactivityinareaLIP. However,EEGpicks upneuralactivity globallyand, sincebuild-up activityfor theselected alternativeismirroredbyaroughlycorrespondingdecreaseintheactivityofneurons coding for the unselected alternative, it wouldbe expected that muchor all of the choice-selective build-up activityoftheLIPwouldbecancelledoutatthelevelofthescalp.Interestingly,LIPneuronshave beenfoundtoencodegoal-relevantstimuluscategories(e.g.,motiondirection)inan effector-independentfashion;however,itisnotknownwhetherthesesignalsexhibitevidence accumula-tiondynamics[90].Moregenerally,muchworkremainstobedonetounderstandtherelationship betweenintracranialandextracranialsignalsexhibitingdecision-predictivedynamicsindifferent species[91](Box4).Thesequestionsnotwithstanding,theidentificationofanabstract accumu-lationprocessinhumanbrainrecordingshighlights the existenceofanadditionalprocessinglayer, thepreciseroleofwhichindecisionformationremainstobedetermined.

Althoughwemaylackacompletepictureoftheessentialcomputationallayersfor decision-making,studiesthathaverecordedneuralactivityatmultipleprocessinglevelsduringthesame taskhavealreadyfurnishedinsightsthatarebeyondthereachofbehaviouralmodellingalone. Forexample,recordingfrombothMTandLIPduringtrainingonamotiondirection discrimi-nationtaskrevealedthatimprovementsinbehaviouralsensitivitywithlearningwereattributable tochangesinthemotion-drivenresponseofLIPneuronsintheabsenceofanychangeinthe evidence-encodingMTneurons,suggestingthatlearningchanges theread-outbutnotthe sensoryrepresentationsthemselves[92].

capturingkeyqualitativefeaturesofthemeasuredFEFactivity,includingincreasedbuild-up rateinthevisualneuronsunderspeedemphasis. Thisstudyhighlightsthat,whileabstract decision models can provide parsimonious accounts of choice behaviour, they may not necessarilycaptureall ofthemechanisticstepsthatthebrainperformsand,therefore,are not always likely to correspond with neurophysiological dynamics observed at any one processinglevel.Italsoillustrateshowmodelsbuiltfromphysiologicalknowledgeof sensori-motorsystemsandtheircapabilitiescanhaveapivotalroleinfacilitatingtheinterpretationof decision-relatedneuralactivitypatterns(Box4).

Combiningcomputationalmodellingwithneuralrecordingsprobingmultipleprocessinglevels (e.g.,sensoryevidenceencoding,motor-independentaccumulation,motorpreparation,and muscleactivation)willbecentraltoresolvingarangeofoutstandingquestionsinthefield.For example,thusfar,muchoftheneurophysiologicalresearchondecision-makinghasfocussed on activity in neural circuits situated close to the motor output end of the sensorimotor hierarchy.Therefore,wehaveafairlyrefinedpictureofhowkeyfactorssuchasspeedpressure, priorprobability,andpayoffinformationaffectdecision-makingatthisneurophysiologicallevel, butamorelimitedpictureonearlierprocessingstages.Ofnote,researchonattention[93], featureexpectation[94],andrewardexpectation[95,96]hasdemonstratedthecapacityofthe braintoexerttop-downinfluencesonbasicsensoryrepresentations.Itremainsuncleartowhat extentsuchmodulationsareusedwhenadaptingdecisionprocessestoaccountforcontextual factors,andmodellingstudiesrarelyconsidertheirpotentialcomputationalbenefits.

ConcludingRemarks

Sequential sampling models have provided a common, principled foundation to diverse investigationsintodecision-making.Behaviouralfits ofthemodels have longbeenused to furnishquantitative,mechanisticallydefinedmetricstoaidinunderstandingdifferencesinhow decisionsareforgedacrossstimulusconditions,taskcontexts,andclinicalgroups.However,

Box4.BridgingacrossRecordingModalitiesinDecisionNeuroscience

Theneuralbasesofdecision-makinghavebeenstudiedatarangeoffunctionallevelsandscales,fromsingleneurons, throughneuronalmicrocircuits,toglobalactivitymeasuredinhumanelectrophysiologyand/orneuroimaging.Withthese expandingviewpointscomestheimperativetointegratefindingsacrosstheselevels.Inpart,thisrequiresmoregeneral understandingofthebiophysicaltranslationsbetweenrecordingmodalities.Forexample,inbridgingfromtheneuronal circuitleveltonon-invasiveelectrophysiology,localfieldpotential(LFP)activityanditsrelationshiptomultiunitspikingforms animportantbridgetoscalpEEG,whichisthoughttoprimarilyreflectpostsynapticactivity[122].Suchresearchhasbeen increasinglyundertakenrecentlyatboththesensorylevel(e.g.,[123])andthelevelofemergingactionplans(e.g.,[124]). StudyingthebiophysicalmechanismsbywhichextracellularLFPstranslatetoelectricand/ormagneticsignalsatthescalp surface(e.g.,[125])andtoBOLDactivations(e.g.,[126])remainsanactiveareaofinvestigation.

Biophysicallybasedcomputationalmodellingrepresentsacomplementaryapproachtointegratingacrosslevelsof descriptionwhilealsospecifyingmechanismsofdecisionformation.Forinstance,spikingneuronalnetworkmodels havesuccessfullycapturedaspectsofspikingdynamicsandbehaviouraldataduringdecision-making[40].More recently,itwasfoundthat,throughtraining,suchrecurrentneuralnetworkscancapturevariousidiosyncrasiesfoundin neuronalpopulation recordings,suchasmixed,time-varying,andheterogeneousselectivity,acrossavarietyof decision-makingtasks[127–129].Suchmodelsrevealanadditionallayerofcomplexityofneuralcomputationin decision-making,whichmaynotbeaccomplishedusingsimplifiedcognitivemodels.

Despitethisprogress,recurrentneuralnetworkscomewithissuesrelatingtostabilityandeaseofinterpretationwith respecttodecisionalgorithmsoflowercomplexity.Onemeanstobridgefromspikingneuronalnetworkmodelsto simplerfiring-rate,population-basedmodelsisthroughtheoreticalmean-field approximations[106,130],butthe applicationofthisapproachtoheterogeneousnetworksisstillinitsinfancy.Achievingaprincipledmappingofcomplex networkmodelstolower-dimensionaldescriptionsisvitaltomakelinkagestothereducedcognitivemodelsin widespreaduseindecisionscience[97],andhasimportantimplicationsformodel-basedanalysesinneuroimaging, giventhealreadyprevalentrelianceonneuralmassmodels(e.g.,dynamiccausalmodelling)tounderstandcausalglobal braindynamics[131],includinginperceptualdecision-making[132,133].

OutstandingQuestions

Variousfactorsareknowntoinfluence decision-making behaviour, among them: prior information, conflicting information, redundant information, energeticcosts,spatialattention, per-ceptual learning, and value assign-ment.Processing ofmany ofthese factorsisdysregulatedinbrain disor-ders.Dosequentialsamplingmodels provide accurate accounts of the essentialneurocomputational adjust-ments through which these factors influence decision-making, and can neural signal analyses be used to determinewhetherthatisthecase? Inadditiontodominantcriteria adjust-ments,aretheremodulationsexerted atthesensorylevelthatmodelfitting alonecannotdetect?

The versatility of popular sequential samplingmodelvariantsispartlyowed totheinclusionofcertainparameters (e.g.,variabilityindriftrateandstarting point)thatrenderthemodelsflexible andenablethemtoaccountfor differ-entbehaviouralpatterns.What predic-tions do these parameters make regarding neural activity, and how can these predictions be tested? Can neural signatures ofsuch pro-cessesbeidentified?

Build-to-threshold decision signals have been observed ina varietyof brainareas.Whatdistinct computa-tionsdothesesignalsandareas per-formduringdecisionformation?

thefieldhasbeengrapplingwithseveraldebatesregardingkeyalgorithmicelementsofthese modelsthataredifficulttoresolvebasedsolelyonquantitativefits tobehaviouraldata.The abilitytoobserveneuralsignaldynamicsunderpinningthedecisionprocessprovidesameans ofguidingmodeldevelopmentfurther.Recentstudiesdemonstratetheuniqueinsightsthatcan be acquired by examining correspondences between abstract mathematical models and neuralsignalsthathavebeenindependentlyverifiedtoreflectelementsofdecisionformation. Itisnowincreasinglypossibletoconstructmodelsthatareneurallyconstrained(e.g., quanti-tatively setting a time-varying stopping criterion based directly on neural measurements), neurally informed (e.g., including and fitting parameters for time-varying criterion settings basedonqualitativepatternsobservedintheneuraldata),oratleastneurallycognisant(e. g., including and fitting a time-varying criterion based on pre-existing neurophysiological evidencefor itsgeneral role).Withtheongoingdevelopmentof techniquesandparadigms formeasuringdecision-relevantneuralprocesses,wecanexpecttoseeincreasingadoptionof suchapproaches that integrate neural evidenceinto computational accounts of decision-making(seeOutstandingQuestions).Adaptingcognitivemodelstoreflectthecriticalneural dynamicsgoverningdecisionformationcanalsohelpsubstantiallyinestablishingmuchneeded linkages betweenthe parametersand mechanisms of cognitive models and biophysically basedneuralcircuit models, whicharerarely broughtinto direct contact[97](Box4). The conceptual and methodological challenges examined in this review have implications that extendbeyondresearchonperceptualdecision-makingbecauseatrendtowardintegrating computationalmodelsandneuraldataisincreasinglyevidentinmanyotherresearchfields [98,99].

Acknowledgments

ThisworkwassupportedbyagrantfromtheU.S.NationalScienceFoundation(BCS-1358955toS.P.K.andR.G.O.),a EuropeanResearchCouncilStartingGrant (63829toR.G.O),a ScienceFoundationIreland ERCSupportAward

(15/ERCS/3267toR.G.O.),anda CareerDevelopmentAward fromScienceFoundationIreland(15/CDA/3591to S.P.K.).

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