modeling response inhibition

Modeling response inhibition

Bram Zandbelt

[email protected]

@bbzandbelt

https://www.bramzandbelt.com

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1. Response inhibition - what, why, how

1.1 What is it?

1.2 Why is it relevant?

1.3 How is it studied?

1.4 What are the main findings?

2. Independent race model

2.1 What is the independent race model?

2.2 What are its assumptions?

2.3 How does it account for response inhibition

findings?

2.5 What are its strengths and weaknesses?

3. Sequential sampling models of response inhibition

3.1 What are sequential sampling models?

3.2 What are their assumptions?

3.3 How do they account for response inhibition

findings?

3.4 What are their strengths and weaknesses?

4. Modeling response inhibition in a broader context

4.1 Response inhibition is multidimensional

4.2 Multiplicity of modeling approaches

Bram Zandbelt

Preview



1.1 What is it?








findings?






findings?


4. Modeling response inhibition in a

broader context



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1.1 What is it?

Sources: Aron (2007) Neuroscientist; see also MacLeod et al. (2003) in Psychology of learning and motivation, B. Ross, Ed., vol. 43, pp. 163–214. Lawrence, Eleanor, ed. Henderson's dictionary of biology. Pearson education, 2005.

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Ubiquitous in everyday life From emergency and sports situations to more complex behavior

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Implicated in many clinical conditions From the obvious (ADHD, OCD, TS) to the less obvious (schizophrenia, Parkinson’s)

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Williams et al. (1999) Dev Psych


Changes across the lifespanStopping latency develops during childhood and declines during aging



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Changes across the lifespanStopping latency develops during childhood and declines during aging

Might have translational value Response inhibition training might improve self-control (food intake, gambling)



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Various paradigms Antisaccade, go/no-go, stop-signal, Stroop

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Sources: Aron (2007) Neuroscientist


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Sources: Thomson Reuters Web of Science

Productive ~150 publications/year, stop-signal task only


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Sources: Verbruggen et al. (2013) Psych Sci


Interdisciplinary Medicine, neuroscience, psychology



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st SS

GO STOP

βGO = 0.005

βSTOP = 0.111

μGO = 5.08

σGO = 26.24

μSTOP = 5.07

σSTOP = 26.34

ΔGO = 51 ΔSTOP = 51

θGO = 1000

Sources: http://www.healthcare.philips.com/,


Converging methodologies Imaging, lesion, modeling, neurophysiology, pharmacology, stimulation



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http://www.healthcare.philips.com/pwc_hc/main/shared/Assets/Images/MRI/product/pg_achieva3T180_01_en.jpg

http://www.healthcare.philips.com/

Sources: http://www.cognitive-fab.com, Schall lab, Schmidt et al. (2013) Nat Neurosci



Different speciesHumans, monkeys, rats



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http://www.cognitive-fab.com

Sources: Massachusetts General Hospital; ; Goonetilleke et al. (2012) J Neurophysiol; Tabu et al. (2012) Neuroimage; Claffey et al. (2010) Neuropsychologia



Different speciesHumans, monkeys, rats

Various effector systemsArm, eye, eye-head, eye-hand, finger, foot, hand, speech



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http://www.massgeneral.org/psychiatry/assets/images/Eye_Tracking_Dara_Manoach_MGH.jpg

Stop-signal task demonstration

1.3 How is it studied? - Stop-signal task

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no-signal trial

time

FixationTarget


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no-signal trial

time

RT

FixationTarget


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time

FixationTarget

no-signal trial

stop-signal trial

time

RT

FixationTarget


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time

SSD

SSD

FixationTarget

no-signal trial

stop-signal trial

time

RT

FixationTarget


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signal-inhibit

time

SSD

SSD

FixationTarget

no-signal trial

stop-signal trial

time

RT

FixationTarget


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signal-inhibit

signal-respond

time

SSD

SSD RT

FixationTarget

or

no-signal trial

stop-signal trial

time

RT

FixationTarget


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signal-inhibit

signal-respond

time

SSD

SSD RT

FixationTarget

or

no-signal trial

stop-signal trial

time

RT

FixationTarget

Dependent variables P(response | stop-signal) RT on no-signal trials RT on signal-respond trials

Independent variable Stop-signal delay (SSD)


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1.4 What are the main findings? - Behavior

1. Ability to stop decreases with delay

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2. Inhibition error RTs are fast …


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2. Inhibition error RTs are fast …

… and increase with delay


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… across effector systemse.g. finger, arm, eye

finger

arm

eye

Remarkable generity of findings


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Sources: Logan & Cowan (1984) Psych Rev; Mirabella et al. (2006) Exp Brain Res; Boucher et al. (2007) Percept Psychophys

auditory

visual

tactile


… across stimulus-modalities e.g. visual, auditory, tactile



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Sources: Logan & Cowan (1984) Psych Rev; Cable et al. (2000) Exp Brain Res; Åkerfelt et al. (2006) Exp Brain Res;

monkey

rat

human


… across stimulus-modalities e.g. visual, auditory, tactile

… across speciese.g. rats, monkeys, humans



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Sources: Logan & Cowan (1984) Psych Rev; Hanes & Schall (1995) Vis Res; Eagle et al. (2003) Behav Neurosci

Signatures of stopping in motor system Neurophysiology shows that build-up of response-related activation is interrupted

FEF PM

M1

SC

Striatum

GP

STN

1.4 What are the main findings? - Brain

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FEF PM

M1

SC

Striatum

GP

STN

Figure courtesy of J.D. Schall

Sources: Hanes et al. (1998) J Neurophysiol; Paré & Hanes (2003) J Neurosci; Mirabella et al. (2012) J Neurophysiol; Schmidt et al. (2013) Nat Neurosci; Emeric & Stuphorn (preliminary data)


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Involvement of cognitive systems Neuroimaging reveals activation of a large network of fronto-parietal and basal ganglia areas when stopping a response

FEF PM

M1

SC

Striatum

GP

STN


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Sources: Aron & Poldrack (2006) J Neurosci; Li et al. (2006) J Neurosci; Zandbelt & Vink (2010) PLoS ONE


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Involvement of cognitive systems Neuroimaging reveals activation of a large network of fronto-parietal and basal ganglia areas on stop trials

Disturbance/damage affects stoppingPerturbance and lesions to cognitive and motor areas influence ability to stop

FEF PM

M1

SC

Striatum

GP

STN


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Sources: Aron et al. (2003) Nat Neurosci; Chambers et al. (2006) J Cogn Neurosci; Floden & Stuss (2006) J Cogn Neurosci; Nachev et al. (2007) Neuroimage; Swick et al. (2008) BMC Neurosci; Chen et al. (2009) Neuroimage; Verbruggen et al. (2010) Proc Natl Acad Sci USA


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1.1 What is it?








findings?






findings?





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Psychological Review1984, Vol. 91, No. 3, 295-327

Copyright 1984 by theAmerican Psychological Association, Inc.

On the Ability to Inhibit Thought and Action:A Theory of an Act of Control

Gordon D. LoganUniversity of British Columbia, Vancouver,

British Columbia, Canada

William B. CowanNational Research Council of Canada, Ottawa,

Ontario, Canada

Many situations require people to stop or change their current thoughts and actions.We present a theory of the inhibition of thought and action to account for people'sperformance in such situations. The theory proposes that a control signal, such asan external stop signal or an error during performance, starts a stopping processthat races against the processes underlying ongoing thought and action. If thestopping process wins, thought and action are inhibited; if the ongoing processwins, thought and action run on to completion. We develop the theory formallyto account for many aspects of performance in situations with explicit stop signals,and we apply it to several sets of data. We discuss the relation between responseinhibition and other acts of control in motor performance and in cognition, andwe consider how our theory relates to current thinking about attentional controland automaticity.

Thought and action are important to sur-vival primarily because they can be controlled;that is, they can be directed toward the ful-fillment of a person's goals. Control has beena central issue in the study of motor behaviorsince the turn of the century (e.g., Sherrington,1906; Woodworth, 1899; see Gallistel, 1980,for a review), and it has been important inpsychology since K. J. W. Craik's seminal pa-pers in 1947 and 1948. Students of motor be-havior have not forgotten the importance ofcontrol and have developed sophisticated the-ories that integrate behavioral and physiolog-ical data (e.g., Feldman, 1981; Kelso & Holt,1980; Navas & Stark, 1968; Robinson, 1973;Young & Stark, 1963). However, psychologistshave strayed from the path somewhat over theyears,

Craik's papers, which described the humanperformer as an engineering system, provideda framework in which to study tracking tasksand stimulated interest in the (possibly inter-mittent) nature of the control system in suchtasks. This approach kindled interest in thepsychological refractory period (e.g., Hick,

This research was supported by Grant U0053 from theNatural Sciences and Engineering Research Council ofCanada to Gordon D. Logan.

Requests for reprints should be sent to Gordon D. Logan,who is now at the Department of Psychological Sciences,Purdue University, West Lafayette, Indiana 47907.

1949; Vince, 1948), which led to the formu-lation of single-channel theory (Davis, 1957;Welford, 1952). In the hands of Broadbent(1958) and others, single-channel theory wasextended to deal with many diverse phenom-ena of attention, and dominated theories ofattention for nearly 20 years. The extendedsingle-channel theory attracted the interest ofcognitive psychologists who dealt primarilywith tasks other than tracking, and, in theirhands, control became less important than didother issues such as memory (Norman, 1968),expectancy (LaBerge, 1973), selectivity (Treis-man, 1969), and time sharing (Posner & Boies,1971). Single-channel theory was replaced bycapacity theory (Kahneman, 1973) and mul-tiple-resource theory (Navon & Gopher, 1979),and little attention was paid to problems ofcontrol (but see Broadbent, 1977; Reason &Myceilska, 1982; Shallice, 1972; more gen-erally, see Gallistel, 1980; Kimble & Perlmuter,1970; Miller, Galanter, & Pribram, 1960;Powers, 1978),

Recently, cognitive psychologists have be-come interested in control once more, in theguise of research on automaticity and skill (e.g.,Anderson, 1982; Hasher & Zacks, 1979; Lo-gan, 1978; Posner, 1978; Shiffrin& Schneider,1977), but the studies bear little resemblanceto the early fruits of Craik's seminal thinkingand even less resemblance to studies of motorbehavior. Whereas the earlier studies in Craik's

295

Sources: Logan& Cowan (1984) Psych Rev; see also Logan et al. (2014) Psych Rev

Theory of performance in stop task Published in 1984 by Logan and Cowan

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Sources: Verbruggen et al. (2013) Psych Sci


Widely used across various fields Medicine, neuroscience, psychology


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Sources: Verbruggen & Logan (2008) Trends Cogn Sci


Widely used across various fields Medicine, neuroscience, psychology

Method for estimating stopping latency Stopping latency cannot be observed directly, but can be estimated from the data with help of the independent race model


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timetarget stop-signal

signal-inhibit

GOSTOP

GOSTOP

signal-respond

RT

RT

SSRT

SSRT


Race between GO and STOP Target triggers GO, stop-signal triggers STOP If GO wins, a response is produced If STOP wins, a response is inhibited

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Stochastic independence

Context independence


STOP and GO are independent Stochastic: random variation is unrelated Context: trial type does not influence GO RT


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Stopping latency derived from data The stop-signal reaction time (SSRT) can be derived by integrating the no-signal RT distribution until the point where it equals P(respond | stop-signal)

STOP and GO are independent Stochastic: random variation is unrelated Context: trial type does not influence GO RT


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2.3 How does it account for the main findings?

Delays bias the race in favor of GOSo ability to stop decreases with longer delays

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Delays bias the race in favor of GOSo ability to stop decreases with longer delays

RTs occur only when RTGO < RTSTOPTherefore, inhibition error RTs are fast

Delays bias the race in favor of GOHence, inhibition error RTs increase with delay


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Criterion Description Evaluation of the independent race model

Falsifiability Do potential observations exist that would be incompatible with the modell?

Plausibility Does the theoretical account of the model make sense of established findings?

InterpretabilityAre the components of the model understandable and linked to known processes?

Goodness of fit Does the model fit the observed data sufficiently well?

Complexity Is the model’s description of the data achieved in the simplest possible manner?

Generalizability Does the model provide a good prediction of future observations?

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Decreasing inhibition function Signal-respond RTs that are slower than no-signal RTs Signal-respond RTs that do not increase with delay







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Assumption of a race seems plausible Assumption of independence appears unlikely It cannot explain deflection of motor-related activity






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SSRT has face validity in psychology and neuroscience It does not specify subprocesses of GO and STOP It does not predict trial-to-trial variation in SSRT





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Lesions Magnetic stimulation Pharmacology

Clinical disorders Development

Sources: Thakkar et al. (2011) Biol Psychiatry; Van de Laar et al. (2011) Front Psychol; Aron et al. (2003); Chambers et al. (2006) J Cogn Neurosci; Chamberlain et al. (2006) Science


FEF PM

M1

SC

Striatum

GP

STN

Figure courtesy of J.D. Schall

Sources: Hanes et al. (1998) J Neurophysiol; Paré & Hanes (2003) J Neurosci; Mirabella et al. (2012) J Neurophysiol; Schmidt et al. (2013) Nat Neurosci; Emeric & Stuphorn (preliminary data)

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Model’s predictions have held for decades It underestimates signal-respond RTs for early SSDs (e.g. Colonius, 2001; Gulberti & Colonius, 2014)




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Complexity Is the model’s description of the data achieved in the simplest possible manner? It makes few assumptions, and is generic, non-parametric



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Complexity Is the model’s description of the data achieved in the simplest possible manner? It makes few assumptions, and is generic, non-parametric


It generalizes across effector systems, stimulus modalities and species


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1.1 What is it?








findings?






findings?





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Moving left or right?

Prefer Doritos or M&M’s?

Models of decision makingChoices between alternatives, based on perceptual evidence or subjective preference

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Choose left

Choose right

+


Explain choice and response time Of all response types, relation between error and correct response times

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Choose left

Choose right



Mechanism: accumulation to thresholdAccumulation of perceptual evidence or subjective preference


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Various sequential sampling models …


… and their relationships

Sources: Bogacz et al. (2006) Psych Rev



Constitute a family of models Diffusion (feed-forward), leaky competitive accumulator (mutual inhibition), linear ballistic accumulator (race)


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Constitute a family of models Diffusion (feed-forward), leaky competitive accumulator (mutual inhibition), linear ballistic accumulator (race)

Extended to other domains Decision making in intertemporal choice, visual search, response inhibition, among others


Visual search

Response inhibition

Sources: Purcell et al. (2012) J Neurosci; Boucher et al. (2007) Psych Rev

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Evidence accumulation to a thresholdEvidence favoring each alternative is integrated over time. A decision is made when sufficient evidence is accumulated.

Evid

ence

Choose left / Doritos

Choose right / M&M’s

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t0

v

θ

Evid

ence


Behavior decomposed into parameters that map onto cognitive processes Non-decision time (t0) - encoding, executionRate (v) - accumulation of evidence/preferenceThreshold (θ) - decision making criterion Leakage (k) - ‘memory loss’ Lateral inhibition (w) - choice competition

LEFT RIGHT

v, t0v, t0

w kk

w

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3.2 What are their assumptions?Ev

iden

ce LEFT RIGHT


Behavior decomposed into parameters that map onto cognitive processes Non-decision time (t0) - encoding, executionRate (v) - accumulation of evidence/preferenceThreshold (θ) - decision making criterion Leakage (k) - ‘memory loss’ Lateral inhibition (w) - choice competition

Subject to random fluctuations Variation in parameters, within and/or across trials, determines fluctuations in performance

Response time distribution

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3.3 How do they account for response inhibition findings?

Extend the model with STOP unit STOP unit races independently or interactively with the GO unit

Sources: Boucher et al. (2007) Psych Rev

Independent race

Interactive race

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Independent race

Interactive race


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Models explain behavior equally wellOther data necessary to resolve model mimicry

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Sources: Schall (2009) Encylop Neurosci



FEFInteractive race explains neural dataIndependent race model cannot explain deflection seen in FEF/SC movement neurons

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Interactive race explains neural dataIndependent race model cannot explain deflection seen in FEF/SC movement neurons

Sources: Hanes et al. (1998) J Neurophysiol

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GO STOPGO STOPΔt



STOP interacts late and potently Weak interaction causes slowing of response times on signal-respond trials


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Sources: Logan et al. (2015) Psych Rev



STOP interacts late and potently Weak interaction causes slowing of response times on signal-respond trials

Lateral inhibition is just one possibility Blocking input to the GO unit is another


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Criterion Description Evaluation of the interactive race model


Neurophysiological assumptions are falsifiable, for behavioral assumptions this is less clear (e.g. Jones & Dzhafarov 2014 Psych Rev)






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Late, potent interaction explains seeming independence Assumes STOP unit is off when model starts processing (but see Logan et al. 2015)





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Parameters map onto plausible cognitive processes Model predicts variability in SSRT




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Goodness of fit Does the model fit the observed data sufficiently well? Model fits both behavior and monkey neurophysiology



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Explaining behavior and neurophysiology, the model is relatively simple


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Explaining behavior and neurophysiology, the model is relatively simple


Generalizes to data from monkeys performing different tasks in different labs and also to human data (e.g. Lo et al. 2009; Ramakrishnan et al. 2012)

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1.1 What is it?








findings?






findings?





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4.1 - Response inhibition is multidimensional

all-or-none(any response)

spur-of-the-moment(without preparation)

all-or-none(any secondary signal)

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stopping some actions,while continuing others

restraining actionsin preparation for stopping

stopping to some stimuli,while ignoring others

non-selective, reactive stopping


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4.2 - Multiplicity of modeling approaches

Neural network Wilson & Cowan (1972)

Rumelhart (1986)

Stochastic accumulator

Usher & McClelland (2001)Brown & Heathcote (2008)

Bayes optimal decision-making

Non-process/descriptive

LATER-likeCarpenter & Williams (1995)

simple stopping

selectivity

choice

simple changing

executivecontrol

RTSSRT

Logan & Cowan (1984)

Camalier et al. (2007)

Zandbelt et al. (in prep.) Wiecki & Frank (2013)

Shenoy & Yu (2011)Liddle et al. (2009)

Leotti & Wager (2010)

Ide et al. (2014)Pouget et al. (2011)

Ramakrishnan et al. (2012)

Boucher et al. (2007)Salinas & Stanford (2013)

Marcos et al. (2013)Yang et al. (2013)

Lo et al. (2009)Mattia et al. (2013)

Schmidt et al. (2013)

Logan et al. (2014)Zandbelt et al. (in prep)

Middlebrooks et al. (in prep)

Ramakrishnan et al. (2010)

GO STOPHanes & Carpenter (1999);

Kornylo et al. (2003); Corneil & Elsley (2005); Walton & Gandhi (2006); Goonetilleke et al. (2012)

GO2 RTGO1 RT

SSRTLogan et al. (2014)

GO STOP

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Further reading

Boucher, L., Palmeri, T. J., Logan, G. D., & Schall, J. D. (2007). Inhibitory control in mind and brain: an interactive race model of countermanding saccades. Psychological Review, 114(2), 376.

Verbruggen, F., & Logan, G. D. (2008). Response inhibition in the stop-signal paradigm. Trends in Cognitive Sciences, 12(11), 418–424

Logan, G. D., Yamaguchi, M., Schall, J. D., & Palmeri, T. J. (2015). Inhibitory control in mind and brain 2.0: Blocked-input models of saccadic countermanding. Psychological Review, 122(2), 115–147

Inhibitory Control in Mind and Brain: An Interactive Race Model ofCountermanding Saccades

Leanne Boucher, Thomas J. Palmeri, Gordon D. Logan, and Jeffrey D. SchallVanderbilt University

The stop-signal task has been used to study normal cognitive control and clinical dysfunction. Its utilityis derived from a race model that accounts for performance and provides an estimate of the time it takesto stop a movement. This model posits a race between go and stop processes with stochasticallyindependent finish times. However, neurophysiological studies demonstrate that the neural correlates ofthe go and stop processes produce movements through a network of interacting neurons. The juxtapo-sition of the computational model with the neural data exposes a paradox—how can a network ofinteracting units produce behavior that appears to be the outcome of an independent race? The authorsreport how a simple, competitive network can solve this paradox and provide an account of what ismeasured by stop-signal reaction time.

Keywords: stop-signal task, cognitive control, frontal eye field, cognitive modeling, stochastic decisionmodels

The task of cognitive neuroscience is to bring behavioral andphysiological data together to explain how mental computationsare implemented in the brain. This task is difficult when behavioraland physiological data appear to contradict each other. In thesesituations, a new theory is required to resolve the contradiction.This article reports results from an endeavor to resolve a paradoxin the behavioral and physiological analyses of the stop-signaltask. For over 20 years, behavioral data have been modeled suc-cessfully in terms of a race between two independent processesthat respond to the stop signal and the go signal (Logan & Cowan,1984). However, the neural systems that control movements com-prise layers of inhibitory interactions between neurons that imple-ment movement inhibition and movement initiation (reviewed byMunoz & Schall, 2003). These two facts present a paradox: Howcan interacting neurons produce behavior that appears to be theoutcome of independent processes? We present a new theory of

performance in the stop-signal task—the interactive race model—which assumes that the stop and go processes are independent formost of their latent periods. After this latent period, a second stageoccurs in which the stop process interacts strongly and briefly tointerrupt the go process. The theory resolves the paradox andunifies behavioral and physiological perspectives on stop-signaltask performance. More generally, our work illustrates a novelapproach to bringing neurophysiological data to bear on quantita-tive computational model testing.

The Stop-Signal Task

The stop-signal task investigates the control of thought andaction by probing subjects’ ability to withhold a planned move-ment in response to an infrequent countermanding signal (seeFigure 1a; e.g., Lappin & Eriksen, 1966; Logan, 1994; Logan &Cowan, 1984). Subjects are instructed to make a response asquickly as possible to a go signal (no-stop-signal trial). On aminority of trials, a stop signal is presented and subjects have toinhibit the previously planned response (stop-signal trial). Sub-jects’ ability to inhibit the response is probabilistic due to vari-ability in reaction times (RTs) of the stop and go processes anddepends on the interval between the go-signal and stop-signalpresentation, referred to as the stop-signal delay (SSD). A trial islabeled signal inhibit (or cancelled) if the subject inhibits theresponse that would have been produced otherwise. A trial islabeled as signal respond (or noncancelled) if the subject is unableto inhibit the response. Typically, as SSD increases, subjects’ability to inhibit the response decreases, so the probability ofsignal-respond trials increases. Plotting the probability of respond-ing given a stop signal against SSD is described as the inhibitionfunction and is illustrated in Figure 1. In addition to the inhibitionfunction, other dependent measures include RTs on trials with nostop signal and RTs on trials in which a response was made despitethe stop signal (i.e., the signal-respond trials).

Leanne Boucher, Thomas J. Palmeri, Gordon D. Logan, and Jeffrey D.Schall, Department of Psychology, Vanderbilt University.

This work was supported by Robin and Richard Patton through the E.Bronson Ingram Chair in Neuroscience; National Science FoundationGrants BCS0218507 and BCS0446806; and National Institutes of HealthGrants F32-EY016679, RO1-MH55806, RO1-EY13358, P30-EY08126,and P30-HD015052. We thank M. Pare for sharing data; J. Brown, C.Camalier, M. Leslie, R. Krauzlis, M. Pare, L. Pearson, E. Priddy, V.Stuphorn, and K. Thompson for comments; D. Shima for computer pro-gramming assistance; K. Reis for figures; and the Vanderbilt AdvancedCenter for Computing for Research and Education for access to thehigh-performance computing cluster (http://www.accre.vanderbilt.edu/research).

Correspondence concerning this article should be addressed to LeanneBoucher, Thomas J. Palmeri, Gordon D. Logan, or Jeffrey D. Schall,Department of Psychology, Vanderbilt University, Nashville, TN 37221.E-mail: [email protected], [email protected], [email protected] or [email protected]

Psychological Review Copyright 2007 by the American Psychological Association2007, Vol. 114, No. 2, 376–397 0033-295X/07/$12.00 DOI: 10.1037/0033-295X.114.2.376

376

Response inhibition in the stop-signalparadigmFrederick Verbruggen1,2 and Gordon D. Logan1

1 Department of Psychology, Vanderbilt University, Nashville, TN 37203, USA2 Department of Experimental Psychology, Ghent University, B-9000 Ghent, Belgium

Response inhibition is a hallmark of executive control.The concept refers to the suppression of actions that areno longer required or that are inappropriate, whichsupports flexible and goal-directed behavior in ever-changing environments. The stop-signal paradigm ismost suitable for the study of response inhibition in alaboratory setting. The paradigm has become increas-ingly popular in cognitive psychology, cognitive neuro-science and psychopathology. We review recent findingsin the stop-signal literature with the specific aim ofdemonstrating how each of these different fields con-tributes to a better understanding of the processesinvolved in inhibiting a response and monitoring stop-ping performance, and more generally, discovering howbehavior is controlled.

People can readily stop talking, walking, typing and so on,in response to changes in internal states or changes in theenvironment. This ability to inhibit inappropriate or irre-levant responses is a hallmark of executive control. Therole of inhibition in many experimental paradigms isdebated, but most researchers agree that some kind ofinhibition is involved in deliberately stopping a motorresponse. Here, we focus on the stop-signal paradigm[1], which has proven to be a useful tool for the study ofresponse inhibition in cognitive psychology, cognitiveneuroscience and psychopathology. We review recentdevelopments in the stop-signal paradigm in these differ-ent fields. The focus is primarily on the inhibition ofmanual responses. Studies of oculomotor inhibition arediscussed in Box 1.

Successful stopping: inhibition and performancemonitoringIn the stop-signal paradigm, subjects perform a go tasksuch as reporting the identity of a stimulus. Occasionally,the go stimulus is followed by a stop signal, which instructssubjects to withhold the response (Figure 1). Stopping aresponse requires a fast control mechanism that preventsthe execution of the motor response [1]. This processinteracts with slower control mechanisms that monitorand adjust performance [2].

The race between going and stoppingPerformance in the stop-signal paradigm is modeled as arace between a ‘go process’, which is triggered by thepresentation of the go stimulus, and a ‘stop process’, which

is triggered by the presentation of the stop signal. Whenthe stop process finishes before the go process, the responseis inhibited; when the go processes finishes before the stopprocess, the response is emitted. The latency of the stopprocess (stop-signal reaction time [SSRT]) is covert andmust be estimated from a stochastic model, such as theindependent race model [3] (Box 2). SSRT has proven to bean important measure of the cognitive control processesthat are involved in stopping. Cognitive neuroscientistsuse SSRT as a criterion to determine whether neuralprocesses participate directly in response inhibition (Box1). Psychopathologists use SSRT to study inhibitory defi-cits in different patient groups (see later). Developmentalscientists found that SSRT is elevated in younger childrenand older adults, compared with young adults. In addition,a comparison of SSRT and go reaction time (RT) showedthat going and stopping develop and decline independently[4–6].

Monitoring and adjusting go and stop performanceSuccessful performance in the stop-signal paradigm alsoinvolves monitoring go and stop performance and adjust-ing response strategies to find an optimal balance betweenthe conflicting demands of the go task (‘respond as quicklyas possible’) and the stop task (‘stop the response’). Severalstudies indicate that subjects change response strategiesproactively when they expect stop signals to occur, tradingspeed in the go task for success in the stop task [2,7]. Manystudies indicate that subjects also change response strat-egies reactively after stop-signal trials [8–11]. Some showthat go RT increases after unsuccessful inhibition, remi-niscent of the post-error slowing observed in choice reac-tion tasks. Others show that go RT increases aftersuccessful stopping, which is inconsistent with error-cor-rection but indicates a shift in priority to the stop task aftera stop signal. Recent studies show that stimulus repetitionmight be a crucial variable: responding after successfulstopping is typically slower when the stimulus from thestop trial is repeated, as if the stimulus was associatedwith stopping, and retrieval of that association impaired goperformance [8]. This stimulus-specific slowing can persistover many intervening trials [10] and might support thedevelopment of automatic inhibition [12].

Interim conclusionsCognitive psychologists have identified the computationalmechanisms underlying performance in the stop-signalparadigm, identifying a fast-acting stop process that pro-

Review

Corresponding author: Verbruggen, F. ([email protected]).

418 1364-6613/$ – see front matter ! 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tics.2008.07.005 Available online 15 September 2008

Inhibitory Control in Mind and Brain 2.0: Blocked-Input Models ofSaccadic Countermanding

Gordon D. LoganVanderbilt University

Motonori YamaguchiVanderbilt University and Edge Hill University

Jeffrey D. Schall and Thomas J. PalmeriVanderbilt University

The interactive race model of saccadic countermanding assumes that response inhibition results from aninteraction between a go unit, identified with gaze-shifting neurons, and a stop unit, identified withgaze-holding neurons, in which activation of the stop unit inhibits the growth of activation in the go unitto prevent it from reaching threshold. The interactive race model accounts for behavioral data andpredicts physiological data in monkeys performing the stop-signal task. We propose an alternative modelthat assumes that response inhibition results from blocking the input to the go unit. We show that theblocked-input model accounts for behavioral data as accurately as the original interactive race model andpredicts aspects of the physiological data more accurately. We extend the models to address thesteady-state fixation period before the go stimulus is presented and find that the blocked-input model fitsbetter than the interactive race model. We consider a model in which fixation activity is boosted whena stop signal occurs and find that it fits as well as the blocked input model but predicts very highsteady-state fixation activity after the response is inhibited. We discuss the alternative linking proposi-tions that connect computational models to neural mechanisms, the lessons to be learned from modelmimicry, and generalization from countermanding saccades to countermanding other kinds of responses.

Keywords: inhibition, cognitive control, executive control, stop signal

The ability to inhibit thought and action is an important com-ponent of cognitive control. It improves over childhood and de-clines in old age. It is strong in healthy adults and weak in peoplewith psychiatric and neurological disorders. It varies betweenindividuals with different personalities and cognitive abilities. It isoften studied in the stop-signal paradigm, in which people areasked to inhibit a response they are about to execute (for reviews,see Logan, 1994; Verbruggen & Logan, 2008). The inhibitoryprocess in the stop-signal paradigm is not directly observable, so itmust be assessed by applying a mathematical model to the data.For 25 years stop-signal behavior was explained in terms of Logan

and Cowan’s (1984) independent race model, which assumes thatstop-signal performance depends on the outcome of a race betweena go process that produces an overt response and a stop processthat inhibits it. The independent race model provides estimates ofthe latency of the unobservable response to the stop signal (stop-signal response time or SSRT), which is the primary measure ofinhibitory control in stop-signal studies of development, aging,psychopathology, and neuropathology (also see Logan, Van Zandt,Verbruggen, & Wagenmakers, 2014). The independent race modeladdresses whether and when a response is inhibited but does notaddress how the response is inhibited. It describes the processesthat run in the race; it does not describe what happens at the endof the race when the stop process wins. Recently, Boucher, Palm-eri, Logan, and Schall (2007) proposed an interactive race modelthat describes what happens when the stop process wins: Theyassumed that a stop unit inhibits the growth of activation in a gounit to prevent it from reaching a threshold that triggers theresponse (also see Lo, Boucher, Paré, Schall, & Wang, 2009;Ramakrishnan, Sureshbabu, & Murthy, 2012; Wong-Lin, Eckhoff,Holmes, & Cohen, 2010; cf. Salinas & Stanford, 2013). Boucher etal. showed that the interactive race model accounts for behavior aswell as the independent race model and goes beyond it to predictimportant properties of the underlying neurophysiology.The purpose of this article is to evaluate alternatives to the

interactive race model that provide different explanations of howresponses are stopped. We focus on blocked-inputmodels that stopresponses by blocking the input to the go unit instead of inhibitingthe growth of activation in the go unit (Band & van Boxtel, 1999;

Gordon D. Logan, Department of Psychology, Vanderbilt University;Motonori Yamaguchi, Department of Psychology, Vanderbilt Universityand Department of Psychology, Edge Hill University; Jeffrey D. Schall andThomas J. Palmeri, Department of Psychology, Vanderbilt University.This research was supported primarily by grant number R01-EY021833

from the National Institutes of Health, and also by grant number BCS0957074, and SMA 1041755 from the National Science Foundation andR01-MH55806, R01-EY008890, and P30-EY08126 from the NationalInstitutes of Health and by Robin and Richard Patton through the E.Bronson Ingram Chair in Neuroscience. We are grateful to Paul Middle-brooks for help with the spike density functions. Data and models can befound at https://sites.google.com/site/cogyamaguchi/.Correspondence concerning this article should be addressed to Gordon

D. Logan, Department of Psychology, Vanderbilt University, Nashville TN3720. E-mail: [email protected]

ThisdocumentiscopyrightedbytheAmericanPsychologicalAssociationoroneofitsalliedpublishers.

Thisarticleisintendedsolelyforthepersonaluseoftheindividualuserandisnottobedisseminatedbroadly.

Psychological Review © 2015 American Psychological Association2015, Vol. 122, No. 2, 000 0033-295X/15/$12.00 http://dx.doi.org/10.1037/a0038893

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