Deep models of superficial face judgments.

RESEARCHARTICLE PSYCHOLOGICALANDCOGNITIVESCIENCES OPEN ACCESS
Deep models of superficial face judgments
JoshuaC.Petersona,1,StefanUddenbergb,ThomasL.Griﬃthsa,c,AlexanderT odorovb,andJordanW.Suchowd
EditedbyWinrichFreiwald,TheRockefellerUniversity,NewYork,NY;receivedAugust17,2021;acceptedMarch7,2022,byEditorialBoardMember
CharlesD.Gilbert
The diversity of human faces and the contexts in which they appear gives rise to an
expansive stimulus space over which people infer psychological traits (e.g., trustwor-
thiness or alertness) and other attributes (e.g., age or adiposity). Machine learningmethods,inparticulardeepneuralnetworks,provideexpressivefeaturerepresentations
of face stimuli, but the correspondence between these representations and various
human attribute inferences is difficult to determine because the former are high-dimensionalvectorsproducedviablack-boxoptimizationalgorithms.Herewecombine
deep generative image models with over 1 million judgments to model inferences of
morethan30attributesoveracomprehensivelatentfacespace.Thepredictiveaccuracyofourmodelapproacheshumaninterraterreliability,whichsimulationssuggestwould
nothavebeenpossiblewithfewerfaces,fewerjudgments,orlower-dimensionalfeature
representations. Our model can be used to predict and manipulate inferences withrespecttoarbitraryfacephotographsortogeneratesyntheticphotorealisticfacestimuli
thatevokeimpressionstunedalongthemodeledattributes.
faceperception |socialtraits |computationalmodels
Facesareamongthemostimportantstimulithatpeople encounter—theyarerecognized
byinfantslongbeforeotherobjectsintheirenvironment(1),recruitspecializedcircuitsin
thebrain(2),andarefundamentaltosocialinteraction(3).Centraltoourexperiencewith
faces are the attributes that we assign to them, often implicitly. These include attributesthatarereadoff,describinglargelyobjectiveattributesoffaces(e.g.,ageandadiposity),and
thosethatarereadinto,suchashowtrustworthyapersonis(4).Althoughtheinferences
of the latter attributes are more subjective and generally inaccurate, they are similarlypsychologicallyconsistentacrosspeople(4–6)aroundtheglobe(7–9)andhaveimportant
consequences (10) ranging from electoral success (11, 12) to sentencing decisions (13,
14). Because any face can be judged with respect to such attributes, these psychologicaldimensions are universal in that they are implicitly defined over the space of nearly all
possible faces, contexts, and observational conditions. These factors combine to form
a diverse landscape of stimuli that makes it challenging to capture the correspondingpsychological content in its entirety. Such content forms the basis of scientific models of
faceperceptionanddefinesthescopeofdownstreamapplicationssuchastrainingpeople
toovercome stereotypes(15).
The importance of face attribute inferences has led to the proliferation of techniques
forscientificmodelingoffaces,whichcanbeorganizedbroadlyintotwoapproaches.The
firstextrapolatesfromfacephotographs,oftenrelatedvialandmarkannotations(16,17).Thesecondgeneratesartificialfacesusingparametricthree-dimensionalfacemeshes(18).
Photographs offer greater realism but are limited to available datasets of face stimuli that
serveasthebasisforinterpolationandbytheinterpolationalgorithmsthemselves,which
oftenrequirehigh-qualitylandmarkannotationsunattainablewithoutcostlymanualwork
(19).Artificiallygeneratedfacesarenotsubjecttotheselimitationsbutlackdiversityandrealism. Neither approach provides workable models that express the full richness and
diversity ofhuman faces.
Machinelearningmethods,inparticulardeepneuralnetworkssuchasgenerativeadver-
sarialnetworks(GANs),canlearntomodelfacesfrommassivecollectionsofphotographs
scraped from image-sharing websites (20–23). These methods present a third option
for developing scientific models of faces, providing expressive feature representationsfor arbitrary realistic face images. However, relating these representations to human
perception is difficult because they are high-dimensional vectors produced via black-box
optimization algorithms(24).
We show that the keys to unlocking the scientific potential of these models and their
downstream applications are large-scale datasets of human behavior unattainable using
traditional laboratory experiments. In particular, such large datasets provide sufficientevidence to determine a robust mapping between expressive high-dimensional repre-
sentations from machine learning models and human mental representations of faces.Significance
Wequicklyandirresistiblyform
impressionsofwhatotherpeople
arelikebasedsolelyonhowtheir
faceslook.Theseimpressions
havereal-lifeconsequencesrangingfromhiringdecisionsto
sentencingdecisions.Wemodel
andvisualizetheperceptualbasesoffacialimpressionsinthemost
comprehensivefashiontodate,
producingphotorealisticmodelsof34perceivedsocialand
physicalattributes(e.g.,
trustworthinessandage).Thesemodelsleverageanddemonstrate
theutilityofdeeplearninginface
evaluation,allowingfor1)generationofaninﬁnite
numberoffacesthatvaryalong
theseperceivedattribute
dimensions,
2)manipulationofanyfacephotographalongthese
dimensions,and3)predictionof
theimpressionsanyfaceimagemayevokeinthegeneral(mostly
White,NorthAmerican)
population.
Author contributions: J.C.P., S.U., T.L.G., A.T., and J.W.S.
designed research; J.C.P. and S.U. performed research;
J.C.P., S.U., T.L.G., A.T., and J.W.S. contributed new
reagents/analytic tools; J.C.P., S.U., and J.W.S. analyzed
data; and J.C.P., S.U., T.L.G., A.T., and J.W.S. wrote the
paper.
Competing interest statement: All authors are listed as
inventors on a related patent (US Patent no. 11,250,245,
“Data-driven, photorealistic social face-trait encoding,
prediction, and manipulation using deep neural
networks”).
This article is a PNAS Direct Submission. W.F. is a guest
editorinvitedbytheEditorialBoard.
Copyright © 2022 the Author(s). Published by PNAS.
This open access article is distributed under Creative
Commons Attribution-NonCommercial-NoDerivatives
License4.0(CCBY-NC-ND) .
1To whom correspondence may be addressed. Email:
joshuacp@princeton.edu.
This article contains supporting information online at
https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.
2115228119/-/DCSupplemental .
PublishedApril21,2022.
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Fig. 1.Correlationmatrixfor34averageattributeratingsforeachof1,000faces.Rowsandcolumnsarearrangedaccordingtoahierarchicalclusteringoft he
correlationvalues.
We quantify an upper bound on the robustness of the mapping
in terms of the reliability of the underlying attribute inferences
and determine how that robustness scales as a function of the
number of faces rated, the number of ratings per face, andthe dimensionality of the deep feature space. We then use this
mapping to predict and manipulate inferences over arbitrary face
images, enabling us, for example, to adjust a photograph so as toincreaseordecreasetheperceivedtrustworthinessofitssubjectto
match a targetrating.
Such a mapping can be computed for any psychologically
meaningful attribute inference. We focus on three classes of such
inferences.First,thereareinferencesdefinedbysubjectiveimpres-
sions of relatively objective properties (e.g., age and adiposity).These more objective properties, which also include hair styling,
presence of accessories (e.g., glasses), gaze, and facial expression,
arecommonlystudiedincomputervision,wheretheyarereferredto as “attributes” (25) or “soft biometrics” (26). Next, there are
inferences of subjective and socially constructed attributes, such
astrustworthy andmasculine/feminine , the conventional targets
of social scientific study (4). Finally, there are inferences of fully
subjective attributes such as familiar,w h e r et h eo b s e r v e ri st h e
only arbiter of truth (27). For ease of presentation, we refer to
inferences of all three classes as “attribute inferences” and the
underlyingattributesas“attributes,”drawingdistinctionsbetweentheclassesinthetextasnecessary.Pleasenotethattheseattribute
inferences,especiallythoseofthemoresubjectiveorsociallycon-
structedattributes,havenonecessarycorrespondencetotheactualidentities, attitudes, or competencies of people whom the images
resemble or depict (e.g., a trustworthy person may be wrongly
assumedtobeuntrustworthyonthebasisofappearance).Rather,theseinferences,andinturnourmeasurements,reflectsystematic
biasesandstereotypesaboutattributessharedbythepopulationof
raters. Nevertheless, these inferences are driven by (combinationsof) physical cues present in the faces themselves—for example,
facesjudged tolook moretrustworthymay have moreneotenous
features(e.g.,largeeyes) orupturnedlips, asin a smile(4).We used online crowdsourcing to obtain attribute inference
ratingsforjustover1,000synthetic(althoughhighlynaturalistic)
face stimuli for 34 attributes, with ratings by at least 30 unique
participants per attribute–stimulus pair, for a total of 1,020,000humanjudgments( MaterialsandMethods ).Wecallthiscollection
of face stimuli and the corresponding behavioral data the One
Million Impressions dataset. A detailed summary of these ratingsandinterattribute relationships can be foundin SI Appendix .
Results
The Structure of Attribute Inferences. To explore the structure
ofattributeinferences,wefirstcomputedthecorrelationbetween
the mean face ratings for each pair of attributes (Fig. 1). Manyattributes were highly correlated, including happy–outgoing(r=
0.93)anddominant–trustworthy (r=−0.81),whileotherswere
largely unrelated, including smart–attractive (r=0 . 0 1),smart–
trustworthy (r=0 . 0 2),liberal/conservative –believes in god (r=
0.08), andelectable–attractive(r=0 . 0 5).
Although some of these correlations are consistent with pre-
vious findings (8), others are not. First, although past work has
foundthatjudgmentsoftrustworthinessanddominanceareoftennegatively correlated, the correlation is generally small (on the
order of –0.2), whereas the correlation observed here (–0.81)
was much stronger (4, 28). Second, judgments of smartness orcompetence have been found to be highly positively correlated
withjudgmentsofattractivenessandtrustworthiness(withvalues
as high as ≈0.8), whereas we found only marginal correlations
between those attribute inferences (8). One explanation for these
discrepancies is that the face stimuli used here are more diverse
thaninthecomparisonstudies,especiallywithrespecttoage;thepresent study includes (simulated) childrens’ faces. This explana-
tionisplausiblegiventhatthecorrelationalstructureofjudgments
of children’s faces is different from the structure of judgmentsof adult faces (29). To probe this hypothesis, we recomputed
interattributecorrelationsonsubsetsofthedatawithrestrictedage
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ranges (SIAppendix ,F i g.S9). We found that the inclusion of the
children’s faces partially explains some discrepancies (e.g., smart–
attractive) and does not explain others ( trustworthy –dominant).
Third,memorable faces were more attractive, as observed in the
positive correlation between the respective ratings (Fig. 1). This
findingisinconsistentwithworkshowingthatactualmemorabil-
ityoffacesisnegativelycorrelatedwithattractivenesstotheextentthat predictions of memorability are veridical (30). Last, familiar
faceswereseenasmoreattractiveandaverage-looking,consistent
with the finding that average faces tend to be perceived as moreattractive(ref. 31,but seeref. 32).
Theattribute outdoors(whetherthephotoappearedtobetaken
outdoors or indoors) was included to assess potential confoundsin using naturalistic face photos. It was found to be the least
correlated with other attributes, having the lowest per-attribute
maximum absolute correlation ( outdoors–electable,r=0 . 2 0). In
comparison, the attribute with the next-lowest maximum was
skinny/fat(skinny/fat–attractive,r=0 . 4 3), which despite having
twice the magnitude was one of the easier attributes to predict
(Fig.2).Furthermore,that outdoorshadthelowestmeanabsolute
correlationwithallotherattributes( r=0 . 0 8)indicatesminimal
contributionofcontextualeffectsduetonaturalisticbackgrounds
andlighting.
Predicting Attribute Inferences. To model an attribute, we
start with the high-dimensional representation vectors zi=
{z1,...zd}assigned to each synthetic face iin our stimulus
set by a pretrained state-of-the-art GAN (21, 22, 33). The GAN
haslearnedamappingfromeachsuchvectortoanimagethrough
extensive training on a large database of real, nonsynthetic facephotographs ( Methods and Materials ). We then model each
psychological attribute, measured via average ratings y
i,a sa
linear combination of features: yi=w0+w1z1+...+wdzd.
Thevectorofweights wk={w1,...wd}representstheattribute
as a linear dimension cross-cutting the representational space
and is fit using cross-validated, L2-regularized linear regression.
A diagram summarizing the modeling pipeline for predicting
attribute inferences is provided in SI Appendix ,F i g.S 1.
Average cross-validated (i.e., out-of-sample) model perfor-
manceforeachattributeisreportedinFig.2.Predictionformost
attributeswasreasonablysuccessful,withmost R2valuesranging
fromabove0.5toalmost0.8,withattributes typical,familiar,and
gaybeing the exceptions.
Because participants partly disagree in their appraisals (34),
perfect prediction is impossible. To better understand the pre-
diction ceiling imposed by limited interrater reliability, we com-
puted the split-half reliability for each attribute, averaging thesquared correlations between the averages of 100 random splits
oftheratingsforeachimage.Thesepredictionceilingsvaryacross
attributes and are plotted in Fig. 2 alongside the correspondingmodel shortfalls they imply. (See Factors Influencing Prediction
Performance for a detailed characterization.)
Interestingly, the models of familiarandlooks like you showed
the smallest gaps between performance and reliability, indicating
that their unpredictability is not due to poor model quality or
lack of useful input features. Rather, it seems likely that familiar
more so than other attributes is based on both a shared concept
or experience and a much larger personal concept or experience;
onlytheformercanbepredictedforparticipantsinaggregate.Thisis corroborated by a similar effect for the attribute looks like you ,
whichcanbepredictedonlyattheaggregateleveltotheextentthat
ourparticipantpoolhasasharedrepresentationoftheirrespectivefacial features, which may be a byproduct of the participant pool
having less diversity in appearance than does the stimulus set.Fig. 2.Average cross-validated model performance (black bars) compared
tointersubjectreliability(redmarkers).
Attributes corresponding to some racial or ethnic social cat-
egories, such as “Black,” exhibited a larger gap between relia-
bility and model performance than did other attributes. One
possible reason for this gap is a sampling bias in the stimulusgenerator. Indeed, rating-distribution violin plots provide some
indication that, for example, Black faces were undersampled
(SI Appendix ,F i g.S 3).Asecondpossiblereasonforthegapisthat
thedegreeofundersamplingofparticipantswhoreportmember-
ship in a racially or ethnically minoritized group might correlate
with the content of the aggregate attribute inferences. However,weobservenosuchcorrelation:thesecondmostcommonpartici-
pant self-identifier was Black, which had one of the largest gaps
between reliability and model performance, whereas attributescorresponding to even less commonly self-reported racial and
ethnic social categories had a smaller gap. A third possible reason
is that the predominantly White participant pool might havesimilarstereotypesofallraciallyorethnicallyminoritizedgroups,
leadingtocomparablepredictabilityacrosstherelevantattributes.
However, this explanation is inconsistent with the lack of strongcorrelation observed across those attributes (Fig. 1). Taken to-
gether, this suggests that the stimulus selection contributes more
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0.8
0.6
0.00.20.4
Model performance R²
Number of ratings per face 5 30
Number of feature dimensions 012 150.8
0.6
0.00.20.4
0.8
0.6
0.00.20.4gay Blackprivileged Asianelectable agehappy liberal/conservativealertsmugMiddle Eastern familiar memorable typicalbelieves in god smart skin color hair color outdoors trustworthywell groomedattractivePaciﬁc Islanderskinny/fatdominantWhite feminine/masculineoutgoingcutelong hair Native American dorkyHispanic looks like you
Number of faces 10000.8
0.6
0.00.20.4
0.8
0.6
0.00.20.4
0.8
0.6
0.00.20.4100
Fig. 3.Modelperformance( R2)foreachattributeasafunctionofthenumberoffaceexamples( Top),thenumberofparticipantratingsforeachfaceexample
(Middle),andthenumberofimagefeaturedimensions( Bottom).Attributesareorderedbythemaximummodelperformanceobservedin Top.
to the observed gap than does the composition of the participant
pool.Evenso,nofirmconclusioncanbedrawnbecausewecannotrule out limitations in the representational capacity of the neural
networkfeatures.
FactorsInﬂuencingPredictionPerformance. Tocharacterizethe
factors influencing prediction performance, we first investigated
the effect of the number of faces rated on predictive performance
(Fig.3,Top).Performancecurvesweregeneratedbyfittingmodels
for each of 30 random samples of images with sizes ranging
from 100 to 1,000. Most attributes benefit from increases in the
numberoffacesrated,withsignificantvariationacrossthemwithrespecttohowperformancescaleswiththenumberofuniquefaces
thatwererated.Interestingly,fewerimageswereneededtosaturate
model performance for the attribute feminine/masculine than for
most other attributes. For all other attributes, adding additional
images improved performance throughthe full range.
Next, we investigated the relationship between the number of
ratingsbyuniqueparticipantsobtainedforeachfacestimulusand
predictiveperformance(Fig.3, Middle).Performancecurveswere
generated by fitting models on down-sampled datasets with sizesranging from 5 to 30 unique ratings per image, with 30 datasets
sampledpersize.Asidefromattributes feminine/masculine andage,
whichelicitlessdisagreement,performanceincreasesconsiderably
as the number of ratings increases for all attributes. Gains due to
the number of ratings diminish with increases in the number ofunique ratings but at a slower rate than gains due to the number
of faces (Fig. 3, Top). It remains to be seen the extent to which
scaling the number of rated faces and the number of ratingsper face beyond the range explored here accounts for the gap
betweenmodelperformanceandtheceilingimposedbyinterrater
reliability.
Finally, we investigated the relationship between the number
of image features (512 total) and predictive performance (Fig. 3,
Bottom). Performance curves were generated by fitting models
using reduced feature sets obtained via principal components
analysis, varying the dimensionality between 10 and 512. In all
cases, performance saturates quickly but is improved marginallywith a greater number of dimensions in some cases. The various
profilesofsaturationindicatethatasfewas10dimensionsofthis
latentfeaturespacemaybeenoughtoaccountforthebulkofvari-ance in attribute inferences, with a subset of attributes benefiting
considerably fromhigher-dimensional feature representations.Itispossiblethatthequalityofthelearnedrepresentationfrom
the particular deep neural network we employed was a limitingfactor in predictive performance. Factors beyond predictive per-formance(specifically,theabilitytogenerateimagesinadditiontorepresentingthem)guidednetworkselectionforthepresentstudy.Other architectures with other forms of supervision may offer
improvement in predictive performance. For example, there is
evidence that identity-supervised models provide representationsthat are highly predictive of diverse attribute information (26,35,36).
Manipulating Attribute Inferences. Because the learned
attribute vectors correspond to linear dimensions, we canmanipulate an arbitrary face represented by features z
iwith
respect to attribute kusing vector arithmetic: zi+βwk,w h e r e
βis a scalar that controls the positive or negative modulation of
theattributes.Weapplyasymmetricrangeof βaround0toeach
attributevectortomanipulateaseriesofbasefacerepresentationsinboththenegativeandpositivedirectionsanddecodetheresultsfor visualization using the same decoder/generator component of
the neural network that was used to derive representations (see
SIAppendix formore details).
The results of these transformations for six sample attribute
inferences are shown in Fig. 4. The manipulations are strikinglysmooth and effective along each attribute dimension. For ex-ample, modulating trustworthiness increases features associated
with perceptions of trustworthiness, such as eye gaze, degree ofsmiling, face shape, and facial femininity (4, 37). Manipulationsof attribute inferences may affect more than one dimension ofappearance. For example, increasing smartnessmay add glasses or
change the facial expression. Increasing outgoingness may increase
smiling, as expected, but also give glasses a more rounded andcartoonish appearance. Other dimensions allow for greater levelsof extrapolation. For example, faces can be made considerablyskinnierorfatterthan any examples in the dataset, yet still
maintain a realistic appearance. Faces with strongly manipulatedhappinessalso resemble convincing caricatures.
It is possible to manipulate one dimension s(e.g.,smartness)
while controlling for another t(e.g.,trustworthiness )b yc r e a t i n g
anorthogonalvector,subtractingtheprojectedcomponentofthe
dimension to be controlled for:
s−ts·t
||t||2. [1]
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B A
Fig. 4.(A)Thefacesjudgedonaveragetohavethehighestandlowestratingsalongsixsampleperceivedattributedimensions.( B)Model-basedmanipulations
oftwosamplebasefacesalongthesampledimensions,demonstratingsmoothandeﬀectivemanipulationsalongeachattribute.
An example of such transformations controlling for trustwor-
thiness on a given exemplar face can be seen in SI Appendix ,
Fig. S11.
Notethattheattribute-inferencemanipulationscanaffectboth
internal facial features and external features. When only internal
face features are altered, it is not because the GAN manipulatesonlyinternalfeaturesbutbecausetheexternalfeaturesareorthog-onal or irrelevant to that attribute inference in the region of the
manipulated face.
Validating Models of Attribute Inferences. Do the attribute
models generated above reliably change participants’ impressions
of faces transformed with them? To answer this question, we
ran a series of 20 preregistered experiments with over 1,000participants to verify that our models can indeed manipulateattributeimpressionsinobservers.Eachoftheexperimentspaired
one of two face image types (artificial vs. real) with one of
10 different attribute dimensions, chosen to represent a widerange of different model performances and levels of objectiv-
ity/subjectivity ( age,feminine/masculine ,skinny/fat,trustworthy ,
attractive,dominant,smart,outgoing,memorable ,a n dfamiliar).
Like in the attribute-modeling experiments, for the artificial faceexperiments we generated 50 unique synthetic faces at randomusing StyleGAN2 (21, 22), a state-of-the-art GAN architecture
(SG2). However, for the real-face experiments, we encoded intoourmodel50uniquefacephotograph,chosenfromacommonlyused database of real faces from the psychological literature (38).
On each trial, participants were shown a single face and asked
to rate it. Critically, each face image was transformed by one(experimentally assigned) perceived attribute model to evoke oneof three levels of that impression; faces could be set to the mean
observed value of the perceived attribute or at ±0.5 SD from
that mean. Every face was shown at every level of the assignedattribute (50 identities ×3 transformation levels = 150unique
faces), and once again, 20% of trials were repeated to measure
test–retest reliability (in order to exclude subjects with negative
such reliability) for a total of 180 trials. If the attribute modeltransformations indeed change participants’ impressions of the
faces,thenweshouldobservethatparticipants’ratingsofthefaces
increase with increasing levels of the manipulation. We foundjust that: repeated measures ANOVAs revealed that all of themanipulations yielded highly significant results [all F(2, 98)s>
14.13, all values of P<0.000005, all values of η
2>0.223].
Critically,alloftheexperiments’datashowedastronglysignificantpositive linear trend [all values of t(98)>2.69, all values of
P≤0.008, with the exception of real faces manipulated along
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thefamiliarattribute dimension, t(98) =−1.60,P= 0.112;s e e
SIAppendix , Fig.S12 for a swarmplotof all the data].*
General Discussion
Wesetouttodevelopacomprehensivemodelofattributepercep-
tionthatcanpredicthumanattributeinferencesfromfaceimages
and manipulate them along psychologically meaningful dimen-
sions. With no explicit featurization or interpolation algorithm,the model accomplishes this in a fully data-driven manner with
relatively high accuracy and generalization. Large datasets (with
respecttoboththenumberoffacestimuliandthenumberofrat-ingsperface)arenecessarytoachievethis.Qualitativeresultsand
validation experiments demonstrate that psychological attribute
manipulations of realistic face photos can be accomplished usingsimple vector arithmetic. Moreover, our pipeline provides a gen-
eralformulaformodelinginferencesofanyattributesthatcanbe
measuredviaimageannotations.Becausethemodelsofattributesareexpressedinthesamemultidimensionalspace,theirsimilarity
isimmediatelygiven,enablingtestingofspecifichypothesesabout
the relation between psychological attributes, predicting novelattributes based on their relationships with models of existing
attributes,andcontrollingforsharedvariancebetweenattributes.
The model broadly characterizes inferences about diverse faces
in their everyday contexts and viewing conditions. For exam-
ple, in any particular image, one can generally discern whether
the photograph is candid or contrived, environment conditions(e.g., outside in direct sunlight near vegetation versus inside of
a building with warm lighting), the subject’s pose and gaze,
grooming habits, and even hints of their culture or tastes basedonpartiallyvisibleclothing,necklines,headwear,jewelry,glasses,
etc. Other factors of variation include viewing angle, head pose,
photo quality, focal length, and depth of field, among others.While capturing behavior in a way that generalizes across these
variations (and includes their effects) is the primary goal, it
has the considerable disadvantage of making interpretation more
challenging. Consider, for example, when one face is inferred
to be more trustworthy than another. Is it because of furrowedbrowsandawidejaworbecauseofahighlyatypicalhatanddark
lighting? Although our stimuli are synthetic, they are not highly
controlled, more comparable to randomly sampled and weaklycurated photographs. Thus, understanding the bases of attribute
inferences will require significant additional lower-level attribute
annotations (e.g., hair color). Fig. 1, for example, implies thatskinny/fat,long hair,a n dhair color (hair darkness) are not partic-
ularly explanatory of attribute inferences, with some exceptions
(e.g.,skinny/fat–attractive). Qualitative inspection revealed that
transformationsdidnotappeartofrequentlyorsignificantlyalter
nonface features (with the notable exception of spawning glasses
when increasing smart-ness).
Another notable consideration when interpreting the current
work is that the diversity of the faces used in the experiment will
almost certainly influence and may even obfuscate the meaningof some attributes. For example, the semantics of the attribute
attractivemaydifferwhenratingimagesofchildrenversusadults.
It is not enough to simply analyze subsets of faces in the data,because the context of the experiment may induce order effects
or serial dependence (39) that influences participant ratings of
all faces. It is also difficult to manipulate the context of theexperiment because so many different contexts are possible. Fu-
*The fact that familiarperformed so poorly is not unexpected, as this dimension was
speciﬁcally chosen to represent a poorly performing attribute model from the model-
generationstudies.ture work could consider two possible solutions. The first is to
exploit the fact that our experiment sampled faces and their
ordering, and thus contexts, at random and relatively densely.
Because some of these contexts will cluster into, e.g., many-children/few-children groups, this provides one possible avenue
for probing relevant effects. The second is to model attributes
as multimodal, wherein attributes are not single linear factors(linear combinations of features) but many potentially correlated
but not wholly colinear factors that cluster in different regions of
the underlying representation space of the attribute model. Thismay also explain part of the current gap between our predictive
models and the corresponding estimated upper bounds based on
intersubject reliability.
Last,itisunclearwhethersyntheticstimuligeneratedbyarchi-
tectures like SG2, despite being generally convincingly realistic,
are in fact different from real faces in ways that could bias
conclusions that make use of them. For this reason, researchers
making use of these stimuli to draw conclusions about humanperceptionshouldtakecaretovalidatefindingsderivedfromthem
usingphotos ofreal facesas appropriate.
EthicalImplications. Importantly,whiletheprimarygoalofthis
work is to support scientific modeling, the framework developedhere adds significantly to the ethical concerns that already en-
shroud image manipulation software. In contrast to traditional
photo editing, which may be limited in effectiveness by theintuitions of a particular artist, the current method may be more
accurate and at the least is faster and more efficient through its
automation. Further, in contrast to other methods making use ofdeepneuralnetworkssuchasDeepFakes(40),whichcanaffectthe
socialperceptionofanindividualbyplacingtheminanunwanted
or compromising context (e.g., superimposed on a body in anarbitrarytargetimage),ourmodelcaninduce(perceived)changes
within the individual’s face itself and may be difficult to detect
when applied subtly enough. We argue that such methods (aswell as their implementations and supporting data) should be
made transparent from the start, such that the community can
develop robust detection and defense protocols to accompanythe technology, as they have done, for example, in developing
highly accurate image forensics techniques to detect synthetic
faces generated by SG2 (41, 42). More generally, to the extentthatimproperuseoftheimagemanipulationtechniquesdescribed
here is not covered by existing defamation law (43, 44), it is
appropriate to consider ways to limit use of these technologies
through regulatory frameworks proposed in the broader context
of face-recognition technologies (45,46).
There is also potential for our data and models to perpetuate
the biases they measure, which are first impressions of the popu-
lation under study and have no necessary correspondence to theactual identities, attitudes, or competencies of people whom the
images resemble or depict. While the bias in our sample of raters
comes from the same population as most crowdsourced studies,it may be particularly important to understand in the context
of social attribute perception, given that it consists of primarily
White participants from the United States. Further, we foundthat the generative model that synthesized our stimuli, while
highly diverse, nonetheless undersamples faces of Black people
and other minoritized groups. Applications of the model willthereby produce face images that are more closely aligned with
this bias than are the original inputs. We quantify part of this
bias beyond participant demographics primarily using the White,
familiar,a n dlooks like you attributes, all of which are moderately
correlated(Fig. 1).
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Conclusion. Modern data-driven methods from machine learn-
ingprovidenewtoolsforrepresentingandmanipulatingcomplex,
naturalistic stimuli but are not explicitly designed to model or
explain human mental representations. However, applying thesame “big data” philosophy to behavioral experiments allows us
toalignthesepowerfulmodelswithhumanperception.Thedeep
modelsofsuperficialfacejudgmentsthatweexploreinthispapercan in turn be used to broaden the range of behavioral data
we can collect because they define an infinite set of realistic
and psychologically controlled stimuli for a new generation ofbehavioral experiments.
Materials and Methods
Stimuli.Ourexperimentsmakeuseof1,004syntheticyetphotorealisticimages
offacesgeneratedusingSG2.ThegeneratornetworkcomponentofSG2modelsthedistributionoffaceimagesconditionedona512-dimensional,unit-variance,multivariate normal latent variable.When a vector is sampled from this distri-
butionandpassedthroughthenetwork,itismappedtoasecond,intermediate
512-dimensionalrepresentation(forwhichthedistributionisunknown),whichisinturnfedthroughmultiplelayersandultimatelymappedtoanoutputimage
resemblingthosefromthedatasetonwhichthemodelwastrained.Thus,either
of thetwo512-dimensional representationscanbeusedforourmodelingap-plications,eachassociatingonefullydescriptive(latent)featurevectorwitheach
face.Weusedthelatterrepresentationthroughoutbecauseityieldedsuperior
resultsinallanalyses.Speciﬁcally,weusetheserepresentationsfromapretrainedmodelthatwastrainedontheFlickr-Faces-HQDataset(21),containing70,000
high-qualityimagesataresolutionof1,024 ×1,024pixels.Imagesgenerated
bythismodelarerenderedatthesameresolution.
The synthetic faces generated by SG2 are diverse and convincingly realistic
in most cases but can occasionally contain visual artifacts that appear odd or
even jarring.We minimized these artifacts in our dataset using two strategies.
First,SG2employsaparameter ψforposttrainingimagegenerationthatbounds
thenormofeachmultivariateinputsampleand,asaresult,tradesoffbetween
sample diversity and sample quality. We set ψto 0.75, which by inspection
appearedtojointlymaximizethecriteriaforourpurposes.Second,wemanuallyinspected and ﬁltered the generated images,removing all instances that con-
tainedobviouslydistortedfaces,multiplefaces,hands,localizedblotchesofcolor,
implausible headdress, or any particularly notable visual artifact. Speciﬁcally,wesampled ∼10,000512-dimensional normal vectors,fedthemthrough the
generatornetworkofSG2toobtain10,000candidatefacestimuliforourdataset,
and took the ﬁrst ≈1,000 that met the criteria for quality.Random examples
fromthestimulussetareprovidedin SI Appendix .
For the model-validation studies,50 real face identities were generated by
encoding 50 faces from the Chicago Face Database (CFD ) (38).The CFD faces
usedinthesereal-faceexperimentswereroughlybalancedintermsofthefourracesandtwogendersavailableinthemainstimulusset.Theﬁnalsetincluded
12 East Asian, 14 Black, 12 Latin American, and 12 White faces (with equal
numbersofmaleandfemalefacesineachracialgroup).The50facesusedintheartiﬁcialfaceexperimentswerechosenviathesameprocedureasintheprevious
attributemodelingstudies.Eachuniquefaceidentitywasthentransformedalong
oneof 10perceivedattributedimensions( age,feminine/masculine ,skinny/fat,
trustworthy ,attractive,dominant,smart,outgoing,memorable ,and familiar)a t
threelevelsoftheattribute(–0.5SD,0SD,and+0.5SDfromthemeanratings
observed in the attribute model studies).This yielded 150 unique images permodel-validationstudyandtherefore3,000uniqueimagesintotal.
Participants. Fortheattributemodelstudies,weusedAmazonMechanicalTurk
torecruitatotalof 4,157participantsacross10,974sessions,of which10,633(≈97%) met our criteria for inclusion ( SI Appendix ,Data Quality ).Participants
identiﬁedtheirgenderasfemale(2,065)ormale(2,053),preferrednottosay
(21),or did not have their gender listed as an option (18).The mean age was
∼39 y old. Participants identiﬁed their race/ethnicity as either White (2,935),
Black/African American (458), Latinx/a/o or Hispanic (158), East Asian (174),
SoutheastAsian(71),SouthAsian(70),NativeAmerican/AmericanIndian(31),
Middle Eastern (12), Native Hawaiian or Other Paciﬁc Islander (3), or somecombinationof twoormoreraces/ethnicities(215).Theremainingparticipantseitherpreferrednottosay(22)ordidnothavetheirrace/ethnicitylistedasan
option(8).
Forthemodel-validationstudies,werecruitedatotalof1,022workersfrom
Amazon Mechanical Turk via CloudResearch (47),of which 1,000 ( ∼98%) met
our criteria for inclusion.Of those,18 participants were excluded for low test–
retestreliability,onewasexcludedforparticipatingintheexperimenttwice,and
three were overrecruited beyond our target sample size of 1,000. Participantsidentiﬁedtheirgenderasfemale(530)ormale(484),preferrednottosay(3),ordidnothavetheirgenderlistedasanoption(5).Themeanagewas ∼42y
old.Participantsidentiﬁedtheirrace/ethnicityaseitherWhite(781),Black/African
American (77), Latinx/a/o or Hispanic (37), East Asian (37), Southeast Asian(11), South Asian (12), Native Hawaiian or Other Paciﬁc Islander (3), or some
combination of two or more races/ethnicities (57). The remaining participants
either preferred not to say (3) or did not have their race/ethnicity listed as anoption(4).
TheInstitutionalReviewBoardatPrincetonUniversityapprovedbothsetsof
studies.Participantsprovidedinformedconsentbeforebeginningthestudy.
Procedure. Fortheattributemodelstudies,weusedabetween-subjectsdesign
whereparticipantsevaluatedfaceswithrespecttoeachattribute.Participantsﬁrst
consented. Then they completed a preinstruction agreement to answer open-ended questions at the end of the study.In the instructions,participants were
given 25 examples of face images in order to provide a sense of the diversity
theywouldencounterduringtheexperiment.Participantswereinstructedtorateaseriesoffacesonacontinuoussliderscalewhereextremeswerebipolardescrip-
torssuchas“trustworthy”and“nottrustworthy.”Wedidnotsupplydeﬁnitionsof
eachattributetoparticipantsandinsteadreliedonparticipants’intuitivenotionsofeach.
Eachparticipantthencompleted120trialswiththesingleattributetowhich
they were assigned. One hundred of these trials displayed images randomlyselected (without replacement) from the full set; the remaining 20 trials wererepeatsofearliertrials,selectedrandomlyfromthe100uniquetrials,whichwe
usedtoassessintraraterreliability.Eachstimulusinthefullsetwasjudgedbyat
least30uniqueparticipants.
Attheendof theexperiment,participantsweregivenasurveythatqueried
whatparticipantsbelievedwewereassessingandaskedforaself-assessmentof
theirperformanceandfeedbackonanypotentialpointsofconfusion,aswellasdemographicinformationsuchasage,race,andgender.Participantsweregiven
30mintocompletetheentireexperiment,butmostcompleteditinunder20
min.Eachparticipantwaspaid$1.50.
Themodel-validation studiesfollowedanidenticalproceduretothatof the
attributemodelingstudiesabove,exceptwherenotedbelow.
Eachparticipantcompletedoneof20preregisteredexperimentsinvolvinga
pair of one of two different face image types (artiﬁcial vs.real) with manipula-
tionsalongoneof 10differentattributedimensions( age,feminine/masculine ,
skinny/fat,trustworthy ,attractive,dominant,smart,outgoing,memorable ,a n d
familiar). In each experiment, observers rated 150 unique images (with 30
repeats)alongtheassignedperceivedattributedimension.Eachparticipantwas
paid$2.00duetothelongerexperimentduration.
Face Attribute Model. Tobroadlycapturehumanfaceattributeperception,a
model should accurately reproduce human judgments about the attributes of
naturalfaces.Moreformally,weseekafunction φ(·)PE(whatwecalla“psycho-
logicalencoder”)thatmapsfromanypossiblefacestimulus xi={x1,...xm}
(i.e.,an m-dimensionalvectorof rawpixelintensities)toagivenpsychological
attributeinference(averagejudgmentforface xi):
φ(xi)PE=yi. [2]
Wefurtherdeﬁne φ(·)PEasadecompositionoffunctions:
φ(x)PE=φ(φ(x)F)S, [3]
whereφ(xi)F=zi={z1,...zd}isarichfeaturerepresentationoffacestim-
ulusxiandφ(·)Smapsthesefeaturestopsychologicaldimensionsof interest.
Thisformulationallowsustoleveragestate-of-the-artneuralnetworkstofeaturizearbitrary,complexfaceimages.
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Wethenrelatethesefeatures zitopsychologicalfeaturesbyassumingthat
φ(·)Sis a linear function and thereby implying that each attribute is a 512-
dimensional (potentially sparse) vector in the overall feature space. The func-
tionφ(·)Sislearnedfromhumanattributejudgmentdata.Inparticular,given
continuous-scaleattributejudgments(i.e.,degreeoftrustworthinessonascale
from1to100),weuselinearregressiontomap512-dimensionalfeaturevectors
zitoaverageattributeratings yi:
yi=φ(zi)S=w0+w1z1+...+wdzd. [4]
Inbothcases,weightvector wk={w1,...wd}representsasingleattribute k
asalinearfactor.Therefore,attheheartof ourmodelisamatrix W∈IRk×d,a
setof d-dimensionallinearfactorsforeachofthe kattributes,eachobtainedby
ﬁttingaseparatelinearmodel.
The above components of the model enable predictions of attributes to be
made for arbitrary face stimuli. We further desire the ﬂexibility to manipulate
theseattributesforagivenface.Becausewerepresenteachattributeasavectorw
kinthefeaturerepresentationspace,wecanmanipulateeachfaceinthisspace
(i.e.,representedby zi)usingvectoraddition:
z/prime
i=zi+βwk, [5]
where z/prime
iisthenewtransformedfaceand βisascalarparameterthatcontrolsthe
strengthofthetransformation,whichcanbepositiveornegative.When β=0,
z/prime
i=zi,andnotransformationtakesplace.Inotherwords, βscalestheattribute
vectorthatisaddedtothegivenfacerepresentation.Finally,inordertogenerate
anewstimuluscorrespondingtoourtransformation,theinversefeaturizer(i.e.,
decoder/generatornetworkofSG2) φ−1(·)Fisemployedtomapfromfeatures
zibacktoafacestimulus xi,suchthatmanipulationoffaceimagescanbefully
describedby
x/prime
i=φ−1(z/prime
i)F=φ−1(zi+βwk)=φ−1(φ(xi)F+βwk), [6]
where x/prime
iistheattribute-transformedversionofinputface xi.
The success of the above formulation (i.e., good prediction of human at-
tributejudgmentsforarbitraryfaces)ishighlydependentonthechoiceof the
feature encoder φ(·)F,which abstracts over raw pixels and provides the basis
formodelingattributes.Ifthefeaturesarenotsufﬁcientlyexpressive,themodel
willfailtomakegoodpredictionsof humanattributejudgments.Likewise,the
ability of the inverse function φ−1(·)Fto generate face stimuli given their
feature representations determines whether attribute-transformed face stimuliwillsuccessfullyavoidtheuncannyvalleyeffect.Therearemanymodernneural
networks that could make for a good choice of featurizer φ(·)
F. For example,
convolutional neural networks, which learn hierarchies of translation-invariantfeatures, can be trained to classify faces to a high level of accuracy, and their
hiddenrepresentationscanbetakenasafeaturerepresentation z.However,this
method does not yield an inverse function from features back to stimuli andattemptstoinvertmodelsafterthefactoftenintroduceartifacts(48).
Instead,weselectedamodelprimarilyaimedatsolvingtheinverseproblem
alone.GANsareaformofdeeplatentvariablemodelthatlearntomodeladis-tributionofimagesusingtwocomponents:ageneratornetworkthatgenerates
images by mapping Gaussian noise to (synthetic) images and a discriminatornetwork that discriminates between real and generated data. When properly
trained in a way that balances the two components,the discriminator network
forces the generator to produce realistic images,and the discriminator can no
longerdistinguishbetweenrealandgeneratedimages.SG2,describedearlier,is one of the most successful applications of this model structure and training
paradigm; it includes several key improvements that yield highly convincing
results(seeexamplefacesin SI Appendix ).
SG2yieldsonlytheinversefunction φ(x
i)−1
F,alearnedconvolutionalgenera-
torordecoderfunctionwhichmapsfromfeaturestoimages.Inordertoapplyour
modeltoarbitraryfaceimagesoutsideofoursetof1,004,invertingthisfunction
isrequired.WhiletheauthorsofSG2supplytheirownsolutiontothisproblem,we ﬁnd that it is not accurate enough for our purposes.Instead,we deﬁne an
encoderfunctionandfeaturizer φ(x
i)Fasanoptimizationprocessthatsearches
viagradientdescentforthevectorinputtoSG2thatproducesanoutputimagewithagoodlikenesstotheonewewishtofeaturize.Thislikenessisdeﬁnedas
Euclideandistanceinthefeaturespaceofanotherexternalconvolutionalnetwork
pretrainedtorecognizefaces(20).Additionally,becausethisprocessisslow,weinitialize the image-encoding vector using a ﬁrst-pass approximation from yet
another convolutional neural network that we trained to regress thousands of
SG2imagesamplestotheoutputvectorsthatgeneratedthem.Thisencoderismuchlessaccurate,butmuchfaster,anddrasticallyspeedsconvergenceof theslowerandmoreaccuratedecodingprocessoutlinedabove.
A summary diagram of our modeling pipeline is provided in SI Appendix ,
Fig.S1.
ModelFittingandGeneralization. Alllinearregressionmodelswereﬁtusing
theleastsquaresalgorithm.Becauseimagefeaturerepresentations(i.e.,vectors
ofpredictorsinthedesignmatrix)arehigh-dimensional,thereisasigniﬁcantriskofoverﬁtting,whichcouldpotentiallyresultinsuboptimalormeaninglessmodel
solutions.Toaddressthis,weuseridgeregression,whichpenalizessolutions w
k
thathavealargeeuclideandistancefromthe 0vector.Thestrengthofthispenalty
anditsinﬂuenceontheresultingsolutioniscontrolledbyafreeparameter λ.
Wesearchfortheoptimalvalueof thisparameterbasedonthegeneralization
performanceofthemodel,speciﬁcallyusing10-foldcross-validation.Allreported
modelscoresareaveragesoverthoseforeachofthe10folds,suchthatweneverreportperformanceondatathatwasusedtoﬁtourmodels.
Data Availability. The One Million Impressions dataset and all behavioral
judgmentsandsynthesizedimageshavebeendepositedinaGitHubrepository(https://github.com/jcpeterson/omi )(49).
ACKNOWLEDGMENTS. A.T. was supported by the Richard N. Rosett Faculty
FellowshipattheUniversityofChicagoBoothSchoolofBusiness.DatacollectionwasfundedbytheInnovationFundforNewIdeasintheNaturalSciencesfrom
PrincetonUniversity’sDeanforResearch.
Author aﬃliations:aDepartment of Computer Science, Princeton University, Princeton, NJ
08540;bBooth School of Business, University of Chicago, Chicago, IL 60637;cDepartment
ofPsychology,PrincetonUniversity,Princeton,NJ08540;anddSchoolofBusiness,Stevens
InstituteofTechnology,Hoboken,NJ07030
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Peterson
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C
Uddenberg
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Griffiths
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L
Todorov
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& Suchow
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W


Complex cognitive algorithms preserved by selective social learning in experimental populations.

COGNITIVE SCIENCE
Complex cognitive algorithms preserved by selective
social learning in experimental populations
B. Thompson1*†, B. van Opheusden2†, T. Sumers2, T. L. Griffiths2,3
Many human abilities rely on cognitive algorithms discovered by previous generations. Cultural
accumulation of innovative algorithms is hard to explain because complex concepts are difficult to
pass on. We found that selective social learning preserved rare discoveries of exceptional algorithms
in a large experimental simulation of cultural evolution. Participants ( N= 3450) faced a difficult
sequential decision problem (sorting an unknown sequence of numbers) and transmitted solutions
across 12 generations in 20 populations. Several known sorting algorithms were discovered. Complexalgorithms persisted when participants could choose who to learn from but frequently became extinct in
populations lacking this selection process, converging on highly transmissible lower-performance
algorithms. These results provide experimental evidence for hypothesized links between sociality and
cognitive function in humans.
Reading, counting, cooking, and sailing
a r ej u s ts o m eo ft h eh u m a na b i l i t i e s
passed from generation to generation
through social learning ( 1,2). Complex
abilities like these often depend on
learned cognitive algorithms: procedural rep-
resentations of a problem that coordinate mem-ory, attention, and perception into sequences
of useful computations and actions. Accumu-
lation of complex algorithms —from ancient
tool-making techniques to bread making, boat
building, or horticulture —is central to human
adaptation ( 3–5) yet challenging to explain
because algorithmic concepts can be difficult
to discover, communicate, and learn from ob-
servation ( 6), making them vulnerable to loss
(7–10). Theories of cultural evolution suggest
that human social learning may help overcome
this fragility ( 11,12). For example, mathematical
models ( 13) predict that choosing to learn from
successful or prestigious individuals can pre-
v e n tt h el o s so fr a r ei n n o v a t i o n s .H o w e v e r ,t h i s
potential link between sociality and complex
abilities ( 14) is challenging to establish.
We conducted large-scale simulations of
cultural evolution with human participants
to assess how selective social learning in-
fluenced the evolution of cognitive algorithms.
Prior research ( 15–22) shows that social learn-
ing can improve decisions in multiple-choice
tasks ( 23), perceptual judgments ( 24), and
search problems ( 25) and can improve arti-
facts such as physical structures ( 26) or com-
puter programs ( 27). However, the evolution of
cognitive algorithms at the population level
has been difficult to study ( 28). We developed
custom software to recruit large numbers of
participants online and organize them intoevolving societies facing a common problem.
Twenty populations tackled a sequential de-
cision problem (Fig. 1A and materials and
methods 1.1). Presented with six images, par-
ticipants attempted to establish hidden arbi-
trary orderings using pairwise comparisons.
Out-of-order pairs swapped positions whencompared. Participants were rewarded for
establishing the ordering using fewer com-
parisons. This task poses a sorting problem,
requiring a strategy for executing appropriate
sequences of actions, analogous to culturally
evolved strategies for making tools or food.
Participants transmitted their strategies
across 12 generations (Fig. 1B). Initial asocial
generations completed the task individually.
Participants in generations 2 to 12 were ran-
domly assigned to either the experimental
selective social learning (SSL) treatment (par-
ticipants could choose demonstrators from the
previous generation based on demonstrator
performance) or to a control random mixing
(RM) treatment (demonstrator performance
was not visible). Participants were incentivizedto improve on strategies that they observed
and provide a helpful description and demon-
stration of their own strategy (materials and
methods 1.1.13).
Figure 2 shows task performance. Asocial
participants achieved the lowest scores [mean
over scored trials = 0.33, SD = 0.19, relative to
a theoretical maximum of 1; supplementary
materials (SM) 3; mean number of success-
ful trials = 6.45 of 10 scored trials, SD = 2.89;
SM 2.1.1]. Asocial participants improved over
trials, confirming withi n-task learning {regres-
sion coefficient p osterior mean ( b)=0 . 1 4 ,9 7 %
highest density interval (HDI) = [0.11, 0.16];SM 2.1.1}. Participants who learned socially
(generations 2 to 12) achieved higher perform-
ance [mean (M) = 0.446, SD = 0.199] than
asocial participants ( b=0 . 1 1 4 ,9 7 %H D I=
[0.083, 0.145]; SM 2.1.2). RM participants (M =
0.399, SD = 0.167) outperformed asocial par-
ticipants ( b= 0.067, 97% HDI = [0.036, 0.098];
SM 2.1.3). SSL participants performed highest
(M = 0.493, SD = 0.216), outperforming asocial
(b= 0.162, 97% HDI = [0.13, 0.193]) and RM
(b= 0.095, 97% HDI = [0.095, 0.107]; SM 2.1.3)
participants.
By the final generations (9 to 12), perform-
ance among SSL (M = 0.514, SD = 0.216) and
RM (M = 0.433, SD = 0.163) participants in-
creased substantially relative to asocial par-
ticipants (SSL: b= 0.181, 97% HDI = [0.147,
0.221]; RM: b= 0.101, 97% HDI = [0.071, 0.132];
SM 2.1.5 and 2.1.6). This was not just a con-
sequence of accumulating more knowledge
of the task: In a follow-up experiment, asocial
participants completed 52 trials (equivalent to
four generations) yet performed worse than
SSL participants (but better than RM partic-
ipants; SM 1.3). In the SSL group, but not the
RM group, a distinct population of high per-
formers emerged (performance > 0.6; Fig. 2B).
Most of these participants (85.2%) learned
from a high-performing demonstrator (Fig.
2C). However, most people who learned fromRESEARCH
Thompson et al.,Science 376,9 5–98 (2022) 1 April 2022 1o f4
1Department of Psychology, University of California, Berkeley,
Berkeley, CA, USA.2Department of Computer Science,
Princeton University, Princeton, NJ, USA.3Department of
Psychology, Princeton University, Princeton, NJ, USA.
*Corresponding author. Email: wdt@berkeley.edu
†These authors contributed equally to this work.
Fig. 1. Problem-solving task and study design. (A) Sorting task. ( B) Participants chose up to three
demonstrators from a sample of eight (out of 15) members of the preceding generation. Ten SSL networks
were paralleled by 10 RM networks yoked to shared initial generations.
Downloaded from https://www.science.org at Princeton University on November 11, 2022

a high-performing demonstrator were not
themselves high performing (64.9%). This
asymmetry indicated an exceptional strategy
that is rarely discovered and difficult to pass on.
To deepen our understanding of these strat-
egies, we analyzed the algorithmic structure
of participant responses. Using recurrent
neural network models (SM 4), we identified
eight classes of algorithms (SM 4.3). Partici-
pants discovered several known sorting algo-
rithms. Two algorithms were more frequent
than all others. The first algorithm is known in
computer science as selection sort. Selection
sort generates 15 specific comparisons (1-2, 1-3,
1-4, 1-5, 1-6, 2-3, 2-4, 2-5, 2-6, 3-4, 3-5, 3-6, 4-5, 4-
6, and 5-6; Fig. 3A) that are guaranteed tosucceed (performance = 0.55). The second algo-
rithm is an even more efficient solution, known
as gnome sort. The comparisons implied by
gnome sort depend on the outcome of earlier
comparisons, so its behavior varies. Participants
using gnome sort made specific sweeps of adja-
cent comparisons until a pair failed to swap, re-
membering where each sweep started (Fig. 3B).
Overall, 80% of participants who used an
identifiable algorithm used selection sort or
gnome sort (SM 4.2.1). Figure 4 shows major
independent lineages of algorithms in four
networks (all networks are shown in the SM).
Only 44% of asocial participants (66 of 150)
used an identifiable algorithm: Among asocial
participants, 16% (26) used selection sort and
just 13% (20) used gnome sort. All other algo-
rithms were even rarer. In early generations,
selection sort began to spread in both the RM
and SSL groups (SM 2.2.2), independently
becoming the most frequent algorithm in 7 of
10 network pairs. In the RM group, selection
sort continued to spr ead, dominating 9 of10 populations by generations 9 to 12 (67% of
identifiable algorithms). However, in the SSL
group, selection sort began to decline aftergeneration 3 (Fig. 4). In the SSL group, but not
the RM group (SM 2.2.3), gnome sort domi-nated 8 of 10 populations. By the final two gen-
erations, more than half of all SSL participants
used gnome sort.
Participants successfully transmitted se-
lection sort and gnome sort from person to
Thompson et al.,Science 376,9 5–98 (2022) 1 April 2022 2o f4Fig. 2. Performance in the sorting task. (A) Performance over generations. Error bars show 95% confidence intervals. A, asocial. ( B) Performance among SSL
(top), RM (middle), and asocial (bottom) participants. The vertical axis shows the number of participants. The vertical dashed line indicates the hi gh-performance
threshold (0.6). ( C) Participant performance relative to their demonstrators. t, time (generation number).
Fig. 3. Selection sort and gnome sort. (AandB) Strategy descriptions and executions by participants
using selection sort [(A); participant 1546] and gnome sort [(B); participant 1281]. Squares show swap (solid)
or no swap (transparent). G, generation.RESEARCH |REPORT
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person. However, transmission fidelity differed
(SM 2.3). Selection sort uses a fixed compar-
ison sequence, so it is easier to describe and
learn. Several algorithms (e.g., comb sort,
bubble sort, insertion sort; SM 4.3) share this
property but were rare, suggesting that selec-
tion sort is particularly intuitive or memorable
[consistent with sequence-learning studies ( 29)
and mathematical analyses of attractors ( 30)].
Gnome sort was harder to pass on. Its condi-
tional logic improved performance (sometimes
needing only five comparisons) but made the
algorithm harder to describe, learn, and use
(SM 7). A follow-up study (SM 1.4) showed
that transmission of complex algorithms in
this task was primarily facilitated by partici-pant demonstrations, not written descriptions
(though descriptions do improve transmis-
sion; SM 2.1.8). Finally, we found that selective
social learning counteracted differences in
algorithm transmission fidelity. SSL partici-
pants chose higher-performing demonstra-
tors and therefore encountered gnome sort
more often (SM 2.4), offsetting the complexity
disadvantage at the population level. Numer-
ical simulations support this dynamic (SM 8).
Our study offers insight into one potential
mechanism linking sociality and the trans-
mission of complex disc overies, supporting
assumptions of mathematical models ( 31).
Random mixing led to an evolutionary process
shaped by how difficult the algorithms wereto learn and convey, favoring highly trans-
missible algorithms (e.g., selection sort). By
contrast, selective so cial learning led to an
evolutionary process heavily influenced by
how efficiently participants could solve the
underlying problem, favoring more complex
algorithms (e.g., gnome sort).
Sequential decision-making problems arise
in many higher cognitive functions such as
planning, social interaction, navigation, and
tool use. Like the sorting problem, these chal-
lenges call for procedural strategies that we
can follow to reliably achieve a goal when in-
teracting with a dynamic task. Our study
showed that a simple form of selective social
learning helped populations establish such
Thompson et al.,Science 376,9 5–98 (2022) 1 April 2022 3o f4Fig. 4. Algorithm lineages. (Top) Major lineages (connected subcomponents exceeding 20 participants) in two network pairs. ( Bottom ) Algorithm frequencies under
RM (left) and SSL (right).RESEARCH |REPORT
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solutions by increasing the take-up of rare
but innovative algorithms. Alternative routes
to increased uptake, such as forms of content-
biased learning ( 13) ,m a yh a v ea n a l o g o u s
evolutionary consequences.
Our study does not address potential con-
sequences of population size, demographic
profiles, or more complex forms of demon-
strator selection that may arise in richer con-
texts (e.g., strategies that account for potential
relationships between expertise and teaching
skills). Our findings highlight interactions be-
tween reconstructive and preservative aspects
of cultural transmission ( 30). Choosing who to
learn from helps complex ideas be preserved
and built on by future generations in evolving
populations.
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ACKNOWLEDGMENTS
Funding: This work was supported by Defense Advanced Research
Projects Agency (DARPA) agreement D17AC00004 and the Schmidt
Family Foundation (T.L.G.) and a National Defense Science and
Engineering Graduate Fellowship (T.S.). Author contributions:
Conceptualization: B.T., B.v.O., T.L.G.; Methodology: B.T., B.v.O., T.S.,
T.L.G.; Investigation: B.T., B.v.O., T.S., T.L.G.; Visualization: B.T.,B.v.O., T.S., T.L.G.; Writing: B.T., B.v.O., T.S., T.L.G. Competing
interests: None declared. Data and materials availability:
Data, materials, and study registrations are available through the
Open Science Framework at https://osf.io/nbc7a/. All other
data needed to evaluate the conclusions in the paper are present
in the paper or the supplementary materials.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.abn0915
Materials and MethodsFigs. S1 to S55
Tables S1 to S15
References ( 32,33)
3 November 2021; accepted 25 February 2022
10.1126/science.abn0915
Thompson et al.,Science 376,9 5–98 (2022) 1 April 2022 4o f4RESEARCH |REPORT
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to original U.S. Government WorksComplex cognitive algorithms preserved by selective social learning in
experimental populations
B. ThompsonB. van OpheusdenT. SumersT. L. Griffiths
Science, 376 (6588), • DOI: 10.1126/science.abn0915
Humans succeed through social learning
Our capacity to accumulate complex algorithms over generations allows human beings to adapt to diverse
environments and solve challenges that go beyond our individual limitations. However, cultural accumulation of
innovative algorithms is difficult to explain. Thompson et al. studied a large number of participants to explore the
evolution of algorithms under different learning conditions (see the Perspective by Henrich). Selective social learning
that involved knowledge of the success level of different strategies or of different models preserved difficult-to-invent,
efficient algorithms more than random social learning or one-attempt asocial learning. Two efficient algorithms were
used by many people, but the most efficient one only spread under selective social learning. —PRS
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