A V IEW F ROM S OMEWHERE :
H UMAN -C ENTRIC F ACE R EPRESENTATIONS
Anonymous authors
Paper under double-blind review
A BSTRACT
Few datasets contain self-identified demographic information, inferring demographic information risks introducing additional biases, and collecting and storingdata on sensitive attributes can carry legal risks.
Besides, categorical demographiclabels do not necessarily capture all the relevant dimensions of human diversity thatare important for developing fair and robust models.
We propose to implicitly learna set of continuous face-varying dimensions, without ever asking an annotator toexplicitly categorize a person.
We uncover the dimensions by learning on a noveldataset of 638,180 human judgments of face similarity (FAX).
We demonstrate theutility of our learned embedding space for predicting face similarity judgments,collecting continuous face attribute values, attribute classification, and comparativedataset diversity auditing.
Moreover, using a novel conditional framework, weshow that an annotator’s demographics influences the importance they place ondifferent attributes when judging similarity, underscoring the need for diverseannotator groups to avoid biases.
I NTRODUCTION
Machine learning models depend on the data that they are trained on (Torralba & Efros, 2011).
Dataset bias can result in models that are discriminatory (Hendricks et al., 2018;
Buolamwini &
Gebru, 2018) or depend on spurious correlations (Sagawa et al., 2019; Geirhos et al., 2020).
Forinstance, a face image restoration model (Menon et al., 2020) may hallucinate features correlatedwith oversampled subgroups, resulting in the inadvertent erasure of minority groups (Vincent, 2020).
Thus, prior to learning, human-centric image dataset users should evaluate the diversity of the data.
The canonical approach is to categorize people using demographic attributes labels.
Many equatediversity with parity across the subgroup distributions (Keswani & Celis, 2021; Kay et al., 2015;
Bolukbasi et al., 2016; Schwemmer et al., 2020), presupposing access to demographically labeledsamples.
However, most human-centric image datasets are web-scraped, lacking ground-truthinformation about the data subjects.
Moreover, data protection legislation considers demographicattributes to be personal information and limits their collection and use (Andrus et al., 2021; 2020).
Even when demographic labels are known, evaluating diversity by examining counts across subgroupsfails to reflect the continuous nature of human phenotypic diversity (e.g., skin tone is often reduced tolight vs. dark ).
Furthermore, such an approach often denies multi-group membership (Rothbart& Taylor, 1992)
(e.g., erasing multi-ethnic and intersex individuals).
When labels are unknown, researchers typically choose certain attributes they consider to be relevantfor human diversity and use human annotators to infer them (Kärkkäinen & Joo, 2019; Schumannet al., 2021; Wang et al., 2019).
Beyond issues such as the inclusion of derogatory and offensivecategories (Koch et al., 2021; Birhane & Prabhu, 2021; Hanley et al., 2020; Crawford & Paglen,2019), inferring labels (in practice) is difficult for ill-defined and highly changeable social constructssuch as race and gender (Hanna et al., 2020; Keyes, 2018; Benthall & Haynes, 2019; Khan & Fu,2021).
Furthermore, discrepancies between, for example, observed and self-identified race, gender, orother sensitive attributes can induce psychological distress (Campbell & Troyer, 2007) by invalidatingan individual’s self-image and identity (Roth, 2016).
Data access request rights through, for example,
GDPR, CCPA or PIPL, have the potential to force data holders into revealing inferred informationheld about data subjects (Andrus et al., 2021), can increase the likelihood of psychological harm.
Contributions.
As an image subject can exhibit certain traits to a greater or lesser extent than others,even within the same subpopulation (Becerra-Riera et al., 2019; Carcagnì et al., 2015; Feliciano,2016), the goal of our work is to learn a similarity function , which measures the similarity betweentwo faces that is aligned with human perception .
In particular, as similarity is inversely connectedto diversity (Leinster & Cobbold, 2012), our model (i.e., similarity function) provides dataset userswith a new type of diversity measure that coincides with human perception.
Concretely, we present amodel of conditional decision-making for learning continuous, human-interpretable face embeddingsdirectly from human judgments of face similarity.
Underlying our approach is FAX, a novel datasetof 638,180 judgments over 4,921 faces, where each judgment corresponds to the odd-one-out (i.e.,least similar) face in a triplet of faces.
Such contextual similarity judgments have been shown to offera window into the factors of variation of object categories (Hebart et al., 2020;
Zheng et al.
, 2018),human actions (Dima et al., 2022), and reachspace environments (Josephs et al., 2021) in the humanmind.
Distinct from other computer vision datasets, each judgment in FAX is accompanied by theidentifier and demographic attributes of the annotator who made the judgment.
Our model concurrently learns an embedding space and the importance distinct annotators place oneach embedding dimension when determining similarity.
By learning importance scores, we inducesubspaces that encode each annotator’s notion of similarity, which increases predictive accuracy.
Significantly, we find that annotator subspaces are not interchangeable, but can be grouped wrt thesociocultural backgrounds (e.g., nationality, ancestry) of the annotators.
Our findings underscorethe need for diverse annotator groups to avoid biases.
Beyond resulting in increased predictiveperformance of human judgments of face similarity, we show that our embeddings are highlycorrelated with the human mental representational space of faces, as compared to face embeddingsinduced by learning to predict face identity or face attributes.
Importantly, we find that the individualembedding dimensions are: related to concepts of gender, race, age, as well as face and hairmorphology; and, positively correlated with human ratings of face prototypicality.
We demonstratethe utility of such dimensions for: collecting continuous (as opposed to discrete) face attribute valuesfor novel faces from annotators; binary attribute classification; and, estimating attribute disparities.
1. R ELATED W ORK
Disentangled Representation Learning.
Our approach is similar in spirit to wholly unsupervisedgenerative approaches (Härkönen et al., 2020;
Peebles et al., 2020; Shen & Zhou, 2021;
Wei et al.,2021).
However, rather than modeling the data generating distribution, our representations are trainedto predict human similarity judgments, reflecting the human mental representational space of faces.
Our baselines primarily center on embeddings induced by training on facial analysis datasets, since inthe face domain, post-hoc interpretation of latent dimensions (Shen et al., 2020; Nitzan et al., 2022;
Wu et al., 2021; Locatello et al., 2019) predominantly rely on CelebA (Liu et al., 2015).
Psychological Embeddings.
The human mind is conjectured by cognitive psychologists to have“a considerable investment in similarity” (Medin et al., 1993).
Significantly, when two entities arecompared they mutually constrain the set of features that are activated or inferred in the humanmind (Markman, 1996)—i.e.
, similarity is dynamic, where features are discovered and aligned basedon what is being compared.
Multidimensional scaling (MDS) is often used to learn psychologicalembeddings from pairwise similarity judgments (Torgerson, 1958;
Zheng et al., 2018; Hebart et al.
,2020; Roads & Love, 2021; Van Der Maaten & Weinberger, 2012; Josephs et al., 2021).
As MDScannot embed images outside of the training set, researchers have used pretrained models to predict
MDS representations (Sanders & Nosofsky, 2020) or directly infer similarity judgments (Petersonet al., 2018; Attarian et al., 2020).
Rather than relying on pretrained models which can introduceimplicit biases (Krishnakumar et al., 2021; Steed & Caliskan, 2021), we perform end-to-end learningfrom scratch.
Further, unlike recent work (Hebart et al., 2020; Josephs et al., 2021; Dima et al.,2022), we focus on human perception of naturalistic face images outside of a face recognitionsetting (McCauley et al., 2021; Sadovnik et al., 2018; Somai & Hancock, 2021), evidenced to beprocessed differently to objects in the human visual system (Sinha et al., 2006).
Annotator Bias.
Categorization by observation depends not only on the subject being categorized, butalso on the annotator’s sociocultural background, perception of the subject, and contextual cues (Segallet al., 1966; Balaresque & King, 2016; Hill, 2002; Roth, 2016; Freeman et al., 2011).
Despite this,annotator positionality has only recently entered into discourse in computer vision (Chen & Joo, 2021;
Zhao et al., 2021), albeit predominantly in the context of natural language processing (Al Kuwatly et al., 2020; Waseem, 2016;
Wich et al., 2020; Binns et al., 2017; Salminen et al., 2018).
Recentempirical studies confirm this (Denton et al., 2021; Geiger et al., 2020), in particular “only fivepublications [from 113 surveyed] provided any [annotator] demographic information” (Scheuermanet al., 2021).
In order to mitigate bias, one must first measure bias (Le Quy et al., 2022).
Addressingthe potential for annotator bias, our conditional model elucidates the importance distinct annotatorsplace on different attributes when judging similarity.
Veit et al.
(2017) employ a similar procedure tolearn subspaces which encode different notions of similarity (e.g., font style, character type).
D ATA AND M ODEL
To learn a human-interpretable similarity function aligned with human perception, we collect, FAX, alarge-scale dataset of odd-one-out similarity judgments An odd-one-out judgment corresponds tothe least similar face in a triplet of face images, representing a three alternative forced choice task .(Refer to Appendices B and C for further details on the data and models used in this paper.) Data.
FAX contains 638,180 quality-controlled triplets over 4,921 faces, representing 0.003% of allpossible triplets.
1 Each triplet is labeled with a judgment, as well as the identifier of the annotator whomade the judgment and their age, nationality, ancestry, and gender identity.
Quality was controlledby excluding judgments from annotators who provided overly fast, deterministic, or incompleteresponses.
As in previous non-facial odd-one-out datasets (Josephs et al., 2021; Hebart et al., 2022; Dima et al., 2022), there is a single judgment per triplet.
In total, 1,645 annotators contributed to FAXvia Amazon Mechanical Turk (AMT), providing their consent.
Compensation was 15 USD per hour.
For our proof of concept, the 4,921 faces were sampled from the CC-BY licensed dataset FFHQ (Karras et al., 2019).
The subset was obtained by first splitting FFHQ into 56 partitions based on estimatedintersectional group labels, and then randomly sampling from each partition with equal probability.
All faces are near-frontal with little to no eye occlusions and an apparent age > 19 years old.
Let x ∈ X and sim : ( x i , x j ) → sim( i, j
) ∈ R denote a face image and a similarity function, resp.
Our motivation for collecting FAX is fourfold.
Most significantly, the odd-one-out task does notrequire an annotator to explicitly categorize people.
Second, for a triplet ( x i , x j , x k ) , repeatedlyvarying x k permits the identification of the relevant dimensions that contribute to sim( i, j ) .
That is,w.l.o.g., x k provides context for which sim( i, j ) is determined, making the task easier than explicitpairwise similarity tasks (i.e., “Is x i similar to x j ?”).
This is because it is not always apparent to anannotator which dimensions are relevant when determining sim( i, j ) , especially when x i and x j areperceptually different.
Third, there is no need to prespecify attribute lists hypothesized as relevant forcomparison (e.g., “Is x i older than x j ?”).
The odd-one-task implicitly encodes salient attributes thatare used to determine similarity.
Finally, compared to judgments for triplets composed of an anchor(i.e. , reference point), x a , a positive, x p , and a negative, x n , odd-one-out judgments naturally providemore information.
Odd-one-out triplets require an annotator to determine sim( i, j ) , sim( i, k ) , andsim( j, k ) , whereas triplets with anchors only necessitate the evaluation of sim( a, p ) and sim( a, n ) .
Model of Conditional Decision-Making.
Zheng et al.
(2018) developed an MDS approach for learning psychological object embeddings from odd-one-out judgments.
The approach is based on threeassumptions.
First, embeddings can be learned solely from odd-one-judgments, where representationsare constrained to be continuous, non-negative, and sparse.
Such properties support interpretabilitysuch that dimensions indicate both feature presence and feature magnitude.
Second, odd-one-outjudgments are a function of sim( i, j ) , sim
( i, k ) , and sim( j, k ) .
Third, odd-one-out judgments arestochastic, where the probability of selecting x k as the odd-one-out is p ( k )
∝ exp(sim( i, j )) .
At a high-level, we want to apply Zheng et al. (2018)’s MDS approach to learn face embeddings.
However, MDS cannot embed data outside of the training set, limiting its utility.
Moreover, MDSpools all judgments, disregarding intra- and inter-annotator stochasticity.
To resolve these issues, wepropose to learn a conditional convolutional neural network (CNN).
Let { ( { x iℓ , x jℓ , x kℓ } , kℓ, a ) } nℓ =1 denote a training set of n (triplet, judgment, annotator) tuples,where a ∈ A .
To simplify notation, we assume that judgments always correspond to index kℓ .
Suppose f : x (cid:55)→ f ( x ) = w ∈ R
d is a CNN, parametrized by Θ , where w ∈ R d is an embeddingof x .
In contrast to Zheng et al.
(2018), we model the probability of annotator a selecting kℓ asp ( kℓ | a ) ∝ exp(sim a ( iℓ, jℓ )) , where sim a ( · , · ) denotes the internal similarity function of a .
Giventwo images x i and x j , we define their similarity according to a as:
[Equation]
where σ ( · ) is the sigmoid function and σ ( ϕ a ) ∈ [0 , 1] d is a mask associated with a .
Each maskplays the role of an element-wise gating function, encoding the importance a places on each of the dembedding dimensions when determining similarity.
Conditioning prediction on annotator identifiersinduces subspaces that encode each annotator’s notion of similarity.
This allows us to study whetherper-dimensional importance scores differ between annotators.
We denote by Φ =
[ ϕ ⊤ 1 , . . . , ϕ ⊤|A| ] ∈ R
d
×|A| a trainable weight matrix, where each column vectorϕ ⊤ a corresponds to annotator a ’s mask prior to applying σ ( · ) .
In our conditional framework, wejointly optimize Θ and Φ by minimizing:
[Equation]
where
[Equation]
is the predicted probability that kℓ is the odd-one-out conditioned on a .
The first term in Eq.
2encourages similar face pairs to result in large dot products.
The second term (modulated by α 1 ∈ R )promotes sparsity.
The third term (modulated by α 2 ∈ R ) supports interpretability by penalizingnegative values.
The last term (modulated by α 3 ∈ R ) penalizes large weights.
When α 3 = 0 and σ ( ϕ a ) =
, 1] ( ∀ a ), Eq.
2 corresponds to the unconditional MDS objectiveproposed by Zheng et al.
In what follows, we refer to unconditional and conditional modelstrained on FAX as FAX-U and FAX-C , resp.
In addition, we refer to conditional models whosemasks are learned post hoc as FAX-C-PH .
A FAX-C-PH model uses a fixed unconditional model(i.e.
, FAX-U ) to obtain face embeddings such that only Φ is trainable.
Our conditional decision-making framework is generally applicable to any task that involves mappingfrom inputs to decisions made by humans; it only requires record-keeping during data collection suchthat each judgment (or annotation) is associated with the annotator who generated it.
Implementation.
All models have ResNet18 (He et al., 2016) architectures and output 128-dimensionalembeddings.
We use the Adam (Kingma & Ba, 2014) optimizer with default parameters, reserving10% of FAX for validation.
Based on grid search, we empirically set α 1 = 5 × 10 − 5 and α 2 =1 × 10 − 2 .
For FAX-C and FAX-C-PH , we additionally set α 3 = 1 × 10 − 5 .
Across independentruns, we find that only a fraction of the 128 dimensions are needed and individual dimensions arereproducible.
Post-optimization, we remove dimensions with maximal values close to zero.
For
FAX-U , this results in 22 dimensions (61.9% validation accuracy).
Note that we observe that 8/22dimensions have a Pearson’s r correlation > 0 .
9 with another dimension.
E XPERIMENTS
We demonstrate the utility of our FAX induced embedding spaces for predicting face similarityjudgments, revealing annotator bias, collecting continuous face attribute values, attribute classification,and comparative dataset diversity auditing.
Throughout this paper, statistical tests correspond to
Mann-Whitney U -tests ( p -value < 0.05).
For comparison, we consider embeddings extracted from face recognition and facial analysis models.
In particular, an ArcFace (Deng et al., 2019) face recognition model trained on CASIA-Webface (Yiet al., 2014); and analysis models trained on CelebA (Liu et al., 2015) (40 binary face attribute labels),
FairFace (Kärkkäinen & Joo, 2019) (perceived binary gender expression, age, and race labels), and FFHQ (binary gender expression, age, and race labels).
3 All models have ResNet18 architectures andoutput 128-dimensional embeddings.
For the analysis models, we also consider unnormalized classlogit representations, as well as the logit representations converted to binary vectors based on classpredictions.
All baseline representations are normalized to unit-length, and the dot product of tworepresentations determines their similarity.
Additional baselines are considered in the Appendix.
Predicting Human Similarity Judgments.
The utility of any face embedding method is typicallydetermined by measuring whether similar faces are closer together in feature space than dissimilarfaces.
We therefore employ two evaluation protocols, evaluating odd-one-out predictive accuracy.
In Protocol 1 , we test whether our embeddings are predictive of human judgments not observed duringlearning.
This is a typical MDS test setting, as MDS cannot embed images outside of the training set.
Using images from the stimulus set of 4,921 faces, we generate 1,000 novel triplets and collect 22–25unique judgments on AMT per triplet (24,060 judgments).
In addition to predictive accuracy, wecompute Spearman’s r correlation between the entropy in human- and model-generated triplet oddone-out probabilities.
Human-generated odd-one-out probabilities are of the form: ( n i , n j , n k )
/n ,where, w.l.o.g., n k /n corresponds to the fraction of n odd-one-out votes for k .
In Protocol 2 , we sample 56 novel face images from FFHQ not contained in the stimulus set.
Wethen generate all (cid:0) 563 (cid:1) possible triplets and collect 2–3 unique judgments on AMT per triplet (80,300judgments).
As an additional performance measure, we compute Spearman’s r between the strictlyupper triangular model- and human-generated similarity matrices.
Entry ( i, j ) in the human-generatedsimilarity matrix corresponds to the fraction of triplets containing ( i, j ) , where neither was judged asthe odd-one-out.
Entry ( i, j ) in a model-generated similarity matrix corresponds to the mean ˆ p ( i, j )over all triplets containing ( i, j ) .
[Table] As we have 22–25 judgments per triplet in Protocol 1 , wecan reliably estimate odd-one-out probabilities.
The Bayesoptimal classifier accuracy corresponds to the best possibleaccuracy any model could achieve given the stochasticityin the human judgments.
The classifier makes the mostprobable prediction, i.e., the majority judgment.
Thus, itsaccuracy is equal to the mean majority judgment probabilityover the 1,000 triplets, corresponding to 65.5 ± 1% (95% CI).
Results for Protocol 1 and Protocol 2 are shown in Table 1.
First, embeddings trained on FAX outperform the baselinesacross all metrics.
In particular, as evidenced by the correlation tests, the human mental representational space isbetter represented by embedding spaces induced by learningon FAX.
This even holds for our FAX-U model trained ononly 72K judgments.
Second, as hypothesized, transforming FAX into a dataset of standard triplets constraints with anchors results in lower performance dueto a reduction in information—i.e., FAX-Triplet trained using a triplet margin with a distanceswap loss (Balntas et al., 2016).
Third, FAX-C and FAX-C-PH have increased performance overtheir unconditional counterparts.
This shows that the learned annotator-specific masks generalize, i.e.,the encoded importance an annotator places on each dimension extends to novel judgments.
Mostsignificantly, in Protocol 1 , our conditional models attain a predictive accuracy at or above the upperbound of the Bayes optimal classifier.
To quantify the number of dimensions required to represent a face while preserving Protocol 2performance, we follow Hebart et al.
(2020)’s dimension-elimination approach .
In Protocol 2 , weiteratively zero out the lowest value per face embedding until a single nonzero dimension remains.
As this is done per embedding, the same dimension is not necessarily zeroed out from all embeddingsduring the same iteration.
To obtain 95–99% of the predictive accuracy 6–13 dimensions are required,whereas to explain 95–99% of the variance in the similarity matrix we require 15–22 dimensions.
This shows that humans utilize a larger number of dimensions to represent the global similaritystructure of faces than for predicting individual odd-one-out judgments. Gaps in Perception.
Peterson et al.
(2019) showed that learning to predict human-generated labeldistributions (i.e., soft labels), reflecting human perceptual categorization uncertainty gave modelshuman-like robustness against distributional shift and adversarial attacks. Most pertinently, the labeldistributions provide a mechanism for measuring the gap between the similarity structure of humansand those inferred by machines, irrespective of predictive accuracy. As shown FAX can be leveragedto evaluate the human-like abilities of machine learning algorithms.
Annotator Bias.
Conditioning prediction on annotator identifiers provides the best predictiveaccuracy, evidencing that knowledge of the annotator determining similarity assists in informingthe outcome.
However, annotators are often framed as interchangeable (Malevé, 2020; Chancelloret al., 2019).
To test the validity of this assumption, in Protocol 2 , we randomly swap the annotatorassociated with each judgment and then recompute the predictive accuracy of FAX-C .
Repeating thisprocess 100 times results in a performance drop from 61.7% to 52.8% ± 0.02% (95% CI) on average.
This shows that annotator subspaces are not interchangeable.
[Table]
An interesting question relates towhether an annotator’s socioculturalbackground influences their decision making.
To evaluate this, wecreate datasets { ( σ ( v a ) , y ) } , whereσ ( v a ) and y ∈ Y are annotator a ’slearned mask and self-identified demographic attribute, resp.
For a particular annotator attribute (e.g., nationality), we limit the dataset to annotators who contributed ≥ 200judgments and belong to one of the two largest groups wrt the attribute.
Using 10-fold cross validation,we train linear support vector machines (SVMs) (Hearst et al., 1998) with balanced class weightsto predict y from σ ( v a ) .
Table 2 shows the average area under the receiver operating characteristic(AUC) for each attribute and the proportion of dimensions with a statistically significant difference(PDSS).
Most significantly, none of the AUC confidence intervals include chance performance.
Moreover, the linear SVMs are able to discriminate between binary groups wrt nationality, regionalancestry and subregional ancestry with high probability (86–88%).
Implications for Active Learning.
Vast amounts of unlabeled data are usually easy to obtain, butexpensive to label.
However, some input-output tuples provide more information than others.
Forsome fixed budget, we often want to focus our efforts on collecting labels for the most informativesubset of the data, representing a classic active learning (AL) scenario (Lindley, 1956; MacKay, 1992).
In AL, the objective is to maximize task performance while minimizing cost. Since our triplets onlyrepresent 0.003% of all possible triplets from 4,921 faces, future triplets could be actively sampledso as to learn additional, finer-grained face-varying dimensions. For instance, this could correspondto triplets composed of faces that are close in embedding space such that similarity judgments areunlikely to be based on, e.g., gender or ethnicity, but rather eye color, interpupillary distance, etc. Most AL approaches implicitly assume that labels come from a single oracle (i.e., annotator)
(Zhanet al., 2022; Ren et al., 2021).
Less than a handful of works consider a more realistic multiple-oraclesetting, selecting at each iteration an unlabeled data point with high label uncertainty for which thereexists an oracle who could confidently label it (Rodrigues et al., 2014; Yan et al., 2011).
Similarly,however, both settings assume the existence of correct labels, in particular as most AL researchcenters on semantic classification tasks.
In contrast, there are no correct judgments in perceptualsimilarity tasks such as ours.
Thus, under a conditional framework such as ours, one may insteadseek at each iteration an unlabeled triplet with high label uncertainty wrt to a specific annotator orannotator group.
We therefore envisage FAX helping to advance multiple-oracle active learningresearch, where the oracles’ social identities shape their understanding of the world (Scheuermanet al., 2021).
Interpretability.
Since we aim to replace the explicit collection of problematic categorical labels, weevaluate whether the individual dimensions are human-interpretable through a qualitative dimensionlabeling task and a quantitative dimension rating task (Hebart et al., 2020; Josephs et al., 2021).
Inwhat follows, let x i and ReLU( w i ) denote an image from the stimulus set of 4,921 faces and itscorresponding 22-dimensional embedding, resp.
Further, let %tile qj denote the q -th percentile of thedimension j embedding values. We define grid j as a 5 × 100 grid of faces. Column q ∈ [100 , . .
. , 1]of grid j corresponds to faces from the stimulus set of 4,921 faces with the top 5 highest dimension j [Figure] SkinColor,FacialExpression Indian
[Figure]
Eyebrows
[Figure]
LatinoHispanic
[Figure]
c
[Figure]
embedding values, satisfying %tile q − 1 j ≤ ReLU( w ) j < %tile qj .
Thus, from left (high) to right (low),grid j shows example faces from each percentile for dimension j .
For the dimension labeling task , we task annotators with writing 1–3 visual characteristics thatdescribe grid j .
For each grid j , we collect 25–62 labels.
As the task is open-ended, we convert thelabels into 35 broad topics .
(Annotator descriptions were sometimes offensive.)
Figure 1 provides evidence of the interpretability for a random subset of FAX-U dimensions.
There isclear relationship between the dimension topics obtained from annotator descriptions and dimensionlabels generated using CelebA and FairFace models.
Across the 22 dimensions, we note the materialization of individual dimensions coinciding with commonly defined demographic groups, i.e., Male ,
Female , Black , White , East Asian , South Asian , and Elderly .
In addition, separatedimensions surfaced for face and hair morphology, i.e., Wide Face , Long Face , Smiling
Expression , Neutral Expression , Balding , Facial Hair , and Dyed Hair .
This isachieved without ever asking an annotator to explicitly categorize a person.
Let µ qj denote the mean value of FAX-U dimension j embedding values of all 4,921 faces from thestimulus set, satisfying %tile q − 1 j ≤ ReLU( w ) j < %tile qj .
For the dimension rating task , annotatorsmust place novel faces (e.g., x ) above a single column q of grid j .
Placement is based on the similaritybetween x and the faces contained in each column q of grid j .
Annotators are not primed with themeaning of grid j .
If x is accurately placed on grid j , then this indicates that the ordering of dimensionj is visually coherent.
To test this, we sample 20 novel faces from FFHQ, i.e., the faces are notcontained in the stimulus set.
∀ ( x, grid j ) , we collect 20 unique judgments (8,800 judgments).
Fromthe judgments, for each x , we create 22-dimensional human-generated embeddings of the form:[ 120 (cid:80) 20 n =1 µ a n 1 , . .
, 120 (cid:80) 20 n =1 µ a n 22 ] , where a n ∈ [100 , . .
, 1] denotes the n -th annotator’s columnchoice q .
Next, we generate all (cid:0) 203 (cid:1) possible triplets to create a human-generated similarity matrix
M ∈ R 20 × 20 .
Entry ( i, j ) in M corresponds to the mean ˆ p ( i, j ) over all triplets containing ( i, j )using the human-generated embeddings.
We create a model-generated matrix in the same way, butthis time using the model-generated embeddings.
Spearman’s r correlation between the strictly upper triangular model- and human-generated similaritymatrices is 0.83 and 0.86 for FAX-U and FAX-C-PH , resp.
This shows that: (i) dimensional valuescorrespond to the feature magnitude; and (ii) image grids can be used to directly collect continuousattribute values for faces, sidestepping the limits of categorical definitions (Keyes, 2018; Benthall &
Haynes, 2019; Khan & Fu, 2021).
Note that the use of an image grid is not restricted to any particularembedding method, as long as the dimension is human-interpretable.
[Table]
Prototypicality. To test whether dimensionalvalues represent the typicality of faces, weuse face images from Chicago Face Database(CFD)
(Ma et al., 2015; Lakshmi et al., 2021; Ma et al., 2021) labeled with prototypicality ratings.
The ratings (obtained from human annotators) correspond to the average prototypicalityof a face wrt a race category from one (less typical) to five (very typical), considering skin color,hair, eyes, nose, cheeks, lips, and other physical features.
For gender expression, ratings correspond to the typicality of the face relative to others of the same race and gender in the United States fromone (not at all typical) to seven (extremely typical).
Table 3 shows that relevant FAX-U dimensions are positively correlated with the typicality ratingsaccording to Spearman’s r .
Although the odd-one-task does not require an annotator to explicitlycategorize any person, category typicality appears to manifest from the similarity judgments forconcepts related to race and gender.
[Table]
Binary Attribute Classification. Facial analysis models are trained for classification,therefore we test the utility of FAX-U dimensions for discriminating between binaryvalued attributes.
For labeled face data, we use
[Table] COCO (Lin et al., 2014), OpenImages MIAP(MIAP) (Schumann et al., 2021), CFD, FFHQ,
CelebA (Liu et al., 2015), and Casual Conversations (CasCon) (Hazirbas et al., 2021).
Table 4 shows that FAX-U dimensions arecompetitive with the baselines, even in challenging unconstrained settings as representedby COCO and MIAP.
Therefore, training on FAX results in interpretable dimensions thatcan serve as classifiers.
Notably, FAX-Udimensions have the highest AUC for selfidentified CFD attributes Black , East Asian , and Indian . [Table] [Figure] [Table]
[Figure] [Table] [Figure] [Table]
[Figure] [Table] Comparative Dataset Diversity Auditing. Drawing inspiration from biodiversity measures (Leinster & Cobbold, 2012), we propose to use ourlearned dimensions for comparativedataset diversity auditing.
Given aset of candidate datasets { c k } nk =1 , weaim to find c
k ⋆ = arg min c k sim( c k ) ,where sim( c k ) measures the similarity of the faces in x ∼ c k .
We denote by q k ∈ [0 , 0 .
, 0 . 99 , 1]and
− q k the proportion of images inc k from D
= { ( x i , y 0 ) }
i and D 1 ={ ( x j , y 1 ) } j , resp., where D 0 ∩ D 1 =∅ .
Here y 0 , y 1 ∈ { 0 , 1 } are sensitiveattribute labels.
Let ˆ y ∈ R denote a proxy continuous attribute value.
We define the similarity between( x i , x j ) ∼ c k as z ij = abs(ˆ y
i − ˆ y j ) − 1 .
Further, let Z k =
( z ij ) ∈ R | c k |×| c k | denote c k ’s similaritymatrix.
In biodiversity terms, the average ordinariness of faces in c k is ∝ (cid:80) i (cid:80)
j z ij ( ∀ i ).
Thisquantity is large when most faces in c k are concentrated into a few very similar faces.
Importantly,concentration is inversely connected to diversity.
Therefore, we can interpret the mean of Z k as adiversity score, which we denote by divscore( Z k ) .
Note that divscore( Z k ) → 0 for homogeneoussets of faces.
For face data, we sample from COCO, MIAP, CFD, FFHQ, CelebA, and CasCon.
To find c k ⋆ ,wrt a label, we use relevant attribute values from FAX-U and relevant unnormalized logits from
CelebA , FairFace , and FFHQ .
Note that we do not compare candidates from multiple datasets,i.e., we sample each c k ∈ { c k } nk =1 from a single dataset (e.g., CFD).
We bootstrap each c k 100 times,where | c k | = [-
-]100 ( ∀ k ).
To measure performance, we compute: (i) the attribute disparity in c k ⋆ , i.e.,∆ = {+abs(
+} q k − 1) ; and (ii) Spearman’s r correlation between the k bootstrapped average diversityscores and the k ground-truth disparity scores.
Results are shown in Table 5.
On CFD, FAX-U has the lowest ∆ for Male and Indian .
On CasCon, FAX-U results in the lowest ∆ for Light skin .
In all other cases, FAX-U is competitive with the baselines.
In particular, Spearman’s r evidences that FAX-U disparity scores are highly correlatedwith ground truth disparity based on labels. Clustering.
We compare representations from the baseline models and our model for the task ofsemantic clustering. Here, we run K -means on the representations of several datasets, where K isequal to the number of underlying subgroups (classes) according to a dataset’s ground-truth labels. Normalized mutual information (NMI) results are shown Table 6. Notably, FAX-U face embeddingsare competitive in most cases.
However, it is clear that the FAX-U embedding which are betteraligned with the human mental representation face are not well-suited to clustering based on semanticcategories.
D ISCUSSION
[Figure] [Table] We proposed a method for implicitly learning continuous face-varying dimensions,without ever asking an annotator to explicitly categorize a person.
We uncoveredthe face embedding space by learning on a [Figure] novel dataset of human judgments of face [Figure]
similarity (FAX). We showed that the indi- [Figure] vidual dimensions are human-interpretableand related to concepts of gender, race, age,as well as face and hair morphology categories.
We demonstrated the utility of our learned embeddingspace for predicting face similarity judgments, collecting continuous face attribute values, attributeclassification, and comparative dataset diversity auditing.
Moreover, using a novel conditional framework, we showed that an annotator’s demographics influences the importance they place on differentattributes when judging similarity, underscoring the need for diverse annotator groups to avoid biases.
As our conditional decision-making framework is generally applicable to any task that involvesmapping from inputs to decisions made by humans, it would be interesting to study the behavior ofannotators in other visual tasks.
However, our work is not without its limitations.
First, we assume that the stimuli set is sufficientlydiverse.
Therefore, our current proposal is limited to the proof of concept that our approach canonly uncover factors that vary in the data and are salient to human perception of face similarity.
Forinstance, if skin color does not vary among data instances, then skin color cannot possibly influencehuman judgments, rendering it impossible to learn skin color as a face dimension.
Second, thenumber of (near) nonzero dimensions depends on the L 1 sparsity penalty, which must be carefullychosen.
Too high of a penalty will result in the entanglement of distinct factors of variation, whereastoo low of a penalty will result in repeated dimensions.
We erred on the side of caution (lowerpenalty) to avoid merging distinct factors, which would reduce interpretability.
Third, we found thatparticipants did not always follow our instructions in full.
Dimensions emerged corresponding tofacial expression, which participants were instructed to ignore.
Finally, our participant pool wasdemographically imbalanced, which is an unfortunate consequence of using AMT.
Despite these limitations, we have shown that similarity judgments are a valuable means by which toreveal the human mental representations of faces.
Of particular note is the fact this was achieved bylearning on 0.003% of all possible triplets from 4,921 faces.
We hope that our work inspires othersto pursue unorthodox tasks for learning the dimensions of human diversity, which do not requireannotators to explicitly categorize people.
Moreover, we aim to increase discourse on annotatorpositionality.
As the philosopher Thomas Nagel suggested, it is impossible to take a “view fromnowhere ” (Nagel, 1989).
Therefore, we need to make datasets more inclusive by integrating a diverseset of perspectives from their inception.
A E XTENDED R ELATED W ORK
Similarity.
Similarity represents a central theoretical construct in cognitive psychology (Medin et al.
,1993; Markman & Gentner, 2005; Goodman, 1972), in particular as the human mind is conjectured bymany scholars to have “a considerable investment in similarity” (Medin et al., 1993).
This is because,similarity, a type of comparison, permits people to make inferences on the basis of incompleteinformation, i.e., transfer learning (Thorndike, 1932).
The process of comparing similarity hingeson the alignment of the attributes of the objects being compared (Markman, 1996).
Alignment iscontended to be weighted, where humans multiplicatively integrate over both similar and dissimilarattributes to arrive at a judgment (Medin et al., 1993).
This involves evaluating the attributes presentin one object and measuring their fit in the other object.
In other words, when two objects arecompared they mutually constrain the set of features that are activated or inferred in the human mind.
For example, determining whether an object is red can depend on the object it is being compared to.
As another example, comparing face A to face B will most likely involve different sets of featuresthan when comparing face A to face C. That is, face A may be associated with different featureswhen we vary the face it is being compared to.
The process of alignment is contended to be centralto similarity comparisons.
Shanon (1988) goes as far as arguing that similarity is not a function offeatures, but that the features themselves are a function of the similarity comparison.
Thus similarityis dynamic, where features are discovered and aligned based on what is being compared.
Contextual Similarity.
Human perception of similarity can vary with respect to context (Barsalou,1987; Roth & Shoben, 1983).
For example, Barsalou (1987) found that a snake and raccoonwere judged to be less similar when participants were not given any context.
However, when thecomparison was contextualized, i.e., by placing snakes and raccoons in the context of pets theirsimilarity increased.
The odd-one-out similarity task (Dima et al., 2022; Josephs et al., 2021; Zhenget al., 2018; Hebart et al., 2020) also provides context.
For instance, it requires annotators to performpairwise comparisons in order to determine the odd-one-out.
By varying the context, e.g., face Cin the triplet (A, B, C), we uncover different sets of features that contribute to the similarity anddissimilarity between A and B.
This is important as there are an uncountable number of ways inwhich two objects may be similar or dissimilar (Love & Roads, 2021).
Odd-one-out similarityjudgments (Zheng et al., 2018; Hebart et al., 2020; Josephs et al., 2021; Dima et al., 2022), or moregenerally contextual similarity comparisons, can be used to uncover the salient features that contributeto pairwise similarity.
As highlighted in several cognitive psychology works (Medin et al., 1993;
Markman & Gentner, 2005; Goodman, 1972), context makes salient: (i) context-related properties;and (ii) the extent to which objects being compared share context-related properties.
Data Protection and Privacy.
Based on the principle of data minimization (i.e., only collect whatyou need), privacy and legal counsel typically advise against collecting demographic informationeven if when it is for fairness purposes, so as to avoid potential privacy violations.
Therefore, manypractitioners avoid collecting such information (Andrus et al., 2021), in particular special, and/orsensitive, category data (e.g., race), which is often subject to stronger restrictions.
However, if weare unable to collect demographic information, as well as other attributes, for developing fairer andmore ethical AI systems, then we require creative solutions to ensure that datasets have some level ofdiversity and are representative.
While labels can be inferred using attribute classifiers, there are concerns with this, which have beenvoiced by many practitioners (Andrus et al., 2021).
Data access request rights (e.g., via GDPR, CCPA,
PIPL) may force data holders into revealing information held about data subjects, including inferredinformation.
Due to this, practitioners are more cautious about inferring labels about people (Andruset al., 2021), especially as mismatches between inferred and self-identified race, gender, or othersensitive and nonsensitive attributes can induce psychological distress (Campbell & Troyer, 2007)by invalidating an individual’s self-image and identity (Roth, 2016).
Our method instead implicitlylearns face-varying axes from similarity judgments, altogether avoiding any explicit labeling of faces.
We show that the axes are meaningful and human-interpretable through the dimension labeling anddimension rating human experiments.
Our model (i.e., similarity function) provides dataset userswith a new type of diversity measure that coincides with human perception, which can be pluggedinto any metric (Friedman & Dieng, 2022; Benhenda, 2018).
Together, our dataset, FAX, and model offer a creative solution to the issues arising from dataprotection and privacy legislation: (i) FAX does not contain any attribute labels; and (2) our modeldoes not explicitly label faces.
Bias Detection.
Several works cluster pretrained embeddings to surface systematic failure modes (Krishnakumar et al., 2021; d’Eon et al., 2022;
Sohoni et al., 2020).
As the clusters are often difficult tointerpret, embeddings that intergrate visual and textual information have been proposed (Eyubogluet al., 2021).
Cross-modal embeddings, however, are trained on datasets that contain negative stereotypes and racist slurs (Birhane et al., 2021), causing downstreams harms (Hundt et al., 2022).
Othersutilize disentangled representations learned by generative models for unknown attribute bias discoveryin classifiers (Li & Xu, 2021; Lang et al., 2021).
Balakrishnan et al.
(2020) find semantic latent spacedirections, via human annotators, which explicitly rely on normative assessments.
Disentangled Representation Learning.
Learning interpretable representations through semantically labeled concepts and prototypes has recently gained attention (Alvarez Melis & Jaakkola,2018;
Koh et al., 2020; Li et al., 2018).
Others reveal meaningful directions inside generative models,where directional distances estimate the magnitude of attributes (Nitzan et al., 2022).
However, theidentification of interpretable directions is performed post-hoc, requiring potentially biased labeledexamples and/or pretrained models (Wu et al., 2021;
Locatello et al., 2019), self-supervision (Plumerault et al., 2019; Jahanian et al., 2019), or paired images sharing at least one factor of variation(Locatello et al., 2020).
Our approach is similar in spirit to wholly unsupervised approaches based on
PCA (Härkönen et al., 2020), Hessian regularization (Peebles et al., 2020), and orthogonal Jacobianregularization (Shen & Zhou, 2021;
Wei et al., 2021).
Rather than modeling the data generatingdistribution, our representations are trained to predict human similarity judgments, reflecting thehuman mental representational space of faces.
Our baselines primarily center on embeddings inducedby training on facial analysis datasets, since in the face domain, post-hoc interpretation of latentdimensions (Shen et al., 2020; Nitzan et al., 2022; Wu et al., 2021; Locatello et al., 2019) predominantly rely on CelebA (Liu et al., 2015).
Models trained on such datasets effectively map from imagespace to concept space, similar to encoders in concept bottleneck models (Koh et al., 2020).
B D ATA
[Figure]
B. F ACE IMAGE STIMULI
[Figure]
[Figure]
The stimulus set was sampled from the publicly available FFHQdataset (Karras et al., 2019) of 70,000 permissively licensed face images.
The FFHQ dataset which includes JSON metadata and documentationis available from the following repository: https://github.com/
NVlabs/ffhq-dataset .
For face detection, as in (Karras et al., 2019), we used the dlibmmod human face detector (King, 2009) ( https://github.com/davisking/dlib-models ).
To align the detected faces, we followed the same procedure as detailed in (Or-El et al., 2020), which usesthe dlib 68 landmark shape predictor (King, 2009)
( https://github.com/davisking/dlib-models ).
As stated in the main text, we used FFHQ-Aging annotations (Or-El et al.,2020), obtained using Face++, for absolute head yaw angle, absolutehead pitch angle, eyewear, and eye occlusion annotations to prune thedataset.
The purpose of these constraints was to reduce the influence ofhead pose on human behavior and to better allow for eye comparisons.
The stimulus set of 4,921 representative examples were then sampledfrom the remaining images such that each intersectional subgroup basedon perceived binary gender expression, age group, and ethnicity wouldbe included.
We only considered face images with an apparent agegreater than 19 years old in an attempt to exclude images of minors.
Ethnicity was estimated using a FairFace (Kärkkäinen & Joo, 2019)trained model (implementation details are in Appendix C.2).
Perceivedbinary gender expressions and apparent age groups were obtained from
FFHQ-Aging crowdsourced annotations.
To mitigate biasing our set toward stereotypical faces, we randomly sampled images from the 56possible intersectional subgroups rather than selecting the most confidently predicted or annotated.
Table 7 shows the group counts at the level of age, gender, and ethnicity, whereas Table 9 reports thecounts at the finer intersectional subgroup level.
Exact balancing was not possible due to the skewedcomposition of FFHQ.
Ideally, we would have sampled images from a dataset with self-reportedattributes.
However, while such datasets do exist, they are typically small, tightly constrained, andlargely unrepresentative.
B. C OLLECTION OF HUMAN BEHAVIORAL JUDGMENTS
All participants were recruited on AMT and were required to have previously completed a minimumof 100 human intelligence tasks (HITs) on AMT with a 95% approval rating.
Eligibility was furtherdetermined through a prescreening survey (nominal fee of 0.01 USD), which included a short multiplechoice English language proficiency test.
Since we placed no restriction on participant location,in order to be eligible, we required participants to answer at least two out of three multiple-choice
English language proficiency questions correctly.
Collection of human behavioral odd-one-out similarity judgments for training and validation.
Based on estimated face image labels, a triplet can comprise 1–2 binary gender expression group(s), 1–3 age group(s), and 1–3 ethnicity group(s) resulting in 18 triplet types which were uniformly sampled.
We sampled 703,300 unique triplets in total.
Participants were presented with triplets alongside thefollowing minimal instructions: “Choose the person that looks least similar to the two other people.
Focus your judgment on the people depicted, ignoring differences in head position/direction, facialexpression/emotion, lighting, accessories, and background/objects”.
Each HIT consisted of 20 uniquetriplets, where each triplet was presented separately and in succession.
We collected 703,300 uniquetriplet similarity judgments (i.e., one judgment per triplet) on AMT from 1,887 eligible participants.
Each triplet was judged once by a single participant, resulting in a single judgment per triplet.
Tocontrol for quality, according to the criteria outlined in Table 8, we excluded triplet judgmentsobtained from any participant who provided overly fast, deterministic, or incomplete judgments.
Thisleft 638,180 judgments from 1,645 participants.
Irrespective of estimated quality, all participantswere compensated at a rate of 15 USD per hour.
Table 10 shows the age, ancestry, gender identity,and nationality group counts of the 1,645 participants.
Collection of human behavioral odd-one-out similarity judgments for testing: Same images,novel triplets.
We sampled an additional 1,000 triplets (images were sampled from the stimulus setof 4,921 images).
We collected 25 unique judgments per triplet on AMT (total: 25,000 judgments).
After excluding responses based on the quality control criteria outlined in Table 8, we were leftwith 22–25 unique judgments per triplet (total: 24,060 judgments) obtained from 355 participants.
Table 11 shows the age, ancestry, gender identity, and nationality group counts of the 355 participants.
Collection of human behavioral odd-one-out similarity judgments for testing: Novel images,novel triplets.
We sampled all possible triplets from 56 novel images (sampled from FFHQ, butdisjoint from the stimulus set) and collected 3 unique judgments per triplet on AMT (total: 83,160judgments).
After excluding responses based on the quality control criteria outlined in Table 8,we were left with 2–3 unique judgments per triplet (total: 80,300 judgments) obtained from 632participants.
Table 12 shows the age, ancestry, gender identity, and nationality group counts of the632 participants.
Collection of dimension labels.
For each of the 22 dimensions, we constructed a scale (measurementunits corresponded to dimensional values which were converted to percentiles) and tasked participantswith providing up to three labels (minimum one label) using words only.
Note that participants were
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table] [Figure] [Table] [Figure]
[Table]
[Figure]
[Table] [Figure] [Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
not restricted to entering single word labels, they were provided with free-text boxes.
Participantswere presented with a scale and were asked: “Which visual characteristics do you think the people atthe high end of the scale have in common compared to the people at the low end of the scale?”.
Inaddition, participants were asked to view and interact with the entire scale before providing any labels.
Figure 4 shows an example of a scale and a novel face image shown to participants.
After qualitycontrol, there were 25–62 labels per dimension.
Quality control roughly entailed removing responsesthat did not correspond to words and those that were derogatory in nature.
The filtered labels werethen converted into 35 broad topic categories: “Age”, “Age related”, “Ancestry”, “Ear shape”, “Eyecolor”, “Eye related”, “Eye shape”, “Eyebrow related”, “Eyebrow shape”, “Face related”, “Faceshape”, “Facial expression”, “Facial hair”, “Forehead shape”, “Gender expression”, “Hair color”,“Hair length”, “Hair related”, “Hair texture”, “Hairstyle”, “Head shape”, “Lip related”, “Lip shape”,“Mouth related”, “Mouth shape”, “Neck related”, “Nose related”, “Nose shape”, “Skin color”, “Skin
[Table]
related”, “Skin texture”, “Teeth related”, and “Weight related”.
Figure 3 shows the top three topics formodel dimensions 1 to 22, as well as the top three labels (i.e. those resulting in the highest AUCs perdimension) using CelebA, FairFace, and FFHQ-Aging annotations.
Table 13 shows the age, ancestry,gender identity, and nationality group counts of the 102 participants.
Collection of dimension ratings.
We tasked participants with placing 20 novel face images alongeach of the 22 dimensions using the unlabeled scales from the dimension labeling task.
We collected8,800 judgments in total (20 per image-dimension tuple).
Participants were presented with a scaleand a novel face image above the scale, and were asked: “Decide where on the scale you wouldplace the person shown based on their similarity to the people shown beneath the scale”.
In addition,participants were asked to view and interact with the entire scale before making their decision.
Figure 5 shows an example of a scale and a novel face image shown to participants.
Table 14 showsthe age, ancestry, gender identity, and nationality group counts of the 164 participants.
C I MPLEMENTATION DETAILSC. FAX MODELS
All images were resized to 128 × 128 and normalized to [ − 1 , 1] .
Standard data augmentation wasused (horizontal mirroring and 112 × 112 random crops).
For the unconditional FAX models, guidedby the validation loss, we empirically set α 1 = 5 × 10 − 5 and α 2 = 1 × 10 − 2 .
(The conditionalmodels used the same hyperparameters with the additional loss term’s weight set to α 3 = 1 × 10 − 4 .)
All models were optimized for 40 epochs with Adam Kingma & Ba (2014) (default parameters),learning rate 1 × 10 − 3 , and batch size 128 on a single Tesla T4 GPU.
Post-optimization, we obtainedour core set of dimensions by dispensing with those whose maximal value was close to zero, resultingin a low-dimensional space.
(For the FAX trained model, this resulted in 22 dimensions.)
The
[Table]
threshold for all models was determined based on maximizing accuracy on the validation set.
Acrossfive independent runs, the 95% confidence interval (CI) for the number of dimensions and validationaccuracy were 27.4 ± 5.8 and 61.9 ± 0.1%, respectively.
Figure 2 shows that the judgments can beencapsulated using a limited number of the available dimensions and that the 22 dimensions areapproximately replicated across the independent runs.
Note that we discovered some redundancy in the dimensions, in particular 8 dimensions have a
Pearson r > 0 .
9 with another dimension.
The number of (near) nonzero dimensions depends onthe L 1 sparsity penalty, which must be carefully chosen: Too high of a penalty will result in theentanglement of distinct factors of variation, whereas too low of a penalty will result in repeateddimensions.
We erred on the side of caution (lower penalty), since it is more difficult to localize thesource of bias when factors are merged, i.e., since our main aim is auditing datasets and models.
C. B ASELINE MODELS
All images were resized to 128 × 128 and normalized to [ − 1 , 1] .
Standard data augmentation wasused (horizontal mirroring and 112 × 112 random crops).
For preprocessing, we used the same
[Table]
[Table]
Vietnamese 1 English
Venezuelan 1 Italian
Icelandic 1 Spanish
[Table]
Lithuanian 1 Canadian
Tunisian 1 German
Greek 1 French alignment procedure as in Or-El et al.
(2020) to produce 128 × 128 face crops.
Image values werenormalized to [ − 1 , 1] .
CelebA model.
Training was performed using a batch size of 512 (across 4 Tesla T4 GPUs) with
SGD for 45 epochs.
The initial learning rate 0 . 1 was divided by 10 at epoch 15, 30, and 40.
L 2 weight
[Table]
decay and SGD momentum were set to 0 . 0005 and 0 .
9 , respectively.
Standard data augmentation [Table] was used (horizontal mirroring and 112 × 112 random crops).
[Table]
FairFace model.
Training was performed using a batch size of 512 (across 4 Tesla T4 GPUs) with
SGD for 45 epochs.
The initial learning rate 0 . 1 was divided by 10 at epoch 15, 30, and 40.
L 2 weight
[Table]
decay and SGD momentum were set to 0 . 0005 and 0 .
9 , respectively.
Standard data augmentationwas used (horizontal mirroring and 112 × 112 random crops). [Table]
CASIA-WebFace models.
We experimented with several face recognition models that differedonly in terms of the loss function minimized: Softmax, ArcFace Deng et al.
(2019), CosFace Wanget al.
(2018), and SphereFace Liu et al.
Training was performed using a batch size of 512(across 4 Tesla T4 GPUs) with SGD for 55 epochs.
The initial learning rate 0 . 1 was divided by 10 atepoch 15, 30, and 40.
L 2 weight decay and SGD momentum were set to 0 . 0005 and 0 .
9 , respectively.
Standard data augmentation was used (horizontal mirroring and 112 × 112 random crops).
D A DDITIONAL BASELINE RESULTS
When appropriate, as baselines, we compare to supervised and self-supervised representation learningmethods.
Supervised models minimize a cross-entropy, ArcFace (Deng et al., 2019), CosFace (Wanget al., 2018), SphereFace (Liu et al., 2017), or triplet margin with distance swap (Balntas et al., 2016)loss.
Self-supervised approaches correspond to MoCo-v2 (Chen et al., 2020), SwAV (Caron et al.,2020), or DINO (Caron et al., 2021).
For data, supervised methods train on CASIA-Webface (Yiet al., 2014), CelebA (Liu et al., 2015), FairFace (Kärkkäinen & Joo, 2019), FFHQ (Karras et al.
,2019; Or-El et al., 2020), or ImageNet-1K (Russakovsky et al., 2015).
Self-supervised approacheslearn on IG-1B (Goyal et al., 2022), ImageNet-1K (Russakovsky et al., 2015), or PASS (Asano et al.,2021).
As is standard, baseline representations are extracted from the final encoder layer of a modeland then normalized to unit-length.
The dot product of two representations determines their similarity.
Results for Protocol 1 and Protocol 2 are shown in Tbl. 15.
E A UDITING MODEL BEHAVIOR
Beyond dataset auditing, as an example, we study the disparate impact of the face image restorationmodel PULSE (Menon et al., 2020).
We select PULSE due to its much discussed racial bias (Salminenet al., 2020; Menon et al., 2020; Vincent, 2020).
Let R : x L (cid:55)→ R ( x L ) =
x ′ H denote the PULSEmodel, which maps a low-resolution face image to a high-resolution face image.
We denote by x Hthe ground-truth high-resolution face image.
Suppose z H and z ′ H denote face attribute representationsof x H and x ′ H , resp.
Disparate outcomes in attribute changes due to R across demographic groupsmay be an indicator of data and/or algorithmic bias.
For face data, we use CFD (Ma et al., 2015),
[Table]
centering our analysis on self-identified sensitive labels: Black , White , Indian
[Table]
and (East)
Asian .
We create low-resolution faces by downsampling from 1024 × 1024 to 32 × 32 .
For eachgroup, we calculate the mean cosine similarity between each ( z H , z ′ H ) pair and report the min-maxgroup ratio, i.e., worst-case scenario (Ghosh et al., 2021).
For the CelebA and FairFace models, attribute representations correspond to unnormalized classifier predictions (logits), whereas for the
FAX and CASIA-WebFace-AF models we use the face embeddings.
The min-max ratio for the FAX, CelebA, FairFace, and CASIAWebFace-AF attribute representations are 0.78, 0.88, 0.58, and0.98, resp.
All attribute representations result in the samemin-max pair, i.e., Black - White .
Using FAX, CelebA, and
FairFace attribute representations, we find statistically significant differences in 22/22, 36/40, and 18/18, resp., for Blackindividuals, whereas for White individuals, we find statistically significant differences in 16/22, 26/40, and 12/18, resp.
All methods show that Black individuals undergo more significant attribute changes.
Fig.
6 plots the mean of z ′ H − z H ,highlighting FAX-model attribute changes per group.
To easepresentation, we combined FAX-model dimensions measuringthe same attribute.
First, Black individuals have highly reduced values in the Black dimension and magnified valuesin the White dimension, corroborating previous qualitativefindings (Vincent, 2020).
Second, the impact of PULSE on
White individuals largely centers on changes in face widthand length, representing a novel insight.
While neither type ofmodification is desirable, the inadvertent erasure of minority groups is extremely harmful.
FAXdimensions are therefore useful as a tool for gaining insight into the behavior of face-based models.
F N AIVE P REDICTIONS
Given that previous works equate diversity with parity across demographic subgroup distributions (Keswani & Celis, 2021;
Kay et al., 2015; Bolukbasi et al., 2016; Schwemmer et al.
, 2020),we test whether categorical labels corresponding to gender, race, and age are predictive of humanjudgments of similarity.
We only consider triplets that are composed of two faces that share thesame attribute(s), whereas the third face does not.
We use a parameterless naive model that alwayspredicts the third face as the odd-one-out.
Protocol 1 and Protocol 2 results are shown in Fig.
Wenote that when two of the faces have at least the same gender and race attribute labels that the naivepredictor starts to approach the predictive accuracy of our models.
This is unsurprising, since themore attributes two faces have in common as compared to the third face, the more likely the thirdface will be selected as the odd-one-out.
Note that this strategy cannot explain judgments for tripletscomposed of faces from the exact same subgroup.
Protocol 1: Age
Protocol 2: Age
Protocol 1: Gender
Protocol 2: Gender
Protocol 1: Race
Protocol 2: Race
Protocol 1: Age, Gender
Protocol 2: Age, Gender
Protocol 1: Age, Race
Protocol 2: Age, Race
Protocol 1: Gender, Race
Protocol 2: Gender, Race
Protocol 1: Age, Gender, Race
Protocol 2: Age, Gender, Race
G D ATASET D OCUMENTATION FOR FAX
Below we follow the datasheets for datasets documentation guidelines Gebru et al.
(2018), answering questions with respect to FAX’s motivation, composition, collection process, preprocessing/cleaning/labeling, uses, distribution, and maintenance.
G. M OTIVATION
For what purpose was the dataset created?
Biases in human-centric computer vision modelsare often attributed to a lack of sufficient data diversity, with many demographics insufficientlyrepresented.
However, auditing datasets for diversity can be difficult, due to an absence of ground-truthlabels of relevant features.
Few datasets contain self-identified demographic information, inferringdemographic information risks introducing additional biases, and collecting and storing data onsensitive attributes can carry legal risks.
Moreover, categorical demographic labels do not necessarilycapture all the relevant dimensions of human diversity that are important for developing fair and robustmodels.
One can instead implicitly uncover a set of continuous face-varying dimensions, without everasking an annotator to explicitly categorize a person.
To do so, we propose a novel dataset of 638,180human judgments of face similarity (FAX).
Notably, each judgment is associated with the identifierand demographic attributes of the annotator who made the judgment.
We demonstrate the utility of
FAX induced embedding spaces for predicting face similarity judgments, collecting continuous faceattribute values, comparative dataset diversity auditing, and studying annotator bias.
Who created the dataset (e.g., which team, research group) and on behalf of which entity (e.g.,company, institution, organization)?
The dataset was constructed by the authors.
Who funded the creation of the dataset?
The dataset was created for research purposes only andwas funded entirely by the authors.
G. C OMPOSITION
What do the instances that comprise the dataset represent (e.g., documents, photos, people,countries)?
The dataset consists of several JSON files, containing information such as randomlygenerated participant identifiers, triplet image identifiers, and odd-one-out triplet judgments.
JSONformat data is provided for each participant and contains their demographic information.
How many instances are there in total (of each type, if appropriate)?
For training and validation,
FAX contains 638,180 triplet-judgment unique tuples (one unique judgment for each unique triplet).
For testing generalization, we include two additional subsets: (a) 1,000 unique triplets, where eachtriplet has 22–25 judgments from distinct participants (total: 24,060 triplet-judgment tuples); (b)27,720 unique triplets, where each triplet has 2–3 judgments from distinct participants (total: 80,300triplet-judgment tuples).
We provide demographic information for each of the 1,663 participants thatcontributed judgment responses.
Does the dataset contain all possible instances or is it a sample (not necessarily random) ofinstances from a larger set?
The training and validation sets represent 0.003% of all possibletriplets that could be sampled from 4,921 images.
The 4,921 images are a subset of the 70,000images contained in FFHQ Karras et al.
We used FFHQ-Aging annotations (Or-El et al.,2020), obtained using Face++, for absolute head yaw angle, absolute head pitch angle, eyewear,and eye occlusion annotations to prune the 70,000 images.
The purpose of these constraints wasto reduce the influence of head pose on human behavior and to better allow for eye comparisons.
The stimulus set of 4,921 representative examples were then sampled from the remaining imagessuch that each intersectional subgroup based on perceived binary gender expression, age group, andethnicity would be included.
We only considered face images with an apparent age greater than 19years old.
Ethnicity was estimated by using a model traned on the FairFace dataset (Kärkkäinen& Joo, 2019).
Perceived binary gender expression and apparent age group were obtained from
FFHQ-Aging crowdsourced annotations.
To mitigate biasing our set toward stereotypical faces, werandomly sampled images from the 56 possible intersectional subgroups rather than selecting themost confidently predicted or annotated.
Additional images (total: 56) used for testing (disjoint fromthe 4,921 stimuli set images) were also sampled in the same manner.
In this case, all possible tripletswere sampled.
Note: No images are contained in our dataset, the images are hosted on NVIDIA
Corporation’s Google Drive, please see the original FFHQ dataset Karras et al.
for moredetails: https://github.com/NVlabs/ffhq-dataset .
What data does each instance consist of?
Each instance in the training and validation set consist ofa randomly generated participant identifier, triplet image identifiers, an odd-one-out triplet judgment,and a training or validation split label.
The test set instances consist of the same information, howeverthey do not have training or validation split labels, since they should be used for testing only.
Is there a label or target associated with each instance?
Each instance is labeled with the oddone-out triplet judgment, as well as a randomly generated participant identifier (i.e., the participantwho generated the judgment).
Each participant’s identifier can be mapped to their demographicinformation (age, nationality, ancestry, and gender identity) using the participant metadata JSON file.
Note: Participant identifiers were randomly generated and do not correspond to their true Amazon
Mechanical Turk worker identifiers.
Is any information missing from individual instances?
No.
Are relationships between individual instances made explicit (e.g., users’ movie ratings, socialnetwork links)?
We make explicit the relationship between a judgment and the participant whogenerated the judgment.
Are there recommended data splits (e.g., training, development/validation, testing)?
The datasetis split into training, validation, and testing splits.
The training and validation data are contained inthe same JSON file, where each instance has a training or validation split label.
The test data subsetsare provided in separate JSON files.
Are there any errors, sources of noise, or redundancies in the dataset?
No.
Is the dataset self-contained, or does it link to or otherwise rely on external resources (e.g.,websites, tweets, other datasets)?
The triplet judgments pertain to images hosted on NVIDIA
Corporation’s Google Drive, please see the original FFHQ dataset Karras et al.
for moredetails: https://github.com/NVlabs/ffhq-dataset .
Does the dataset contain data that might be considered confidential (e.g., data that is protectedby legal privilege or by doctor-patient confidentiality, data that includes the content of individuals’ non-public communications)?
The dataset includes the demographic information (age,nationality, ancestry, and gender identity) of each participant.
Participants who contributed judgmentsconsented to the collection and use of this data as well as the information being made public.
Does the dataset contain data that, if viewed directly, might be offensive, insulting, threatening,or might otherwise cause anxiety?
No.
Does the dataset relate to people?
If not, you may skip the remaining questions in this section.
FAX contains judgments gathered from human participants about the similarity of human faces inimages.
Does the dataset identify any subpopulations (e.g., by age, gender)?
Each judgment in the datasetis explicitly linked to the participant who generated the judgment.
Moreover, each participant’s age,nationality, ancestry, and gender identity is available, which were provided when obtaining informedconsent.
Note:
Participant identifiers were randomly generated and do not correspond to their true
Amazon Mechanical Turk worker identifiers.
Is it possible to identify individuals (i.e., one or more natural persons), either directly orindirectly (i.e., in combination with other data) from the dataset?
We replaced each participant’s
Amazon Mechanical Turk worker identifier with randomly generated identifiers.
Therefore, it is notpossible to directly identify individuals.
Does the dataset contain data that might be considered sensitive in any way (e.g., data thatreveals racial or ethnic origins, sexual orientations, religious beliefs, political opinions orunion memberships, or locations; financial or health data; biometric or genetic data; forms ofgovernment identification, such as social security numbers; criminal history)?
Each instance the dataset is associated with the participant who generated the judgment and each participant is associated with their age, nationality, ancestry, and gender identity, which were provided when we obtained informed consent.
G. C OLLECTION PROCESS
[Table]
How was the data associated with each instance acquired?
All judgments were collected on
Amazon Mechanical Turk directly from participants.
What mechanisms or procedures were used to collect the data (e.g., hardware apparatuses orsensors, manual human curation, software programs, software APIs)?
The Amazon Mechanical
Turk API was used to deploy human intelligence tasks and collect responses.
If the dataset is a sample from a larger set, what was the sampling strategy (e.g., deterministic,probabilistic with specific sampling probabilities)?
Based on estimated face image labels, atriplet can comprise 1–2 binary gender expression group(s), 1–3 age group(s), and 1–3 ethnicitygroup(s) resulting in 18 triplet types which were uniformly sampled.
Ethnicity was estimated using amodel trained on the FairFace dataset (Kärkkäinen & Joo, 2019), whereas perceived binary genderexpression and apparent age group were obtained from FFHQ-Aging crowdsourced annotations Or-Elet al.
Who was involved in the data collection process (e.g., students, crowdworkers, contractors)and how were they compensated (e.g., how much were crowdworkers paid)?
The authors andparticipants were involved in the data collection process.
For the prescreening survey (which includedthe consent form), participants were paid a nominal fee of 0.01 USD.
For all other tasks, participantswere compensated at a rate of 15 USD per hour, regardless of whether their work passed our qualitychecks.
Over what timeframe was the data collected?
Data was collected on Amazon Mechanical
Turkbetween 6 November 2021 and 20 February 2022.
Were any ethical review processes conducted (e.g., by an institutional review board)?
No.
Did you collect the data from the individuals in question directly, or obtain it via third partiesor other sources (e.g., websites)?
The judgments and participant demographic information werecollected directly from the participants on Amazon Mechanical Turk.
Were the individuals in question notified about the data collection?
The participants whocontributed judgments were provided with an “Information Sheet and Consent Form” as well as aseparate “Notification and Consent for Collection and Use of Study Data Form”.
Did the individuals in question consent to the collection and use of their data?
Yes.
Participantswho contributed judgments consented to the collection and use of the following Study Data: Amazon
Mechnical Turk worker identifier, age, gender identity, nationality, and ancestry, as well as any otherdata provided while performing human intelligence tasks.
Note: Participant identifiers were randomlygenerated and do not correspond to their true Amazon Mechanical Turk worker identifiers.
If consent was obtained, were the consenting individuals provided with a mechanism to revoketheir consent in the future or for certain uses?
Participants were informed that their Study Datais regulated in the European Economic Area under the General Data Protection Regulation (the“GDPR”) and in the UK under the UK GDPR.
GDPR gives them rights relating to their Study Data,including the right to: (a) Access, correct or withdraw their Study Data; (b) Restrict the types ofactivities that can be done with their Study Data; (c) Object to using their Study Data for specifictypes of activities; (d) Withdraw their consent to use their Study Data for the purposes outlined in theoriginal consent form.
In addition, residents in the EU, EEA or the UK were informed who to contactin the event that they wish to exercise their rights under the GDPR or UK GDPR.
Has an analysis of the potential impact of the dataset and its use on data subjects (e.g., a dataprotection impact analysis) been conducted?
A privacy impact assessment was conducted.
G. P REPROCESSING / CLEANING / LABELING
Was any preprocessing/cleaning/labeling of the data done (e.g., discretization or bucketing,tokenization, part-of-speech tagging, SIFT feature extraction, removal of instances, processingof missing values)?
To control for quality, according to the criteria outlined, we excluded triplet judgments obtained from any participant who provided overly fast, deterministic, or incomplete judgments.
Was the “raw” data saved in addition to the preprocessed/cleaned/labeled data (e.g., to supportunanticipated future uses)?
Yes.
The authors retain a copy of the raw data.
Is the software that was used to preprocess/clean/label the data available?
No software was usedper se.
The quality controls used to clean the data are conditional statements.
G. U SES
Has the dataset been used for any tasks already?
We have shown that the dataset can be usedto implicitly uncover human-interpretable dimensions corresponding to perceptual face-varyingaxes, aligned with the human mental representational space of faces.
We have also shown that thelearned embedding dimensions may be used to audit the visual diversity of unlabeled datasets andthe behavior of pretrained face-based models.
Furthermore, since each judgment in the dataset isassociated with the generating participant’s identifier and their demographic attributes, we haveshown that this permits the identification and study of annotator bias.
Is there a repository that links to any or all papers or systems that use the dataset?
We will listthese on the dataset’s GitHub repository which will be made public in August 2022.
What (other) tasks could the dataset be used for?
The dataset can be used to mitigate bias duringmodel training.
Is there anything about the composition of the dataset or the way it was collected and preprocessed/cleaned/labeled that might impact future uses?
The triplet judgments pertain to imagesfrom Flickr.
While we made attempts to ensure the subset of images that we collected judgments forwere demographically diverse, the subset is not representative of the entire population.
Moreover,although the images have permissive licenses that allow free use, redistribution, and adaptation fornon-commercial purposes, image subjects and/or image creators are free to revoke the use of theirdata.
When this is the case, we will remove any affected judgments from our dataset.
The sameapplies when a participant who contributed judgments withdraws their consent.
Our participant pool was demographically imbalanced, which is an unfortunate consequence of using
Amazon Mechanical Turk.
Therefore, the criteria used by our participants and the importance of eachcriterion when performing judgments does not necessarily generalize to demographically dissimilarparticipants.
Are there tasks for which the dataset should not be used?
The dataset was created for researchpurposes only, in particular for those wishing to study the human mental representational space offaces.
The dataset is not intended for, and should not be used for, development or improvement offacial recognition technologies.
G. D ISTRIBUTION
Will the dataset be distributed to third parties outside of the entity (e.g., company, institution,organization) on behalf of which the dataset was created?
Yes, the dataset will be made publiclyavailable on Zenodo: https://zenodo.org/ .
How will the dataset be distributed (e.g., tarball on website, API, GitHub)?
The dataset will behosted on Zenodo: https://zenodo.org/ .
When will the dataset be distributed?
The dataset will be made publicly available in August 2022on Zenodo: https://zenodo.org/ .
Will the dataset be distributed under a copyright or other intellectual property (IP) license, and/or under applicable terms of use (ToU)?
Creative Commons BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0/ .
Have any third parties imposed IP-based or other restrictions on the data associated with theinstances?
No.
Do any export controls or other regulatory restrictions apply to the dataset or to individualinstances?
We are not aware of any controls or restrictions.
G. M AINTENANCE
Who will be supporting/hosting/maintaining the dataset?
The dataset is supported by the authors.
How can the owner/curator/manager of the dataset be contacted (e.g., email address)?
Contactinformation removed for peer review.
Is there an erratum?
In the event that any errors are found, an erratum file will be added to thedataset.
Will the dataset be updated (e.g., to correct labeling errors, add new instances, delete instances)?
The dataset will be versioned.
If the dataset relates to people, are there applicable limits on the retention of the data associatedwith the instances (e.g., were the individuals in question told that their data would be retainedfor a fixed period of time and then deleted)?
Participants were informed that their public Study
Data (age, gender identity, nationality, and ancestry) would be kept indefinitely.
However, participantsare free to withdraw their consent at any time and for any reason.
Will older versions of the dataset continue to be supported/hosted/maintained?
Older versionsof the dataset will continue to be hosted, except when a participant withdraws their consent or whenan image subject and/or image creator revokes the use of their data.
In this case, older versionscontaining such data instances will be removed and a new version will be created.
If others want to extend/augment/build on/contribute to the dataset, is there a mechanism forthem to do so?
External parties are free to extend the dataset, or contact us directly if they wish tocollaborate on extending the dataset.
G. A UTHOR STATEMENT OF RESPONSIBILITY
The authors confirm all responsibility in case of violation of rights and confirm the license associatedwith the dataset.