Unbiased Supervised Contrastive Learning
Authors: Carlo Alberto Barbano
Benoit Dufumier
Enzo Tartaglione
Marco Grangetto
Pietro Gori
Venue: ICLR 2023 poster (2023)
Keywords: contrastive learning
debiasing
supervised learning
representation learning
deep learning
neural networks

Abstract: Many datasets are biased, namely they contain easy-to-learn features that are highly correlated with the target class only in the dataset but not in the true underlying distribution of the data. For this reason, learning unbiased models from biased data has become a very relevant research topic in the last years. In this work, we tackle the problem of learning representations that are robust to biases. We first present a margin-based theoretical framework that allows us to clarify why recent contrastive losses (InfoNCE, SupCon, etc.) can fail when dealing with biased data. Based on that, we derive a novel formulation of the supervised contrastive loss ($\epsilon$-SupInfoNCE), providing more accurate control of the minimal distance between positive and negative samples. 
Furthermore, thanks to our theoretical framework, we also propose FairKL, a new debiasing regularization loss, that works well even with extremely biased data. We validate the proposed losses on standard vision datasets including CIFAR10, CIFAR100, and ImageNet, and we assess the debiasing capability of FairKL with $\epsilon$-SupInfoNCE, reaching state-of-the-art performance on a number of biased datasets, including real instances of biases "in the wild".

Published as a conference paper at ICLR 2023
UNBIASED SUPERVISED CONTRASTIVE LEARNING
Carlo Alberto Barbano" " University of Turin LTCI, Telécom Paris, IP Paris
Benoit Dufumier
Enzo Tartaglione
LTCI, Télécom Paris, IP Paris
LTCI, Télécom Paris, IP Paris
Marco Grangetto University of Turin
Pietro Gori
LTCI, Télécom Paris, IP Paris
ABSTRACT
Many datasets are biased, namely they contain easy-to-learn features that are highly correlated with the target class only in the dataset but not in the true un- derlying distribution of the data. For this reason, learning unbiased models from biased data has become a very relevant research topic in the last years. In this work, we tackle the problem of learning representations that are robust to biases. We first present margin- based theoretical framework that allows us to clarify why recent contrastive losses (InfoNCE, SupCon, etc.) can fail when dealing with biased data. Based that, derive a novel formulation of the supervised contrastive loss (c-SupInfoNCEE) providing more accurate control of the minimal distance between positive and negative samples. Furthermore, thanks our the- oretical framework, we also propose FairKL, new debiasing regularization loss, that works well even with extremely biased data. We validate the proposed losses on standard vision datasets including CIFAR1O. 10, CIFARIO0. and ImageNet, and we assess the debiasing capability of FairKL with e-SupInfoNCE, reaching state- of-the-art performance on a number of biased datasets, including real instances of biases "in the wild".
INTRODUCTION
Deep learning models have become the predominant tool for learning representations suited for a variety of tasks. Arguably, the most common setup for training deep neural networks in supervised classification tasks consists in minimizing the cross-entropy loss. Cross-entropy drives the model towards learning the correct label distribution for given sample. However, it has been shown in many works that this loss can be affected by biases in the data (Alvi et al.] [2018] Kim et al., 2019) Nam et al.) 2020 Sagawa et al., 2019 Tartaglione et al. 2021 Torralba et al. 1011)) or suffer by noise and corruption in the labels Elsayed et al. (2018): Graf et al.] (2021). ). In fact, in the latest years, has become increasingly evident how neural networks tend to rely on simple patterns the data (Geirhos et al. 2019 Li et al. (021I. As deep neural networks grow in size and complexity, guaranteeing that they do not learn spurious elements in the training set is becoming a pressuring is- sue to tackle. It is indeed known fact that most of the commonly-used -used datasets are biased (Torralbal jet al. (201)) and that this affects the learned models (Tommasi et al., (017). In particular, when the biases correlate very well with the target task, is hard obtain predictions that are independent of the biases. This can happen, e.g., in presence of selection biases in the data. Furthermore, if the bias easy to learn (e.g. a simple pattern or color), we will most likely obtain a biased model, whose predictions majorly rely on these spurious attributes and not on the true, generalizable, and discriminative features. Learning fair and robust representations of the underlying samples, espe- cially when dealing with highly- data, is the main objective of this work. Contrastive learning has recently gained attention for this purpose, showing superior robustness to cross-entropy Crraf et al. (202I). For this reason, in this work, we adopt metric learning approach for supervised representation learning. Based on that, we provide a unified framework to analyze and compare existing formulations of contrastive losses such the InfoNCE loss (Chen et al. 2020: Oord et al.
"Corresponding author; carlo . ba Barbano@unne to. it We refer any contrastive loss and necessarily losses based on pairs of samples in Sohn 2016

---

Published as a conference paper at ICLR 2023
3
2
d5
d
#1
(b)
(c)
Figure I: With e-SupInfoNCE (a) we aim at increasing the minimal margin between the distance dt of positive sample x+ (+ symbol inside) from an anchor x and the distance d' of the closest negative sample x (- symbol inside). By increasing the margin, we can achieve a better separation between positive and negative samples. We show two different scenarios without margin (b) and with margin (c). Filling colors of datapoints represent different biases. We observe that, without imposing a margin, biased clusters might appear containing both positive and negative samples (b). This issue can be mitigated by increasing the margin (c).
2019), the InfoL10 loss (Poole et al. 2019) and the SupCon loss (Khosla al. 2020). Further- more, we also propose a new supervised contrastive loss that can be seen as the simplest extension of the InfoNCE loss (Chen al. 2020 Oord
2019) to supervised setting with multiple positives. Using the proposed metric learning approach, we can reformulate each loss as set of contrastive, and surprisingly sometimes even non-contrastive, conditions. We show that the widely used SupCon loss is not "straightforward" extension of the InfoNCE loss since it actually contains a set of "latent" non-contrastive constraints. Our analysis results in an in-depth understanding the different loss functions, fully explaining their behavior from a metric point of view. Furthermore, by leveraging the proposed metric learning approach, we explore the issue of biased learning. We outline the limitations of the studied contrastive loss functions when dealing with biased data, even the loss on the training set is apparently minimized. By analyzing such cases, we provide a more set of regularization
formal characterization of bias. This eventually allows to derive straints for debiasing that is general and can be added to any contrastive or non-contrastive loss. Our contributions are summarized below:
1.
We introduce a simple but powerful theoretical framework for supervised representation learning, from which derive different contrastive loss functions. We show how exist- ing contrastive losses can be expressed within our framework, providing a uniform under- standing of the different formulations. We derive generalized form of the SupCon loss (e-SupCon), propose a novel loss e-SupInfoNCE, and demonstrate empirically its effective- ness;
2. We provide a more formal definition of bias, thanks to the proposed metric learning ap- proach, which is based on the distances among representations, This allows us to derive a set of effective debiasing regularization constraints, which call FairKL. We also an- alyze, theoretically and empirically, the debiasing power the different contrastive losses, comparing e-SupInfoNCE and SupCon.
RELATED WORKS
Our work is related to the literature in contrastive learning, metric learning, fairness, and debiasing. Contrastive Learning Many different contrastive losses and frameworks have been proposed (Chen)
al. 2020 Khosla al.) 2020 Oord et al.) 2019 Poole et al.) 2019). Supervised contrastive learn- ing approaches aim at pulling representations of the same class close together while repelling repre- sentations of different classes apart from each other. It has been shown that, in supervised setting, this kind of optimization can yield better results than standard cross-entropy, and can be more robust against label corruption (Khosla et al. 2020 Graf et al. 2021). Related to contrastive learning,
2

---

Published as a conference paper at ICLR 2023
Hermans et al. 2017) and based on distance metrics Schroff et al. (2015); Weinberger et al. (006). The latter are the most relevant for this work, we propose metric learning approach for supervised representation learning.
can also find methods such as triplet losses (Chopra et al. 2005
Debiasing Addressing the issue of biased data and how it affects generalization in neural networks has been the subject of numerous works. Some approaches in this direction include the use of differ- ent data sources in order to mitigate biases (Gupta et al. (2018) and data clean-up thanks to the use of a GAN (Sattigeri et al. 2018; Xu et al. 2018). However, they share some major limitations due to the complexity of working directly on the data. In the debiasing related literature, we can most often find approaches based on ensembling or adversarial setups, and regularization terms that aim at obtaining an unbiaved model using biased data. The typical adversarial approach is represented by BlindEye (Alvi et al., 2018). They employ an explicit bias classifier, trained on the same repre- sentation space as the target classifier, in an adversarial way, forcing the encoder to extract unbiased representations. This is also similar to Xie ct al. (2017). Kim et al. (2019) use adversarial learning and gradient inversion to reach the same goal. Wang et al. (2019b) adopt an adversarial approach to remove unwanted features from intermediate representations of a neural network. All of these works share the limitations of adversarial training, which is well known for its potential training instability. Other ensembling approaches can be found in Clark et al. (2019); Wang el | (2020), where feature independence among the different models is promoted. [Baing al. (2020) propose ReBias, aiming at promoting independence between biased and unbiased representations with a min-max optimiza- tion. In (Lee al. 2021) disentanglement between bias features and target features is maximized to perform the augmentation in the latent space. Nam et al. (2020) propose LiF, where bias-capturing model trained with focus on easier samples (hias-aligned)), while a debiased network trained by giving more importance to the samples that the bias-capturing model struggles to discriminate.
Another approach is proposed in Wang et al. (2019a) with HEX, where a neural cowural-eetorr-bbaee gray-level co-occurrence matrix (Haralick et al. 1973 Lam 1996), is employed for learning invari- ant representations to some bias. However, all these methods require training additional models, which in practice can be resource and time-consuming. Obtaining representations that are robust and/or invariant to some secondary attribute can also be achieved by applying constraints and reg- ularization the model. Using regularization terms for debiasing has gained traction also due to the typically lower complexity when compared to methods such as exembling. For example, recent works attempt to discourage the learning of certain features with the aim of data privacy (Barbano itt al. [02T]] Song et al.) 2017) and fairness (Beutel et al. 2019). For example, Sagawa et al. (2019) propose Group-DRO, which aims at improving the model performance on the worst-group, dehned based on prior knowledge of the bias distribution. In RUBi (Cadene et al. (0199), logits re- re-eeighting used to promote the independence of the predictions on the bias features. Tartaglione et al. (2021) propose EnD, which is a regularization term that aims at bringing representations of positive sam- ples closer together in case of different biases, and pulling apart representations of negative samples sharing the same bias attributes. A similar method is presented in (Hong & Yang 2021), where contrastive formulation is employed to reach a similar goal. Our method belongs to this latter class of approaches, it consists of regularization term which can be optimized during training.
3 CONTRASTIVE LEARNING: AN E-MARGIN POINT OF VIEW
Let & E X' be an original sample (i.e., anchor), x;² a similar (positive) sample, 25 a dissimilar (neg- ative) sample and P and N the number of positive and negative samples respectively. Contrastive learning methods look for a parametric mapping function f X' + gd-1 that maps "semantically" similar samples close together in the representation space (a (d- (d-Der-pherre and dissimilar samples far away from each other. Once pre-trained, ʃ is fixed and its representation is evaluated on a downstream task, such as classification, through linear evaluation on a test set. In general, positive samples 27 can be defined in different ways depending on the problem: using transformations of I (unsupervised setting), samples belonging to the same class as x (supervised) or with similar im- age attributes of x "weakly-supervised)) The definition of negative samples 2,, varies accordingly. Here, we focus on the supervised case, thus samples belonging to the same/different class, but the proposed framework could be easily applied to the other cases. We define s(f()), (bb) as a similar- ity measure (e.g., cosine similarity) between the representation of two samples a and b. Please note
that since [a)ll [[f(b]]22 lg = 1, using cosine similarity is equivalent to using L2-distance (d(f(a) f(6) = f(a) f(b] (3). Similarly to Chhhpr et al. (2005): Hadsell et al. (2066): Schroff
et al. (2015)) Sohn 2016): Wang et al. (2014) 2019c); Weinberger et al. (2066); Yu & Tao (0199)
3

---

Published as a conference paper at ICLR 2023
metric learning approach which allows us to better formalize recent contrastive losses, such as InfoNCE (Chen et al. 2020 Oord et al., 2019). InfoLIO (Poole et al. 2019) and SupCon (Khosla et al. 2020D, and derive new losses that better approximate the mutual information and can take into account data biases. Using an e-margin metric learning point of view, probably the simplest contrastive learning formulation is looking for mapping function such that the following e-condition is always satisfied:
propose
d( (((x), d(f()), = - Vj (1)
where 2 0 is margin between positive and negative samples and consider, for now, single positive sample.
Derivation of InfoNCE The constraint of Eq. D can be transformed in optimization problem using, as is common in contrastive learning, the max operator and its smooth approximation LogSumExp (full derivation in the Appendix A.1.II:
8j
Vj
exp(xt) exp(st - +)+ E, exp(s))
arg min max(-c, 18j st Jj:.....N) N) s arg min - log
e-InfoNCE
Here, we can notice that when e = 0, we retrieve the InfoNCE loss, also known as N-Pair loss (Sohn 2016), whereas when - co we obtain the InfoL.O loss. It has been shown in Poole et al. 2019
that these two losses are lower and upper bound of the Mutual Information T(X+ X respectively:
exp st
exp s+
log stpst + expsy
SI(x ,X) S log Σ, exp
(3)
InfoNCE
InfoL1O
By using value of E oo), might find tighter approximation of I(X+, xxx+,x X) since the exponential function at the denominator exp(-c) monotonically decreases as increases.
Proposed supervised loss (c-SupInfoNCE) The inclusion of multiple positive samples (8 can lead to different formulations. Some of them be found in the Appendix[A.13 Here, considering a supervised setting, we propose to use the following one, that we call e-SupInfoNCE:
s S - Vi.j
exp(x:) Σ max(-ce -c, -st -t s=) N) - Σ log exp(s: c) + E, exp(s7)
(4)
C-SupInfoNCE
Please note that this loss could also be used in other settings, like in an unsupervised one, where positive samples could defined as transformations of the anchor. Furthermore. even here, the value can be adjusted in the loss function, in order to increase the e-margin. This time, contrarily to what happens with Eq. and InfoNCE, if we consider O, we do obtain the SupCon loss.
Derivation of c-SupCon (generalized SupCon) It's interesting to notice that Eq. 4 is similar to Coup, which is one of the two SupCon losses proposed Khosla et al. (2020), but they differ for sum over the positive samples at the denominator. The Cour loss, presented as the "most straight- forward way to generalize" the InfoNCE loss, actually contains another non-contrastive constraint on the positive samples: s, x < Vi, Fulfilling this condition alone would force all positive samples to collapse to a single point in the representation space. However, does not take into account negative samples. That is why define non-contrastive condition. Considering both

---

Published as a conference paper at ICLR 2023
contrastive and non-contrastive conditions, we obtain:
$j - s S -E Vi,j and
57 - 5 5 Vi,tzi
Σ max(0, 10j - ot + tejs 1st st teas) RE P
1
1 Σ log p
exp(s;)
Σ. exp(s7 - + E, exp(17
e- --SupCon
(5)
when e we retrieve exactly Lour The second loss proposed in Khosla et al. (200)) called Lim
minimizes a different contrastive problem, which is a less striet condition and probably explains the fact that this loss did not work well in practice (Khosla et al.) 2020):
max()7) < max(s;)) R logí Σ
exp(87) )) log exp(s <0
(6)
exp(s,) (s
arg min max(0, max(s,) - max(s;)) ~= log Σ
E. exp(st) + E, exp(s7)
(7)
It's easy to see that, differently from Eq. and Lour: this condition is fulfilled when just one positive sample is more similar to the anchor than all negative samples. Similarly, another contrastive con- dition that should be avoided is: Σ, s(f(x), fxx, )) - Σ, (f((),, f(;)) < -e since one would need only one (or few) negative samples far away from the anchor in the representation space (i.e.. orthogonal) fulfil the condition.
3.1 FAILURE CASE OF INFONCE: THE ISSUE OF BIASES
Satisfying the e-condition I can generally guarantee good downstream performance, however, it does not take into account the presence of biases (e.g. selection biases). model could therefore take its decision based on certain visual features, i.e. the bias, that are correlated with the target downstream task but don't actually characterize it. This means that the same bias features would probably have a worse performance if transferred to a different dataset (e.g. different acquisition set- tings or image quality). Specifically, in contrastive learning, this can lead to settings where we are still able to minimize any InfoNCE-based loss (e.g. SupCon or e- e-SuplnfoNCE), but with degraded classification performance (Fig. [bp. To tackle this issue, this work, we propose the FairKL regu- larization technique, set of debiasing constraints that prevent the use of the bias features within the proposed metric learning approach. In order to give a more in-depth explanation of the e-InfONCE failure case, employ the notion of bias-aligned and bias-conflicting samples in Nam et al. (020). In our context, a bias-aligned sample shares the same bias attribute of the anchor, while a bias-confficting sample does not. In this work, assume that the bias attributes either known priori or that they can be estimated using a bias-capturing model, such as in Hong & Yang (202I).
Characterization of bias We denote bias-aligned samples with xib and bias-conflicting samples with .'.6' Given an anchor x, if the bias is "strong" and easy-to-learn, a positive bias-aligned sample æ t. will probably be closer to the anchor x in the representation space than positive bias- conflicting sample (of course, the same reasoning can be applied for the negative samples). This is why even in the case in which the r-condition is satisfied and the c-SupInfoNCE is minimized, we could still be able to distinguish between bias-aligned and bias-conflicting samples. Hence, we say that there is a bias if we can identify ordering on the learned representations, such as:
d(f(x),
d(f(z). f(xt + < d(f(z), c < d(f(x),f() " -e Vi,k,t,
4.
d,
(8) This represents the worst-case scenario, where the ordering is total (i.c., Vi, k. t) Of course, there can also be cases in which the bias is not as strong, and the ordering may be partial.
FI regularization for debiasing Ideally, we would enforce the conditions d -
d
0 Vi, ks and d, d/ d.." Vi, meaning that every positive (resp. negative) bias-confticting
5

---

Published as a conference paper at ICLR 2023
sample should have the same distance from the anchor any other positive (resp. negative) bias- aligned sample. However, in practice, this condition is very strict, as it would enforce uniform distance among all positive (resp. negative) samples. A more relaxed condition would instead force the distributions of distances, {dk } and { to be similar. Here, we propose two new debiasing constraints for both positive and negative samples using either the first moment (mean) of the distributions or the first two moments (mean and variance). Using only the average of the distributions, we obtain:
Pa E
1
1
P. =0
!
Eist
1 Pa
(9)
Pc
where Pa and Pa are the number of positive bias-aligned and bias-conflicting samples, respectively
Denoting the first moments with p++6 = P. E, d E.
p+. = Ex Dx and the second mo-
ments of the distance distributions with o E - =+.))² o = Ex
|+.b-) } and making the hypothesis that the distance distributions follow normal distribution, can define a new set of debiasing constraints using, for example, the Kullback- divergence:
}) 1 + (1+.6 p 3/ )²
7
DRLlld: "HH
-) -
log
(10)
-
+.V
In practice, one could also use another distribution such as the log-normal, the Jeffreys divergence (pll() + (x(())))) simplified version, such the difference of the two statistics (e.g., (u+.6 - p+.00²2 )2 (o+b6 )²) The proposed debiasing constrains can be easily added to any contrastive loss using the method of the Lagrange multipliers, as regularization term R FairKL
(Hatt"""1la }). Thus, the final loss function that propose minimize is:
exp(s,)
f= -= Σ log exp(s - -() Exp((()
XR Fair KT.
(11)
C-SupInoNNCE
where a and are positive hyperparameters.
3.1.1 COMPARISON WITH OTHER DEBIASING METHODS
Vi, * are actually all fulfilled only when s s Vi, t * i. This means that one tries to align all positive samples, regardless of their bias b, to single point in the representation space. In other terms, at the optimal solution, one would also fulfill the following conditions:
SupCon is interesting to notice that the contcontrae conditions in Eq.
-
s S
(12) Realistically, this could lead to suboptimal solutions: argue that the optimization process would mainly focus on the easier task, namely aligning bias-aligned samples, and neglecting the bias- conflicting ones. In highly biased settings, this could lead to worse performance than e-SupInfoNCE.
s7 =
82 55 st s + b +.b'
st vi,t
More empirical results supporting this hypothesis are presented in Appendix C.2
End The constraint in Eq. 1is very similar what was recently proposed in Tartagllone et al.) (2021) with EnD. However, EnD Jacks the additional constraint on the standard deviation of the distances, which is given by Eq, 10 An intuitive difference can be found Fig. 33 and of of the Appendix. The constraints imposed by EnD (only first moments) can be fulfilled even if there is an effect of the bias features on the ordering of the positive samples. The use constraints on the second moments, as in the proposed method, can remove the effect of the bias. An analytical comparison can be found in Appendix A.3
BiasCon In Hong & Yang (021). authors propose the BiasCon loss, which is similar to SupCon but only aligns positive bias-conflicting samples. It looks for an encoder f that fulfills:
<0 Vi, (13) The problem here is that we try to separate the negative samples from only the positive bias- conflicting samples, ignoring the positive bias-aligned samples. This is probably why the authors proposed to combine this loss with a standard Cross Entropy.
s 5j <-c Vi.j and sp ++b s < 0 Vi,p p and s7 -5-- +
Thhe same reasoning be applied negative samples (omitted for brevity.)

---

Published as a conference paper at ICLR 2023
4 EXPERIMENTS
In this section, we describe the experiments we perform to validate our proposed losses. We perform two sets of experiments. First, we benchmark our framework, presented in Sec. on standard vision datasets such as: CIFAR- 10 (Krizhevsky et a). CIFAR-100 (Krizhevsky et al. b) and ImageNet- 100 (Deng et al. 2009). Then, we analyze biased settings, employing BiasedMNIST (Bahng et al.) 2020). Corrupted CIFARIO (Hendrycks & Dietterich 2019), bFFHQ (Lee al., 2021p. 9-Class ImageNet (Ilyas et al. 2019) and ImageNet-A (Hendrycks et al. (021). The code can be found at rast ve- learning
https://gt http://..tuuu.... com http//ETDOSAAB/UUI
4.1 EXPERIMENTS ON GENERIC VISION DATASETS
We conduct an empirical analysis of the e-SupCon and e-SupInfoNCE losses on standard vision datasets to evaluate the different formulations and to assess the impact of the parameter. We compare our results with baseline implementations including Cross Entropy (CE) and SupCon.
Experimental details We use the original setup from SupCon (Khosla et al. 2020), employing ResNet-50, large batch size (1024). learning rate of 0.5, a temperature of 0.1, and multiview aug- mentation, for CIFAR-10 and CIFAR- 100. Additional experimental details (including ImageNet- D and the different hyperparameters configurations are provided Sec. of the Appendix.
Table I: Comparison of e-SupInfoNCE and e-SupCon on ImageNet-100.
Results First, we compare our proposed c-SuuInfoNCE
loss with the e-SupCon loss derived in Sec. 3 As re- ported in Tab. D e-SupInfoNCE performs better than e- SupCon: conjecture that the lack of the contrastte term of Eq. 5 Ilaads to increased robustness, as it will also be shown in Sec. 4.2 For this reason, focus SupInfoNCE. Further comparison with different values can be found in Sec. C.I. showing that SupCon S SupCon I e-SupInfoNCE in terms of accuracy. Results on general computer vision datasets are presented in Tab. 2 in terms of top-1 accuracy. We report the performance for the best value of c; the complete results can be found in Sec. C.I. The results are averaged across trials for every configuration, and we also report the standard deviation. We obtain significant improvement with respect to all baselines and, most importantly, SupCon, all benchmarks: on CIFAR-10 (+0.5%), on CIFAR- 100 (+0.63%), and on ImageNet-100 (.11%)
Loss
Acc@) I
c-SupInfoNCE e-SupCon
83.3
82.83+0.11
Table 2: Accuracy on vision datasets. SimCLR and Max-Margin results from Khosla et al. Results denoted with * are (re)implemented with mixed precision due memory constraints.
2020
Dataset
Network
SimCLR
Max Max-Margin
SimCLR*
CE*
SupCon
--SupInfoNCE**
CIFAR-10
R0
93.6 70.7
92.4
91. 11.75
94.7310.18
95 1002
96.141001
CIFAR-100 100
55
70.5
68. 9412
13.43.10.5
75.41 81.99=008
76.041001
ImageNet-100
50
66. 14.008
82.1
83.3
4.2 EXPERIMENTS ON BIASED DATASETS
Next, move on analyzing how our proposed loss performs on biased learning settings. We employ five datasets, ranging from synthetic data to real facial images: Biased-MNIST, Corrupted- CIFARIO, bFFHQ, and 9-Class ImageNet along with ImageNet-A. The detailed setup and experi- mental details are provided in the appendix B
Biased-MNIST a biased version of MNIST Deng 2012). proposed in Bahng al. (2020). A
color bias is injected into the dataset, by colorizing the image background with ten predefined colors associated with the ten different digits. Given an image, the background is colored with the prede- fined color for that class with probability p. and with any one of the other colors with a probability 1 1-p. p. Higher values of p will lead to more biased data. In this work, we explore the datasets in
'Due computing resources constraints, we were not able evaluate ImageNet-1k:
7

---

Published as a conference paper at ICLR 2023
0099
=0.997
0=0.995
0=0.990
35-
86-
91.5
54-
91.0
Accuracy
25
00.5
SupCon
65
90.0
-SupCCo
80.6
+SuplrroNCE
0.0
0.1
0.25
0.5
0.0
0.1
0.25
2.5
0.0
0.1
0.25
1.0
2.5
0.0
0.1
0.25
1.0
2.5
Figure 2: Comparison of e-SupCon and e-SupInfoNCE on Biased-MNIST is noticeable that for p 0.997, e-SupInfoNCE and c-SupCon comparable, while for 0.999 the gap is signifi- cantly larger: this could be due to the additional non-contrastive condition of SupCon.
different values of p: 0.999, 0.997, 0.995 and 0.99. An unbiased test is built with p == 0.1. We compare with cross entropy baseline and with other debiasing techniques, namely EnD Tartaglione al. 202T), LNL (Nam et al. 2020) and BiasCon and BiasBal (Hong & Yang 202T).
Analysis of E-SupInfoNCE and e-SupCon: First, we perform an evaluation of the e-SupCon and c-SupInfoNCE losses alone, without our debiasing regularization term. Fig. shows the accuracy on the unbiased test set, with the different values of p. Baseline results of a cross-entropy model (CE) are reported in Tab. 3 Both losses result in higher accuracy compared to the cross entropy. formulations is also confirmed by the related 2020). Interestingly. the most biased setting (p = 0.999), we observe that -SSupInoNCCE obtains higher accuracy than e-SupCon. Our conjecture is that the non-contrastive term of SupCon in Eq. 5 (s+-s" st S Vi, t) can lead, in highly biased settings, to more biased representations as the bias-aligned samples will be especially predominant among the positives. For this reason, we focus on c-SupInfoNCE the remaining this work.
The generally higher robustness of contrastive-bass
literature (Khosla et al.,
Debiasing with FairKL: Next, apply SupInfoNCE, and compare it with the other debiasing methods. The results are shown in Tab. Our technique achieves the best results in all experiments, with high gaps in accuracy, especially in the most difficult settings (lower p). For completeness, we also evaluate the debiasing power of FairKL with different losses, i.c. CE and e-SupCon. With FairKL we obtain better results than most of the other baselines with either CE, c-SupCon or c-SupInfoNCE; the latter achieves the best performance, confirming the results observed in Sec 4.1 For this reason, in the rest of the work, we focus on c-SupInfoNCE.
regularization technique FairKL jointly with
Top-1 accuracy (%) on BiNSTT-MNIST. Reference results from Hong & Yang 2022). Re- sults denoted with are re-implemented without color-jittrrigg and bias-conflicting oversampling.
Table 3:
Method
0.999
0.997
0.995
0.99
Hong & Yana 2021
11.8=0.7
62.5+29
79.5+0.1
90.8+0.3
LNL
2019
18.2
57.2+22
72.5
86.0102
SupCon
24.36
74.35-10.09
84.1341.11
91.12:10335
SSpInffNCC
33. 33.1623.57
73.8640081
83.654.0.66
91.18=0.49
EnD
Tartaglione et al.
2021
59.5+2.3
82.70+t0.3
94.0+..6
94.8+.0.3
BiasCon+ Bons-BaaBaa
Hong & Yang 2021
30.26+11.08
82.83+4.17
88.20+2.27
95 95,04=0.86
BiasBal Hong & Yang 2021
76.8=1.6
91.2++022
93.9+001
96,3+02
BiasCon+CE Hong & Yang 2021
15.06=2.22
90.48+5.26
95.95+0.11
97.67=0.09
CE + FairKL
79.944.29
93.86+1113
94.85+0.55
95.92=0.17
e-SupCon + FairKL
89.45
95.75+0.16
96.31
96.72+0.2
<SSupInfoNCE + FairKL
1..55
96.19.1.23
97.00
97.86
Corrupted CIFAR-10 is built from the CIFAR-10 dataset, by correlating each class with certain texture (brightness, frost, etc.) following the protocol proposed in HHHedryykks & Dietterich (2019).
Similarly BinSed-MNIST,, the dataset is provided with five different levels of ratio between bias-
8

---

Published as a conference paper at ICLR 2023
conflicting and bias bias-aligned samples. The results are shown in Tab. Notably, obtain the best results in the most difficult scenario, when the amount of bias-conficcinn samples is the lowest. Again, for the other settings, we obtain comparable results with the state of the art.
bFFHQ is proposed by Lee et al. (202)) and contains facial images. They construct the dataset in such way that most of the females are young (age range 10-29), while most of the males are older (age range 40-59). The ratio between bias-conflicing and bias-aligned provided for this dataset is 0.5. The results are shown in Tab. 4 where our technique outperforms all other methods.
9-Class ImageNet and ImageNete Net-A We also test our method on the more complex and realistic 9-Class ImageNet (Iyas et al. 2019) dataset. This dataset is a subset of ImageNet, which is known to contain textural biases (Geirhos et al. 2019). It aggregates 42 of the original classes into 9 macro categories. Following Hong & Yang (2021), we train a BagNet18 (Brendel Bethge| 2019) as the bias-capturing model, which we then use to compute a bias score for the training samples, to apply within our regularization term. More details and the experimental setup can be found in the Sec. B..24] We evaluate the accuracy (UNB), computed with the texture labels assigned in |rendel & Bethge (011)). We also report accuracy results on ImageNet-A A (IN-A) dataset, which contains bias cons-coni samples (Hendrycks) jet al. (021). Results are shown in Tab, 5 On the biased test set, the results are comparable with SoftCon, while the harder sets unbiased and ImageNet-A we achieve SOTA results.
the test set (biased) along with the unbiased accuracy
Table 4: Top-1 accuracy (%) Corrupted CIFAR-10 with different corruption ratio (%) and bFFHQ. Reference results are taken from Lee et al. (221))
Corrupted CIFAR-10
bFFHQ Ratio
Ratio
Method
0.5
1.0
2.0
5.0
0.5
Vanilla Lee et al
202
23.08
25.82.0..3
30.06-0.71
39.42:1064
56.87+2.69
EnD
Tartaglione
2021
19.38
23.12
34.07=4.81
36.57+3.98
56.87+1142
HEX Wang et al.
(019a
13.8710.06
14.81
15.20=0.54
16.0440.63
52.83++0.0
Bias Bahng
22.27:1041
25.72.10.0
31.66-00.43
43.43
59.46.1064
LfF Nam et al.
2020
28.57
33.07
39.91 20.30
50.27.1.55
62,2.1.0
DFA
29.95
36.49
41.78 2.229
51.13
63.87.1.31
c-SupInfoNCE FairKL
33.33
36.53
41.45 10.42
50.73 10.90
64.8
Table 5: Top-1 accuracy (%) on 9-Class ImageNet biased and unbiased (UNB) sets, and ImageNet-
A (IN-A), Reference results from Hong & Yang 222T
Vanilla
SIN
LM
RUBi
ReBias
LfF
SoftCon
c-SupInfoNCE FairKL
Biased
94.010.1
88.4
79.2
93.910.2
94.010.2
91.2.0.1
95.3..02
95.1 10.1
UNB 92.7+02
86.6+1.0
76.6+1.
92.5+0.2
92.7+0.2
89 99.6203
94.1
94.8
IN-A
30.5+a0
24.6+24
19.0+1.
31.0+0.2
30.5
29.4 29.4
34.1=06
35.7
5 CONCLUSIONS
In this work, we propose a metric-leaming-based framework for supervised representation learn- ing. We propose a new loss, called e-SupInfoNCE, that is based on the definition of the e-margin, which is the minimal margin between positive and negative samples. By adjusting this value, we are able to find a tighter approximation of the mutual information and achieve better results compared to standard Cross Cross-Entropy and to the SupCon loss. Then, we tackle the problem of learning unbi- ased representations when the training data contains strong biases. This represents a failure case for InfoNCE-like losses. We propose FairKL, debiasing regularization term derived from our frame- work. With it, we enforce equality between the distribution of distances of bias bins-confiicting samples and bias-aligned samples. This, together with the increase of the margin, allows us reach state- of-the-an performances in the most extreme cases of biases in different datasets, comprising both synthetic data and real-world images.

---

Published as a conference paper at ICLR 2023
REFERENCES
Mohsan Alvi, Andrew Zisserman, and Christoffer Nelläker. Turning a blind eye: Explicit removal of biases and variation from deep neural network embeddings. In Proceedings of the European Conference on Computer Vision (ECCV), pp. 0-0, 2018.
Hyojin Bahng, Sanghyuk Chun, Sangdoo Yun, Jaegul Choo, and Scong Joon Oh. Learning de-biased representations with biased representations. In International Conference on Machine Learning (ICML). 2020.
Carlo Alberto Barbano, Enzo Tartaglione, and Marco Grangetto. Bridging the gap between debias- ing and privacy for deep learning. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops, pp. 3806-3815 3815, October 2021.
Alex Beutel, Jilin Chen, Tulsee Doshi, Hai Qian, Allison Woodruff, Christine Luu, Pierre Kreit- mann, Jonathan Bischof, and Ed H Chi. Putting fairnsss principles into practice: Challenges, metrics, and improvements. In Proceedings of the 2019 AAAI/ACM Conference on AI, Ethics, and Society, pp. 453 149.459,00 2019.
Wieland Brendel and Matthias Bethge. Approximating enns with bag-of-local-featune models works surprisingly well on imagenet. 7th International Conference on Learning Representa- tions, ICLR 2019, 2019. doi: 10448550arxiv.1144..00 URL https://arxiv
abs/1904. 00760v1
Remi Cadene, Corentin Dancette, Matthieu Cord, Devi Parikh, et al. Rubi: Reducing unimodal biases for visual question answering. In Advances in neural information processing systems, pp. 841-852, 2019.
Ting Chen, Simon Korbblith, Mohammad Norouzi, and Geoffrey Hinton. A Simple Framework for Contrastive Learning of Visual Representations. In International Conference Machine Learn ing, pp. 1597-1607. PMLR, November 2020. URL http:t/p: http:://proceeeeeee wgw.oeedding....... ml .tt.gssssss...s////// press/ v1 2119/chen201 htm
ISSN: 2640-3498.
S. Chopra, R. Hadsell, and Y. LeCun. Learning a Similarity Metric Discriminatively, with Applica- tion to Face Verification. In CVPR, volume 1, pp. $36-546. IEFE, 2005. ISBN 978-0-7695-2372. 9. doi: N0.1109/CVR..2005.000
URL.
14673147
Christopher Clark, Mark Yatskar, and Luke Zettlemoyer. Don't take the easy way out: En semble based methods for avoiding known dataset biases. In Kentaro Inui, Jing Jiang, Vin- cent Ng, and Xiaojun Wan (eds.), Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Lan- guage Processing, EMNLP-IJCNLP 2019, Hong Kong, China, November 3-7, 2019, pp. 4067- 4080. Association for Computational Linguistics, 2019. doi: 10.18653/11/119-4411 URL
https://doo 11530/10011...13311111111111111. -418
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hi- erarchical image database. In 2009 IEEE conference on computer vision and pattern recognition,
pp. 248-255 Ieee, 2009.
Li Deng. The mnist database of handwritten digit images for machine learning research. JEEE Signal Processing Magazine, 2916):141-442 2012.
Gamaleldin Elsayed, Dilip Krishnan, Hossein Mobahi, Kevin Regan, and Samy Bengio. Large margin deep networks for classification. Advances in Neural Information Processing Systems, 2018-December:842 852, 2018. ISSN 10495258. doi: 104485500arxxv..100..5555 URL https://arxiv..ort abss///////// 180803..0 05598v2
Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A. Wichmann, and Wieland Brendel. Imagenet- trained CNNs are biased towards texture; increasing shape bias im- proves accuracy and robustness. In International Conference on Learning Representations, 2019.
10

---

Published as a conference paper at ICLR 2023
Florian Graf, Christoph D Hofer, Mare Niethammer, and Roland Kwitt. Dissecting supervised constrastive learning. 2021.
Abhinav Gupta, Adithyavairavan Murali, Dhiraj Prakashchand Gandhi, and Lerrel Pinto. Robot Improving generalization and reducing dataset bias. In Advances in Neural Information Processing Systems, pp. 9094-9104, 2018.
learning homes:
R. Hadsell, S. Chopra, and Y. LeCun. Dimensionality Reduction by Learning Invariant Mapping. In CVPR, volume 2, pp. 1735-1742 IEEE, 2006.
Robert M. Haralick, K. Shanmugam, and Its Hak Dinstein. Textural features for image classification. IEEE Transactions Systems, Man, and Cybernetics, SMCC33)):10-621,, 1973, doi: 10.1 109/ ISMC.1973.430931.
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for im- age recognition. Proceedings of the IEEE Computer Society Conference on Computer Vi- sion and Pattern Recognition, 2116-Decembber:70--777, 12 2015. ISSN 10636919. doi: 10.48550/arxiv.1112.333 /ttps////...aaeaaaaaoooooo/////a
Dan Hendryeks and Thomas Dietterich. Benchmarking neural network robustness to common cor- ruptions and perturbations. 7th International Conference on Learning Representations, ICLR 2019, 3 2019. doi: 11.50//aa URL httpss//arrxiv.orr//bb////// 12261v1
Dan Hendrycks, Kevin Zhao, Steven Basart, Jacob Steinhardt, and Dawn Song. Natural adversarial examples. CVPR, 2021.
Alexander Hermans, Lucas Beyer, and Bastian Leibe. In defense of the triplet loss for person re- identification. arXiv preprint arXiv: /703.07737 2017.
Youngkyu Hong and Eunho Yang. Unbiased classification through bias-contrastive and bias- balanced learning. In Thirty-Fifth Conference on Neural Information Processing Systems, 2021. URL httphtttts////peeeeeeee
www.//e//orrrre 1d=20q2ZAqxmm
Andrew llas,, Shibani Santurkar, Dimitris Tsipras, Logan Engstrom, Brandon Tran, and Aleksander Madry. Adversarial examples are not bugs, they are features. Advances in Neural Informa- fion Processing Systems, 32, 5 2019. ISSN 10495258. doi: 10-48550/arxxv110050017.. URL
https: org/ abs 1905... 021 75v4
Prannay Khosla, Piotr Teterwak, Chen Wang, Aaron Sarna, Yonglong Tian, Phillip Isola, Aaron Maschinot, Ce Liu, and Dilip Krishnan. Supervised contrastive learning. volume 33, pp. 18661-18673. Curran Associates, Inc., 2020. URL httpss//prroeeeedgggg/ neurips. 0c//ppprr2220//11e///aaaaa 9t http:////2....bbbabaaaaaaaaaaaaa
Paper. pdf
Byungju Kim, Hyunwoo Kim, Kyungsu Kim, Sungjin Kim, and Junmo Kim. Learning not to lear:: Training deep neural networks with biased data. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2019.
Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. Cifar-10 (canadian institute for advanced re- search). a. URL/ttp:: www. cs. toronto. edu/ "kriz/ htt//iiaa F.......mlmm...mmm..............
Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. Cifar-100 (canadian institute for advanced research). URL URL http::tttw//.tt toronto wwt.ooott..euuukiiii/iaaaaaaaa html
S. S.W.-C. Lam. Texture feature extraction using gray level gradient based co-occurence matrices. In 1996 IEEE International Conference Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929), volume 1, pp. 267-271 vol.1, 1996. doi: 10.1109/ICSMC. 1996.569778.
Jungsoo Lee, Eungyeup Kim, Juyoung Lee, Jihyeon Lee, and Jaegul Choo. Learning debiased representation via disentangled feature augmentation. In Thirty-Fifth Conference Neural Information Processing Systems, 2021. URL /tttps://openeviiit www.:orumtteeeoet.c....o
=ohhJJTL.Hbb

---

Published as a conference paper at ICLR 2023
Yingwei Li, Qihang Yu, Mingxing Tan, Jieru Mei, Peng Tang, Wei Shen, Alan Yuille, and cihang xie. Shape-texture debiased neural network training. In International Conference on Learning Representations, 2021. URL
Junhyun Nam, Hyuntak Cha, Sungsoo Ahn, Jaeho Lee, and Jinwoo Shin. Learning from failure: Training debiased classifier from biased classifier. In Advances in Neural Information Processing Systems, 2020.
Aaron den Oord, Yazhe Li, and Oriol Vinyals. Representation Learning with Contrastive Pre- dictive Coding, arXiv: 1807.0070030 000.003448/0 fcs, stat], January 2019. URL 1807. 03748
arXiv: 1807.03748.
Ben Poole, Sherjil Ozair, Aaron van den Oord, Alexander A. Alemi, and George Tucker. On Varia- tional Bounds of Mutual Information. In ICMI., 2019.
Shiori Sagawa, Pang Wei Koh, Tatsunori Hashimoto, and Percy Liang. Distributionally robust neural networks. In International Conference Learning Representations, 2019.
Prasanna Sattigeri, Samuel C Hoffman, Vijil Chenthamarakshan, and Kush R Varshney. Fairness gan. arXiv preprint arXiv:1805.099 0090100000000,,...00 2018.
Florian Schroff, Dmitry Kalenichenko, and James Philbin. FaceNet: A Unified Embedding for Face 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 815-823, June 2015. doi: 10.1 101///CCR.201..22266666 URL
Recognition and Clustering.
Noggabs/15000 1503.. 03832 arXiv: 1503.03832.
Kihyuk Sohn. Improved Deep Metric Learning with Multi-class N-pair Loss Ob- jective. In Advances in Neural Information Processing Systems, volume 29, Cur- ran Associates, Inc., 2016. URL https://papers nips. cc cct/papper/211//aas. .ttll
Congzheng Song, Thomas Ristenpart, and Vitaly Shmatikov. Machine learning models that re- member too much. In Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, pp. 587-601. ACM, 2017.
Enzo Tartaglione, Carlo Alberto Barbano, and Marco Grangetto. End: Entangling and disentan- gling deep representations for bias correction. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition (CVPR), pp. 13508-13517, June 2021.
Tatiana Tommasi, Novi Patricia, Barbara Caputo, and Tinne Tuytelaars. A deeper look at dataset bias. In Domain adaptation computer vision applications, pp. 37-55. Springer, 2017.
Antonio Torralba, Alexei A Efros, et al. Unbiased look at dataset bias. In CVPR, pp. 7. Citeseer, 2011.
Haohan Wang, Zexue He, Zachary L. Lipton, and Eric P. Xing. Learning robust representations by projecting superficial statistics out. In International Conference on Learning Representations, 2019a.
wet.eeiwwwwweeeeeeeeeeee....eeee / hwtp://ntt//etteeeeeeee /tt////ouumn.xx---10..---
Jiang Wang. Yang song, Thomas Leung. Chuck Rosenberg, Jinbin Wang, James Philbin, Bo Chen, and Ying Wu. Learning Fine-grained Image Similarity with Deep Ranking. In CVPR, 2014.
Tianlu Wang, Jieyu Zhao, Mark Yatskar, Kai-Wei Chang, and Vicente Ordonez. Balanced datasets enough: Estimating and mitigating gender bias in deep image representations, In Interna- tional Conference on Computer Vision (ICCV), October 2019b.
Xinshao Wang. Yang Hua, Elyor Kodirov, and Neil M. Robertson. Ranked List Loss for Deep Metric Learning. In CVPR, 2019c.
Zeyu Wang, Klint Qinami, loannis Karakozis, Kyle Genova, Prem Nair. Kenji Hata, and Olga Rus- sakovsky. Towards fairesss in visual recognition: Effective strategies for bias mitigation. In IEFF/CVF Conference Computer Vision and Pattern Recognition (CVPR), 2020.
12

---

Published as a conference paper at ICLR 2023
Kilian Q Weinberger, John Blitzer, and Lawrence Saul. Distance Metric Learning for Large Margin Nearest Neighbor Classification. In Advances in Neural Information Processing Systems, vol- ume 18. MIT Press, 2006. URL https: httptp::/ppocceeingg..... www.inng.....rrr... wwwp:rrippp..ppppp//0/0000 hash/a7f592ce 8b 13 a 696 6 7 9061 7db5681b wbw.t.batt...................... (ttstraatttttl
Qizhe Xie, Zihang Dai, Yulun Du, E. Hovy, and Graham Neubig. Controllable invariance through adversarial feature learning. In NIPS, 2017.
Depeng Xu, Shuhan Yuan, Lu Zhang, and Xintao Wu. Fairgan: Fairness-aware generative adver- sarial networks. In 2018 IEEE International Conference on Big Data (Big Data), pp. 570-575. IEEE, 2018.
Baosheng Yu and Dacheng Tao. Deep Metric Learning With Tuplet Margin Loss. In JEEE ICCV, pp. 6499-6498, 2019.
13

---

Published as a conference paper at ICLR 2023
A THEORETICAL RESULTS
A.1 COMPLETE DERIVATIONS FOR SECTION
In this section, present the complete analytical derivation for the equations found in Sec. All of the presented derivations are based on the smooth max approximation with the LogSumEXp (LSE) operator:
m2 ..., x3) xe log Σ exp(x;))
(14)
A.1.1 COMPUTATIONS OF G-INFONCE
We consider Eq. and we obtain:
exp(x*)
arg min max(-e, 137 st s*} x arg min
log
(15)
exp(s* - + E3 exp(s7)
e-InfoNCE
Starting from left-hand side, we have:
max(-c, 187 -s +)=i.....)) = log
exp(-c) + Expp(s st)
log
exp(-c) exxp--st> Σ exp(s5)
log
exp(-s-) [exp(st -e) Σ exp(s5)
(16)
=logexp(-st) + log exp(st -))+ Σ exp($5)
exp(st)
log exp(st -)) E, exp(s;)
c-InfoNCE
A.1.2 MULTIPLE POSITIVE EXTENSION
Extending Eq. 2 to multiple positives be done in different ways. Here, list four possible choices. Empiriclll, we found that solution c) gave the best results and is the most convenient to implement for efficiency reasons.
14

---

Published as a conference paper at ICLR 2023
exp(E, 855)
a) max( - (0j - -st i=....))) = log
exp 87 - (c) + (2, exp(s 5f )) exp(E 8
j=1..,
expl) E 8t))
6) Σ max -E, 18j of )i=l....)) = Σ log
exp(E, 17 - exp(s) (3 ) exp (0 80
explst)
max( -c, 18j of }== Σ log
exp(xt - e) + E exp()7)
exp(s*)
-- log max G,g - - -- -
exp(st E) + exp(s3]
(17)
A.1.3 COMPUTATIONS OF C-SUPINFONCE
The computations very similar to Eq. 16
We obtain:
arg min Σ max(-cx (-e, [s, -s, }J=L...N) arg min
Σ log exp(-e) exp(s] 87)
Eexpps
(18)
Starting from the left-hand side, we have:
Σ (mxx--e,1 15 - -8, b so Σ log exp(-c) + Σ exp(s -st) st))
Σ log exp( E, exp(s;) )
exp(st)
(19)
(exp(st - 6) =)E,, exp(ss) exp(stt)
Σ log
exp(s!)
Σ log
exp(st - -5 exp(x7)
C-SupInoNCCE
A.1.4 COMPUTATIONS OF -SPPCON 5
We extend Eq. by adding the non contrastive conditions:
$j -s st < - Vi,j and sf - st 50 vi,
(20)
and we show
exp(st)
P Σ max(O, (0j -87
-8t++800 +ebss (st - -otte)) - Σ log
Σ, exp(s - E) + E, exp
SupConn
(21)
15

---

Published as a conference paper at ICLR 2023
Starting from the left-hand side, have:
1 P Σ max(0, 18j - -It N:1s - s, -5
1 Σ log 1+ Σ exp(s} -s + + Σ exp(=5 - 55))
tesi) 2 p
log 1+ exp((57
Eljt exp(st) exp(s7) )
1
+
p
exp(s) -e)
exp(s, -e) + E, exp(s,) Eiye exp(s: -c)
P Σ log
exp(s: -c)
exp(s, c)
p Σ log
Σ, exp(s -c) + E, exp(s7)
cxp(s.)
E Σ log
Ex -() + Eg exp(85)
E-SupCon
(22)
A.1.5 COMPUTATIONS OF Coup 7
Here we show that:
exp(s²)
max(s7) < max(s+) = - -log
Σ
(23)
E, exp(s)) (st) E, exp(s,) })
Starting from the left-hand side, and given that:
max($7) max(s+)) z log( Σ cxp(s))) - -log( Σ exp(s:) )) <0
have:
16

---

Published as a conference paper at ICLR 2023
log( Σ exp(s7)) - log Σ exp( sono(st)))
max 0, 1og( Σ exp($7)) - -log( E exp(st))
~ log
1 + exp
Σ; exp(8)
log
1 ex log
Σ, exp(s
E, exp(s;)) )) Σ, exp(s:))
log
1+
Σ exp(s:) + E, exp(s) E; exp(xx)
log
exp(st)
- loo
Σ
Ee explxt) Eg exp(s,
(24)
A.1.6 COMPUTATIONS OF T7
T7-A
(csp(-e)+
arg min mim max(-e, - 8 p).....)) z arg min log eep(-cc+ + ΣΣ exp(s] - -s)) (25)
j=l...,
We have:
P.
exp((3))
)) =log
exp(-
E, exp(s7)
log eep((cc+ Σ
Σ
=
exp(s:))
P
cxp(s:))
P
exp(s; c) + P(E, exp(s)))
)) log Σ
eexp(st - c)) + E, exp(s,
= log
P(exp(st)))
exp(x+)
Σ p exp(s, -E) exp(s: )) + (E3 exp(s) (T exp(s:))
log
11. exp(x:))
[I, + E, exp(x)))) () Mags exp(st))
log
II. exp(s;t)
expl Σ; x5
= log explE, s/ cc) (E, exp(s, ) exp((1ee 8t
(26)
A.2 BOUNDNESS OF THE c-MARGIN
In this section, we give insights on how an optimal value of can be estimated. First of all, it is easy show that is bounded and cannot grow infinity. Given that [][(2)] then
17

---

Published as a conference paper at ICLR 2023
d=1
(a)
(b)
Figure 3: When considering only Eq. a-left (average of distances) or Eq. Ph-right (average of similarities), that when using EnD Tartaglione al. (202T), we may obtain suboptimal config- uration such (a), where anchor based on the bias features. We can see that the conditions in Eq. 9 are fulfilled, namely the average of the distances of bias-aligned and bias-conflicting samples from the anchor (J+.,6 = 1,4 = 2). This is only partially mitigated when using a margin é > 0 (b). However, the standard deviations of the distances of bias-aligned and bias-conflicting samples in (a) and (b) different (a+.6 = O, while d+.6 1). This can be computed using the distances d reported in the figure. If also consider the conditions the standard deviations of the distances, as proposed in FairKL (Eq. IOP, the ordering is removed and thus also the effect of the bias (c). In (c), we show the case in which both mean and standard deviation of the distributions match (in simplified case with o=0). A simulated example is shown in Fig.
still (partially) order the distances of positive samples from the
the same
max 2. This is the case in which the two samples are aligned opposite poles of the hypersphere. We can conclude that, in general, e will be less than 2. If we also take into account the temperature т, when e < 2/T. This always true, however, stricter upper bound can found we consider the geometric properties of the latent space. For example, Graf et al. (2021) show that when the SupCon loss converges to its minimum value, then the representations of the different regular simplex. This property could be used to compute precise upper
classes are aligned bound of the margin, depending on the number of classes the dataset. We leave further analysis on this matter future work.
A.3 THEORETICAL COMPARISON WITH END
Here, we present more detailed theoretical analysis of EnD (Tartaglione et al. that the EnD regularization term can be equivalent to the condition Eq.
2021). and we show
18
1
b)
18g
Σ 18 1
(27)
P
Pa
N.
N₂
which can be turned into a minimization term R, using the method of Lagrange multipliers:
R ー
Σ
+ 88
1 Pa i
Σ $7 s1
A
18
Σ
(28)
P.
No
No
Now, if we assume \ι A2 = 1, we can re-arrange the terms, obtaining:
R =
P
N
59 -bb
P
k
+
N
1
|
(29)
k
R
RI
18

---

Published as a conference paper at ICLR 2023
aligned conflicting
Figure 4: Toy example with simulated data better explain the suboptimal solution of Fig. We make the hypothesis that the distributions of the distances do follow a Gaussian distribution. In blue and in orange are shown bias-aligned and the bias-conflicting samples respectively. The green sample represents the anchor. On the left, data points are sampled from two normal distributions with the same mean but different std. We can see that the two distributions do not match. This shows that, even if the first order constraints of EnD the bias. On the contrary, on the right, the two distributions have almost the same statistics (both average and std) and the KL divergence is almost O. In that case, the bias effect is basically removed.
fulfilled, there might still be effect of
The two terms obtain are equivalent to the disentangling term R- and the entangling term Rll of EnD: R-L tries decorrelate all of the samples which share the same bias attribute, while the Rll tries to maximize the correlation of samples which belong to the same class but have different bias attributes. However, some practical differences between the two formulation remain in how the different terms are weighted: for Eq. 9 we would have:
R = A1(14.0 -4.00 + de(m- --
(30)
while for EnD would have:
R = 11 p)) + d2(M+. W)
(31)
B EXPERIMENTAL SETUP
All of our experiments were run using PyTorch 1.10.0. We used a cluster with 4 NVIDIA V100 GPUs and cluster of 8 NVIDIA A40 GPUs. For consistency, when training with constrastive losses we use a temperature value = 0.1 across all of our experiments.
B. GENERIC VISION DATASETS
B.1.1 CIFAR-10 10 AND CIFAR-100
We use the original setup from SupCon (Khosla et al. (020), employing a ResNet-50, large batch size (1024), learning rate of 0.5, temperature of 0.1 and multiview augmentation, for CIFAR-10 and CIFAR-100, We use SGD as optimizer with momentum 0.9, and train for 1000 epochs. Learning rate is decayed with cosine policy with warmup from 0.01, with 10 warmup epochs.
1.1 IMAGENET-100
For ImageNet- 100 we employ the ResNet50 architectures (He et al., 2015). We use SGD as opti- mizer with weight decay of 10-1 and momentum of 0.9, with an initial learning rate of 0.1. We
19

---

Published as a conference paper at ICLR 2023
train for 100 epochs with batch size of 512, and we decay the learning by factor of 0.1 every 30 epochs.
B.2 BIASED DATASETS
When employing debiasing term, find that scaling the e-SupInfoNCE loss by small factor (< 1) and using À closer to I, is stabler then using values of À >> (as done in Tartaglione et al. do not make of the projection head used in Khosla et al. (2020); Chen et al. (2020). For this reason, we also avoid the aggressive augmentation usually employed by contrastive methods (more on this Sec. C.3). Furthermore, as also done by Hong & Yangl (022), we also experimented with small contribution of the cross entropy loss for training the model end-to-end; however, we did not find any benefit in doing so, compared to training linear classifier separately.
202T and tends produce better results. For biased datasets,
B.2.1 BIASED-MNIST
We emply the network architecture SimpleConvNer proposed by |Bahng et al. (2020), consisting of four convolutional layers with 7 kernels. We the Adam optimizer with learning rate of 0.001, a weight decay of 10-5 and batch size of 256. We decay the learning rate by a factor of 0.1 1/3 and 2/3 of the epochs (26 and 53). We train for 80 epochs.
Hyperparameters configuration The hyperparameters for Tab. B are reported in Tab. 6
Table 6: Biased-MNIST hyperparameters of Tab.
Corr (p)
0.999
0.997
0.995
0.990
0.03
0.03
0.03
0.03
c-SupCon
0.75
0.5
0.5
0.5
0.25
0
0.5
0.03
0.03
0.03
0.03
S-SuunffoCCE
X
0.75
0.75
0.75
0.5
0.5
0.5
0.5
0.5
B.2.2 CORRUPTED CIFAR-10
For this dataset we employ the ResNet-18 architecture. We use the Adam optimizer, with initial learning rate of 0.001, a weight decay of 0.0001. The other Adam parameters are the pytorch default ones (31 0.9, B2 0.999, 10- We train for 200 epochs with batch size of 256. We decay the learning rate using a cosine annealing policy.
Hyperparameters configuration: Table 7 shows the hyperparameters for the results reported in Tab. of the main paper.
Table 7: Corrupted CIFAR-10 hyperparameters
Ratio (%)
0.5
1.0
2.0
5.0
0.1
0.1
0.1
0.1
X
1.0
1.0
1.0
0.1
0.25
0.5
0.25
B.2.3 BFFHQ
Following Lee et al. (202T) we use the ResNet- 18 architecture. We use the Adam optimizer, with an initial learning rate of 0.0001, and train for 100 epochs. For this experiment, 0.1,
20

---

Published as a conference paper at ICLR 2023
0.25 and À 1.5. Differently from Lee et al. (2021) as contrastive losses benefit more from larger batch sizes (Chen et al.) 2020; Khosla et al. 2020 Additionally, also use weight decay of 10 rather than O. These changes do not provide advantages to the debiasing task: we obtain an accuracy of 54.8% without FairKI,, which is line with the 56.87% 87% reported for the vanilla model.
batch size of 256 (vs 64)
B.2.4 9-CLASS IMAGENET AND IMAGENET-A
Our proposed method can also be applied in cases in which prior label about the bias attributes given, with only slight change formulation. For example, for ImageNet. Similarly to other works (Nam et al. 2020 Hong & Yang 2021) we exploit a bias-capturing model for this purpose.
FairKL with capturrg model To use continuous score, rather than discrete bias label, we compute the similarity of the bias features b, = s(g(z), )), where g(.) is the bias-capturing BagNet18 model. The bias similarity b, is used to obtain weighted sample similarity: s = s b for bias-aligned samples, and 8.--8/ 8 - b,t for bias-conflicting. By doing so, for example, the terms p+.b //2 Σ, di and μ4.6' Pe Σx di" become u+.6 N Σ, di b and u4.0
N D, b; ) where N is the batch size.
1
Setup We pretrain the capturan model BagNet18 (Brendel Bethge, 2019) for 120 epochs. For the main model R8 we use the Adam optimizer, with learning rate 0.001, B 0.9 and
82 = 0.999, weight decay 0.0001 and a cosine decay of the learning rate. We use a batch size of 256 and train for 200 epochs. We employ augmentation: random resized crop, random flip, and, as done in Hong & Yang (202I) random color jitter and random gray scale (p 0.2). We use 0,5 and À= I. Given the higher complexity of this dataset, we employ 0.5.
C ADDITIONAL EXPERIMENTS
In this section, we present some additional experiments we conducted, for more in depth analysis of our proposed framework.
C.I COMPLETE RESULTS FOR COMMON VISION DATASETS
In Table 8 report the results CIFAR-I0. CIFAR- 100 and ImageNet-100 for different values of e. In Table 9 the full comparison between e-SupCon and e-SupInioNCE on ImageNet-100 is presented. Our proposed c-SupInfoNCE outperforms SupCon in all datasets for all the values, reaching the best results. Furthermore, on ImageNet- 100, we observe that the lowest accuracy obtained by e-SupInfoNCE (83.02%) still higher than the best accuracy obtained by e-SupCon (82.83%) on the same dataset, even though e-SupCon is always higher than SupCon. In terms of accuracy, the results in Tab. show that SupCon S SupCon
SupInfoNCC
Table 8: Complete results for common vision datasets, for different values of c, in terms of top-1 accuracy (%). With every value of e we obtain better results than SupCon (and CE) on the same dataset.
Dataset
CE
SupCon
e-SupInfoNCE = 0.25
= 0.1
= 0.5
CIFAR-10
94.73
95.6440.02
95.93+1002
96.14
95.95-0.12
CIFAR-100
73.43
75.41 19
75.85+0007
76.04+0.01
75.99=006
ImageNet-1000
82. 1 10.59
81.991...0
83.25
83.02...41
83.3
C.2 ANALYSIS OF -SUPCONN FOR DEBIASING
We perform more in-depth analysis the debiasing capabilities of c-SupInfoNCE and e-SupCon. In Sec. 4,2 of the main text, we hypothesize that the non-constrastive condition of Eq. 20
Vi,
21

---

Published as a conference paper at ICLR 2023
Table Complete comparison e-SupInfoNCE and e-SupCon on ImageNet-100) in terms of top-1 accuracy (%). The results of c-SupInfoNCE are higher than any results of c-SupCon.
Loss
= 0.1
= 0.25
0.5
C-SupInfoNCE
83.25
83.02.0.1
83.3
c-SupCon 82.83
82.54
82.77
might actually be the reason for the loss of accuracy in e-SupCon when compared to e-InfoNCE, as shown on the analysis on Biased-MNIST in Fig. 2 of the main text.
In this section, we provide more empirical insights supporting this hypothesis. We plot the similarity
of bias-aligned samples (s and bias-conflicting samples (st..6) during training, to understand how they are affected. Fig. 5 shows the bivariate histogram of the similarities obtained with the two loss functions, at different training epochs and values of c, Biased- MNISS, with training of 0.999. Focusing on the bias-aligned samples (first two columns), we observe that, in both cases, most values are close to 1. However, while this is true for most of the shown histograms, the presence of the non-contrastive condition of Eq, 20 produces a much tighter distribution for e-SupCon, when compared to e-SupInfoNCE. In fact, with e-SuuInfoNCE
obtain significantly more bias- bias-aligned samples with a similarity smaller than 1. This is especially evident we focus on the last training epochs.
More interestingly, if we focus on the bias-conflicting similarities (last two columns), we can also notice how, average, the distribution of similarities of bias-conflicting samples for c-SupCon tends to be more concentrated around the value O. This means that plas-conflicting samples have dissimilar representations even if they are both positives and should be mapped to the same point in the representation space. The effect of the bias is thus still quite important and it has not been discarded. On the other hand, with e-SupInfoNCE, we obtain a much more spread distribution, especially as the number of training epochs increases. This means that a higher number of bias- conflicting samples have greater similarity (in the representation space), leading to more robust representations.
Clearly, c-SupCon focuses more on bias-aligned samples as most of them have a similarity close to 1, whereas most of the bias-conflicting samples have a similarity close to O. With our proposed loss e-SupInfoNCE, this behavior is less pronounced, as the lack of the non-contrastive condition leads the model to be less focused on bias-aligned samples. This could explain why e-SupInfoNCE can perform better than e-SupCon in highly biased settings.
C.3 TRAINING WITH A PROJECTION HEAD
In Tab. 10 we show the results on Corrupted CIFAR-10 with and without using projection head. When employing a projection head, the loss term and the regularization are applied on the projected and original space respectively, and the final classification is performed in the original latent space before the projection head. We conjecture that the loss in accuracy is likely due i.) to the absence of the aggressive augmentation typically used for generating multiviews in contrastive setups, which are probably attenuated by the projection head ii.) minimizing e-SupInfoNCE and the FairKI. term on the same latent space rather than two different ones, could be more beneficial for the optimization process.
Table 10: Accuracy on Corrupted CIFAR-10 with and without projection head
Ratio (%)
0.5
1.0
2.0
5.0
With Head
30.85
37.95 32.75
45.67
Without Head
33.33
36.53 10.38
41.45 10.42
50.73
22

---

Published as a conference paper at ICLR 2023
e-SupCon
e-SupIntoNCE
e-SupCon
c-SullfoNCC
1.0
10
Similanty
0.5
Similariyy
0.0
25
75
25
30
75
Epach
Epoch
Epoch
Epoch
e-SupCon
e-SupInfoNCC
e-SuCoo
e-SupIffoNCE
1.0
0.1
Similarity
0.5
Similarity
0.3
0.00
0.0
-0.3
75
25
10
75
-1.0
Epoch
Epoch
Epach
Epach
<-SupCon
<SSulInoNNCE
e-SupCon
cSSulIfoNCE
0.255
1.0
Simiarity
Similarity
0.0
-0.3
25
25
Epoch
Epoch
Epoch
Epoch
bias-aligned
bins-conflicting
Figure 5: (first and second columns) Distribution of positive bias-aligned similarities t.b, Here c-SupCon tends to produce much tighter distribution, with similarities close 1; (third and fourth columns) Distribution of positive bias-conflicting similarities st.6' Here e-SupInfoNCE, even marginally, is able to increase the number of similar bias-conflicting samples. e-SupCon focuses more on bias-aligned samples, resulting in more biased representations. With e-SupInfoNCE, this behavior is less pronounced, the lack of the non-contrastive condition leads to be less focused on bias-aligned samples and more focused on the cla-coonfiiting ones. We hypothesize that this the reason c-SupInfoNCE. appears obtain better results than c-SupCon in more biased datasets.
23

---

Published as a conference paper at ICLR 2023
C.4 ABLATION STUDY OF DEBIASING REGULARIZATION
We perform an ablation study of our debiasing regularization on Corrupted CIFAR-10 and on bFFHQ. We test variants of the regularization term:
1. Only with the conditions on the mean of the representations μ4+ and μ.- (Eq. equation 9 and equation 9)b), similarly to (Tartaglione et al. 2021), but with the differences in formu- lations of Sec. A.3
2. Full FairKI. debiasing term of Eq. 9 and Eq. d
The results are shown Tab. I1 As can be easily observed, employing the full regularization
constraint consistently results in better accuracy.
Table 11: Ablation study of R Fairkl, on Corrupted CIFAR- 10 and bFFHQ
Corrupted CIFAR-10
bFFHQ Ratio (%)
Ratio (%)
0.5
1.0
2.0
5.0
0.5
FairKL (mean)
12.37
35.6541075
39.94.1050
50.25
60.55
FairKL (full)
33.33
36.53
41.45
50.73
63.70
C.5 IMPORTANCE OF THE REGULARIZZTION WEIGHT
We conduct an analysis on the importance and stability the the weights a and À of Eq. 11 We perform multiple experiments selecting E f0.01, 0.1, 1.0). For simplicity, the accuracy scored on the Biased-MNIST test. The results are show in Tab. 12 There seems to be correlation between the value of and the strength of the bias: for stronger biases it is better to give more importance to the regularization term rather than the target loss function. Additionaly, we also find that a depends on the complexity of the dataset: for example on Corrupted-CIFARI and bFFHQ we use = 0.1, for 9-Class ImageNet we use a 0.5.
fix
O, and report
Table 12: Importance of the weights and X.
= 0.5
=
Comr.) a
0.01
0.1
1.0
0.01
0.1
1.0
0.999
89.55-1.43
31.63++2.00
38.38+1.26
84.98
43.21
31.84
0.997
94.08
82.1 12244
78.91
91.08
84.98
79.03
0.995
92.42.13.76
90.6043.5
86.6342.26
88.394..00
93.97-11.3
88,27
0.99
95.00=0.21
96.60+t.17
93.75+0025
90.72+0.51
97.13
94.74+0.40
24


Reviews:
[{"review_id": "ehQfQeGxkZu", "reviewer": "Reviewer_pTc7", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The authors use a common approximation of the max operator to simply motivate and formulate eps-SupInfoNCE, their proposed loss for contrastive learning, and FairKL, their proposed regularization term for mitigating effects of bias in datasets. Also using this approximation, they formulate prior work such as InfoNCE, InfoL1O, and SupCon, and highlight some of their deficiencies. They demonstrate eps-SupInfoNCE and FairKL across a variety of common vision datasets and their biased variants, showing that eps-SupInfoNCE performs favorably to alternatives on CIFAR-10, CIFAR-100, and a small variant of ImageNet, and showing that the combination of eps-SupInfoNCE + FairKL performs favorably on Biased-MNIST, Corrupted CIFAR-10, bFFHQ (faces of younger females and older males), and small variants of ImageNet with known biases.", "summary_of_the_review": "The 'Summary of the Paper' and 'Strengths and Weaknesses' sections speak for themselves: overall, the simple derivation of related work + new methods is easy to follow and leads to convincing results across various datasets.", "strength_and_weaknesses": "The paper is very clear, especially when taking into account the derivations in the appendix that would usually be glossed over. I liked that the authors include both a thorough related work section *and* section 3.1.1, which makes direct comparisons with closely related work after introducing the method (for a more in-depth understanding). In addition to formulating eps-SupInfoNCE and eps-SupCon, the discussion around prior work, particularly Equations 6 and 7, is interesting and insightful. Calling Equation 2 a 'theoretical framework' might be a bit much, but still it is insightful, both in the context of prior work and the proposed methods. The experiments do admittedly lie on the toy-ish side, but are for the most part convincing.\n\nI see only one potential weakness: it appears to me that FairKL is applicable to many constrastive learning methods; is this correct or incorrect? If correct, then there is an experimental gap, in that, with respect to handling bias, the comparison is always between eps-SupInfoNCE + FairKL vs. other methods. Why are they intertwined in the experiments? To evaluate FairKL, wouldn't it make sense to include many experiments without eps-SupInfoNCE?", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "WUrnnZJjCZ4", "reviewer": "Reviewer_BLxm", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper tackles the problem of learning representation robust to biased data, i.e. data containing easy-to-learn but unrelated features. It first derives \\epsilon-SupInfoNCE, which adds control of the minimal distance between positive and negative samples to the traditional contrastive losses. Then it proposes FairKL, a regularization loss minimizing the KL divergence between the distribution of distances to bias-conflicting samples and the distribution of distances to bias-aligned samples. Experiments show \\epsilon-SupInfoNCE + FairKL outperforms other debiasing methods on several biased datasets.", "summary_of_the_review": "This paper investigates an interesting problem - how to learn a good representation that is robust to data bias. It proposes a generalized version of contrastive losses and a regularization loss to address the problem. However, it lacks important experiments and the writing should be improved. Therefore, it still needs a lot of work before it is ready to be published. ", "strength_and_weaknesses": "Pros:\n- The topic of this paper is interesting. It discusses whether traditional contrastive losses can deal with biased data, and how to learn a good representation that is robust to biased data. \n- This paper proposed a natural and reasonable generalization of the traditional contrastive losses which has more control of the minimal distance between positive and negative samples. Figure 1 presents a nice illustration of how it can mitigate the biased issue.\n- The proposed FairKL regularization addresses the biased issue directly, and shows better performance compared with existing methods on biased datasets, including synthesized and real-world datasets.\n\nCons:\n- The related works section is very hard to follow. It just lists a lot of literature on debiasing without organization. It does not discuss how those works are related or different from this paper either. The literature of contrastive learning is totally missing.\n- The empirical validation of \\epsilon-SupInfoNCE is not convincing. The SimCLR and Max-Margin results in Table 2 are collected from [Khosla et al. (2020)]. However, the results of CE and SupCon are re-implemented and are worse than that reported in [Khosla et al. (2020)]. (The results of SupCon reported in the original paper is 76.5 for CIFAR-100, which is even slightly better than the proposed \\epsilon-SupInfoNCE.) How could those four columns be put together in a table? Also, the results on ImageNet are not included - the performance of the proposed method on large-scale datasets has not been validated.\n- The experiments on biased datasets are not enough. It does not investigate how the traditional contrastive losses(e.g. SupCon) performs empirically and how much the proposed method can outperform them on biased datasets, as it discusses analytically in the method section. Moreover, it is not clear how much the improvement on the biased datasets comes from \\epsilon-SupInfoNCE and how much comes from FairKL. How well will \\epsilon-SupInfoNCE perform without FairKL? How much benefit will FairKL add to methods other than \\epsilon-SupInfoNCE? \n\nQuestion:\n- For the FairKL, it is reasonable that considering the standard deviation in addition to the mean value of the distances is helpful. However, I do not think the argument of the standard deviation in 3.1.1 (the discussion for EnD)  is correct. The centroid of samples is not the mean of distances, right? In Figure 1(b), even if the green samples and other-color samples have the same centroid, their average distance to the anchor is not the same - the average distance of the green ones is smaller.  Also, why can we assume the distance distribution follows a normal distribution? \n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "A_rKXBPZM5F", "reviewer": "Reviewer_DYGt", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper tackles the problem of learning representations that are robust to biases in the data. The authors first clarify why existing contrastive losses fail to deal with biased data, and further derive a novel formulation of supervised contrastive loss to provide more accurate control of minimal distance between positive and negative samples. Moreover,the authors propose a new debiasing regularization loss to deal with extremely biased data. \n\nTo evaluation the proposed losses, the authors first provide a benchmark on standard classification datasets CIFAR10, CIFAR100, ImageNet to evaluate different formulations of the proposed loss terms. The authors further conduct experiments on biased datasets Biased-MNIST, Corrupted CIFAR-10, bFFHQ and 9-Class ImageNet and ImageNet-A, which contains color biases or texture biases in the data. The experiments show better results in comparison to other debiasing techniques  ", "summary_of_the_review": "The paper studies an important problem and proposes reformulations upon the contrastive loss. Experiments are conducted to verify the effectiveness of the proposed method. However, the writing about proposed method is suggested to be improved with better clarity as mentioned above in the section of Strength And Weaknesses.", "strength_and_weaknesses": "+ The paper studies an important problem and proposes reformulations upon the contrastive loss to address the biases in the data.\n\n- The motivation that drive the model formulation is not clear. In particular, t is not very clear why contrastive losses should be used as for the formulations to address the biases in the data. Why can't one also consider other metric loss such as the triplet loss, or consider classification loss that also allow to introduce margin or temperature to address the biases in the data? \n\n- The proposed method lacks intuitive explanations about why the reformulations of contrastive loss can properly address the biases in the data. From the formulations, it turns out the authors introduce an additional margin parameter to ensure the relevant distance of a positive wrt an anchor and the nearest negative. The formulations are quite similar to the idea of triplet loss  [a,b], but it is unclear why and how it resolve biases in data. \n\n- What kinds of biases do the paper aims to tackle? It seems that the bias in this paper is quite related to domain drift across datasets. How does the proposed technique compared to ones that address the domain drift in data? \n\n- There is an existing formulation of supervised contrastive loss proposed in [c]. What is the difference between the SupInfoNCE proposed in this paper and the one proposed in [c]? \n\n[a] FaceNet: A Unified Embedding for Face Recognition and Clustering. CVPR 2015\n[b] In Defense of the Triplet Loss for Person Re-Identification. arXiv2017\n[c] Supervised Contrastive Learning. NeuRIPS 2020\n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster