Avoiding spurious correlations via logit correction
Authors: Sheng Liu
Xu Zhang
Nitesh Sekhar
Yue Wu
Prateek Singhal
Carlos Fernandez-Granda
Venue: ICLR 2023 poster (2023)
Keywords: spurious correlation
robust learning
empirical risk minimization

Abstract: Empirical studies suggest that machine learning models trained with empirical risk minimization (ERM) often rely on attributes that may be spuriously correlated with the class labels. Such models typically lead to poor performance during inference for data lacking such correlations. In this work, we explicitly consider a situation where potential spurious correlations are present in the majority of training data. In contrast with existing approaches, which use the ERM model outputs to detect the samples without spurious correlations and either heuristically upweight or upsample those samples, we propose the logit correction (LC) loss, a simple yet effective improvement on the softmax cross-entropy loss, to correct the sample logit. We demonstrate that minimizing the LC loss is equivalent to maximizing the group-balanced accuracy, so the proposed LC could mitigate the negative impacts of spurious correlations. Our extensive experimental results further reveal that the proposed LC loss outperforms state-of-the-art solutions on multiple popular benchmarks by a large margin, an average 5.5% absolute improvement, without access to spurious attribute labels. LC is also competitive with oracle methods that make use of the attribute labels.

Published as a conference paper at ICLR 2023
AVOIDING SPURIOUS CORRELATIONS VIA LOGIT COR- RECTION
Sheng Liu If
Xu Zhang² Nitesh Sekhar
Yue Wu?
Prateek Singhal Carlos Gernandez-Granda'
'New York University, USA; shengliuunyu...
3 3Amazon Alexa AL, USA
ABSTRACT
Empirical studies suggest that machine learning models trained with empirical risk minimization (ERM) often rely on attributes that may be spuriously correlated with the class labels. Such models typically lead to poor performance during inference for data lacking such correlations. In this work, we explicitly consider a situation where potential spurious correlations are present in the majority of training data. In contrast with existing approaches, which use the ERM model outputs to detect the samples without spurious correlations and either heuristically upweight or upsample those samples, we propose the logit correction (LC) loss, simple yet effective improvement on the softmax cross-entropy loss, to correct the sample logit. We demonstrate that minimizing the LC loss is equivalent to maximizing the group-balanced accuracy, so the proposed LC could mitigate the negative impacts of spurious correlations. Our extensive experimental results further reveal that the proposed LC loss outperforms sfate-of-the-- art solutions multiple popular benchmarks by a large margin, an average 5.5% absolute improvement, without access to spurious attribute labels. LC is also competitive with oracle methods that make use of the attribute labels
INTRODUCTION
In practical applications such self-driving cars, robust machine learning model must be designed to comprehend its surroundings in rare conditions that may not have been well-represented in its training set. However, deep neural networks can be negatively affected by spurious correlations between observed features and class labels that hold for well-represented groups but not for rare groups. For example, when classifying stop signs versus other traffic signs in autonomous driving, 99% of the stop signs in the United States are red. A model trained with standard empirical risk minimization (ERM) may learn models with low average training error that rely on the spurious background attribute instead of the desired "STOP" text on the sign, resulting in high average accuracy but low worst-group accuracy (e.g., making errors on yellow color or faded stop signs). This demonstrates fundamental issue: models trained on such datasets could be systematically biased due to spurious correlations presented in their training data (Ben-Tal et al. 2013 Rosenfeld et al.. 2018 Beery et al. 2018 Zhang al. 2019). Such biases must be mitigated in many fields, including al algorithmic fairness (Du et al. 2021 machine learning in healthcare (Oakden-Rayne) et al. 2020
Liu et al. 2020b 2022a and public policy Rodolfa al. (021).
Formally, spurious correlations occur when the target label is mistakenly associated with one or more confounding factors presented in the training data. The group of samples in which the spurious correlations occur is often called the majority group since spurious correlations are expected to occur in most samples, while the minority groups contain samples whose features correlated. The performance degradations of ERM on dataset with spurious correlation (Nagarajan al. 202T Nguyen al. 202T) are caused by two main reasons: 1) the geometric skew and 2) the statistical skew. For robust classifier, the classification margin on the minority group should be much larger than that of the majority group (Nagarajan et al., (021). However, a classifier trained with ERM maximizes margins and therefore leads to equal training margins for the majority and
spuriously
Work primarily done during an internship at Amazon.
Codee is available at athttps: /tttpa://githb.. com/ cww.s/engg 1666/1C

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minority groups. This results in geometric skew. The statistical skew is caused by slow convergence of gradient descent, which may cause the network to first learn the "easy-to-leams spurious attributes instead of the true label information and rely on it until being trained for long enough (Nagarajan et al.
2021
Liu et al. 2020a 2022b).
To determine whether samples are from the majority minority groups, need know the group information during training, which is impractical. Therefore, many existing approaches consider the absence of group information and first detect the minority group (Nguyen al. 2021; Liu al. 20216 Nam et al., 2020) and then upweightuusample the samples in the minority group during training Li & Vasconcelos, 2019) Nam al. 2020; Lee al. 2021; ; Liu et al.) 2021a). While intuitive, upweighting only addresses the statistical skew (Nguyen et al. 2021). and it is often hard
to define the weighted loss with an optimal upweighting scale in practice. Following Menon et al.
(2013); Collell 2 et al. (2016) on learning from imbalanced data, we argue that the goal of training debiased model is to achieve a high average accuracy over all groups GGroup-Balance
Accuracy, GBA, defined in Sec. (3, implying that the training loss should be Fisher consistent with GBA (Menon ct al. 2013; Collell et al. 2016). In other words, the minimizer of the loss function should be the maximizer of GBA.
In this paper, we revisit the logit adjustment method (Menon et al. 2021) for long-tailed datasets, and propose new loss called logit correction (LC) to reduce the impact of spurious correlations. We show that the proposed LCC loss is able to mitigate both the statistical and the geometrical skews that cause performance degradation. More importantly, under mild conditions, its solution is Fisher consistent for maximizing GBA. In order to calculate the corrected logit, we study the spurious correlation and propose use the outputs of the ERM model estimate the group priors. To further reduce the geometrical skew, based on MixUp (Zhang et al. 2018), we propose a simple yet effective method called Group MixUp to synthesize samples from the existing ones and thus increase the number of samples in the minority groups.
The main contributions of our work include:
We propose logit correction loss mitigate spurious correlations during training. The loss ensures the Fisher consistency with GBA and alleviates statistical and geometric skews.
We propose the Group MixUp method to increase the diversity of the minority group and further reduce the geometrical skew.
The proposed method significantly improves GBA and the worst-group accuracy when the group information is unknown. With only 0.5% of the samples from the minority group, the proposed method improves the accuracy by 6.03% and 4.61% on the Colored MNIST dataset and Corrupted CIFAR- 10 dataset, respectively, over the state-of-the of-the-art.
2 RELATED WORK
Spurious correlations are ubiquitous in real-world datasets. A typical mitigating solution requires to first detect the minority groups and then design learning algorithm to improve the group-balanced accuracy and/or the worst-group accuracy. We review existing approaches based on these two steps.
Detecting Spurious Correlations. Early researches often rely on the predefined spurious correla- tions (Kim et al. 2019 Sagawa et al. 2019 Li & Vasconcelos 2019). While effective, annotating the spurious attribute for each training sample is very expensive and sometimes impractical. Solutions that do not require spurious attribute annotation have recently attracted a lot of attention. Many of the existing works (Sohoni al. 2020 Nam al.) 2020 Liu et al. [021a] Zhang al. 2022) assume that the ERM model tend to focus on spurious attribute (but may still learn the core features Kirichenko al. (2022): Wei et al. (202))) thus "hard" examples (whose predicted labels conflict with the ground-truth label) are likely to be in the minority group. (Shhoni et al.) (2020); Sco et al. (2022), on the other hand, propose to estimate the unknown group information by clustering. Our work follows the path of using the ERM model.
Mitigating Spurious Correlations. Previous works (Naaraaja et al. 202 Nguyen et al. 2021 show that the geometric skew and the statistical skew are the two main reasons hurting the performance of the conventional ERM model. Reweighting (resampling), which assigns higher weights (sampling rates) minority samples, is commonly used to remove the statistical skew (Li & Vasconcelos 2019
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Nam al. 2020: Lee et al. 2021 Liu et al. 2021a). While intuitive, reweighting has limited effects to remove the geometric skew (Nagarajan et al. 2021). Also, there are surprisingly few discussions on how to set the optimal weights. We argue that the reweighting strategy should satisfy the Fisher consistency (Menon et al. 2013), which requires that the minimizer of the reweighted loss is the maximizer of the balanced-gee group accuracy (see Sec. (.T). On the other hand, synthesizing minority samples/teatures is widely utilized in removing the geometric skew. Minderer et al. (2020); Kim al. (202I) propose directly synthesize minority samples using deep generative models. Yao et al. (2022) Han et al. (2022) synthesize samples by mixing samples across different domains. While synthesizing the raw image is intuitive, the computation complexity can be high. DFA (Lee et al.)
2021 mitigates this issue by directly augmenting the minority samples in the feature space.
DFA (Lee et al. 202T is the most related work to our approach. applies reweighting to reduce the statistical skew and feature swapping to augment the minority feature, thus removing the geometric skew. However, our approach uses logit corrected loss and is proved to be Fisher consistent with the group-balanced accuracy. The proposed legit corrected loss has a firmer statistical grounding and can reduce both the statistical skew and the geometric skew. By combining the logit correction loss and the proposed Group MixUp, our approach outperforms DFA, especially on the dataset containing very few minority samples.
3 PROBLEM FORMULATION
Let's first consider a regular multi-class classification problem. Given a set of n. training input samples X' {(x, 9:)} i 1...., n, where, IR has input dimension of d and y y {1..... with total number of L categories. Our goal is to learn function (neural network), f() X' + R to maximize the classification accuracy Px(y arg maxy'y (x)). With ERM, we typically minimize a surrogate loss, egg., softmax cross-entropy (CE(.) where,
(CE(y, log Σ Eelv(t))
[x(x).
(1)
We assume there is spurious attribute A with K different values in the dataset. Note that K and the number of classes L. may not equal. We define combination of one label and one attribute value a group (a, y) E A x y. The spurious correlation means attribute value and label y commonly appear at the same time. Different from ERM, the goal of training a model to avoid spurious correlation is to maximize the Group-Balande Balanced Accuracy (GBA):
-P (I (y= arg max for (x)) 9ES
GBA(F) = KL
(2)
V'E
Note that spurious correlation is "harmful" when it is not present during the evaluation. The spurious attribute can not be disentangled from other features if spurious correlations are present in all samples.
OUR APPROACH: LOGIT CORRECTION
Following
Nam et 2020 we adopt a two-branch network (as shown in Figure D.. The top branch
(denoted as (()) is a network trained with ERM using generalized cross-entropy (GCE) loss Zhang
& Sabuncu 2018) :
LOCE p(x)"
where p(x) represents the probability outputs (after softmax layer) of the ERM model f. q E [0. 1) a hyperparameter. Compared to the standard cross-entropy loss, the gradient of GCE loss upweights examples where f(x:) large, which intentionally biases to perform better on majority (easier) examples and poorly minority (harder) examples. The second (bottom) branch is trained to learn from the first branch. To be more specific, we use the probability output of the first branch to correct the logit output of the second branch. We further adopt Group Mix to increase the number of unique examples in minority groups. The details of the method are demonstrated in the following sections.
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Land
Sottrax
LGCF
In(-)
3428 samples
samples
Coerection
Waterbile
Rebust
LeB
semples
Figure 1: The overview of our proposed logit correction approach on the Waterbirds dataset, where the background (water/land) spuriously correlated with the foreground (waterbird/landbird) Most training samples belong to the group where the background matches the bird type (highlighted in red); While only small fraction belongs to the groups where the background mismatches the bird type (highlighted in green). To address this issue, we train both an ERM network and robust network simultancously. The ERM network is trained with a generalized cross-entropy (GCE) loss that intentionally biases it toward the majority groups. The logit correction loss corrects the logits of the robust network by a term p. which is generated by the probability predictions of the ERM network. After logit correction, the robust network is trained with the standard cross-entropy loss.
4.1 LOGIT CORRECTION AS MAXIMIZING GBA
Recall that our goal maximize GBA in Eq 2 which depends on the (unknown) underlying distribu- tion P(r, y, a). the Bayes-optimal prediction function under this setting is f* E arg max GBA().
Proposition 1. Let Ply, a) be the prior of group (y, a), and P(y, alx) is the true posterior probability of group (y, a) given x, the prediction:
P(y, alx)
Plyla, P()
arg max (x) arg max yEy
Σ
a) arg max Σ
P(y,a)
the solution to Eq. See proof in Appendix
Assume each example x can only take one spurious attribute value (e.g. waterbirds can either be on the water land, and can not be on both), that is to say, the prior probability P(a|x) is 1 when the spurious attribute ox and 0 otherwise. We have
arg max J (x) arg max P(y axx x)/P(y,,a))) yEy
Note that although ax is unknown in the dataset, can be estimated using the outputs of ERM model (see Sec.
Because we are using the second branch to estimate the posterior probability P(ylax, x), supposing the underlying class probability P(y (xx, x) x ex)(f(x) for (unknown) scorer can rewrite Eq. as
arg max (x) = arg max (xx(fxx))))))))))) ax). yEy
arg (xx(f,(x) In P(y. ox)).
wey
In other words, optimizing the GBA solution f" is equivalent to optimizing the ERM solution f minus the logarithm of the group prior In P(y, (x). In practice, we could directly bake logit correction into the softmax cross-entropy by compensating the offset. Specifically, we can use the corrected logits f(x) + In Py,a, instead of the original logits f(x) to optimize the network, where Py.,, are estimates of the group priors P(y, ax). Such that by optimizing the loss function usual, we can derive the solution for f* (Menon et al. 2021). The logits corrected softmax cross entropy function can be written as,
Σ efv (x) Py - (fo(x) + In P..o.)..
(xcly.((x)) = log
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A
A
A
e
O
q
one-to-one
many-to-one
one-to-many
many-to-many
Figure 2: Example of different situations for spurious correlation that can be considered for the colored MNIST dataset. Spurious correlations existed the majority groups: the many-to-one situation, multiple digits share the same color; for the many-to-one situation, multiple digits are colored by the same color; Conversely, in the one-to-many situation, a single digit can colored by several different colors. The many-to-man situation encompasses all of these possibilities, allowing for spurious correlations to occur in multiple directions. Note that the figure only illustrates how labels are spuriously correlated with the attributes.
We show that when P(a]x) follows one-hot categorical distribution, Eq. 7 is Fisher consistent with maximizing the GBA (Eq.2) 2). Intuitively, the more likely the combination of (y. 4x) appears in the training dataset, the less we subtract from the original logits. Meanwhile, the less likely the combination of (y, (x) appears the training dataset, the more we subtract from the original logits, resulting in less confidence in the prediction. It leads larger gradients for samples in the minority group, making the network learns more from the minority group. To this end, the logit corrected loss helps reduce the statistical skew. Moreover, Eq. 7 can be further rewritten as
LiCly, = log 1 Σ (xxx)+) (PPss) P y'
(8)
It's a pairwise margin loss (Menon et al. 2013), which introduces a desired per example margin
In (y PPy.an/Py.a into the softmax cross-entropy. A minority group example demands a larger margin since the margin is large when Py.a, is small. To this end, LC loss is able to mitigate the geometric skew resulting from maximizing margins. We also empirically compare the training margins of minority groups and majority groups in Figureffor different methods. In the next section, we will introduce, given a sample the training dataset, how to estimate ax and the group prior.
4.2 ESTIMATING THE GROUP PRIOR
In this section, we analyze different spurious correlation relations. The spurious correlation between the target label and the spurious attribute can be categorized into different types (Figure 2): 1) one-to-one, where each label only correlates with one attribute value and vice versa; 2) many-to-one. where each label correlates with one attribute value, but multiple labels can correlate with the same attribute value; 3) one-to-many, where one label correlates with multiple attribute values; and 4) many-to-many. where multiple labels and multiple attribute values can correlate with each other. In the next section, will first discuss the most common one-to-one situation and then extend it to other situations.
4.2.1 ONE-TO-ONE
One-to-one the most common situation studied in the previous works, egg. the original Colored MNIST dataset. To estimate the group prior probability P(y, a), we consider
a) / P(y, a, x)dx
P / P(y, ((xxxxx))(xxxxx NV P(r,
The last approximation is the empirical probability estimation estimate the prior, where N is the number of total samples. It's impractical to use the whole dataset to estimate the group prior after each training iteration is finished. In practice, try different estimation strategies and find out that
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using moving average of the group prior estimated within each training batch seems to produce reasonable performance (see Figure 3 We apply this method to all the experiments in the paper.
For training sample of (x,, Us, a.), since the label ys is known, have
P(y. = P(a[x), if = y/. otherwise.
(10)
Since the spurious correlation is one-on-one, the number categories and the number of different attribute values are the same. Without loss of generality, we assume that the j-th category (gls) is correlated with the j-th attribute value (a()), where [l,..., LJ and L K. L and K the number of categories and the number of different attribute values respectively.
Since the ERM network would be biased the spurious attribute instead of the target label, the prediction of the ERM network can be viewed as an estimation of P(a[x)) Formally, denote the output logits of the ERM network as f(x:), and the j-th element of f(x) is denoted as fy (x,), we have
(xp(f)(xx))
P(a ((a=aa)0 x,)
(11)
Σ exx(fx(xx))
Given Eq. 9 to Eq. 11
we can estimate the group prior P(y,a). The associated attribute value in Eq. can be estimated as 0x arg max, P(a)x).
4.2.2 MANY-TO-ONE
Under this scenario, multiple labels can be correlated with the same attribute value. Without loss of generality, we assume that y() and y22) are correlated with a(1), and yd), , >> 2 is correlated with a)i-1). We consider that the first 2 label predictions spuriously correlated with attribute value (!)), i..., fx) ((y(1), (()))),; 1,2 and other predictions similar the one-to-one situation, where (x) x P(a(i-1(xx,) > 2. Compared to the one-on-one mapping, the only difference the calculation of P(a- = a()) x;) in Eq. 11 Considering both y()) and y( contribute to (!),, we have,
P(a = a (44) ((y()), = (2)) xx) + P(y (2) = a
K
(exp(fi + (xx(f((x))) / exp(ff
(12)
The associated attribute value can then be estimated as well, iee. 0x = arg max, P(a|x).
4.2.3 ONE-TO-MANY
In this scenario, one label can be correlated with multiple attribute values. Since we don't t have the attribute label, to distinguish different attributes correlated with the same label,
follow [Seo et al. (202)) to create pseudo labels for multiple attribute values. Without loss of
generality, we assume y()) is correlated with (!!) and a? Therefore, P(a aها) x
wy exp(fi Ek exp(ff(xx))) = 1, 2, where w is the weight defined Seo et al. 2022
Eq. (6). The associated attribute value can also be estimated with the estimated posterior.
4.2.4 MANY-TO-MANY
Since this a combination of the previous cases, we can apply the solutions mentioned above together. In order to accurately calculate the prior probability P(y, a). we need to at least know how the label set y and the attribute set A are correlated. Annotating the category- relation much easier than annotating the sample-lvel attribute. In the case where even the category-level relation is not available, we show in Sec. E that directly applying the one-to-one assumption in other situations (one-to-many and many-to-one still shows reasonable performance.
4.3 GROUP MIXUP
To further mitigate the geometric skew and increase the diversity of the samples in the minority group, proposed simple group MixUp method. We also start with the one-to-one situation and other

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situations can be derived similarly. Same as Sec. 4.2.1 without loss of generality, we assume the j-th category (1(6) is correlated with the j-th attribute value (aV)). An training sample (x,, 24) is in the minority group when arg maxy' () # ys. else it is in the majority group. Given one sample X; in the minority group, we randomly select one sample x; in the majority group with the same label (yy- = Yj). instead of using the original x; in training, following the idea of MixUp (Zhang et al.) 2018), we propose to generate a new training example (X,: 1/5) as well as its correction term via the linear combination of the two examples,
(13) where À ~ U0055 1) to assure that the mixed example is closer the minority group example. Since both samples are with the same label, we expect their convex combination shares the same label. Using such convex combination technique increases the diversity of minority groups. The pseudo code of the implementation can be found in Appendix B
X Ax; Ax; (1 A)x;, PS. 2i.
= AP mnaato P + (1 P) al::
5
EXPERIMENTS
In this section, we evaluate the effectiveness of the proposed logit correction (LC) method on five
computer vision benchmarks presenting spurious correlations: Colored MNIST (C-MNIST) (Arjovsky)
jet al. 2020). Corrupted CIFAR-10 (C-CIFAR10) (Hendrycks & Dietterich] 2019 Nan Nam et al. [2020].
Biased FFHQ (bFFHQ) (Karras et al., 2019, Lee al. (021), Waterbird (Wah et al. [00 I), and
CelebA (Liu et al.
2015). Sample images in the datasets can be found in Figure of Appendix.
5.1
EXPERIMENTAL SETUP
Datasets. C-MNIST, C-CIFAR-10 and Waterbird are synthetic datasets, while CelebA and bFFHQ are real-world datasets. The above datasets are utilized to evaluate the generalization of baselines over various domains. The C-MNIST dataset is an extension of MNIST with colored digits, where each digit is highly correlated to certain color which constitutes its majority groups. In C-CIFAR- 10, each category of images is corrupted with a certain texture noise, as proposed in Hendrycks & Dietterich (2019). Waterbird contains images of birds as "waterbird" "landbird", and the label is spuriously correlated with the image background, which is either "land" or "water". CelebA and bFFHQ are both human face images datasets. On CelebA, the label is blond hair or not and the gender is the spurious attribute. The group containing samples of male with blond hair is the minority group. bFFHQ uses age and gender as the label and spurious attribute, respectively. Most of the females are "young" and males are "old".
Following Nam et al. (2020), for C-MNIST and C-CIFAR-10 datasets, we train the model with different ratios of the number of minority examples to the number of majority examples and test the accuracy on croup-balanced test set (which is equivalent to GBA) The ratios are set to 0.5%, 1 1% 2%, and 5% for both C-MNIST and C-CIFAR-10. For bFFHQ dataset, the model is trained with 0.5% minority ratio and the accuracy is evaluated on the minority group Lee et al. (2021) ). For Waterbird and CelebA datasets, we measure the worst group accuracy (Sohoni al. 2020).
Evaluation.
Baselines. We consider six baselines methods:
Empirical Risk Minimization (ERM): training with standard softmax loss on the original dataset.
Group-DRO (Sagawa al., 2019): Using the ground truth group label to directly maximize the
worst-group accuracy.
2020 Using ERM to detect minority samples and estimate weight to reweight minority samples.
Learn from failure (LfF) (Nam et al.
Just train twice (JTT) (Liu et al. 20216): Similar to LfF but weight the minority samples by a hyperparameter.
Using the generalized cross entropy loss (Zhang& & Sabuncu, 2018) to detect minority samples and reweight the minority. Using feature swapping to augment the minority group.
Disentangled feature augmentation (DFA) (Lee et al. 2021):
I
Implementation details. We deploy a multi-layer perception (MLP) with three hidden layers as the backbone for C-MNIST, and ResNet-18 for the remaining datasets except ResNet-50 for Waterbirds and CelebA. The optimizer is Adam with 3 = (0.9, 0.999). The batch size is set to 256. The learning rate is set to 1 x 10 for C-MNIST, 1 10 for Waterbird and C-CIFAR- 10. and x 10 for CelebA and bFFHQ. For in Eq. 3 it's set to 0.7 for all the datasets except for Waterbird which is set to 0.8. More details are described in Appendix. D
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Table 1: Classification accuracy (%) evaluated on group balanced test sets of C-MNIST and C-CIFAR- 10 with varying ratio (%) of minority samples. The baseline method results are taken from Lee al. | (202T) as the same experiment settings are adopted. We denote whether the model requires group or spurious attribute annotations in advance by X(i.e., not required), and (i.e., required). Best performing results are marked bold.
Methods
Group
C-NNIST
C-CIFAR-10
Info
1.0
2.0
1,0
200
5,0
Group
38.30
ERM JTT
(3.49)
$2.09 (2.88)
65.86 (3.59)
82.17 (0.74)
23.08 (1.25)
25.82 (0.33)
30,06 (0.71)
39,42 (0.64)
X
(3.89)
62.9 (3.01)
74,23 (3.21)
$4.03 (1.10)
24.7340.600 60)
26 26.9000.31)
33/40(1.00 (.00)
42.2010.313
LIF
x
(2443)
61 (1.97)
71.03 (2.44)
$4.79
28.57
53.07 (0.77)
39.91 30)
50.27 (1
81.73 (4,41)
(0.95)
(2.29)
(1.28)
I.Coun))
(3.17)
82.25 (2.11) 86.21 (1.02)
91.16 (0.97)
34.56 (0.69)
(1.26)
47.81 (2.00)
(1.36)
Table 2: Worst-group accuracies on Waterbirds, CelebA, and minority-group accuracy on bFTHQ. For the ERM, JTT and Group-DRO baselines, we provide the results reported in Liu et al. (2021a).
except for bFFHQ, we rerun the baseline methods. The Group Info column shows whether group labels are available during training.
Waterbirds Worst
CelebA Worst
CivilComments Worst
bFFHQ Minority
Method
Group Info
Group-DRO
91.4
88.9
ERM
62.9 (0.3)
46.9 (2.2)
(1.7)
56.7 (2.7)
JTT
85.8 (1.2)
81.5 (1.7)
69.3 (-)
65.3 (2.5)
LIF
78.0 (0.9)
77.2 (-)
(0.5)
62.2 (1.6)
DFA
X
87.7 (0.2)
84.1 (1.2)
63.9 (0.3)
LC(ours)
90.5 (1.1)
88.1 (0.8)
70.3 (1.2)
70.0 (1.4)
6 RESULTS
6.1
CLASSIFICATION ACCURACY
Table reports the accuracies on group balanced test sets for all baseline approaches and the proposed method when trained with various pinority-to-majoory ratios. Models trained with ERM commonly show degraded performance and the phenomenon is aggravated by the decrease in the number of examples in the minority groups. Compared to other approaches, LC consistently achieves the highest test accuracy. The performance gain is example, compared to DFA Sohoni et al. (020), LC improves the accuracy by 6.03%. 4.61 % on C-MNIST and C-CIFAR-10 datasets respectively, when the minority ratio is 0.5%. While at 5% minority ratio, the improvements are 1.51 % and 3.42%. It shows the superior performance of the proposed method in datasets with strong spurious correlations. Even compared to the approach which requires the ground truth attribute label during training (Group DRO), LC still achieves competitive or even better performance. Table shows the model performances on Waterbird, CelebA and bFFHQ datasets. LC again achieves the highest worst/minority ggroup accuracy among all methods without group information. The clear performance gaps again prove the effectiveness of the proposed method.
more significant when the minority ratio is low. For
Note that all results demonstrated in both Table I and 2 are on datasets with one-to-one one spurious correlation. We also tested the proposed algorithm on datasets with many-to-one and one-to-many correlations as well. The proposed method also outperforms the best baseline methods. Additional experiments can be found in Appendix
6.2 ABLATION STUDY
Effectiveness of each module. Table Jeblonssamontrratte the effectiveness of the LC loss and the Group MixUp in the proposed method. The evaluation is conducted on the bFFHQ dataset. The first row shows the performance of the baseline ERM network. From rows 2-4, each proposed module helps improve the baseline method. Specifically, adding Group MixUp brings 6.35% of the performance boost, and introducing logit correction is able to improve the performance by 9.64%. Combining both of the elements achieves 12.80% accuracy improvement. Compared our method without Group MixUp (third row in Table 3) to LfF in Table 2 both methods use the same pipeline and the only difference is that we apply LC loss while LfF uses reweighting. The experiment result shows that the proposed LC loss clearly outperforms reweighting (62.2% 66.51%) The reasons may be due to
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the proposed LC loss 1) is Fisher consistent with the balanced- reduce the geometric skew as well as the statistical skew.
aalanced-group group accuracy; and 2) is able to
Table 3: Ablation studies on 1) Group MixUp, 2) cor- recting logit on bFTHQ. Each row indicates different training setting with / mark denoting the setting applied. While correcting the logit individually brings a signifi- cant performance boost, adding Group MixUp further improves the performance.
Groap Ralanoed Acmuracy
60
40
30
Group Logit MixUp
Minority Group
Correction
Accuracy
Dataset Avg. Batch Avving Avg.
x
56.87
Figure 3: The performance comparison of different strategies for estimating the group prior (on CMNIST with ratio 0.5%).
63.22
66.51
69.67
Influence of group prior estimate method. We test how different group prior estimation strategies in Eq. Paffect the final performance. We tested updating the prior using all samples in the datasets after finishing each training epoch (Dataset Avg.); 2) updating the prior using all samples in one training mini-batch (Batch Avg.): ); and 3) keeping a moving average for the batch-level prior (Moving Avg.). The result is shown in Fig. 3 Dataset Avg. performs significantly worse than the other two strategies. This may because the Dataset Avg. only updates the prior after each epoch. The delay in the prior estimation may mislead the model training, especially in the early training stage when the model prediction can change significantly.
Group
Group
Group
majority
majority minerity
majerity minority
Margin
minority
Margin
Margin
CMNIST
Waterbird
CMNIST
Waterbird
CMNIST
Waterbird
(a) ERM
(b) ERM Group MixUp
(c) LC Loss
Figure 4: The effect of the proposed logit correction (L.C) method on classification margins (defined in Appendix (C) CMNIST and Waterbird datasets. ERM produces ratio (between the majority group margin and the minority group margin) > 1, ERM Group Mixup has a ratio < 1 and the proposed LC loss achieves ratio << 1.
Analysis of training margins. We show how the proposed LC loss and Group MixUp help reduce the geometric skew. In Sec. [ we mentioned that balanced classifier prefers a larger margin on the minority group compared to the margin on the majority group. i.e., the ratio between the majority group margin and the minority group margin should less than 1. Figure 4 we show the minority group margin and the majority group margin (defined in Appendix ( of the model trained with ERM, ICC loss, and FRM + Group MixUp on both C-MNIST and Waterbird datasets respectively. Figure shows that both the proposed LC loss and the Group MixUp reduce the geometric skew since both of them have a ratio that is less than
CONCLUSION
In this work, we present novel method consisting of logit correction loss with Group MixUp. The proposed method can improve the group balanced accuracy and worst group accuracy the presence of spurious correlations without requiring expensive group labels during training. LC is statistically motivated and easy-to-use. It improves the group-balanced accuracy by encouraging large margins for minority group and reducing both statistical and geometric skews. Through extensive experiments, The proposed method achieves state-of-the-ur balanced accuracy and worst-group accuracy across several benchmarks.

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ACKNOWLEDGEMENT
SL was partially supported by Alzheimer's Association grant AARG-NIF-21-84022 NSF grant DMS 2009752, and NSF NRT-HDR Award 1922658. CFG acknowledges support from NSF OAC- 2103936.
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APPENDIX
A PROOF OF PROPOSITION
Proposition 1. Let Py, a) is the prior group (y, a), and P(y,alx) is the true posterior probability of group (y, a) given x, the prediction:
P(yla, P(aa)x
arg max Σ ,ly',a)
max
P(y,a)
the solution Eq.
Proof. To simplify the notation, we define the output of the classifier as = arg m Ey' fy (x).
Following Collell et al. (2016), for group (y)²), ( the accuracy in this group can be written as,
[ P(y = yb), (1) xx) P(c= y P(x)dx.
Acc(y ab))))
(14)
P(u = yu), a(*))
GBA in Eq. 2 thus can be rewritten as:
(ΣΣ
Ply = ا(0, a = (1*) (x) (x) y
GBA = KL x y0) alk)
P(x)dx.
(15)
Ply = y(), a = (t+))
Maximizing Eq. 15 equivalent obtain the optimal choice of P(c = y x) at each x. Since what
inside of the integral is
Ply = yb), P(cc (x)
P(y = yl5), =a(+))
UI a(k)
Ply y(8) , alk) alx1/x)
P(y = y0) = a(k)) P(c = y(0lx),
(16)
y
(a(k)
which is convex combination, and is maximized at each x if and only if we place probability largest term. That is say, at each x, we assign to P(c y x) where En P(a=y a= (2) xx) the largest term among all possible y values in y and assigning to other terms. Formally,
P(y=y(n a=at))
1, if ( arg max, E Ea(
Ply=e'.a=aa" Ply=y',a=a
P(c ) =
(17)
0,
Otherwise.
The second equation can be derived by Bayes' theorem.
B PSEUDO CODE OF THE PROPOSED ALGORITHM
We provide the pseudo-code of the proposed logit correction and Group MixUp in Algorithm
C DEFINITION OF CLASSIFICATION MARGIN
Let f(x)
Rd R be a model that outputs logits, following previous works Koltchinskii &
Panchenko 2002 Cao al. 2019). we define the margin of an example (x., y)
m(z. y) f(x), max f(x),- jøy
(18)
We can then define the training margin for a group g = (a, y) as the minimum margin of all classes
my = min m mxx:;y)).
(19)
iEg
The margins for minority groups and majority groups are defined as the average margin of minor- ity/majority groups.
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Algorithm 1: L.C. for one-to-one mapping
Input :Triining set (X, Y), Initialize the ERM model fo and the robust model fo. # epochs
K, # rampup epoch T, moving average momentum a.
for epoch K do
Sample mini-batch {xx,y); y)}:
Update ERM network f(0) parameters by training on f(x, y)} with Equation for (x, v) E (xx y)} do
Let p(..)) be the ERM model's probability outputs on sample (x, y)-
Let ax arg max ((x.)) be the estimated value of the spurious attribute.
Update the group priors by Py.o= aPy, + a)pa (x:9)
end
(Optional) Perform Group MixUp obtain the synthesized batch:
0.5 exp(-x() epoch) /Ty sigmoid ramp up function {x, y. p(x]] = GroupMixup( (x, y: ax), P,
11
for (x, y, p(x)) {x, p(x) do
13
for == to # labeled classes do
Correct the cth logit of the robust mode by f(x). == f(x), + log ((x) c.ax
15
end
16
end
17
Update robust model's parameters 0 with softmax cross entropy loss on fo(x).
18
end
19
Function SroupMixup (1x, 1/, 4x 7,
20
Obtain set of samples {8,, 77 ag) that are estimated to be from minority groups i.e. y & ax
21
{(E, y. az)] := shuffle (zz (. d;)));
22
Sample À Uniform(1 2T, 1-7,1-71 -)T);
for i, (x, y, ax) E enumerate ((x, y. (xx) do
23
Sample (7, ag) from {(T, V, ag)) such that
25
x == Ax + (1 A)T
:: y
p(x) = Xp, v. (1 P) y.a. the correction term for MixUp sample x.
27
28
end
End Function
D EXPERIMENT DETAILS
We utilize Adam optimizer with 3 = (0.9, 0.999) without weight decay except for CelebA, we set weight decay to 10-4 and batch size 256. For Waterbird, we use SGD optimizer with weight decay of 1 10-4. Learning rates of 1 x 10 2 10-3 and 1 10 are used for Colored MNIST, Waterbird, and CelebA, respectively. We use learning rate of 5 x 10-4 for 0.5% ratio Corrupted CIFAR- 10 and 1 10 for the remaining ratios. We decay the learning rate 10k iteration by 0.5 for both Colored MNIST and Corrupted CIFAR1O. For CelebA, we adopt a cosine annealing learning schedule. For Waterbird, ramp-up epoch set as 50 for waterbird and CelebA and for other datasets, and the moving average momentum set to 0.5 for all datasets.
the in GCE 0.8 and 0.7 for other datasets. The
E RESULTS ON OTHER SPURIOUS CORRELATION
In the previous section, report the results one-to-one mapping which is common scenario considered by previous works. In this section, we further examine the performance of previous approaches as well as LC other spurious correlation types.
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2
3
4
5
6
7
8
0
/
2
3
4
S
6
7
8
9
O
/
2
3
4
5
6
9
BFFHQ
10
Waterbirds
[e] CelebA
Figure 5: Example images of datasets used in our work. In each dataset, the images above the dotted line demonstrate the majority groups while the ones below the dotted line minority groups. For Colored MNIST and Corrupted CIFAR-10, each column demonstrates each class.
2
3
4
5
7
8
9
0
/
2
3
4
S
6
7
8
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3
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5
+
9
(a) Many to-one spurious correlation.
2
3
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5
6
7
8
9
0
/
2 3
4
S
6
7
8
9
O
2 3
4
5
6
4
9
(b) One-to-many spurious correlation.
Figure Sample images for datasets containing one-to-many and many-to-one correlations. The first two rows show the training samples from the majority groups and the third row shows the validation set where groups are balanced. For many-to-one, both digits 0''s and I's are colored browns. For one-to-many, digit 0's colored in different colors (red and dark green).
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E. MANY-TO-ONE
The digits in the MNIST training dataset is injected with different colors (similar to the original Colored MNIST). However, we inject the color into digits 0 and to obtain the many-to-one relationships between the label and the spurious attribute (Figure 6ap. We evaluate the accuracy of the proposed logit correction method on the many-to-one setting mentioned in Sec. 4.2.2 (LC+). We also apply LC loss with the one-to-one assumption as LC.
Table 4: Test accuracy on Colored MNIST data with many-to-one correlation.
Group Info
Colored MNIST
Methods
Train
Val
0.5
1.0
2.0
5.0
ERM
X
31.13
50.89
$7.92
82.19
LIF
x
<
46.22
69.32
73.33
82.57
DFA
X
V
64.7
77.28
84.19
90.17
LC(ours)
x
/
65.32
78.05
84.24
90.3
LC+(ours)
X
65.06
78.57
84.5
90.3
In Table 4 report the accuracies the balanced test set for Colored MNIST. The proposed method (LC and LC+) constantly outperforms all baselines, Although using the exact mapping information shows the best performance (LC+), directly applying the one-to-one assumption shows very similar performance.
E.2 ONE-TO-MANY
We augmented the MNIST training dataset with colors (similar to Colored MNIST) except that digit 0 has two colors as its major color attribute, shown in We evaluate the accuracy of the proposed logit correction method on the one-to-many setting mentioned See 4.2.3 (LC+). We also apply LC loss with the one-to-one assumption as LC.
Table 5: Benchmark results on the One-to-Many correlation Test accuracy on Colored MNIST
data with one-to-many mapping.
Group Info Train
Colored
MNIST
Methods
Val
0.5
1.0
2.0
5.0
ERM
X
38.47
48.41
67.41
80.61
LfF
x
52.79
66.07
75.09
83.5
DFA
X
/
70.11
78.75
83.06
90.41
LC(ours)
X
/
72.02
79.5
83.24
90.83
LC+(ours)
X
72.26
80.1
84.1
91.25
In Table 5 We report the accuracies the balanced test set for Colored MNIST. The proposed method (T.C and I.++) constantly outperforms all baselines. Although using the exact mapping information shows the best performance (LC++,, directly applying the one-to-one assumption shows very similar performance.
MORE ABLATION STUDY
F.I ABLATION ON
We conduct an ablation study to better understand in the GCE loss. Intuitively, when ş is closer to results loss function with gradient that emphasizes the hard example (e.g. cross-entropy), and when is closer to I, it results in loss closer mean absolute error which produces gradient that emphasizes less on hard examples. The choice of q depends on different datasets of how fast the easy examples (i.e. the spurious correlated example) can be learned. We conducted ablation study on the waterbird dataset, it turns out the proposed method is quite robust to different values of q, as illustrated in Table 6
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Table 6: Ablation study on q of GCE,
9
0.1
0.3
0.5
0.7
0.8
0.9
LC
84.2
88.6
88.9
89.9
90.7
89.4
F.2 LOGIT CORRECTION V.S. REWEIGHTING
We also conduct experiments to compare logit correction with re-weighiin//r-sampphee There both theoretical and empirical evidence showing that LC is more effective than reweighting for training linear classifier since it is not only Fisher consistent, but also able to address the geometric skew. Theoretically, recent papers Xu et al. (2200); Sagawa et al, (2020) proved that overparametrized linear model, regardless of trained with reweighted cross entropy and original cross-entropy, would eventually result in the max-mas max-margin classifier with enough training. This is also validated by our experiments in which classifier on Corrupted CIFAR10 (5%), we obtain that reweighting with the group prior (GBA: 23.75%) results in slightly better results than ERM (GBA: 20.77%) Both are worse than logit correction (GBA: 30.20%)
adopt ImageNet pre-trained ResNet- 18, and only train the last linear
We further compare reweighting with logit correction the fully trained model when ground truth group information are available. LC also outperforms the Fisher-Consisten reweighting (
Table 7: Comparison of reweighting and logit correction with ground truth group information.
Method
ERM
Fisher-Consistent Reweighting
logit correction
Test acc.
39.51
42.13
54.31
17


Reviews:
[{"review_id": "oNbHSgsdcZC", "reviewer": "Reviewer_5Aoq", "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": "This paper tackles the problem that deep neural nets trained for classification learn spurious correlations that can negatively impact generalization. For this purpose, the authors propose Logit Correction (LC) loss to mitigate the effects of spurious correlations. Further, to synthesize more samples from the minority groups, the authors propose Group MixUp.\n", "summary_of_the_review": "Although the contributions are interesting, according to me the paper needs to be refactored to improve the flow and in its current shape, the overall impression is not positive.  ", "strength_and_weaknesses": "Strengths: \n1. The proposed method is simple to implement.\n2. The authors provided theoretical justification.\n3. The study is supported through detailed empirical analysis and ablations\n\nWeakness \n1. I believe the proposed approach shares some similarities with LfF which also uses a two-branch network with generalized cross-entropy loss for mitigating spurious correlations. The authors should provide a detailed discussion of the difference between the two papers.\n\n2. The average accuracy is not reported in Table 1 and 2. Further, the authors also do not report variances over multiple runs, which slightly diminishes the trustworthiness of the results.\n\n3. According to me, writing can be improved. There are some grammatical mistakes that make it hard to understand the concept in some places. (Minor)\n\nQuestions:\n1. I am confused about how you get the samples from minority groups while doing GroupMixup if the group labels are not assumed. Further, to the best of my knowledge, both JTT and LfF use group-labeled validation sets for hyperparameter tuning. It's not very clear why the authors indicated that they do not require group information. \n\n2. Can this proposed method be also applied for spuriously correlated NLP datasets such as MultiNLI and CivilComments. It would be interesting to see the performance.\n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "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": "hS7YFrhvaP5", "reviewer": "Reviewer_tcpr", "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": "This paper presents a loss function for classification that allows to mitigate the issue of spurious correlations in data where there is a majority group in which correlations are present, and a minority group without spurious correlations.  \n\nThe proposed method consists of training two networks: 1) a ERM network that uses the generalized cross entropy loss, and that is therefore biased to be better at predicting elements containing spurious correlations (in the majority group), 2) a robust network trained with the standard cross entropy loss, but after having scaled the logits by a correction term produced from network 1. \n\nExperiments show that the method is able to reduce geometry and statistical skews, and outperforms competing method in a number of standard benchmarks. \n\n ", "summary_of_the_review": "The presented method is interesting and has potential, but in its current state the impact of this paper is limited by the lack of clarity in the theoretical section. ", "strength_and_weaknesses": "**Strengths**\n1. Spurious correlations are very common in real data. This paper proposes an interesting solution to learning classifiers that can avoid them, importantly without assuming that the spurious attribute is known during training \n\n2. The LC loss is theoretically grounded, since as the authors show minimizing the logit-correction loss is equivalent to maximizing the group-balanced accuracy \n\n3. The proposed method outperforms competing ones in popular benchmarks for the task. Ablation studies show the importance of all the novel components introduced in the paper. \n\n\n**Weaknesses**\n \n_Clarity_ \n\nThe logic correction term is the key ingredient of the proposed method. As such, from section 4.1 it should be obvious and very clear to the reader how the correction term is computed and why it works, which I believe it is not the case. \n\n1. While Equations (4) -> (7) provide all the mathematical steps in detail, the authors should provide the reader intuition on what each of those equations represent. I really liked the simple waterbird example from Figure 1, and I believe it could be used as a running example throughout section 4.1 to give a more concrete intuition of the formula and assumptions presented in the section. \n\n2.  $\\Delta_{y, a_x}$ is never even defined explicitly with a formula. \n\n3. Section 4.2 would also greatly benefit from providing some intuition to the reader \n\n\n_Applicability to more realistic datasets_\n\n1. While the authors perform experiments on standard benchmarks, I would have liked more real-world experiment, to make sure that the proposed method generalizes to more realistic tasks where the spurious attributes might be very subtle and hard to infer (as is the case for example in medical imaging datasets). \n\n2. I have some doubts that the linear combination assumption of the group mixup will work in a real dataset with higher dimensional images and objects that might have different scale/positions. Would you expect it to generalize well to more realistic tasks? \n\n \n\n ", "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": "eNXZd6wNVI", "reviewer": "Reviewer_H482", "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 authors tackle the spurious correlation problem in the setting where spurious attribute values are unknown. They propose a method where a two-branch neural network is trained, one branch with the generalized cross-entropy, and the other with a logit correction loss which depends on estimated class priors computed from the first branch. Unlike prior two-stage methods like JTT, the proposed method only requires training a single network. The evaluate their method on standard spurious correlation datasets, finding that it improves over the baselines.", "summary_of_the_review": "Due to inherent issues with the method (Weaknesses #1-2) and issues with the empirical evaluation (Weaknesses #3-6), I recommend rejection at this time pending the authors' rebuttal.\n\nPost-rebuttal update: The authors have addressed my major concerns with the empirical evaluations through new experiments. I am now leaning towards accept.", "strength_and_weaknesses": "Strengths:\n- The paper is generally well-written.\n- The proposed method outperforms the baselines on standard benchmark datasets.\n\n\nWeaknesses:\n1. The main weakness of the paper is the novelty of the proposed method, which is limited by two factors:\n- The proposed group MixUp method is nearly identical to intra-label LISA [1], which the authors do not reference. It is also similar to [2], which I do not expect the authors to have referenced as it is too recent.\n- The GCE loss is the same as the loss used in training the biased model in Learning from Failure, which the authors also do not mention.\n\n2. It seems that, for the method to work, the user needs to know in advance which of the four spurious attribute to label mappings is present within the data. In particular, in Sections 4.2.2-4.2.4, it seems that we would need to know the values of the spurious attribute that are correlated with each value of the label. If so, this seems like a major drawback of the method. The authors should discuss this further, and perhaps conduct experiments in the case where the mapping is misspecified (e.g. we assumed it was one-to-one but it was actually many-to-one).\n\n3. The authors should show the performance of the estimation of the group prior over training. Does this converge to the real values?\n\n4. The authors should evaluate their method on the CivilComments dataset, which is standard in the spurious correlation setting. This might be a tricky setting for the method to define the spurious attribute to label mapping.\n\n5. For transparency, the authors should show the performance of more recent methods such as CNC [3]. They should also show the performance of all methods on all datasets (for example, JTT is missing in Table 1, and there are a couple missing from Table 2). \n\n6. The authors should conduct an experiment showing the effect of varying $q$ in the appendix. Why have they been set to 0.7 and 0.8?\n\n[1] https://arxiv.org/abs/2201.00299\n[2] https://arxiv.org/abs/2209.08928\n[3] https://arxiv.org/abs/2203.01517", "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": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "RBP8Lh4Wa9", "reviewer": "Reviewer_aF7f", "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": "This paper considers the problem of spurious correlations in deep learning, using image classification as a case study.\nThis problem arises when some attribute can be observed in the training set that is correlated with the class label, however the correlation does not hold in general.\nThe formulation assumes that there is one discrete spurious \"attribute\" variable, for which we know (or can determine) the values that frequently co-occur with each class.\nIn practice, this is generally the possibly-incorrect class predicted by a model trained with an ERM loss.\nThe proposed method comprises two components: Logit Correction loss and Group Mixup.\nSimilar to logit correction for class-imbalanced learning, the LC loss seeks a greater margin for examples in the less frequent groups, where groups are defined as a (class, attribute) pair.\nGroup Mixup replaces each minority example with a convex combination of itself and a majority example with the same label, mixing both the inputs and the logit corrections.\nThe method is compared to several baselines on both synthetic and realistic datasets.", "summary_of_the_review": "Overall, the approach is well-motivated and the results seem strong. However, I have some concerns about the justifications and the evaluation. Also, it seems that all experiments in the main paper use a particular choice of attribute, and are thus less general than the formulation. I'm leaning towards accept, but I may downgrade my rating if my concerns are not addressed.", "strength_and_weaknesses": "**Strengths**\n\n1. Based on the work of Menon et al., logit correction seems like a highly effective tool for enforcing different margins from different classes in deep learning. Using this to address spurious correlations makes sense.\n\n1. Both Logit Correction and Group Mixup made a significant contribution to the improvement in results.\n\n1. The inference rule in Proposition 1 was unfamiliar to me and the derivation seems good.\n\n1. Empirical evaluations show the method to be highly effective across all datasets.\n\n1. Algorithm 1 helps to understand the method.\n\n**Weaknesses: Experimental**\n\n1. The ablative study was only conducted for one dataset. It would be better if these 3 ablations were added as rows in Tables 1 and 2 for all datasets.\n\n1. DFA missing from Table 2, JTT missing from Table 1.\n\n1. No confidence intervals (standard deviations) in Tables 1 and 2, even for experiments on relatively small datasets (MNIST, CIFAR). This could be especially important for the \"Worst Group\" metrics, which would probably higher variance than the mean-based metrics.\n\n1. It is stated that the ERM results in Tables 1 and 2 were taken from past papers. To ensure an apples-to-apples comparison, it would be better to run at least the ERM baseline in the exact same pipeline, only disabling your features. (Like the first row of Table 3, but for all the datasets in Tables 1 and 2? Note that Table 3 differs from Table 2, i.e. 56.87 vs 55.47 for MGA with bFFHQ.)\n\n**Weaknesses: Method and text**\n\n1. Was it not necessary to stop the gradients from the ERM branch to the Robust branch?\n\n1. For continuous attributes, it seems like the LC loss could still be used, but Group Mixup would not be directly applicable.\n\n1. The use of the predicted label as the correlated attribute is quite a specific choice (line 6 of Algorithm 1 in appendix). This attribute will always be one-to-one, with ground-truth and predicted labels coinciding in the majority groups. I feel like this particular choice should be given more attention in the formulation. Otherwise, the method seems much more general than the empirical evaluation, since IIUC all experiments in the main paper use this specific configuration. (Only Appendix E contains results that do not.)\n\n1. When the attribute is not the predicted label, it seems necessary to specify which attribute values are correlated with which class labels (Sections 4.2.2, 4.2.3). This is not necessarily a weakness, as sometimes it may be useful to specify this manually. However, it seems that it might also be automatically determined from a class-attribute confusion matrix? How would the accuracy be affected if it was specified incorrectly?\n\n1. It's not clear whether logit correction being more effective than re-weighting/re-sampling is specific to deep learning. For example, Kang et al. (ICLR 2019; \"Decoupling Representation and Classifier for Long-Tailed Recognition\") found that it was best to learn features using instance-balanced sampling and then learn a linear classifier using class-balanced sampling. Does the LC loss still improve the results when training a linear classifier with frozen features?\n\n1. It is hypothesized that the effectiveness of the LC loss is due to being Fisher consistent. However, it seems that re-weighting samples rather than adjusting the margin might also be Fisher consistent (w.r.t. the group-balanced distribution)? If this is not the case, can you state this in the paper and provide a reference?\n\n**Uncertain**\n\nI'm not an expert on spurious correlations, so I'm not sure whether the choice of datasets is appropriate, in particular the use of datasets with only two classes. I'll defer to other reviewers here.", "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": "4: The contributions are significant, and do not exist in prior works.", "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