Paper: Removing Multiple Shortcuts through the Lens of Multi-task Learning (ICLR-2024)

Reviewer comment (Novelty):
Debiased training actually seems closer to multi-domain learning (MDL) [W1] rather than MTL. Because MTL clearly means learning different tasks (i.e. task labels are different) as the paper also mentions on Page 2.

Author response:
Thank you for interesting and insightful suggestions! As you mentioned, both long-tailed classification and multi domain learning are relevant in mitigating spurious correlation in the context of data imbalances. Based on your comments, we will consider integrating techniques from MDL or long-tailed learning for debiasing in the future work. However, we believe MTL can be more naturally incorporated with debiased training for the following reasons. Debiasing focuses on training an unbiased model with respect to spurious correlations. While MDL addresses data imbalance among different domains and long-tailed classification deals with data imbalance among target classes, debiasing tackles the imbalance among bias attributes within a given target label in training dataset. For instance, in bird species classification, if most waterbirds in the dataset are with water background and ERM erroneously uses the water background as a shortcut for classifying waterbirds, waterbirds and water background have  spurious correlation. Therefore, we designed a learning algorithm that causes task conflicts when a model relies on shortcuts by defining tasks according to adherence of samples to spurious correlations using our grouping policy. Adopting MOO to resolve task conflicts is an effective approach for training an unbiased model by removing shortcuts.

Reviewer comment (Novelty):
It is unclear how MultiCelebA is a new dataset compared to CelebA. There are no new images or new labels. Even the choice of attributes is based on the analysis from a prior work.

Author response:
Thanks for the comment, and we have replaced “new dataset” with “new benchmark” in the manuscript to address the concern. Despite this change, we still believe that, as a realistic and challenging benchmark, MultiCelebA will contribute substantially and promote future research in the field of debiased training. We also would like to highlight that reprocessed datasets/benchmarks like MultiCelebA have long been recognized by the community; examples include bFFHQ, a dataset for debiasing derived from FFHQ, and those for long-tailed classification such as ImageNet-LT (from ImageNet), CIFAR-LT (from CIFAR), and Places-LT (from Places).

Reviewer comment (Novelty):
The contribution of a new dataset seems misleading; only a new experimental setting based on an existing dataset is proposed.

Author response:
Thanks for the comment, and we have replaced “new dataset” with “new benchmark” in the manuscript to address the concern. Despite this change, we still believe that, as a realistic and challenging benchmark, MultiCelebA will contribute substantially and promote future research in the field of debiased training. We also would like to highlight that reprocessed datasets/benchmarks like MultiCelebA have long been recognized by the community; examples include bFFHQ, a dataset for debiasing derived from FFHQ, and those for long-tailed classification such as ImageNet-LT (from ImageNet), CIFAR-LT (from CIFAR), and Places-LT (from Places).

Reviewer comment (Writing):
The design choices for the main algorithm are not well explained.

Author response:
Our algorithm is designed to update $\alpha$ and $\lambda$ once every time $\theta$ is updated $U$ times. For computational efficiency, we occasionally updated $\bar{\alpha}$ and $\lambda$, and empirically demonstrated that this maintains consistent performance, regardless of updating frequency $U$. As you mentioned, we can update $\bar{\alpha}$ and $\lambda$ at different frequencies. Updating them at every $U$ iteration is a special case of updating with $U1$ and $U2$, so the performance could potentially be improved by using these distinct updating frequencies $U1$ and $U2$. We however have objections to introducing additional hyperparameters that increase the training complexity.

Reviewer comment (Experiments):
Ideally, one would expect new datasets or benchmarks to improve over existing datasets by providing more challenging scenarios (or at least more data). While the overall accuracy numbers of MultiCelebA seem lower than UrbanCars (but similar to Multi-Color MNIST), upsampling and upweighting are consistently good on all three datasets.

Author response:
**The difficulty of MultiCelebA compared to existing datasets**

Due to the differences in model architectures used for datasets, a direct comparison of overall accuracy numbers not fully represents the relative difficulty of each dataset; Unlike MulticelebA and UnbarCars, where ResNet18 was used, a simple three-layed MLP was utilized in Multi-Color MNIST, resulting in lower overall accuracy numbers for Multi-Color MNIST for its difficulty. 

**MultiCelebA provide more challenging scenarios**

MultiCelebA provides various experimental settings, including a two bias setting in Table 1, a three bias setting in Table 2, and a three bias setting with one missing bias label for training in Table A7. Additionally, it is a 8.4 times larger-scale dataset (66592 training images) compared to UrbanCars (8000 training images). This aspect is noteworthy, as illustrated in Figure 1, where the intersection of bias-conflicting samples (i.e., the smallest group) becomes extremely small as the number of bias types increases.

Reviewer comment (Experiments):
Whether complicated debiased training methods (like the proposed method) provide any significant improvements to be deemed of practical significance is questionable, given that upsampling and upweighting perform very well compared to all the supervised debiased learning methods.

Author response:
First of all, we would like to correct an erratum in Table 1 of the main paper: the 'Unbiased' accuracy of 'Upweighting' should be 79.4, not 81.2. We deeply apologize for our mistake, and would like to confirm that it was indeed a simple erratum and we did not retrain the model to obtain a new result as follows:
- The 'Unbiased' accuracy, by its definition, equals the average of 'GG', 'GC', 'CG', and 'CC' scores, as described in Section 5.1 ‘Evaluation metrics’.
- The average of the four scores is 79.4 for 'Upweighting' in Table 1, i.e.,  (79.0+79.2+80.8+78.7)/4 = 79.4.
This erratum has been rectified in the revision. Again, we sincerely apologize for the mistake.

Given the updated score, our method clearly outperformed prior arts including 'Upweighting' in Table 1 (and in the other tables too). In particular, existing debiasing methods designed for single bias settings are on par with or even underperform 'Upweighting' on MultiCelebA. These results suggest that MultiCelebA presents new challenges in the area of debiased training and that advanced debiased training algorithms are required to improve performance on the dataset.

Reviewer comment (Reproducibility):
In Algorithm 1, why is $\theta$ updated again (outside the "for loop") after updating it for $U$ number of times?

Author response:
Our algorithm is designed to update $\alpha$ and $\lambda$ once every time $\theta$ is updated $U$ times. For computational efficiency, we occasionally updated $\bar{\alpha}$ and $\lambda$, and empirically demonstrated that this maintains consistent performance, regardless of updating frequency $U$. As you mentioned, we can update $\bar{\alpha}$ and $\lambda$ at different frequencies. Updating them at every $U$ iteration is a special case of updating with $U1$ and $U2$, so the performance could potentially be improved by using these distinct updating frequencies $U1$ and $U2$. We however have objections to introducing additional hyperparameters that increase the training complexity.

Reviewer comment (Theory):
In Algorithm 1, why do $\bar{\alpha}$ and $\lambda$ need to be updated once every $U$ iterations and not every iteration?

Author response:
Our algorithm is designed to update $\alpha$ and $\lambda$ once every time $\theta$ is updated $U$ times. For computational efficiency, we occasionally updated $\bar{\alpha}$ and $\lambda$, and empirically demonstrated that this maintains consistent performance, regardless of updating frequency $U$. As you mentioned, we can update $\bar{\alpha}$ and $\lambda$ at different frequencies. Updating them at every $U$ iteration is a special case of updating with $U1$ and $U2$, so the performance could potentially be improved by using these distinct updating frequencies $U1$ and $U2$. We however have objections to introducing additional hyperparameters that increase the training complexity.

Reviewer comment (Experiments):
In Algorithm 1, why not have $\bar{\alpha}$ and $\lambda$ updates be at different frequencies like every $U_1$ and every $U_2$ iterations instead of together after $U$ iterations?

Author response:
Our algorithm is designed to update $\alpha$ and $\lambda$ once every time $\theta$ is updated $U$ times. For computational efficiency, we occasionally updated $\bar{\alpha}$ and $\lambda$, and empirically demonstrated that this maintains consistent performance, regardless of updating frequency $U$. As you mentioned, we can update $\bar{\alpha}$ and $\lambda$ at different frequencies. Updating them at every $U$ iteration is a special case of updating with $U1$ and $U2$, so the performance could potentially be improved by using these distinct updating frequencies $U1$ and $U2$. We however have objections to introducing additional hyperparameters that increase the training complexity.

Reviewer comment (Presentation):
Page 3 (5th line of “Fairness with MTL” paragraph): use \cite instead of \citet.

Author response:
We have fixed them. We appreciate your thoughtful comments.

Reviewer comment (Writing):
Sec. 3.1 (first paragraph): mention dimensions of $\theta$, should be $\mathbb{R}^n$ as per usage in Definition 2.

Author response:
We have fixed them. We appreciate your thoughtful comments.

Reviewer comment (Presentation):
Fig. 3: x-axis title has typos: “interation” → “iteration”.

Author response:
We have fixed them. We appreciate your thoughtful comments.

Reviewer comment (Writing):
Page 10: Citation for Fernando et al. (MoCo) is incorrect; it should be ICLR 2023 and not ICLR 2022.

Author response:
We have fixed them. We appreciate your thoughtful comments.

Reviewer comment (Writing):
The paper is not easy to follow. The writing could have been better.

Author response:
We have made revisions in line with comments from other reviewers. If there are any aspects that remain unclear or if you have any additional questions, please let us know.

Reviewer comment (Reproducibility):
No code, so limited reproducibility.

Author response:
In camera ready, we are committed to making our code publicly available. We understand the importance of transparency and community access in research, and we will ensure to adhere to these principles.

Reviewer comment (Experiments):
There is a recent notion of difficulty in shortcuts. For example, some shortcuts are easy to learn, and some are difficult to learn. If the authors are using different subgroups to design multitask losses, the losses should be weighted corresponding to the shortcut difficulty. For example, a hard shortcut loss will be penalized less than an easy shortcut loss, as the model is more prone to latching on to the easy shortcut. The paper on shortcut difficulty is as follows: Beyond Distribution Shift: Spurious Features Through the Lens of Training Dynamics. Murali et al. TMLR 2023. This setting will be more realistic.

Author response:
According to the ICLR 2024 Reviewer Guidelines, the paper by Murali et al., published one month after our submission date, is considered concurrent work. We sincerely appreciate your diligence in bringing this to our attention and will revise the draft to discuss the paper and compare our method with it. To clarify, Murali et al. categorize spurious correlation as either benign or harmful, while our goal is to eliminate ‘shortcuts’ stemming from easy-to-learn spurious correlations. We empirically demonstrated that the bias types in MultiCelebA are such easy-to-learn spurious correlations, as shown in Section A.3.

Reviewer comment (Experiments):
The dataset MultiCelebA is good for evaluation, but a more realistic dataset like NIH-chesttube in the shortcut paper in Point 5 would be preferable.

Author response:
Thank you for your suggestion! However, the metrics used for evaluating models on the NIH-chesttube benchmark differ from those commonly used to evaluate debiasing methods, which makes direct comparisons of debiasing methods on this benchmark challenging. Currently, it is difficult to complete the experiment immediately due to the lack of time, but we aim to include it in the camera-ready if it is completed in time.

Reviewer comment (Experiments):
With multiple groups involved in the multitask loss, the overall performance may drop.

Author response:
If you could kindly provide more details regarding your comments, it would be helpful for us to address them appropriately.

Reviewer comment (Experiments):
The relationship between multiple biases issue and multi-task learning is intriguing. However, the absence of comparisons with traditional multi-task learning (MTL) methods raises a question. If traditional MTL methods can also effectively optimize the problem, it would strengthen the connection between multiple biases issue and multi-task learning.

Author response:
Thank you for your valuable comments! As you mentioned, the application of an existing MOO/MTL method along with our grouping policy showed improved performance compared to not adjusting group weights, as shown in Table 5, which strengthened the connection between multiple biases and MTL/MOO. However, the methods fall short of the desired level of unbiased performance. This highlights the superiority of our method in scenarios involving multiple spurious correlations.
Specifically, in response to your comment, we have included the results of GradNorm in Table 5, as well as in the subsequent Table R1. GradNorm adjusts group weights based on a specific criteria, namely the inverse training rate. However, it has been known that reweighting task losses based on specific criteria can lead to instability [1], as demonstrated by the high standard deviation in Table W1. GradNorm improved the performance on bias-guiding samples, but it showed lower performance on bias-conflicting samples, even compared with that of (i) No adjusting grouping weights. Therefore, under our grouping policy, finding Pareto optimal with MOO is effective in training an unbiased model. 

**[Table R1] Comparison among different strategies for adjusting $\alpha$**
|  | GG | GC | CG | CC | Unbiased | Worst | InDist |
 |----------|----------|----------|----------|----------|----------|----------|----------|
| (i) No adjusting group weights | 79.6$_{\pm \text{2.9}}$ | 80.0$_{\pm \text{2.2}}$ | 79.0$_{\pm \text{1.9}}$ | 78.4$_{\pm \text{1.3}}$ | 79.2$_{\pm \text{1.4}}$ | 70.8$_{\pm \text{2.7}}$ | 78.5$_{\pm \text{5.7}}$ | 
| (ii) MGDA | 81.6$_{\pm \text{3.5}}$ | 85.1$_{\pm \text{2.1}}$ | 80.1$_{\pm \text{1.3}}$ | 82.3$_{\pm \text{3.2}}$ | 82.3$_{\pm \text{0.4}}$ | 73.9$_{\pm \text{0.2}}$ | 82.7$_{\pm \text{3.7}}$ | 
| (iii) GradNorm | **85.9**$_{\pm \text{5.8}}$ | **86.9**$_{\pm \text{2.4}}$ | 78.1$_{\pm \text{3.5}}$ | 76.6$_{\pm \text{6.5}}$ | 81.9$_{\pm \text{0.6}}$ | 70.9$_{\pm \text{4.9}}$ | **86.5**$_{\pm \text{5.4}}$ |
| (iv) MoCo | 81.7$_{\pm \text{1.3}}$ | 81.8$_{\pm \text{2.6}}$ | 77.2$_{\pm \text{0.9}}$ | 74.9$_{\pm \text{1.2}}$ | 78.9$_{\pm \text{1.5}}$ | 72.1$_{\pm \text{2.7}}$ | 83.8$_{\pm \text{1.6}}$ | 
| (v) Ours | 82.4$_{\pm \text{0.9}}$ | 85.1$_{\pm \text{0.4}}$ | **81.7**$_{\pm \text{0.4}}$ | **82.6**$_{\pm \text{1.0}}$ | **82.9**$_{\pm \text{0.2}}$ | **77.9**$_{\pm \text{0.2}}$ | 84.3$_{\pm \text{0.9}}$ |

[1] Fernando, Heshan, Han Shen, Miao Liu, Subhajit Chaudhury, Keerthiram Murugesan, and Tianyi Chen. “Mitigating Gradient Bias in Multi-Objective Learning: A Provably Convergent Stochastic Approach.” ICLR 2023.

Reviewer comment (Novelty):
GradNorm [1] also adopts the gradient of loss weight to optimize the loss weight. Could you please discuss the relation and the difference between your algorithm and GradNorm? In addition, GradNorm is an important reference for this paper.

Author response:
Thank you for informing us! Our algorithm updates group weights by minimizing the weighted sum of group losses and the norm of the weighted sum of gradients to perform well on all groups, while GradNorm updates group weights towards inverse training rate so that different tasks train at similar rates. We will add GradNorm in our revised manuscript. 

[2] Chen, Zhao, Vijay Badrinarayanan, Chen-Yu Lee and Andrew Rabinovich. “GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks”. ICML 2018.

Reviewer comment (Experiments):
Could you please conduct additional comparisons with traditional MTL methods to solidify the connection between multiple biases issue and multi-task learning?

Author response:
Please see our answer to [Weakness 1].

Reviewer comment (Experiments):
The MultiCelebA dataset appears inadequate in distinguishing between spurious and non-spurious correlations. The authors have not elaborated on the dataset's construction, even in supplementary materials. Furthermore, while they label certain correlations between target attributes and specific attributes as spurious, these correlations seem to compose of the spurious and non-spurious ones. An isolated evaluation of spurious correlations is essential for gauging the efficacy of methods designed to counteract them. Thus, relying on experiments with the MultiCelebA dataset might be questionable.

Author response:
We would like to kindly note that Section A.3 and Figure A3 empirically demonstrated that the bias types in MultiCelebA are spuriously correlated to the target class, High Cheekbones. Additionally, Figure 2 and Table A1&A2 present statistics of MultiCelebA. If you have already reviewed these sections and find any aspect unclear or have specific concerns, we would greatly appreciate further clarification on which parts you found problematic.

Reviewer comment (Evaluation):
Tables 2-4 present diverse evaluation metrics, raising concerns about potential cherry-picking to favor the proposed method. Without including metrics both UNBIASED and WORST consistently, the experiments might come off as biased and not entirely objective.

Author response:
In Table 2, we presented the results of previous methods with respect to both UNBIASED and WORST metrics. However, for Table 3 and Table 4, we followed the evaluation protocols used in prior studies [1, 2] for UrbanCars and Multi-Color MNIST to ensure a fair comparison, which led to the absence of certain metrics in Table 3 and Table 4.

[1] Zhiheng Li, Ivan Evtimov, Albert Gordo, Caner Hazirbas, Tal Hassner, Cristian Canton Ferrer, Chenliang Xu, and Mark Ibrahim. A whac-a-mole dilemma: Shortcuts come in multiples where mitigating one amplifies others. In Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 20071–20082, 2023.

[2] Zhiheng Li, Anthony Hoogs, and Chenliang Xu. Discover and mitigate unknown biases with debias- ing alternate networks. In Proc. European Conference on Computer Vision (ECCV), pp. 270–288. Springer, 2022.

Reviewer comment (Evaluation):
The credibility of evaluating spurious correlations using the MultiCelebA dataset is questionable, as mentioned above. While results derived from Multi-Color MNIST might be more reliable, the proposed method's minimum group-wise accuracy is lower than that of GroupDRO. This undermines the claim that the proposed method is superior to GroupDRO.

Author response:
Please see our answer to [Weakness 2].

Our method outperforms GroupDRO on UrbanCars, MultiCelebA, Waterbirds, and bFFHQ. This underscores the effectiveness of our framework, showcasing superior performance in both multiple bias scenarios and conventional single bias settings. 

We recognize that neither GroupDRO nor our method is better than the other overall on Multi-Color MNIST. While GroupDRO achieved the highest CC accuracy on Multi-Color MNIST, it exhibited lower performance in GG, GC, CG, Unbiased accuracy compared with Ours. 

It is important to note that the experiments on Multi-Color MNIST were conducted using a three-layered MLP, whereas ResNet18 was employed for UrbanCars and MultiCelebA. Since GroupDRO is designed to improve worst group accuracy and is particularly effective when the complexity of model parameters is strongly regularized, it could achieve the best CC on Multi-Color MNIST. However, it tends to underperform when serving more complex networks than a simple MLP, as demonstrated on  UrbanCars and MultiCelebA.

Reviewer comment (Theory):
What underpins the expectation that the proposed method will effectively address multiple spurious correlations?

Author response:
In multiple bias scenarios, some samples may align with one spurious correlation but may conflict with another. The common strategy in single bias scenarios, which involves upweighting the worst group or clean samples that disagree with all the spurious correlations, underperforms in the multiple bias scenarios, as shown in Table 1 & 2 & 3. Since mitigating one bias often exacerbates another in the multiple bias scenarios [3], it is important to simultaneously mitigate multiple spurious correlations. Our method defines tasks according to adherence of samples to spurious correlations. When a model relies on shortcuts from spurious correlations, these are exposed as task conflicts. By optimizing to resolve these task conflicts simultaneously, we effectively eliminate multiple spurious correlations.

[3] Li, Zhiheng, Ivan Evtimov, Albert Gordo, Caner Hazirbas, Tal Hassner, Cristian Canton Ferrer, Chenliang Xu, and Mark Ibrahim. “A Whac-A-Mole Dilemma: Shortcuts Come in Multiples Where Mitigating One Amplifies Others.” CVPR 2023.

Reviewer comment (Novelty):
W1. While MultiCelebA is interesting and useful, selling it as a "new dataset" is too much of a stretch for my taste.

Author response:
Thank you for your constructive suggestion! In response to your comment, we have replaced "new dataset" with "new benchmark" in the manuscript. Despite this change, we still believe that, as a realistic and challenging benchmark, MultiCelebA will contribute substantially and promote future research in the field of debiased training. We also would like to highlight that reprocessed datasets/benchmarks like MultiCelebA have long been recognized by the community; examples include bFFHQ, a dataset for debiasing derived from FFHQ, and those for long-tailed classification such as ImageNet-LT (from ImageNet), CIFAR-LT (from CIFAR), and Places-LT (from Places).

Reviewer comment (Novelty):
W2. Saying that this is the first work connecting "unbiasing" with MOO or MTL (which is quite freely interpreted) is arguable at best. First, one could argue that even importance-weighting approaches are already interpreting the problem as MOO, but there are even works such as FairGrad [4] that connect biases (this one, in the context of fairness, which does not necessarily imply data-imbalance) which adaptively scale gradients.

Author response:
Thank you for your valuable and insightful feedback! We recognize the widespread use of reweighting methods like GroupDRO in the field. It is important to note that none of such prior work, including GroupDRO, explicitly relates their frameworks with MOO/MTL. However, our work explicitly frames debiasing from a perspective of MOO for the first time, which enables us to develop a new and effective algorithm based on recent advances in MOO. Our algorithm substantially outperformed standard reweighting techniques, and we believe its outstanding performance highlights the impact of viewing debiasing through a lens of MOO explicitly. 

Regarding FairGrad (TMLR 2023): According to the ICLR 2024 Reviewer Guidelines, FairGrad, published one month before our submission date, is considered as concurrent work. However, we sincerely appreciate your diligence in bringing this to our attention, and have revised the draft to discuss the paper and compare our method with it. Moreover, we would like to clarify that FairGrad focuses on grouping based on sensitive labels for fairness, a notable distinction from our work that aims to remove spurious correlations by MOO. Despite the existence of FairGrad, we thus assert that our paper is still the first to introduce MOO for mitigating spurious correlations.

Reviewer comment (Theory):
W3. Statements about MOO and Pareto Optimality in the manuscript make me worry about whether the authors have fully understood these concepts.

Author response:
Thank you for your perceptive observation. You correctly note that, in typical MTL settings, Pareto optimality does not necessarily guarantee unbiased performance across groups: there is a trade-off between tasks in terms of performance due to the conflicts between them (i.e., different tasks have different goals), and consequently a Pareto optimal model may be biased towards a certain task. However, in our setting, since tasks share exactly the same objective, a single model that works for all the tasks exists in principle (i.e., a model free from spurious correlations); “the” Pareto optimal parameter indicates such a single, ideal model in our paper. We will clarify this in the draft soon!

Reviewer comment (Writing):
W3 subpoint – I don't understand what it means to "address spurious correlations based on a theory of MOO".

Author response:
Thank you for your perceptive observation. You correctly note that, in typical MTL settings, Pareto optimality does not necessarily guarantee unbiased performance across groups: there is a trade-off between tasks in terms of performance due to the conflicts between them (i.e., different tasks have different goals), and consequently a Pareto optimal model may be biased towards a certain task. However, in our setting, since tasks share exactly the same objective, a single model that works for all the tasks exists in principle (i.e., a model free from spurious correlations); “the” Pareto optimal parameter indicates such a single, ideal model in our paper. We will clarify this in the draft soon!

Reviewer comment (Theory):
W3 subpoint – "Finding _the_ Pareto-optimal parameter". There are _many_ Pareto-optimal parameters.

Author response:
Thank you for your perceptive observation. You correctly note that, in typical MTL settings, Pareto optimality does not necessarily guarantee unbiased performance across groups: there is a trade-off between tasks in terms of performance due to the conflicts between them (i.e., different tasks have different goals), and consequently a Pareto optimal model may be biased towards a certain task. However, in our setting, since tasks share exactly the same objective, a single model that works for all the tasks exists in principle (i.e., a model free from spurious correlations); “the” Pareto optimal parameter indicates such a single, ideal model in our paper. We will clarify this in the draft soon!

Reviewer comment (Theory):
W3 subpoint – The goal is that "performance should not be biased towards a certain group". Pareto-optimality does not guarantee this. Indeed, MGDA is known to be biased towards tasks with low magnitudes. The concept the authors refer to is known as "task impartiality" in MTL (see, e.g., [1, 2]).

Author response:
MGDA tends to be biased towards tasks with low magnitudes as commented, and such a behavior is in fact beneficial for our framework. We first would like to note that, as demonstrated in Section A.2, our grouping strategy and group-wise loss result in the minority group (CC) with significantly low loss magnitude. This is mainly because (1) all the groups contribute to training equally, regardless of their population, through the group-wise loss, and (2) it is easy to reduce the loss for the minority group due to the low complexity of its data distribution. Hence, MGDA allows our algorithm to focus more on the minority group (with low loss magnitudes) during training and consequently resolve the data imbalance issue between the groups.

Reviewer comment (Theory):
W4. The arguments towards "finding a flat optima" are rather hand-wavy and unconvincing.

Author response:
This statement does not imply that a flat minima leads to an unbiased model. Our intention in the paper was that the second term in Eq. (3), which is originally introduced to achieve Pareto stationarity, can be also interpreted as an approximate curvature of the loss, according to previous work [1]. 
To be specific, the trace norm of hessian tr(H) is known to represent loss curvature, and the trace norm of the empirical Fisher information $tr(F)=\mathbb{E}\left[\left\lVert \boldsymbol{\alpha}^{\top}(\nabla L(\theta))\right\rVert_2^2\right]$, which is equivalent to the second term in Eq. (3), approximates $tr(H)$ [2, 3]. Therefore, minimizing the second term in Eq. (3) encourages to find a flat optima. Also, such a flat optima has been known to improve models’ generalization capability [1, 4, 5, 6]. 
To further understand the impact of the term on the loss curvature, **we have included a new ablation study in Section A.7.** The experimental results suggest that a higher weight on this term leads to a smaller loss curvature in the model parameter space.

[1] Xian Li and Hongyu Gong. Robust optimization for multilingual translation with imbalanced data. In Proc. Neural Information Processing Systems (NeurIPS), volume 34, 2021.

[2] Stanislaw Jastrzebski, Devansh Arpit, Oliver Astrand, Giancarlo Kerg, Huan Wang, Caiming Xiong, Richard Socher, Kyunghyun Cho, and Krzysztof Geras. Catastrophic ﬁsher explosion: Early phase ﬁsher matrix impacts generalization. arXiv preprint arXiv:2012.14193, 2020.

[3] Yu Sun, Shuohuan Wang, Yukun Li, Shikun Feng, Xuyi Chen, Han Zhang, Xin Tian, Danxiang Zhu, Hao Tian, and Hua Wu. Ernie: Enhanced representation through knowledge integration. arXiv preprint arXiv:1904.09223, 2019.

[4] Nitish Shirish Keskar, Dheevatsa Mudigere, Jorge Nocedal, Mikhail Smelyanskiy, and Ping Tak Pe- ter Tang. On large-batch training for deep learning: Generalization gap and sharp minima. In Proc. International Conference on Learning Representations (ICLR), 2017.

[5] Gintare Karolina Dziugaite and Daniel M Roy. Computing nonvacuous generalization bounds for deep (stochastic) neural networks with many more parameters than training data. arXiv preprint arXiv:1703.11008, 2017.

[6] Yiding Jiang, Behnam Neyshabur, Hossein Mobahi, Dilip Krishnan, and Samy Bengio. Fantastic generalization measures and where to find them. In Proc. International Conference on Learning Representations (ICLR), 2020.

Reviewer comment (Theory):
W5. Related with W3, it is quite unclear to me what makes the proposed method work at all.

Author response:
The key ideas in our method involve framing the mitigation of spurious correlation as MTL and adapting MOO for debiasing. Specifically, due to the following reason, achieving Pareto optimality under our grouping policy aligns that the model learns a feature space free from spurious correlations. 
1. There is an optimal solution that fits perfectly across all groups since they all share the same objective. (Please see our answer to [Weakness 3-1].)
2. If a model falls into shortcuts during training, the model’s performance will be reduced on certain groups, which deviates from Pareto optimality in the context of our grouping policy. 
3. Hence, optimization towards Pareto optimality with our grouping policy drives the model towards being unbiased.

Reviewer comment (Experiments):
W5 subpoint – MGDA minimizes in each iteration the regularizer in Eq. 3, and it is biased towards dominated tasks (which is observed in Table 5). However, the proposed approach (which is an interpolation between ERM and MGDA, similar to CAGrad [3]) works well. Is it the interpolation? Or learning $\alpha$ using along the parameters?

Author response:
First of all, we would like to correct potential misunderstandings: The records of MGDA in Table 5 suggest that it works well for the minority task (CC) **but not for the dominant task (GG)**. Please note that G and C indicate whether a group includes bias-guiding or bias-conflicting samples for each bias type, respectively, as defined in Section 5.1. This is also discussed in our answer to [Weakness 3-2]. 

Our objective is not an interpolation between ERM and MGDA since both the first and the second terms of Eq. (3) involve $\alpha$. Furthermore, $\alpha$ is not a scalar weight but a learnable vector, enabling dynamic adjustment of group-wise importance during training. This is a significant departure from CAGrad, which employs a constant $c$ for interpolation of ERM and MGDA. Please check out Algorithm 1 in the paper, which clearly illustrates how our method utilizes $\alpha$ in a fundamentally different way from interpolation.

Reviewer comment (Evaluation):
W6. Experiments lack statistics like standard deviations, making the effectiveness of some design choices (e.g. the update frequency $U$) quite unclear.

Author response:
Thank you for your valuable comment. We have revised the draft so that now all the tables except Table 3 report both mean and standard deviation values of three trials; the updated tables still demonstrate the superiority of our method.
Please note that we could not report the standard deviations in Table 3 since the table was sourced directly from Li et al. [7], in which the standard deviations are not available. 

[7] Li, Zhiheng, Ivan Evtimov, Albert Gordo, Caner Hazirbas, Tal Hassner, Cristian Canton Ferrer, Chenliang Xu, and Mark Ibrahim. “A Whac-A-Mole Dilemma: Shortcuts Come in Multiples Where Mitigating One Amplifies Others.” CVPR 2023.

Reviewer comment (Evaluation):
W7. The results in UrbanCars are quite different from those that can be found in other works. Just as an example, the worst variant of ERM recorded in [Papers with code](https://paperswithcode.com/sota/out-of-distribution-generalization-on) has a gap of -15.4, while the one reported in the paper is of -69.2 (worse than any result of the PwC table).

Author response:
We would like to clarify that there is no such discrepancy in the results. The -15.4 performance gap referenced from Papers with Code pertains to scenarios assuming a single bias, specifically, background bias in UrbanCars. In contrast, the results we have reported in our paper are the performance under multiple bias conditions (BG+CoObj gap). 
Moreover, Table 3 in our manuscript was directly sourced from Table 5 of the paper that originally introduced UrbanCars. The results correspond perfectly with the BG+CoObj performance metrics listed in Papers with Code.

Reviewer comment (Reproducibility):
Q1. When using MGDA in Table 5, does it mean that $\alpha$ is tuned as in Eq. 3 but only with the regularization? Or is $\alpha$ fully solved in each iteration?

Author response:
For MGDA in Table 5, we updated $\alpha$ with only the regularization term, $\left\lVert \boldsymbol{\alpha}^{\top}(\nabla L(\theta))\right\rVert_2^2$.