Experimental Setup
Datasets: We evaluate the performance of DeNetDM across diverse domains using two synthetic datasets (Colored MNIST [ 1 ] , Corrupted CIFAR10 [ 9 ] ) and two real-world datasets (Biased FFHQ [ 15 ] , BAR [ 23 ] ).
In Colored MNIST (CMNIST), the digit identity is spuriously correlated with color, whereas in Corrupted CIFAR10 (C-CIFAR10), the texture noise corrupts the target attribute. Biased FFHQ (BFFHQ) consists of human face images and is constructed from the FFHQ dataset [ 13 ] such that the age attribute is spuriously correlated with gender. BAR consists of human action images where six human action classes are correlated with six place attributes. We conduct experiments with varying proportions of bias-conflicting points in the training set to demonstrate the efficacy of our approach across diverse scenarios. Following the experimental settings used by the previous works [ 20 , 16 , 25 ] , we vary the ratio of bias-conflicting samples, specifically setting it at {0.5%, 1%, 2%, 5%} in the case of CMNIST and C-CIFAR10, {0.5%} in BFFHQ and {1%, 5%} in BAR datasets.

Baselines: We compare the performance of our proposed approach to the following bias mitigation techniques:

Empirical Risk Minimization (ERM) [ 32 ] : Standard ERM using cross-entropy loss.

Group DRO (GDRO) [ 26 ] : A supervised approach utilizing group labels to identify the worst group and learn an unbiased classifier.

Learning from Failure (LfF) [ 23 ] : Identifies bias-conflicting points through the Generalized Cross Entropy (GCE) loss and upweighting for debiasing.

Just Train Twice (JTT) [ 19 ] : Treating misclassified points by ERM-based classifiers as bias-conflicting and upweighting them for debiasing.

Disentangled Feature Augmentation (DFA) [ 16 ] : Introducing feature augmentation to improve the diversity of bias-conflicting points and enhance unbiased accuracy.

Logit Correction (LC) [ 20 ] : Proposes logit correction for bias mitigation along with MixUp [ 36 ] inspired data augmentation for increasing diversity.

Evaluation protocol: Evaluation of CMNIST and C-CIFAR10 is conducted on unbiased test sets, with target features being randomly correlated to spurious features. This evaluation protocol is commonly followed in the prior debiasing works [ 23 , 19 , 16 ] .
Nevertheless, in the case of BFFHQ, we do not use the unbiased test set since half of them are bias-aligned points. In order to ensure a fair evaluation on debiasing, we adhere to the previous methods [ 20 , 16 ] by utilizing a test set, which exclusively comprises bias-conflicting points from the unbiased test set. It is notable that the test set of BAR is composed solely of bias-conflicting samples, introducing a significant challenge for evaluation. Our primary metric is classification accuracy. We calculate aligned accuracy and conflicting accuracy separately for some of the ablations on CMNIST and C-CIFAR10 presented in Sec. 4.4 . Aligned accuracy is computed solely on bias-aligned data points while conflicting accuracy is determined exclusively based on the bias-conflicting points. We conduct five independent trials with different random seeds and report both the mean and standard deviation to ensure statistical robustness.

Implementation details: We perform extensive hyperparameter tuning using a small unbiased validation set with bias annotations to obtain the deep and shallow branches for all the datasets. We consistently utilize the same debiasing model architectures used by the previous methods for our target branch to ensure a fair comparison. Additionally, a linear layer is employed for the classifier for all the datasets. The additional architecture details for different datasets are as follows:

CMNIST: we use an MLP with three hidden layers for the deep branch and an MLP with a single hidden layer corresponding to the shallow branch. During the second phase of DeNetDM, we use an MLP with three hidden layers for the target branch.

C-CIFAR10, BAR: we use the ResNet-20 architecture for the deep branch and a 3-layered CNN model for the shallow branch. The target branch used in the second stage of DeNetDM is ResNet-18.

BFFHQ: we use the ResNet-18 architecture as the biased branch and a 4-layered CNN as the shallow branch. We also use the ResNet-18 architecture for the target branch, following the approaches of [ 20 , 16 ] .

Further details on the datasets and implementation are presented in Section D of the supplementary.