Fairness Continual Learning Approach to Semantic Scene Understanding in Open-World Environments

Maintaining fairness is one of the most important factors in learning CSS as it reduces the bias of the model toward a certain group of classes. Formally, under the fairness constraint in semantic segmentation, the error rate of each class should be equally treated by the segmentation model. Given classes $c_{a}$ and $c_{b}$ in the set of classes $\mathcal{C}^{1..T}$, this constraint can be formulated as follows:

where $y_{i,j}$ and $\hat{y}_{i,j}$ is the prediction and ground truth at the pixel location $(i,j)$, respectively; the loss function $\mathcal{L}$ measures the error rates of predictions. Intuitively, Eqn. (2) aims to maintain the differences in the error rates between classes lower than a small threshold $\epsilon$ to guarantee fairness among classes. For simplicity, this constraint can be considered as an additional loss while optimizing Eqn. (1). However, this approach could not guarantee the model being fair due to Eqn. (3).

As shown in the above inequality, the constraint of Eqn. (2) has been bounded by the loss function in Eqn. (1). Although minimizing Eqn. (1) could also impose the constraint in Eqn. (2), the fairness issue still remains unsolved due to the imbalanced class distributions indicated through Eqn. (4).

where $p(\cdot)$ is the data distribution, $\mathbf{y}_{\setminus(i,j)}$ is the predicted segmentation map without the pixel at position $(i,j)$, $p(y^{k})$ is the class distribution of pixels, and $p(\mathbf{y}_{\setminus(i,j)}|y_{(i,j)})$ is the conditional structural constraint of the predicted segmentation $\mathbf{y}_{\setminus(i,j)}$ conditioned on the prediction $y_{i,j}$. Practically, the class distributions of pixels $p(y_{i,j})$ suffer imbalanced issues, where several classes in the majority group significantly dominate other classes in the minority group. Then, learning by gradient descent method, the model could potentially bias towards the class in the majority group because the produced gradients of classes in the majority group tend to prevail over the ones in the minority group. Formally, considering the two classes $c_{a}$ and $c_{b}$ of the dataset where their distributions are skewed, i.e., $p(c_{a})<p(c_{b})$, the gradients produced are favored towards class $c_{b}$ as shown in Eqn. (5).

where $||\cdot||$ is the magnitude of gradients, $\mathbf{y}_{(c_{a})}$ and $\mathbf{y}_{(c_{b})}$ are the predictions of classes $c_{a}$ and $c_{b}$.

Learning Fairness from Ideally Fair Distribution To address this problem, we first assume that there exits an ideal distribution $q(\cdot)$ where the class distributions $q(y_{i,j})$ are equally distributed. Under this assumption, the model learned is expected to behave fairly among classes as there is no bias toward any groups of classes. It should be noted that our assumption is used to derive our learning objective and is going to be relaxed later. In other words, the ideal data is not required at training. Then, our learning objective in Eqn. (4) could be rewritten as follows:

The fraction between the ideal distribution $q(\cdot)$ and the actual data distribution $p(\cdot)$ is the residual learning objective for the model to achieve the desired fairness goal. Let us further derive Eqn. (6) by taking the log as follows:

The detailed derivation of Eqn. (6) and Eqn. (7) will be available in the supplementary. As shown in the Eqn. (7), there are three learning objectives as follows:

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  The Continual Learning Objective The first term, i.e., $\mathcal{L}({\mathbf{y},\mathbf{\hat{y}}})$, represents the task-specific loss which is the continual learning objective. This objective aims to address the catastrophic forgetting and background shift problems. To achieve this desired goal, we introduce a novel Prototypical Contrastive Clustering Loss that will be discussed in Sec. 3.2.

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  The Fairness Objective The second term, i.e., $\mathcal{L}_{class}=\log\left(\frac{q(y_{i,j})}{p(y_{i,j})}\right)$, maintains the fairness in the predictions produced by the model. This objective penalizes the prediction of classes forcing the model to behave fairly based on the class distribution. Under the ideal distribution assumption where the model is expected to perform fairly, the $q(y_{i,j})$ will be considered as a uniform distribution $\mathcal{U}$, i.e., $q(y_{i,j})\sim\mathcal{U}(C)$ ($C$ is the number of classes).

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  The Conditional Structural Consistency Objective The third term, i.e., $\mathcal{L}_{cons}=\log\left(\frac{q(\mathbf{y}_{\setminus(i,j)}|y_{i,j})}{p(\mathbf{y}_{\setminus(i,j)}|y_{i,j})}\right)$, regularizes the structural consistency of the prediction. This objective acts as a metric to constrain the structure of the predicted segmentation under the ideal distribution assumption. To model this conditional structure consistency, we introduce a conditional structural constraint based on the Markovian assumption discussed in Sec. 3.4.

A successful continual learning approach should be able to model background classes without explicit supervision and confront the forgetting problem of previously learned classes when the labels of the task are provided to update the knowledge of the model [20]. A straightforward adoption of Softmax could not be enough to handle. Indeed, the unlabeled pixels will be ignored during training. Thus, it results in these unannotated pixels could be treated as negative samples. Consequently, the segmentation model tends to produce indiscriminative features for these unknown classes that limit the capability of learning new classes in future tasks or recognizing the classes learned previously.

To address this limitation, in addition to the Softmax loss, we introduce a novel Prototypical Contrastive Clustering Loss. In particular, the semantic segmentation pixel belonging to each class can be represented in latent space. Inspired by [20, 2, 21], the features representing the classes can be separated by defining it as a contrastive clustering problem [20] where features of the same class would be pulled closer while features of different classes would be pushed far away. In addition, the deep representations of unknown classes will be grouped into the same cluster of unknown classes to produce discriminative features against other classes.

Formally, for each class $c\in\mathcal{C}^{1..t}$, it is represented by a prototypical vector $\mathbf{p}_{c}$. In addition, the additional prototypical vector $\mathbf{p}_{0}$ represents a cluster of unknown classes. Let $f^{t}_{i,j}$ be a feature representation of pixel at location $(i,j)$ of the input $\mathbf{x}^{t}$. Then, the Prototypical Contrastive Clustering Loss $\mathcal{L}_{cluster}$ can be defined via a distance $\mathcal{D}$ as follows:

where $\ell$ is a distance metric, $\Delta$ is a margin between the feature vectors of different classes, and $\hat{y}^{t}_{i,j}$ is the label of pixel $(i,j)$. Minimizing this loss separates the classes represented in the latent space. For step $t>1$, $\hat{y}^{t}_{i,j}$ of an unknown-class pixel will utilize a pseudo label where its assigned label is computed based on the closest cluster. In addition, since the prototypical vectors of classes $c\in\mathcal{C}^{1..t-1}$ have been well learned to represent for classes, these vectors $p_{c}$ (where $c\in\mathcal{C}^{1..t-1}$) will be frozen at step $t$ to maintain its learned knowledge of classes $\mathcal{C}^{1..t-1}$.

The set of prototypical vectors at current step $t$, i.e., $\mathbf{p}_{0}$ and $\mathbf{p}_{c}$ where $c\in\mathcal{C}^{t}$ are updated gradually with respect to the growth of feature vectors. In particular, the prototypical vector $\mathbf{p}_{c}$ will be periodically updated (after every $M$ iterations) with momentum $\eta$ based on the set of features $\mathbf{f}_{i,j}$ of class $c$. Following common practices [20, 16], to effectively support the updating step and memory efficiency, for each class $c$, we only maintain a set of features $\mathcal{S}_{c}$ with a fixed length of $L$. Algorithm 1 in the supplementary illustrates an overview of computing the prototypical contrastive clustering loss while updating the class prototypes. Fig. 2 illustrates our proposed FairCL framework.

Knowledge Distillation is a common continual learning approach [36, 3, 12, 46] where the knowledge of the previous model will be distilled into the current model. This mechanism prevents the segmentation model from diverging knowledge learned previously and avoiding the catastrophic forgetting problem. This continual learning paradigm has been widely adopted due to its efficiency in computation. In addition, this approach also does not require data rehearsal, i.e., storing the data samples of previous tasks. In this paper, we demonstrate that our Prototypical Constrative Clustering approach is a comprehensive upper limit of the Knowledge Distillation approach. In particular, the common knowledge distillation approach can be formulated as follows:

where $\mathbf{f}^{t}$ and $\mathbf{f}^{t-1}$ are the features of the input $\mathbf{x}^{t}$ produced by the segmentation model at step $t$ and step $t-1$, respectively; and the distance metric $\mathcal{D}$ measure the knowledge gap between $\mathbf{f}^{t}$ and $\mathbf{f}^{t-1}$.

Proposition 1: The Prototypical Constrative Clustering Approach is the generalized upper bound of the Knowledge Distillation Approach.

Proof: Without lack of generality, we assume that $\mathcal{D}$ is a metric that measures distance between features. Given a set of fixed prototypical vectors $\mathbf{p}_{c}$, we consider the following triangle inequality of the metric $\mathcal{D}$ as follows:

where $|\mathcal{C}|$ is the number of prototypical vectors. The prototypical vectors $\mathbf{p}_{c}$ and the feature vectors $\mathbf{f}^{t-1}$ produced by the segmentation model at step $t-1$ are considered as constant features as the model in the previous model $t-1$ has been fixed at step $t$. Thus, the distance $\mathcal{D}(\mathbf{p}_{c},\mathbf{f}^{t-1})$ could be considered as constant number. Then, Eqn. (12) can be further derived as follows:

Intuitively, under this upper bound in Eqn. (13), by only optimizing our prototypical contrastive clustering loss, the knowledge distillation constraint has also been implicitly imposed. Beyond the property of generalized upper bound stated in Proposition 1, our approach offers other benefits over the knowledge distillation approach. In particular, our approach is computationally efficient, where our method only requires a single forward pass of the segmentation model. Meanwhile, the knowledge distillation demands two forward passes for both the current and previous models, which also requires additional computational memory for the previous model. Moreover, our approach provides a better representation of each class $c$ through the prototypical vector $\mathbf{p}_{c}$. This mechanism helps to effectively maintain the knowledge of classes learned previously while allowing the model to update the new knowledge without rehearsing the old data.

The conditional structural constraint plays an important role as it will ensure the consistency of the predicted segmentation map. However, modeling the conditional structural constraint $\log\left(\frac{q(\mathbf{y}_{\setminus(i,j)}|y_{i,j})}{p(\mathbf{y}_{\setminus(i,j)}|y_{i,j})}\right)$ in Eqn. (7) is a quite challenging problem due to two factors, i.e., (1) the unknown ideal conditional distribution $q(\mathbf{y}_{\setminus(i,j)}|y_{i,j})$, and the complexity of the distribution $q(\mathbf{y}_{\setminus(i,j)}|y_{i,j})$. To address the first limitation of unknown ideal distribution, let us consider the following tight bound as follows:

The inequality in Eqn. (14) always hold with respect to any form ideal distribution $q(\cdot)$. Thus, optimizing the negative log-likelihood of $\log p(\mathbf{y}_{\setminus(i,j)}|y_{i,j})$ could also regularize the conditional structural constraint due to the upper bound of Eqn. (14). More importantly, the requirement of ideal data distribution during training has also been relaxed. However, up to this point, the second limitation of modeling the complex distribution $q(\mathbf{y}_{\setminus(i,j)}|y_{i,j})$ has still not been solved.

To address this problem, we adopt the Markovian assumption [5, 39] to model conditional structural consistency. In particular, we propose a simple yet effective approach to impose the consistency of the segmentation map through the prediction at location $(i,j)$ and predictions of its neighbor pixels. Formally, the conditional structure consistency can be formed via the Gaussian kernel as follows:

where $\mathcal{N}(i,j)$ is the set of neighbor pixels of $(i,j)$, $\{\sigma_{1},\sigma_{2}\}$ are the scale hyper-parameters of the Gaussian kernels. The conditional structural consistency loss defined in Eqn. (15) enhance the smoothness and maintain the consistency of the predicted segmentation map by imposing similar predictions of neighbor pixels with similar contextual colors.

Datasets ADE20K [49] is a semantic segmentation dataset that consists of more than 20K scene images of 150 semantic categories. Each image has been densely annotated with pix-level objects and objects parts labels. Cityscapes [10] is a real-world autonomous driving dataset collected in European. This dataset includes $3,975$ urban images with high-quality, dense labels of 30 semantic categories. PASCAL VOC [13] is a common dataset that consists of more than $10$K images of $20$ classes.

Implementation Two segmentation network architectures are used in our experiments, i.e., (1) DeepLab-V3 [6] with the ResNet-101 backbone, and (2) SegFormer [45] with MiT-B3 backbone. Further details of our implementation will be available in our supplementary.

Evaluation Protocols:  Following [12], we focus on the overlapped CSS evaluation. Our proposed method is evaluated on several settings for each dataset, i.e., ADA20K 100-50 (2 steps), ADA20K 100-10 (6 steps), ADA20K 100-5 (11 steps), Cityscapes 11-5 (3 steps), Cityscapes 11-1 (11 steps), Cityscapes 1-1 (21 steps), Pascal VOC 15-1 (3 steps), and Pascal VOC 10-1 (11 steps). The mean Intersection over Union (mIoU) metric is used in our experiments. The mIoU is computed after the last step for the classes learned from the first step, the later continual classes, and all classes. The mIoU for the initial classes shows the robustness of the model to catastrophic forgetting, while the metric for the later classes reflects the ability to learn new classes. To measure the fairness of the model, we also report the standard deviation (STD) of IoUs over all classes.

Our ablative experiments study the effectiveness of our proposed FairCL approach on the performance of the CSS model and fairness improvement on the ADE20K 100-50 benchmark (Table 1).

Effectiveness of the Network Backbone Table 1 illustrates the results of our approach using the DeepLab-V3 [5] with the Resnet101 backbone and the SegFormer [45] with a Transformer backbone, i.e. MiT-B3 [45]. As shown in our results, the performance of segmentation models using a more powerful backbone, i.e., Transformer, outperforms the models using the Resnet backbone. The capability of learning new classes has been improved notably, i.e., the mIoU of classes 101-150 in the full configuration has been improved from $19.86\%$ to $25.46\%$ while the model keeps robust to catastrophic forgetting, the mIoU has been increased from $41.96\%$ to $43.56\%$ in the classes 0-100. Additionally, fairness between classes has been promoted when the standard deviation of the IoU over classes has been reduced from $21.67\%$ to $21.10\%$.

Effectiveness of the Prototypical Contrastive Clustering Loss We evaluate the impact of the Prototypical Contrastive Clustering Loss ($\mathcal{L}_{cluster}$) in improving the performance in the continual learning problem compared to the fine-tuning approach. As shown in Table 1, the clustering loss has significant improvements in the catastrophic forgetting robustness compared to using only the Softmax loss. In particular, the mIoU of classes 0-100 for both DeepLab-V3 and SegFormer backbones has been improved by $+41.63\%$ and $+43.30\%$ respectively that makes the overall mIoU increase by $+26.45\%$ and $+28.44\%$, and the average mIoU between classes increases by $+13.17\%$ and $+14.03\%$. Although the STD of IoUs has slightly increased in this setting, the major target of our $\mathcal{L}_{cluster}$ is used to model the catastrophic forgetting and background shift problems in CSS illustrated by the significant performance improvement of mIoU.

Effectiveness of the Fairness Treatment Loss As reported in Table 1, the fairness treatment from the class distribution loss $\mathcal{L}_{class}$ significantly improves the overall performance and the accuracy of classes. In detail, the STD of IoU from classes has been reduced by $0.96\%$ and $0.46\%$ for both backbones while the mIoU has been improved from $32.97\%$ to $34.40\%$ and from $36.18\%$ to $36.78\%$, respectively. The results have shown that our approach has promoted the fairness of the model.

Effectiveness of the Conditional Structural Consistency The full configuration in Table 1 shows experimental results of our model using conditional structure constraint loss $\mathcal{L}_{cons}$. As illustrated in our results, the conditional structure constraint demonstrates effective improvement. Indeed, it promotes the accuracy of the initial classes and the novel classes when the mIoU has been increased from $43.35\%$ to $43.56\%$ and from $23.50\%$ to $25.46\%$ respectively with the Transformer backbone. The fairness of classes is also improved as the standard deviation of the IoU of classes 0-100 and classes 101-150 is reduced from $19.03\%$ to $18.71\%$ and from $20.75\%$ to $19.99\%$.

Cityscapes As shown in Table 2, our FairCL outperforms previous SOTA methods evaluated on Cityscapes benchmarks. In particular, in the 11-5 task, our method using Resnet and Transformer achieves the mIoU of $66.96\%$ and $67.85\%$ respectively which shows better performance than prior methods. Meanwhile, the results for the 11-1 task are $66.61\%$ and $67.09\%$ w.r.t. the Resnet and Transformer backbones. For the 1-1 task, the mIoU of our method is $49.22\%$ and $55.68\%$.

ADE20K Table 3 presents our experimental results using ResNet and Transformer backbones compared to prior SOTA approaches. Our proposed approach achieves SOTA performance and outperforms prior methods. In particular, our approach achieves the final mIoU of $36.99\%$ for Resnet and $37.56\%$ for Transformer in the 100-50 tasks. For the 50-50 tasks, the model reaches the final mIoU of $34.55\%$ and $35.15\%$ for the Resnet and Transformer backbones, respectively while the result of the prior method [15] is $33.50\%$. Meanwhile, the overall results of our method for the 100-10 task are $34.65\%$ and $35.49\%$ which shows outperforming previous approaches. Fig. 3 visualizes the qualitative result of our method compared to PLOP [12]. Initially, the ground truth contains the class “car” in the first step and the class “minibike” in the third step. Then, in the fourth step, the class “bicycle” is included. As a result, PLOP [12] partly forgets the “minibike” information when learning the class “bicycle” information. Meanwhile, our method consistently maintains the information of “minibike” and predicts segmentation correctly.

Pascal VOC As shown in Table 4, the proposed method outperforms the prior approaches evaluated on the Pascal VOC 2012 dataset. In detail, our method achieves the overall mIoU of $61.5\%$ in the 15-1 task while the result of the previous method [46] is $59.4\%$. Meanwhile, the mIoU in the 10-1 task is $36.6\%$ which shows better performance than the prior methods.

To illustrate the performance improvement of our proposed method in major and minor classes, we include the results of the mIoU (all) and the STD among IoUs of the major group and the minor group on the ADE20K 100-50 (Table 5) and Cityscapes 11-5 (Table 6) benchmarks. As shown in the table below, our proposed approach has improved the performance of both major and minor groups. Thus, these results illustrated that the performance improvement in mIoU is also coming from the minority classes. It helps to enhance the mIoU performance and reduce the STD in both major and minor classes, thus, improving the fairness of the model predictions.

Similarly, to illustrate the effectiveness and robustness of our method in the non-incremental setting. We report our results after the first learning step on the ADE20K 100-50 (Table 7) and Cityscapes 11-5 (Table 8) benchmarks. Our proposed fairness approach has also contributed to the performance improvement of both major and minor classes in non-incremental settings. The comparison table of major and minor groups in the first step is illustrated below.

The goal of conditional structural consistency is to improve the prediction gap among neighbor pixels, thus, enhancing the smoothness of the predictions. In addition, it helps to increase fairness among classes. It is because this loss helps to clean up the spurious or ambiguous predictions produced by the major classes around minor classes. Therefore, the loss alleviates the dominance of the major groups and improves the accuracy of the minor groups, thus, resulting in fairness that has also been further improved (as illustrated in Table 1 in the main paper).

We also perform an additional ablation study on the ADE20K (100-50) benchmark to investigate the impact of the delta. As shown in Table 9, the impact of $\Delta$ does not significantly influence the results due to the minor performance drop.

We have observed the performance improvement of our approach on Pascal VOC is less significant than the ADE20K and Cityscapes because of the minor bias in Pascal VOC. In particular, the data distributions of these datasets are visualized in Figure 4 in the rebuttal file (the PDF file of the rebuttal is attached in Global Response). We calculated the entropy value of the data distributions that illustrate the balance level of the datasets (the higher value of entropy, the more balance the dataset as the data distribution tends to be more uniform). Then, based on the data distributions and entropy values, we observe the data distributions of ADE20K and Cityscapes suffer more bias than the Pascal VOC since the entropy value of Pascal VOC (H = 0.81) is higher than ADE20K (H = 0.69) and Cityscapes (H = 0.62). Thus, ADE20K and Cityscapes suffer severe fairness issues compared to Pascal VOC. Our approach aims to improve the fairness of the model. Therefore, on the more severe bias datasets (ADE20K and Cityscapes), our approach performs more significantly.

We would like to highlight that storing prototypical vectors requires significantly less memory than using the additional teacher model as used in distillation approaches [12]. For example, in the ADE20K benchmark, storing DeepLab-V3 (151 classes) requires $58.664$M parameters, while storing $152$ prototypical $2048$-D vectors (including the unknown cluster) only uses $0.311$M parameters. In addition, the computation of loss with is cheaper than a forward pass of the entire network used in distillation. Therefore, in terms of computational cost and memory, our approach remains more efficient compared to knowledge distillation approaches.