Title: FairDD: Fair Dataset Distillation
Venue: NeurIPS 2025
Accepted: yes
Keywords: Dataset Distillation

Dataset Condensation
Abstract: Condensing large datasets into smaller synthetic counterparts has demonstrated its promise for image classification. However, previous research has overlooked a crucial concern in image recognition: ensuring that models trained on condensed datasets are unbiased towards protected attributes (PA), such as gender and race. Our investigation reveals that dataset distillation fails to alleviate the unfairness towards minority groups within original datasets. Moreover, this bias typically worsens in the condensed datasets due to their smaller size. To bridge the research gap, we propose a novel fair dataset distillation (FDD) framework, namely FairDD, which can be seamlessly applied to diverse matching-based DD approaches (DDs), requiring no modifications to their original architectures. The key innovation of FairDD lies in synchronously matching synthetic datasets to PA-wise groups of original datasets, rather than indiscriminate alignment to the whole distributions in vanilla DDs, dominated by majority groups. This synchronized matching allows synthetic datasets to avoid collapsing into majority groups and bootstrap their balanced generation to all PA groups. Consequently, FairDD could effectively regularize vanilla DDs to favor biased generation toward minority groups while maintaining the accuracy of target attributes. Theoretical analyses and extensive experimental evaluations demonstrate that FairDD significantly improves fairness compared to vanilla DDs, with a promising trade-off between fairness and accuracy. Its consistent superiority across diverse DDs, spanning Distribution and Gradient Matching, establishes it as a versatile FDD approach.

FairDD: Fair Dataset Distillation

Abstract

Condensing large datasets into smaller synthetic counterparts has demonstrated its promise for image classification. However, previous research has overlooked a crucial concern in image recognition: ensuring that models trained on condensed datasets are unbiased towards protected attributes (PA), such as gender and race. Our investigation reveals that dataset distillation fails to alleviate the unfairness towards minority groups within original datasets. Moreover, this bias typically worsens in the condensed datasets due to their smaller size. To bridge the research gap, we propose a novel fair dataset distillation (FDD) framework, namely FairDD, which can be seamlessly applied to diverse matching-based DD approaches (DDs), requiring no modifications to their original architectures. The key innovation of FairDD lies in synchronously matching synthetic datasets to PA-wise groups of original datasets, rather than indiscriminate alignment to the whole distributions in vanilla DDs, dominated by majority groups. This synchronized matching allows synthetic datasets to avoid collapsing into majority groups and bootstrap their balanced generation to all PA groups. Consequently, FairDD could effectively regularize vanilla DDs to favor biased generation toward minority groups while maintaining the accuracy of target attributes. Theoretical analyses and extensive experimental evaluations demonstrate that FairDD significantly improves fairness compared to vanilla DDs, with a promising trade-off between fairness and accuracy. Its consistent superiority across diverse DDs, spanning Distribution and Gradient Matching, establishes it as a versatile FDD approach. Code is available at https: //github.com/zqhang/FairDD .

1 Introduction

Deep learning has witnessed remarkable success in computer vision, particularly with recent breakthroughs in vision models [45, 28, 47, 33, 72]. Their vision backbones, such as ResNet [20] and ViT [16], are data-hungry models that require extensive amounts of data for optimization. Dataset Distillation (DD) [60, 67, 69, 6, 58, 32, 12, 38, 18, 22, 7, 8, 71] provides a promising solution to alleviate this data requirement by condensing the original large dataset into more informative and smaller counterparts [42, 10]. Despite its appeal, existing researches focus on ensuring that models trained on condensed datasets perform comparable accuracy to those trained on the original dataset in terms of target attributes (TA) [13, 40, 56]. However, they have overlooked enabling the fairness of trained models with respect to protected attributes (PA).

Unfairness typically arises from imbalanced sample distributions among PA in the empirical training datasets. When the original datasets suffer from the PA imbalance, the corresponding datasets condensed by vanilla DDs inherit and amplify this bias in Fig. 1(e). Since vanilla DDs tend to cover TA distribution for image classification, and as a result, it naturally leads to more synthetic samples located in majority groups compared to minority groups w.r.t. PA, as shown in Figs. 1(a), 1(b), 1(c), and 1(d). In this case, these condensed datasets retain the imbalance between protected attributes,

DM

FairDD+DM

(a) C-MNIST (FG).

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(b) C-FMNIST (BG).

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(c) CIFAR10-S.

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(d) CelebA (Each row denotes one class)

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IDC

(e) Fairness comparison(IPC=50)

thereby rendering the model trained on them unfair. Moreover, the reduced size of the condensed datasets typically amplifies the bias present in the original datasets, especially when there is a significant gap in size between the original and condensed datasets, such as image per class (IPC) 1000 vs. 10. Therefore, it is worthwhile to broaden the scope of DDs to encompass both TA accuracy and PA fairness. Recent works [14, 41] attempt to address the class/TA-level long-tailed phenomenon [71] and spurious correlations [13] to improve the classification performance [56, 59], but the exploration on visual fairness is still blank.

To bridge this gap, we propose FairDD, a novel FDD framework that achieves PA fairness in models trained on condensed datasets, even when the original data exhibit PA imbalance. Note that FDD addresses data-level fairness: how to generate a distilled dataset that is inherently unbiased, agnostic to the downstream model. Instead, traditional fairness literatures focus on model-level fairness: how to train a fair model given a dataset. These two perspectives approach fairness from distinct yet complementary directions. FDD requires simultaneously maintaining TA accuracy and improving PA fairness. It is challenging, as the algorithm must properly balance the emphasis across all groups reducing the dominance of majority groups while maintaining their TA distributional coverage, and preserving minority groups to mitigate PA bias.

FairDD tackles this challenge by (1) partitioning the empirical training distribution into different groups according to PA and decomposing the single alignment target of vanilla DDs into PA-wise subtargets. (2) synchronously matching synthetic samples to these PA groups, which equally bootstraps synthetic datasets to each PA group without involving the specific group size. In doing so, we reformulated the optimization objectives of vanilla DDs into fairDD-style versions. This allows FairDD to mitigate the effect of imbalanced PA on the generation of S and prevents S from collapsing into the majority group. In Fig. 1(d), FairDD synthesizes more male samples (highlighted by blue squares) within an attributive class originally dominated by females. Meanwhile, FairDD could also achieve the comprehensive coverage of the entire distribution for TA accuracy. We provide a theoretical guarantee that FairDD could improve PA fairness while maintaining TA accuracy.

Extensive experiments demonstrate that our framework effectively mitigates the unfairness in datasets of highly diverse bias. FairDD substantially improves data fairness trained on condensed datasets compared to various vanilla DDs. FairDD demonstrates its versatility across diverse DDs, including Distribution Matching (DM) and Gradient Matching (GM) 2 . Our main contributions are as follows:

To the best of our knowledge, our research is the first attempt to incorporate visual fairness into DDs explicitly. We reveal that vanilla DDs fail to mitigate the bias in original datasets and may exacerbate it due to the limited synthetic samples, leading to severe PA bias in the model trained by the resulting condensed dataset.

We introduce a novel FDD framework called FairDD, which proposes synchronized matching to align synthetic samples to all PA groups partitioned from the original data distribution. This allows the generated synthetic samples to be agnostic to PA imbalance of original datasets while maintaining the overall distributional coverage of TA.

Extensive empirical experiments demonstrate that FairDD is a generalist to significantly mitigate the unfairness of vanilla DDs. Its consistent superiority is observed across various DDs, including DM and GM.

2 Related Work

Dataset distillation Dataset distillation has been broadly applied to many important fields [30, 21, 17, 9]. The first work [60] attempts to formulate dataset distillation as a bi-level optimization problem. However, the two folds of the optimization process are time-consuming. Neural tangent kernel [23] is utilized to obtain the closed form of the inner loop [44, 37, 73]. Some previous works propose surrogate objectives to achieve comparable even better performance, including matching-based methods like GM [70, 67, 31], DM [69, 58, 68], TM [6, 12], soft label learning [4, 54, 62, 52], and factorization [27, 15, 35, 31]. Recent works [14, 41] attempt to mitigate bias to improve classification accuracy on the TA without considering protected attributes (PA), staying within the traditional setting of DD [13, 71, 56, 59]. The work [13] mitigates sample-wise bias by assigning higher weights to samples located in low-density regions of the original data distribution, while they neglect fairness concerning PA. It fails to guarantee that the alignment objective is unbiased across all attribute groups, nor does it ensure adequate distribution coverage. Instead, our methods have a fairness alignment objective to facilitate unbiased data distillation; In addition, we provide a theoretical proof to guarantee the distribution coverage for TA. This makes FairDD with a good balance between fairness and accuracy. We provide a performance comparison in Appendix E.

Visual fairness Current literature on fairness aims to train a model that outputs fair logits under class-imbalanced datasets [5]. According to the stage of bias mitigation, the research field of fairness algorithm [3] can be classified into three branches: Pre-processing [11, 39, 46, 51], Inprocessing [1, 24, 64, 66, 26, 61, 25, 65], and Post-processing [2, 19]. They learn fair representations without involving information condensation [53, 55, 57, 48]. Fairness-aware synthetic data generation serves as a pre-processing for fairness. They frame fairness mitigation as a data-to-data translation problem, and utilize generative models [63] to produce fairer datasets with respect to protected groups [46, 50]. However, they do not consider the aspect of information condensation. Instead, our work aims to reduce bias in condensed datasets by: (1) ensuring that the information from the original datasets is effectively distilled into the condensed datasets, and (2) simultaneously mitigating both the inherent bias of the original dataset and the bias exacerbated by vanilla dataset condensation. Once the data is condensed, we can train a fair model without any further human intervention.

3 Preliminaries

Dataset Distillation. Given a vast dataset T = { ( x i , y i ) } N i =1 , DDs aim to condense original dataset T into a smaller dataset S = { ( x i , y i ) } i M =1 via distillation algorithm Alg with nerual networks, parameterized by θ . Randomly initialized classification network g ψ should maintain the same empirical risk whether it is trained on S or T .

where Ψ and ℓ ( · ) represent the parameter space and loss function, respectively. The pioneering work [60] formulates Alg as a bi-level optimization problem. However, such an optimization process is time-consuming and unstable. Recent works circumvent it and propose surrogate matching objectives to achieve comparable and even better performance. This research line is collectively referred to as the DMF, and our paper primarily studies one-stage GM [70, 67] and DM [69, 58, 68]. We leave it for future exploration.

Visual Fairness Visual fairness is an important field to mitigate discrimination against minority groups. Group fairness requires no statistical disparity to different groups in terms of PA, such as race and gender. This means that an ideal fair model should make independent predictions between TA and PA. One of the common fairness criteria is equalized odds (EO), which computes the prediction accuracy of PA conditioned on TA, to evaluate the level of conditional independence between PA and TA. We use two types of difference of equalized odds DEOM and DEOA from the worst and averaged levels. Formally, given the PA set A = { a 1 , a 2 , ..., a p } , where p denotes the number of protected attributes. DEOM and DEOA [26] can be formulated mathematically as follows:

̸

̸

4 A Close Look at Dataset Distillation

A unified perspective for Data Match Framework. The essence of the DMF lies in choosing the target signs of original samples that effectively represent their characteristics for image recognition, and then aligning these signals as a proxy task to optimize the condensed dataset. The target signal ϕ ( x ; θ ) is typically the key information from feature extraction or optimization process using a randomly initialized network parameterized by θ . For example, GM aligns the gradient information produced by T with that of the condensed S . Instead, DM matches the embedding distributions of T and S . As for these approaches in DMF. we can unify the optimization objective as L ( S ; θ, T ) :

where E [ ϕ x ∼T y ( x ; θ )] ∈ R C and E [ ϕ x ∼S y ( x ; θ )] ∈ R C are represented expectation vectors of the target signs on T and S , respectively. D ( · , · ) is a distance function. In DMF, MSE is adopted in DM and DREAM, and MAE is used in IDC.

Why do vanilla DDs fail to mitigate PA imbalance? Given the dataset T = { ( x i , y i , a i ) } N i =1 , a i ∈ A , let us define the class-level sample ratio R y = { r a 1 y , r a 2 y , ..., r a p y } , where r a i y = |T a i y | / |T y | , and | · | represents the cardinal number of a set. Current DDs' paradigms focus on preserving TA representativeness for image recognition. Here, we decompose the whole expectation into the expectation of PA-wise groups, i.e, E [ ϕ x ∼T y ( x ; θ )] = ∑ a i ∈A r a i y E [ ϕ x ∼T a i y ( x ; θ )] , and thus Eq. 1 can be rewritten as follows:

̸

From Eq. 2, the optimization objective of class y is weighted by the sample ratio r a i y from different groups. When T suffers from PA imbalance, e.g., r a j y ≫ ∑ i = j r a i y , the majority group indexed by i contributes more to the alignment compared to minority groups. In other words, S tends to produce more samples belonging to group i for the total loss minimization. The objective of vanilla DDs suffers from PA imbalance within T .

Next, we further study how the resulting S is affected by sample ratio r a i y of different groups. To this end, we assume that the optimization process could reach the optimal solution for each class, and as a result, the final resulting S satisfies the condition that the derivative of the objective function with

∂ [ ϕ x ∼S y ( x ; θ )] Now, let's delve into the specific distance metrics used in vanilla DDs, where the most commonly used metrics are MAE, MSE, and cosine distance. We could compute the optimal point of E [ ϕ x ∼S y ( x ; θ )] could reach under these metrics:

Where λ is a constant shared across all groups, equal to 1 for MAE and MSE, and equal to ∥ E [ ϕ x ∼S y ( x ; θ )] ∥ 2 ∥ ∑ a i ∈A r a i y E [ ϕ x ∼T a i y ( x ; θ )] ∥ 2 for the cosine loss. Eq. 3 presents that the expectation of synthetic sam- ples E [ ϕ x ∼S y ( x ; θ )] ultimately converges to an average on expectations of all PA groups, weighted by their respective sample ratios r a i y . This indicates that vanilla DDs naturally favor majority groups, causing S to shift towards them and inherit their biases.

̸

When original datasets suffer from PA imbalance, e.g., r a j y ≫ ∑ i = j r a i y , the unfairness of the synthetic dataset stems from two different aspects: 1) The majority group renders synthetic samples to locate its region from Eq. 3. 2) According to Eq. 2, the large sample quantities of the majority group contribute more to the total loss. As a result, minority groups experience higher loss during testing, which limits the model to represent them accurately. These factors prompt us to reduce the impact of PA imbalance on the generation of S .

5 FairDD

Overview In this paper, we propose a novel FDD framework that achieves both PA fairness and TA accuracy for the model trained on its generation S , regardless of whether the original datasets exhibit

PA fairness. As illustrated in Fig. 2, FairDD first partitions the dataset into different groups w.r.t. PA and then introduces an effective synchronized matching to equally align S with each group within T . Compared to vanilla DDs, which pull the synthetic dataset toward the majority group in the synthetic dataset, FairDD proposes a group-level synchronized alignment, in which each group attracts the synthetic data toward itself, thus forcing it to move farther from other groups. This synchronized pull prevents the generation from collapsing into majority groups (fairness) and ensures class-level distributional coverage (accuracy).

Synthesized dataset

Space of target signals

Original dataset

alignment

FairDD

…

…

alignment

Synchronized matching As mentioned in Sec. 4, vanilla DDs fail to mitigate PA imbalance and even amplify the discrimination. The relation behind the failure is that the majority group dominates the generation direction of S and leads to the resulting S inheriting the PA imbalance, i.e., preference to fitting to the majority group. To avoid the synthetic samples collapsing into the majority group, we decompose the single target (dominated by the majority group) into PA-wise sub-targets, and simultaneously align S with these sub-targets, without incorporating the specific sample ratio of each group into the optimization objective. The samples assigned to one group have the same PA within the same class label. In this way, we obtain the unified objective function of FairDD:

The reformulation forms synchronized matching, where different sub-targets attempt to pull S into their corresponding PA regions. Each PA group holds equal importance in generating S , ultimately converging to a balanced (fair) status. Subsequently, we present a theoretical analysis illustrating how FairDD effectively mitigates PA imbalance and aligns TA distribution.

Theorem 5.1. For any PA set A , network parameters θ , and target signs ϕ ( · ) , L FairDD ( S ; θ, T ) could mitigate the influence of PA imbalance of original datasets on generating synthetic samples. Especially when D ( · ) is MAE or MSE, synchronized matching ensures that the signal expectation of S is situated at the center of the expectation across all PA groups within T .

Proof. We assume that E [ ϕ x ∼S y ( x ; θ )] could reach the optimal solution for each class. Hence, we have ∂ L FairDD ( S y ; θ, T y ) /∂ E [ ϕ x ∼S y ( x ; θ )] = 0 :

According to Eq. 5, the resulting E [ ϕ x ∼S y ( x ; θ )] are independent on the sample ratio R y , indicating the corresponding S unaffected by R y . As a result, the condensed S will not be dominated by majority groups that happened in vanilla DDs. All PA centers contribute equally to the generation of S , which succeeds in mitigating the PA imbalance of T . Especially when D ( · ) is MAE or MSE, the expectation of target signs of S is equal to the arithmetic mean of centers of all PA groups. This shows that S generated by FairDD is not biased towards any groups.

Although we mitigate the bias inheritance in vanilla DDs by synchronously aligning S to fine-grained PA-wise groups, it is also crucial to investigate whether L FairDD ( S ; θ, T ) (synchronized matching) ensures that the resulting S achieves comprehensive distributional coverage for T . As mentioned above, L ( S ; θ, T ) matches S and T in a global view to fully cover T 's distribution. Below, we provide a theoretical guarantee that L FairDD ( S ; θ, T ) could maintain comprehensive coverage compared to L ( S ; θ, T ) when D ( · , · ) is a convex distance function, commonly used in diverse DDs 3 .

Theorem 5.2. For any PA set A and target signs ϕ θ ( · ) , L FairDD ( S ; θ, T ) is the upper bound of vanilla unified objective L ( S ; θ, T ) , i.e., L FairDD ( S ; θ, T ) ≥ L ( S ; θ, T ) , when D ( · , · ) is convex. Optimizing L FairDD ( S ; θ, T ) can guarantee the comprehensive distribution coverage for T .

The proof is given in Appendix D. L FairDD ( S ; θ, T ) serves as the upper bound of L ( S ; θ, T ) , meaning that minimizing L FairDD ( S ; θ, T ) ensures the minimization of L ( S ; θ, T ) . Hence, optimizing S in FairDD can guarantee the distributional coverage by bounding L ( S ; θ, T ) tailored for accuracy.

6 Experiment

6.1 Experiment Setup

Datasets Comprehensive experiments are conducted on publicly available datasets with diverse types of bias, including foreground bias (FG), background bias (BG), combined BG & FG bias, and real-world bias. The evaluated datasets include synthetic datasets: C-MNIST (FG), C-MNIST (BG), Colored-FMNIST (FG), Colored-FMNIST (BG), and CIFAR10-S (BG & FG), as well as real-world datasets: CelebA, UTKFace, and BFFHQ. For more details on these datasets, please refer to Appendix B and C. We also explore Tiny-ImageNet-S and ImageNet Subsets-S with the same operations as those performed on CIFAR10 for CIFAR10-S.

Baselines & Evaluation metrics FairDD is a general fairness framework applicable to diverse DDs in DMF. We apply FairDD to diverse DMF approaches including DM method DM [69] and GM methods DC [70], IDC (DC version) [27], and DREAM (DC version) [36]. To provide an overall evaluation for model bias toward PA, we use DEOM ( ↓ ) ∈ [0 , 100] and DEOA ( ↓ ) ∈ [0 , 100] to measure the worst and average fairness levels. Also, we report accuracy ( ↑ ) to assess the model's prediction of TA. We also provide a comparison with MTT in Appendix R. Sometimes, we will abuse DM+FairDD and FairDD for clarification.

Implementation details We default to BR of 0.9 for all synthetic original datasets to induce significant PA skew. In Table 16, we conduct the ablation study on BR. All baselines are reproduced using official implementations. FairDD doesn't introduce extra hyperparameters or learnable parameters. Experiments are conducted on PyTorch 2.0.0 with a single NVIDIA RTX 3090 24GB GPU.

6.2 Main results

Weuse distilled datasets S from different DDs to train and evaluate ConvNet with the same parameters, and then report the corresponding fairness and accuracy. Random refers to sampling defined IPC from the original dataset to create smaller datasets. Besides, Whole means we train the model using the entire training dataset without distillation or sampling.

FairDD significantly improves the fairness of vanilla DDs We provide comprehensive fairness comparisons across various DDs, including DM and DC. As illustrated in Table 1, vanilla DDs fail to mitigate the bias present in the original datasets and even exacerbate unfairness towards biased groups. In C-MNIST (FG), the distilled datasets from DM suffer from severe unfairness at IPC=10 compared

to Whole , with DEOM and DEOA reaching 100.0 and 99.96 vs. 10.10 and 5.89. In some cases, Random presents better fairness than vanilla DDs, particularly when dealing with complex objects like CelebA. This suggests that while vanilla DDs effectively condense information into smaller samples, their inductive bias, which favors the majority group, worsens the fairness to the minority group. However, when FairDD is applied to vanilla DDs, there is a significant improvement in fairness performance, with DEOM dropping substantially from 100.0 to 17.04, and DEOA decreasing from 99.96 to 7.95 in C-MNIST (FG). This indicates that FairDD's synchronized matching ensures the equal treatment of each group, effectively mitigating the bias that vanilla DDs exacerbate. FairDD further reduces the bias originally present in the original datasets. For example, DC + FairDD outperforms Whole in C-FMNIST (FG) and CIFAR10-S, as well as in the real-world dataset CelebA, achieving the overall improvement on DEOM and DEOA metrics. Similar performance gains are also observed in other baselines.

FairDD maintains the comparable and even higher accuracy than vanilla DDs A fairness framework must maintain TA accuracy in addition to improving fairness across PA groups. We report the TA accuracy of FairDD in comparison to other baselines in Table 2. Compared to Random , training the model by vanilla DDs yields better performance. This shows that vanilla DDs capture the informative patterns of majority groups, improving their TA accuracy. However, by focusing on dominant patterns in majority groups, they neglect the important patterns in minority groups within the training datasets. Thus, their representation coverage is limited. In contrast, FairDD proposes synchronized matching to push the S to cover each group, and as a result, the generated S retains key patterns of all groups and achieves comprehensive coverage. For example, DM obtains 25.01 at IPC = 10 on C-MNIST (FG), and its accuracy boosts to 94.61 when applying FairDD. In real-world CelebA, FairDD obtains comparable performance for DC and presents superiority over vanilla DDs. These demonstrate that FairDD could mitigate the bias without compromising accuracy.

Generalization to diverse architectures Here, we investigate the cross-model generalization of FairDD, where ConvNet is used to condense datasets, and we evaluate S on other architectures, including AlexNet, VGG11, and ResNet18. We compare DM and FairDD across four datasets at IPC = 50, evaluating performance against BG, FG, BG & FG, and real-world biases. As shown in Table 3, among these architectures, FairDD achieves DEOM of 10.05, 10.35, 9.55, and 8.40 on C-MNIST (FG), DEOA of 14.47, 14.11, 14.36, and 14.96 on C-FMNIST (BG), and accuracy of 58.84, 49.16, 52.65, and 50.93 on CIFAR10-S. These steady results suggest that S generated by FairDD is not restricted to the model used for distillation but generalizes well across diverse architectures. Additionally, with the model capacity increasing, the model generally tends to be more fair to all groups. However, the accuracy sometimes decreases, such as when it drops from 58.84 (ConvNet) to 50.93 (ResNet18) in CIFAR10-S and from 68.50 (ConvNet) to 61.80 (ResNet18) in CelebA. We assume that while increased attention from larger models can lead to accuracy gains for minority groups, it may limit the representations for majority groups at certain levels. The accuracy gains for minority groups may be smaller than the accuracy losses for majority groups, particularly in larger models that have limited potential improvement in recognizing minority groups.

Discussion FairDD employs a bias-free alignment objective, where the expectation of the distilled data is unbiased across all groups, as shown in Eq. 5. To ensure fairness during optimization, each PA group contributes equally to the total loss, with gradients that are independent of group sample sizes. This design leads to balanced sample generation across all protected groups. Regarding TA, the loss used in vanilla DDs is designed to align with TA-wise classification accuracy. In FairDD, as proven in Thm. 5.2, the loss function serves as an upper bound on the loss of vanilla DDs. This implies that minimizing the FairDD objective ensures distributional coverage across TA. As a result, models trained on FairDD-distilled datasets achieve higher accuracy on minority PA groups, while maintaining stable performance on majority groups. The main takeaways of FairDD are summarized as follows: Fairness-Aligned Objective: The distilled dataset should be constructed such that its expected representation is unbiased across all attribute groups, aligning with fairness principles at the objective level; Equal Group Contribution: Each group should contribute equally to the overall loss, encouraging balanced optimization and preventing group-specific bias during training; Distributional Coverage of TA: It is essential to ensure that the distilled dataset maintains adequate distributional coverage over the TA, supporting both fairness and classification accuracy.

6.3 Result Analysis

Visualization analysis on fairness and accuracy To intuitively present the effectiveness of FairDD, we train g ψ using S of C-MNIST (FG) distilled by DM and FairDD, and then extract the features from the test dataset. Different colors paint these resulting features according to PA and TA, respectively. As shown in Figs. 3(a) and 3(b), features with the same PA tend to form a cluster, indicating that the model trained on DM is sensitive to PA and thus failing to guarantee fairness among all PA. In contrast with DM, the feature distributions in Fig. 3(b) exhibit nearly complete overlaps across all PA. It shows that the model trained on FairDD is agnostic to PA and does not exhibit bias towards these PA. Besides the PA fairness, we also study the feature distribution from the TA perspective. Fig. 3(c) shows that features belonging to one TA scatter and fail to provide compact representations for one class. The failure of DM can be attributed to model bias toward PA. Combined with Fig. 3(a), it can be observed that PA has a stronger influence on the feature distribution compared to TA. As a result, PA-wise representations are tightly clustered, but representations from the same TA are divided into

(a) PA t-SNE of DM.

(b) PA t-SNE of FairDD.

(c) TA t-SNE of DM.

(d) TA t-SNE of FairDD.

PA-wise parts. In contrast, FairDD proposes synchronized matching effectively mitigates this by treating each PA group equally within one TA. The equal treatment allows different PA groups within the same TA to cluster more easily, leading to more compact representations that benefit capturing class semantics in Fig. 3(d). These results highlight the superiority of FairDD in improving PA fairness and TA accuracy. Additional analysis on computation overhead and representation coverage on S generation are provided in Appendix J and F. We also visualize on S generation in Appendix G.

Exploring the scalability on arge datasets To further evaluate the scalability of FairDD, we conduct experiments on large datasets such as ImageNet Subset and Tiny-ImageNet. To introduce bias, we apply the same procedure used for CIFAR10-S, resulting in biased versions: ImageNet Subset-S and Tiny-ImageNet-S. The results are shown in Table 4. As observed, FairDD outperforms the vanilla DDs on these datasets, demonstrating its superior scalability.

6.4 Ablation Study

Ablation on fair extractor General DDs treat the extractor as a non-linear transformation, where the randomly initialized extractor either does not require training or only updates parameters after a few iterations. Here, we investigate whether vanilla DDs can mitigate bias when the extractor is fair to PA. We employ two fairness approaches LW and LfF to train the extractor fairly to PA [43]. Then, we use the extractor for condensation, resulting in DM+LW and DM+LfF models. From Table 5, we can observe that DM+FairDD still outperforms DM+LW and DM+LfF on both fairness and accuracy across FG, BG, and FG&BG. Although they use fair extractor towards PA, which helps provide a balanced feature space, Eq. 3 illustrates that vanilla DDs shift synthetic datasets toward the majority group. This biased shift still causes S to inherit the bias of the original dataset during the condensation. In contrast, FairDD is agnostic to whether the extractor is fair and consistently mitigates the bias in the condensed dataset.

Ablation on initialization of synthetic images The initialization of S determines the prior information obtained by DDs. We examine the effect of different initialization using three strategies: random : randomly drawing samples from the original datasets to initialize S ; Noise : using noise obeying the standard normal distribution for initialization; and balanced : initializing with the equal number of each group. In Table 6, DEOM and DEOA metrics of DM suffer from the bias present in the original dataset across these strategies. Especially in balanced , we keep the synthetic dataset without group imbalance, vanilla DDs still inherit the imbalance from the original dataset. This again demonstrates the disadvantage of vanilla DDs when condensing biased datasets. In contrast, FairDD achieves robust performance in fairness and accuracy.

Ablation on fairness-aware learning in vanilla DDs In this work, we explore fairness-aware learning for vanilla models through distillation fairness (DF) and model training fairness (MF). During distillation, DF assigns weights to each group inversely proportional to its sample proportion to achieve fairness-aware learning, while keeping the rest of the training procedure unchanged. MF, on the other hand, keeps the distillation process unchanged and applies fairness-aware learning only during the model training stage. We apply DF to the DC framework and obtain DC+DF, and similarly incorporate MF into DC to derive DC+MF. As illustrated in Table 7, applying these fairness regularizations can alleviate distillation bias to some extent; however, they do not ensure that the alignment objective remains unbiased across all attribute groups, nor do they guarantee comprehensive coverage of the target attribute distribution. Consequently, the distilled data of certain minority groups may be lost due to biased distillation.

We provide a summary to guide the reader through the appendix in Appendix A. We conduct performance comparison with [13] in Appendix E and more ablation study on weighting mechanism in Appendix H, additional experiments on CelebA in Appendix I, computation overhead in Appendix J, attribute missing in test dataset in Appendix K, ablation study on the biased ratio of original datasets in Appendix L, group label noise and missing in Appendix M, balanced original dataset in Appendix N, nuanced PA groups in Appendix O, imbalanced PA groups in Appendix P, exploration on vision transformer as the backbone in Appendix Q, comparison with MTT in Appendix R.

7 Conclusion

This is the first work to introduce attribute fairness into the field of dataset distillation and to systematically provide a theoretical analysis of why vanilla dataset distillation fails to mitigate attribute bias. To address the problem, we propose a unified fair dataset distillation framework called FairDD, broadly applicable to various DDs in DMF. FairDD requires no modifications to the architectures of vanilla DDs and introduces an easy-to-implement yet effective attribute-wise matching. This method mitigates the dominance of the majority group and ensures that synthetic datasets equally incorporate representative patterns with all protected attributes from both majority groups and minority groups. By doing so, FairDD guarantees the fairness of synthetic datasets while maintaining their representativeness for image recognition. We provide extensive theoretical analysis and empirical results to demonstrate the superiority of FairDD.

Limitations Since FairDD relies on PA's prior information to conduct attribute-wise matching, it is valuable to explore the scenario where PA is unavailable [34]. A potential solution is to generate pseudo-labels to guide FairDD through self-supervised learning or unsupervised learning.

Broader Impacts This paper aims to improve data efficiency and enhance data fairness in modern machine learning, fully compliant with legal regulations. Since training a fair model from scripts with extensive data is time-consuming, our work in providing a fair condensed dataset for effective model training can have significant societal impacts. We hope our research raises attention to achieving fairness and accuracy for dataset distillation in academia and industry.

Acknowledgments

This work was supported by NSFC 62088101 Autonomous Intelligent Unmanned Systems and NSFC U23A20326. We thank Joey Tianyi Zhou for feedback on the draft. We also thank Ninghao Liu for helpful discussion.

References

Alekh Agarwal, Alina Beygelzimer, Miroslav Dudík, John Langford, and Hanna Wallach. A reductions approach to fair classification. In International Conference on Machine Learning , pages 60-69. PMLR, 2018.

Wael Alghamdi, Shahab Asoodeh, Hao Wang, Flavio P Calmon, Dennis Wei, and Karthikeyan Natesan Ramamurthy. Model projection: Theory and applications to fair machine learning. In 2020 IEEE International Symposium on Information Theory (ISIT) , pages 2711-2716. IEEE, 2020.

Rachel KE Bellamy, Kuntal Dey, Michael Hind, Samuel C Hoffman, Stephanie Houde, Kalapriya Kannan, Pranay Lohia, Jacquelyn Martino, Sameep Mehta, Aleksandra Mojsilovi´ c, et al. Ai fairness 360: An extensible toolkit for detecting and mitigating algorithmic bias. IBM Journal of Research and Development , 63(4/5):4-1, 2019.

Ondrej Bohdal, Yongxin Yang, and Timothy Hospedales. Flexible dataset distillation: Learn labels instead of images. arXiv preprint arXiv:2006.08572 , 2020.

Simon Caton and Christian Haas. Fairness in machine learning: A survey. ACM Computing Surveys , 56(7):1-38, 2024.

George Cazenavette, Tongzhou Wang, Antonio Torralba, Alexei A Efros, and Jun-Yan Zhu. Dataset distillation by matching training trajectories. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 4750-4759, 2022.

Xuechao Chen, Wenchao Meng, Peiran Wang, and Qihang Zhou. Distributed boosting: An enhancing method on dataset distillation. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management , CIKM '24, page 3689-3693, New York, NY, USA, 2024. Association for Computing Machinery.

Xuechao Chen, Wenchao Meng, Peiran Wang, and Qihang Zhou. Distributed boosting: An enhancing method on dataset distillation. CIKM '24, page 3689-3693, New York, NY, USA, 2024. Association for Computing Machinery.

Xuxi Chen, Yu Yang, Zhangyang Wang, and Baharan Mirzasoleiman. Data distillation can be like vodka: Distilling more times for better quality. arXiv preprint arXiv:2310.06982 , 2023.

Ming-Yu Chung, Sheng-Yen Chou, Chia-Mu Yu, Pin-Yu Chen, Sy-Yen Kuo, and Tsung-Yi Ho. Rethinking backdoor attacks on dataset distillation: A kernel method perspective. arXiv preprint arXiv:2311.16646 , 2023.

Elliot Creager, David Madras, Jörn-Henrik Jacobsen, Marissa Weis, Kevin Swersky, Toniann Pitassi, and Richard Zemel. Flexibly fair representation learning by disentanglement. In International conference on machine learning , pages 1436-1445. PMLR, 2019.

Justin Cui, Ruochen Wang, Si Si, and Cho-Jui Hsieh. Scaling up dataset distillation to imagenet1k with constant memory. arXiv preprint arXiv:2211.10586 , 2022.

Justin Cui, Ruochen Wang, Yuanhao Xiong, and Cho-Jui Hsieh. Ameliorate spurious correlations in dataset condensation. arXiv preprint arXiv:2406.06609 , 2024.

Justin Cui, Ruochen Wang, Yuanhao Xiong, and Cho-Jui Hsieh. Mitigating bias in dataset distillation. arXiv preprint arXiv:2406.06609 , 2024.

Zhiwei Deng and Olga Russakovsky. Remember the past: Distilling datasets into addressable memories for neural networks. arXiv preprint arXiv:2206.02916 , 2022.

Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, and Neil Houlsby. An image is worth 16x16 words: Transformers for image recognition at scale. ArXiv , abs/2010.11929, 2020.

Yunzhen Feng, Shanmukha Ramakrishna Vedantam, and Julia Kempe. Embarrassingly simple dataset distillation. In The Twelfth International Conference on Learning Representations , 2023.

Ziyao Guo, Kai Wang, George Cazenavette, Hui Li, Kaipeng Zhang, and Yang You. Towards lossless dataset distillation via difficulty-aligned trajectory matching. arXiv preprint arXiv:2310.05773 , 2023.

Moritz Hardt, Eric Price, and Nati Srebro. Equality of opportunity in supervised learning. Advances in neural information processing systems , 29, 2016.

Kaiming He, X. Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , pages 770-778, 2015.

Yang He, Lingao Xiao, Joey Tianyi Zhou, and Ivor Tsang. Multisize dataset condensation. In The Twelfth International Conference on Learning Representations , 2024.

Yang He and Joey Tianyi Zhou. Data-independent module-aware pruning for hierarchical vision transformers. In The Twelfth International Conference on Learning Representations , 2024.

Arthur Jacot, Franck Gabriel, and Clément Hongler. Neural tangent kernel: Convergence and generalization in neural networks. Advances in neural information processing systems , 31, 2018.

Heinrich Jiang and Ofir Nachum. Identifying and correcting label bias in machine learning. In International Conference on Artificial Intelligence and Statistics , pages 702-712. PMLR, 2020.

Sangwon Jung, Sanghyuk Chun, and Taesup Moon. Learning fair classifiers with partially annotated group labels. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 10348-10357, 2022.

Sangwon Jung, Donggyu Lee, Taeeon Park, and Taesup Moon. Fair feature distillation for visual recognition. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 12115-12124, 2021.

Jang-Hyun Kim, Jinuk Kim, Seong Joon Oh, Sangdoo Yun, Hwanjun Song, Joonhyun Jeong, Jung-Woo Ha, and Hyun Oh Song. Dataset condensation via efficient synthetic-data parameterization. In International Conference on Machine Learning , pages 11102-11118. PMLR, 2022.

Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander C Berg, Wan-Yen Lo, et al. Segment anything. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pages 4015-4026, 2023.

Yann LeCun, Corinna Cortes, Chris Burges, et al. Mnist handwritten digit database, 2010.

Dong Bok Lee, Seanie Lee, Joonho Ko, Kenji Kawaguchi, Juho Lee, and Sung Ju Hwang. Self-supervised dataset distillation for transfer learning. In The Twelfth International Conference on Learning Representations , 2023.

Hae Beom Lee, Dong Bok Lee, and Sung Ju Hwang. Dataset condensation with latent space knowledge factorization and sharing. arXiv preprint arXiv:2208.10494 , 2022.

Saehyung Lee, Sanghyuk Chun, Sangwon Jung, Sangdoo Yun, and Sungroh Yoon. Dataset condensation with contrastive signals. In International Conference on Machine Learning , pages 12352-12364. PMLR, 2022.

Junnan Li, Dongxu Li, Caiming Xiong, and Steven Hoi. Blip: Bootstrapping languageimage pre-training for unified vision-language understanding and generation. In International conference on machine learning , pages 12888-12900. PMLR, 2022.

Evan Zheran Liu, Behzad Haghgoo, Annie S. Chen, Aditi Raghunathan, Pang Wei Koh, Shiori Sagawa, Percy Liang, and Chelsea Finn. Just train twice: Improving group robustness without training group information. ArXiv , abs/2107.09044, 2021.

Songhua Liu, Kai Wang, Xingyi Yang, Jingwen Ye, and Xinchao Wang. Dataset distillation via factorization. arXiv preprint arXiv:2210.16774 , 2022.

Yanqing Liu, Jianyang Gu, Kai Wang, Zheng Hua Zhu, Wei Jiang, and Yang You. Dream: Efficient dataset distillation by representative matching. 2023 IEEE/CVF International Conference on Computer Vision (ICCV) , pages 17268-17278, 2023.

Noel Loo, Ramin Hasani, Alexander Amini, and Daniela Rus. Efficient dataset distillation using random feature approximation. Advances in Neural Information Processing Systems , 35:13877-13891, 2022.

Noel Loo, Ramin Hasani, Mathias Lechner, Alexander Amini, and Daniela Rus. Understanding reconstruction attacks with the neural tangent kernel and dataset distillation. arXiv preprint arXiv:2302.01428 , 2023.

Christos Louizos, Kevin Swersky, Yujia Li, Max Welling, and Richard Zemel. The variational fair autoencoder. arXiv preprint arXiv:1511.00830 , 2015.

Yao Lu, Jianyang Gu, Xuguang Chen, Saeed Vahidian, and Qi Xuan. Exploring the impact of dataset bias on dataset distillation. ArXiv , abs/2403.16028, 2024.

Yao Lu, Jianyang Gu, Xuguang Chen, Saeed Vahidian, and Qi Xuan. Exploring the impact of dataset bias on dataset distillation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 7656-7663, 2024.

Ninareh Mehrabi, Fred Morstatter, Nripsuta Saxena, Kristina Lerman, and Aram Galstyan. A survey on bias and fairness in machine learning. ACM computing surveys (CSUR) , 54(6):1-35, 2021.

Jun Hyun Nam, Hyuntak Cha, Sungsoo Ahn, Jaeho Lee, and Jinwoo Shin. Learning from failure: Training debiased classifier from biased classifier. ArXiv , abs/2007.02561, 2020.

Timothy Nguyen, Roman Novak, Lechao Xiao, and Jaehoon Lee. Dataset distillation with infinitely wide convolutional networks. Advances in Neural Information Processing Systems , 34:5186-5198, 2021.

Maxime Oquab, Timothée Darcet, Théo Moutakanni, Huy Vo, Marc Szafraniec, Vasil Khalidov, Pierre Fernandez, Daniel Haziza, Francisco Massa, Alaaeldin El-Nouby, et al. Dinov2: Learning robust visual features without supervision. arXiv preprint arXiv:2304.07193 , 2023.

Novi Quadrianto, Viktoriia Sharmanska, and Oliver Thomas. Discovering fair representations in the data domain. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 8227-8236, 2019.

Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In International conference on machine learning , pages 8748-8763. PMLR, 2021.

Harsh Rangwani, Sumukh K Aithal, Mayank Mishra, and R. Venkatesh Babu. Escaping saddle points for effective generalization on class-imbalanced data. ArXiv , abs/2212.13827, 2022.

Shiori Sagawa, Pang Wei Koh, Tatsunori B. Hashimoto, and Percy Liang. Distributionally robust neural networks for group shifts: On the importance of regularization for worst-case generalization. ArXiv , abs/1911.08731, 2019.

P. Sattigeri, S. C. Hoffman, V . Chenthamarakshan, and K. R. Varshney. Fairness gan: Generating datasets with fairness properties using a generative adversarial network. IBMJournal of Research and Development , 63(4/5):3:1-3:9, 2019.

Prasanna Sattigeri, Samuel C Hoffman, Vijil Chenthamarakshan, and Kush R Varshney. Fairness gan: Generating datasets with fairness properties using a generative adversarial network. IBM Journal of Research and Development , 63(4/5):3-1, 2019.

Xinyi Shang, Peng Sun, and Tao Lin. GIFT: Unlocking full potential of labels in distilled dataset at near-zero cost. In The Thirteenth International Conference on Learning Representations , 2025.

Shivashankar Subramanian, Afshin Rahimi, Timothy Baldwin, Trevor Cohn, and Lea Frermann. Fairness-aware class imbalanced learning. In Conference on Empirical Methods in Natural Language Processing , 2021.

Ilia Sucholutsky and Matthias Schonlau. Soft-label dataset distillation and text dataset distillation. In 2021 International Joint Conference on Neural Networks (IJCNN) , pages 1-8. IEEE, 2021.

Davoud Ataee Tarzanagh, Bojian Hou, Boning Tong, Qi Long, and Li Shen. Fairness-aware class imbalanced learning on multiple subgroups. Proceedings of machine learning research , 216:2123-2133, 2023.

Saeed Vahidian, Mingyu Wang, Jianyang Gu, Vyacheslav Kungurtsev, Wei Jiang, and Yiran Chen. Group distributionally robust dataset distillation with risk minimization. arXiv preprint arXiv:2402.04676 , 2024.

Robin Vogel, Mastane Achab, Stéphan Clémençon, and Charles Tillier. Weighted empirical risk minimization: Sample selection bias correction based on importance sampling. ArXiv , abs/2002.05145, 2020.

Kai Wang, Bo Zhao, Xiangyu Peng, Zheng Zhu, Shuo Yang, Shuo Wang, Guan Huang, Hakan Bilen, Xinchao Wang, and Yang You. Cafe: Learning to condense dataset by aligning features. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 12196-12205, 2022.

Shaobo Wang, Yantai Yang, Qilong Wang, Kaixin Li, Linfeng Zhang, and Junchi Yan. Not all samples should be utilized equally: Towards understanding and improving dataset distillation, 2024.

Tongzhou Wang, Jun-Yan Zhu, Antonio Torralba, and Alexei A Efros. Dataset distillation. arXiv preprint arXiv:1811.10959 , 2018.

Zeyu Wang, Klint Qinami, Ioannis Christos Karakozis, Kyle Genova, Prem Nair, Kenji Hata, and Olga Russakovsky. Towards fairness in visual recognition: Effective strategies for bias mitigation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 8919-8928, 2020.

Lingao Xiao and Yang He. Are large-scale soft labels necessary for large-scale dataset distillation? In The Thirty-eighth Annual Conference on Neural Information Processing Systems , 2024.

Depeng Xu, Shuhan Yuan, Lu Zhang, and Xintao Wu. Fairgan: Fairness-aware generative adversarial networks. 2018 IEEE International Conference on Big Data (Big Data) , pages 570-575, 2018.

Muhammad Bilal Zafar, Isabel Valera, Manuel Gomez Rogriguez, and Krishna P Gummadi. Fairness constraints: Mechanisms for fair classification. In Artificial intelligence and statistics , pages 962-970. PMLR, 2017.

Rich Zemel, Yu Wu, Kevin Swersky, Toni Pitassi, and Cynthia Dwork. Learning fair representations. In International conference on machine learning , pages 325-333. PMLR, 2013.

Brian Hu Zhang, Blake Lemoine, and Margaret Mitchell. Mitigating unwanted biases with adversarial learning. In Proceedings of the 2018 AAAI/ACM Conference on AI, Ethics, and Society , pages 335-340, 2018.

Bo Zhao and Hakan Bilen. Dataset condensation with differentiable siamese augmentation. In International Conference on Machine Learning , pages 12674-12685. PMLR, 2021.

Bo Zhao and Hakan Bilen. Synthesizing informative training samples with gan. In NeurIPS 2022 Workshop on Synthetic Data for Empowering ML Research , 2022.

Bo Zhao and Hakan Bilen. Dataset condensation with distribution matching. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision , pages 6514-6523, 2023.

Bo Zhao, Konda Reddy Mopuri, and Hakan Bilen. Dataset condensation with gradient matching. arXiv preprint arXiv:2006.05929 , 2020.

Zhenghao Zhao, Haoxuan Wang, Yuzhang Shang, Kai Wang, and Yan Yan. Distilling long-tailed datasets, 2024.

Qihang Zhou, Guansong Pang, Yu Tian, Shibo He, and Jiming Chen. Anomalyclip: Objectagnostic prompt learning for zero-shot anomaly detection. In The Twelfth International Conference on Learning Representations , 2023.

Yongchao Zhou, Ehsan Nezhadarya, and Jimmy Ba. Dataset distillation using neural feature regression. arXiv preprint arXiv:2206.00719 , 2022.

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A Appendix summary

We summarize the appendix contents as follows:

Dataset details: Appendix B

Dataset statistics: Appendix C

Proof of the theorem: Appendix D

Additional performance comparison: Appendix E

Visualization analysis on representation coverage: Appendix F

Visualization analysis on S generation: Appendix G

Ablation study on weighting mechanism: Appendix H

Additional experiments on CelebA: Appendix I

Computation overhead: Appendix J

Attribute missing in test dataset: Appendix K

Ablation study on biased ratio of original datasets: Appendix L

Group label noise and missing labels: Appendix M

Balanced original dataset: Appendix N

Nuanced PA groups: Appendix O

Imbalanced PA groups: Appendix P

Exploration using Vision Transformer as the backbone: Appendix Q

Comparison with MTT: Appendix R

More visualizations: Appendix S

B Datasets

Comprehensive experiments have been conducted on publicly available datasets of diverse biases, including foreground bias (FG), background bias (BG), BG & FG bias, and real-world bias. C-MNIST (FG) is a variant of MNIST [29] used to evaluate model fairness, where the handwriting numbers in each class are painted with ten different colors. To correlate the TA (digital number) and PA (color) within the training dataset, each training class is predominantly associated with one color according to the same biased ratio (BR), while the remaining samples are evenly painted with the other nine colors. BR is the ratio of the majority group samples to the total samples across all groups. For the test dataset, we evenly paint the numbers for each class with ten colors to test the model bias trained on S . C-MNIST (BG) adopts the same operation on the background and keeps the foreground unchanged. Colored-FMNIST (FG) is the modified version of Fashion-MNIST, originally aiming to classify object semantics. Like C-MNIST (FG), we color the objects for the training and test datasets. Colored-FMNIST (BG) paints the background similarly to C-MNIST (BG). CIFAR10-S (BG & FG) introduces a PA by applying grayscale or not to CIFAR10 samples. Following [61], we grayscale a portion of the training images, correlating TA and PA among different classes. For fairness evaluation, we duplicate the test images, apply grayscale to the copies, and add them to the test dataset. We also test FairDD on the real-world facial dataset CelebA, a widely used fairness dataset. We follow the common practice of treating attractive attribute as TA and gender as PA (evaluations on other attributes refer to Appendix I).

C Datasest statistics

In this section, we provide detailed statistics for all datasets used in the manuscript for reproduction. As shown in Table 8, we present the target attribute (TA), protected attribute (PA), the sample number of the training set, the sample number of the test set, and the BR in the training set. Additionally, all test sets are balanced, with equal sample sizes across groups. We also report the condensed ratio at IPC 10, 50, and 100, which is computed by the ratio of the condensed dataset size to the training set size.

D Proof of the theorem

Theorem D.1. For any PA set A and target signs ϕ θ ( · ) , L FairDD ( S ; θ, T ) is the upper bound of vanilla unified objective L ( S ; θ, T ) , i.e., L FairDD ( S ; θ, T ) ≥ L ( S ; θ, T ) , when D ( · , · ) is convex. Optimizing L FairDD ( S ; θ, T ) can guarantee the comprehensive distribution coverage for T .

Eq. 6 is obtained according to Jensen Inequality, and Eq. 7 is given since group ratios are smaller than one. L FairDD ( S ; θ, T ) serves as the upper bound of L ( S ; θ, T ) , meaning that minimizing L FairDD ( S ; θ, T ) ensures the minimization of L ( S ; θ, T ) . Hence, optimizing S in FairDD can guarantee the distributional coverage by bounding L ( S ; θ, T ) tailored for accuracy.

E Additional performance comparison

Since the work does not release its code, we follow the implementation details presented in their paper. We conduct experiments on CMNIST-FG and CIFAR10-S using DM at IPC=10. Their method can mitigate the distillation bias to some extent. However, this approach does not guarantee that the alignment objective is unbiased across all attribute groups, nor does it ensure adequate distribution coverage. Instead, our methods have a fairness alignment objective to facilitate unbiased data distillation; In addition, we provide a theoretical proof to guarantee the distribution coverage for TA. We summarize the three main advantages of FairDD over theirs:

Better preservation of target attribute representations: Their approach assigns higher weights to samples in low-density regions of the data distribution. However, these samples may lie on the periphery of the data manifold and carry low information. As a result, the distilled dataset presents the patterns with low information and hinders the distillation of informative patterns. In contrast, our method explicitly aligns the centroids of each group (defined by protected and target attributes) between the distilled and original datasets. This ensures that

each group in the distilled dataset preserves representative and informative patterns, thereby maintaining the semantic integrity of the original distribution.

Better support for protected attribute fairness: Their weighting strategy can still underrepresent minority groups if those groups are dense in the data manifold. This results in biased generation against minority group attributes. In contrast, our method is agnostic to sample density and directly aligns groups across both PA. This ensures fair representation for all attribute groups, regardless of their density, and effectively mitigates PA-related bias.

Stronger theoretical foundations: Their work primarily relies on empirical evaluation and does not provide a theoretical explanation for why distilled datasets inherit biases from the original data, or how their method mitigates these biases. In contrast, we offer a formal theoretical analysis that explains why dataset distillation naturally inherits bias from the source data. Furthermore, we provide provable guarantees on both target attribute accuracy and protected attribute balance.

F Visualization analysis on representation coverage

Figure 4: Feature coverage comparison on TA between DM and DM+FairDD. We visualize features extracted by ϕ θ on training and synthetic datasets. One class is highlighted and the remaining classes are transparent. The S generated by DM and FairDD are marked by stars in (a) and (b).

We investigate whether the FairDD effectively covers the whole distribution of the original datasets. For this purpose, we first feed the original training set into the randomly initialized network used in the distillation to extract the corresponding features. Subsequently, we use the same network to extract features of the distilled dataset S from DM and FairDD. As shown in Fig. 4(a), the synthetic samples in vanilla DDs almost locate the majority group for optimizing the original alignment objective. In this case, vanilla DDs neglect to condense the key patterns of minority groups. This leads to the information loss of minority groups in S . FairDD achieves overall coverage for both majority and minority groups in Fig. 4(b). This is because FairDD introduces synchronized matching to reformulate the distillation objective for aligning the PA-wise groups rather than being dominated by the majority group like vanilla DDs. In doing so, FairDD avoids S collapsing into the majority group and retains informative patterns from all groups.

G Visualization analysis on S generation

We aim to investigate whether FaiDD renders the expectation of S locate the center among all groups, as clarified in Eq. 5. If the clarification holds, S should contain all PA at IPC = 1 because the expectation of S is equal to S when IPC =1. We visualize S at IPC=1 on C-MNIST (FG), where each class (digital number) is dominated by one color, and the rest is colored by the rest nine colors. As shown in Fig. 5, the S generated by FairDD combines all colors from PA groups. This suggests that FairDD can effectively incorporate all PA into resulting S , indirectly validating the Theorem 5.1. Meanwhile, we observe that the majority groups dominate vanilla DDs according to Eq. 3, where the resulting S contains the colors from the corresponding majority groups.

Vanilla DDs

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H Ablation on weighting mechanism

Our approach treats groups separately, similar to the weighting mechanism used in the traditional fairness field. Here, we explore diverse weighting mechanisms based on our proposed groupwise alignment strategy: (1) FairDD+IW weights groups by inverse proportion to their respective sample size 1 |T a i y | . (2) FairDD+LDAM adopts a soft exponential weighting 1 -β 1 -β |T a i y | [53] (3)

FairDD+GroupDRO optimizs the group with the maximum alignment loss instead of simultaneous alignment of all groups [49]. As illustrated in Table 10, DM + FairDD outperforms other weighting mechanisms in terms of both fairness and accuracy. We attribute the inferior performance of FairDD+IW and FairDD+LDAM to the excessive penalization of groups with larger sample sizes. Penalizing groups based on sample cardinality reintroduces an unexpected bias related to group size in the information condensation process. This results in large groups receiving smaller weights during alignment, placing them in a weaker position and causing synthetic samples to deviate excessively from large (majority) groups. Consequently, majority patterns become underrepresented, ultimately hindering overall performance. On the other hand, FairDD+GroupDRO shows that inadequate alignment also makes it difficult to equally represent each group. The success of FairDD lies in making each group equally contribute to the total alignment, mitigating the effects of imbalanced sample sizes across all groups. Meanwhile, FairDD performs synchronized alignment to enable the expectation of S to locate the expectation over all group centers of T . Hence, FairDD can be generally applied to datasets with highly varied biases.

I More attributes Analysis on CelebA

We explore additional facial attributes in CelebA to further demonstrate the robustness of FairDD. To this end, we regard gender as the PA, and young , big_nose , and blond_hair as the TA, which results in CelebA y , CelebA b , CelebA h and respectively. We also exchange the PA and TA for CelebA h , resulting in CelebA h The performance is reported on fairness and accuracy in Tables 11 and 12.

J Computation overhead

In this section, we investigate the computational efficiency of FairDD. The only computational difference between FairDD and vanilla DDs is that FairDD replaces the whole alignment with group-level alignment.

Assume we have m real samples and n synthetic samples with G attributes in a batch. For DM, the computational complexity of group-level alignment involves computing the group center. FairDD

has a complexity of G * O(m/G) + O(n). In contrast, the computational complexity of vanilla DDs is O(m) + O(n). If we ignore GPU parallelism, the computational complexity should be the same. However, since GPU parallelism is highly efficient for large batches, it results in G * O(m/G) > O(m), raising additional time consumption in FairDD. As for DC, the additional time consumption comes from two parts: one is the backward pass for gradients, and the other is to compute the average of the gradients. FairDD incurs additional memory consumption twice due to the above-mentioned GPU parallelism.

Therefore, our additional memory overhead is not related to the dataset scale but to the group number of the dataset. We evaluate the impact of the number of groups on training time (min) and peak GPU memory consumption (MB). As shown in Table 13, FairDD requires more time than vanilla DDs on C-MNIST (FG), and the time increases as the number of groups (PA) grows. This phenomenon is particularly noticeable in DC because DC suffers from GPU parallelism twice. Regarding GPU memory usage, FairDD incurs no obvious additional overhead compared to vanilla DDs.

Here, we further supplement the overhead analysis with respect to image resolutions. We conduct experiments on CMNIST, CelebA (32), CelebA (64), and CelebA (96) on DM and DC at IPC=10. DMand DC align different signals, which would bring different effects. As illustrated in Table 14, it can be observed that FairDD + DM does not require additional GPU memory consumption but does necessitate more time. The time gap increases from 0.42 minutes to 1.79 minutes as input resolution varies (e.g., CelebA 32 × 32, CelebA 64 × 64, and CelebA 96 × 96); however, the gap remains small. This can be attributed to FairDD performing group-level alignment on features, which is less influenced by input resolution. FairDD + DM requires no additional GPU memory consumption. Its additional time depends on both input resolutions. As for DC, FairDD requires additional GPU memory and time.

K Attribute missing in test dataset

Here, we investigate whether FairDD is agnostic to the attribute missing in the test dataset. We conduct our experiment by training the model on all PAs and testing on datasets that are missing one, two, or three PAs.

The missing attribute does not actually affect our performance for the following reasons. First, although the color (PA) is missing in the test dataset, its TA still contributes to the model's ability to make accurate classifications on the corresponding TA. Therefore, these missing attributes are not considered outliers in terms of TA. Second, the absence of the color in the test dataset does not impact fairness performance because FairDD is designed to generate attribute-balanced synthetic datasets. Models trained on these attribute-balanced distilled datasets are expected to treat each attribute equally. Even though the test dataset misses some existing attributes in training datasets, the model trained on such distilled datasets could still present no bias to the remaining attributes in the test dataset.

L Ablation on biased ratio of original datasets

BR reflects the extent of unfairness in the original datasets and indicates the level of PA skew that the distillation process of S will encounter. We investigate the impact of BR values on fairness performance by setting BR to { 0 . 85 , 0 . 90 , 0 . 95 } on C-MNIST (FG), C-FMNIST (BG), and CIFAR10S. The results at IPC = 50 in Table 16 show that DM is sensitive to the BR of original datasets, with its DEOM decreasing from 70.13 to 100.0 as BR increases from 0.85 to 0.95. A similar trend is observed in other datasets. Compared to DM, FairDD maintains consistent fairness and accuracy levels across different biases. This is attributed to the synchronized matching, which explicitly aligns each PA-wise subtarget, reducing sensitivity to group-specific sample numbers. This shows FairDD's robustness to PA skew in the original datasets.

M Ablation study on group label noise and missing

Here, we evaluate the robustness of spurious group labels could provide more insights. We randomly sample the entire dataset according to a predefined ratio. These samples are randomly assigned to

group labels to simulate noise. To ensure a thorough evaluation, we set sample ratios at 10%, 15%, 20%, and 50%. As shown in the table, when the ratio increases from 10% to 20%, the DEOM results range from 14.93% to 18.31% with no significant performance variations observed. These results indicate that FairDD is robust to noisy group labels. However, as the ratio increases further to 50%, relatively significant performance variations become apparent. It can be understood that under a high noise ratio, the excessive true samples of majority attributes are assigned to minority labels. This causes the minority group center to shift far from its true center and thus be underrepresented.

We investigate the experiment when the labels are missing. To provide attribute-level pseudo labels, we choose an unsupervised clustering method DBSCAN. Specifically, we do not have any group labels and use DBSCAN to cluster the samples within a batch. The clustering label is regarded as the pseudo-group label. From Table, FairDD achieves 94.77% accuracy, and 12.38% DEOM and 6.80% DEOA. This demonstrates the potential of FairDD combined with an unsupervised approach when group labels are unavailable.

N Ablation study on balanced original dataset

We synthesized a fair version of CelebA, referred to as CelebA Fair . The target attribute is attractive (attractive and unattractive), and the protected attribute is gender (female and male). In the original dataset, the sample numbers for female-attractive, female-unattractive, male-attractive, and maleunattractive groups are imbalanced. To create a fair version, CelebA Fair samples the number of instances based on the smallest group, ensuring equal representation across all four groups. We tested the fairness performance of FairDD and DM at IPC = 10, as well as the performance of models trained on the full dataset. As shown in Table 19, vanilla DM achieves 14.33% DEOA and 8.77% DEOM. In comparison, the full dataset achieves 3.66% DEOA and 2.77% DEOM. While DM still exacerbates bias with a relatively small margin, this is primarily due to partial information loss introduced during the distillation process. FairDD produces fairer results, achieving 11.11% DEOA and 6.68% DEOM.

O Ablation study on nuanced PA groups

We perform a fine-grained PA division. For example, we consider gender and wearing-necktie as two correlated attributes and divide them into four groups: males with a necktie, males without a necktie, females with a necktie, and females without a necktie (CelebA g & n ). Similarly, we consider gender and paleskin and divide them into four groups (CelebA g & p ). Their target attribute is attractive. As shown in the Table 20, FairDD outperforms vanilla DM in the accuracy and fairness performance

on these two experiments. The performance for necktie and gender is improved from 57.50% to 25.00% on DEOM and 52.79% to 21.73% on DEOA. Accuracy is also improved from 63.25% to 67.98%. Similar results can be observed for gender and paleskin. Hence, FairDD can mitigate more fine-grained attribute bias, even when there is an intersection between attributes.

P Ablation study on imbalanced PA groups

To further study FairDD robustness under more biased scenarios, we keep the sample number of the majority group in each class invariant and allocate the sample size to the remaining 9 minority groups with increasing ratios, i.e., 1:2:3:4:5:6:7:8:9. We denote this variant CMNIST unbalance This could help create varying extents of underrepresented samples for different minority groups. Notably, the least-represented PA groups account for only about 1/500 of the entire dataset, which equates to just 12 samples out of 6000 in CMNIST unbalance . As shown in Table 21, FairDD achieves a robust performance of 16.33% DEOM and 9.01% DEOA compared to 17.04% and 7.95% in the balanced PA groups. A similar steady behavior is observed in accuracy, which changes from 94.45% to 94.61%. This illustrates the robustness of FairDD under different levels of dataset imbalance.

Q Exploration on Vision Transformer as backbone

Although the Vision Transformer (ViT) is a powerful backbone network, to the best of my knowledge, current DDs, such as DM and DC, have not yet utilized ViT as the extraction network. We conducted experiments using 1-layer, 2-layer, and 3-layer ViTs. As shown in Table 22, vanilla DM at IPC=10 suffers performance degradation in classification, dropping from 25.01% to 18.63%. Moreover, as the number of layers increases, the performance deteriorates more severely. This suggests that current DDs are not directly compatible with ViTs. While FairDD still outperforms DM in both accuracy and fairness metrics, the observed improvement gain is smaller compared to results obtained on convolutional networks. Further research into leveraging ViTs for DM and FairDD is a promising direction worth exploring.

R Comparison with MTT

Unlike DMF, MTT uses a two-stage method to condense the dataset. First, it stores the model trajectories, and then it uses these trajectories to guide the generation of the synthetic dataset. To provide a comprehensive comparison, we compare FairDD with MTT, as shown in Tables 23 and 24.

From the results, FairDD outperforms MTT in both fairness and accuracy. Notably, MTT surpasses DMby a large margin, which we attribute to two factors: 1) Unlike DMF, which is directly influenced by biased data, MTT aligns the model parameters to optimize the synthetic dataset, and this indirect alignment reduces the impact of bias in the data. 2) An accurate model typically conceals its inherent unfairness, as it can better classify each class despite underlying biases. For example, when Whole model achieves high accuracy on the C-MNIST (FG) dataset, MTT inherits this accuracy and conceals its biases. However, when the model's accuracy declines on the C-FMNIST (BG) dataset, MTT reveals its underlying unfairness in Fig. 6(a). In contrast, FairDD directly addresses unfairness rather than relying on high accuracy to obscure biased behavior in Fig. 6(b).

(a) MTT visualization.

(b) FairDD visualization.

S More visualizations

We provide more visualizations at IPC = 50 on different datasets in Figures 7, 8, 9, 10, 11, and 12.

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(b) Visualization of the condensed dataset at IPC = 50 in C-MNIST (BG) using Vanilla DM. The background of each class inherits the bias.

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(c) Visualization of the condensed dataset at IPC = 50 in C-MNIST (BG) using FairDD + DM. The background of each class mitigates such bias.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a fair dataset distillation (DD) framework called FairDD, which matches synthetic datasets to protected attribute (PA)-wise groups of original datasets. The matching prevents collapsing into majority groups and balances generation more evenly across PA groups. Experiments show that FairDD significantly improves the fairness of vanilla DD methods.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\n* Improving fairness in data distillation is an important problem.\n* The paper is overall a smooth read.\n\nWeaknesses\n\n* The novelty of this work is questionable as there is a very similar work that has already been published at ICML 2024:\n**Cui et al., \"Mitigating bias in dataset distillation,\" ICML 2024**. The authors need to cite this work, which uses sample reweighting scheme utilizing kernel density estimation, and clearly explain and demonstrate why FairDD outperforms it. The above approach may be more advanced or at least comparable to the proposed alignment approach. Currently the baselines are just adding FairDD to existing DMF approaches, which is not sufficient.\n\n* This work is not the first work to point out that vanilla DDs fail to mitigate bias as claimed in the Conclusion. In addition to the ICML 2024 work above, here is an earlier work whose ArXiv version is cited in the paper: **Lu et al., \"Exploring the Impact of Dataset Bias on Dataset Distillation,\" CVPRW 2024**.\nThe authors should tone down their contributions.\n\n* How do you know the right ratio without looking at the final model's fairness? The paper emphasizes reflecting the sample ratio of each group, but does not consider the learnability of groups at all. For example, even if two groups A and B have a ratio of 2:1, but B is more challenging to learn, it may be better to weight them 1:3 instead of 1:2 in order to maximize fairness.\n\n* Another practical concern is whether the sensitive attributes are always available in image datasets. Unlike structured datasets, it is rarer for images to have this information. There needs to be a discussion what to do when this information is not available.\n\n* If sensitive attributes are available, there are actually more fairness measures (in addition to Visual Fairness) to consider including demographic parity and equal opportunity, which should also be supported in the paper.\n\nQUESTIONS:\nPlease see the weaknesses above.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-10"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a method to address fairness issues in the topic of dataset distillation (DD). Specifically, when distilling image instances in DD, the recognition performance for minor catetories / attributes drops, amplifying unfairness. Therefore, in this paper, by organizing protected attributes (PAs) separately and then processing & performing DD, the paper realizes a method called FairDD for the purpose of fairness treatment.\n\nSTRENGTHS AND WEAKNESSES:\n- S1. The FairDD paper tackles the problem of unfairness in DD. The conventional DD distillates a labeled image dataset into a smaller synthetic dataset for training, however, the distillated image dataset tends to eliminate image instances which have minor categories / attributes. It tends to focus on majority categories / attributes. In order to achieve fairer image recognition in this context, this work, FairDD, preserves the truly protected instances during the process of dataset distillation, this is defined as a FairDD in this paper.\n\n- S2. The proposed approaches and their established model used to improve both performance and fairness scores in the proposed FairDD are quite reasonable. For example, as shown in Figure 2, PA groups are split, and image instances can be separately distilled. By processing all PA groups simultaneously, FairDD avoids focusing only on major categories / attributes and ensures that minority categories / attributes are also represented at that time. Theoretical guarantees are further shown that the FairDD removes imbalance and improves fairness inside of the distillated datasets.\n\n- S3. In the experimental results against baseline / vanilla DD methods, the proposed FairDD successfully improves fairness metrics (DEO_M / DEO_A; lower is better) while also enhancing recognition accuracy (higher is better). The proposed method, FairDD, is evaluated comprehensively on representative datasets, namely C-MNIST, C-FMNIST, CIFAR10-S, CelebA, UTKFace, BFFHQ as shown in Tables 1, 2, and 3, and outperforms baselines on almost all metrics in the presented paper. Additional analyses include visualizations, scalability studies, and an ablation study examining the fair extractor and synthetic image initialization.\n\n- W1. Although extensive experiments in the experimental section at the main paper and appendices partially clarify FairDD’s merits and limitations, the paper will gain greater value by including a more comprehensive discussion. Specifically, a comprehensive description why FairDD works so well in terms of fairness scores and recognition performance. Here, this description should be appeared in the main paper rather than the appendices.\n\nQUESTIONS:\n- In the proposed FairDD, does treating fairness (protect PAs) generally tend to improve accuracy as well? By protecting minor yet important image feature representations, does FairDD reduce the visually similar features in the distillated image dataset, this means that it is acting as a training regularization? Moreover, if we consider other factors beyond fairness, DD may be further enhanced by the preserved and improved image features and enhanced overall performance?\n\n- The reviewer believes that [Nakamura et al., ECCV 2024] is closely related work. The research work uses a \"1p-frac dataset\" generated by fractal geometry to successfully pre-train a Vision Transformer (ViT) from a single synthetic sample. In the appendix, the present paper mentions that applying ViT did not work very well at this moment. The insights from their fractal-based approach for ViT pre-training help the next approach for using ViT as a backbone in the topic of FairDD / DD? Also, clarifying the relationship between DD and such that approaches, formula-driven supervised learning (FDSL), might further advance the DD topic.\n\n[Nakamura et al., ECCV 2024] R. Nakamura et al. “Scaling Backwards: Minimal Synthetic Pre-training?”, ECCV 2024.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-20"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces FairDD, a fairness-aware dataset distillation framework designed to reduce bias towards protected attributes in synthetic datasets, without sacrificing target attribute accuracy. By aligning distilled data to protected attribute-wise distributions rather than majority-dominated global ones, FairDD improves fairness across multiple dataset distillation paradigms and shows strong performance that is justified theoretically.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: \n1. The paper addresses a critical yet underexplored issue, namely bias amplification in dataset distillation, and suggests FairDD, the first method to address this challenge.\n2. The authors provide formal proofs that FairDD mitigates protected attribute imbalance and ensures target attribute distributional coverage.\n3. Evaluation involves both synthetic and real-world datasets, showing consistent fairness improvements. Also, comprehensive ablations are reported in the appendix.\n\nWeaknesses\n1. The method requires known protected attribute labels, limiting its applicability to real-world scenarios where such labels are often unavailable and inferring pseudo-labels can be very challenging.\n\n2. While the technical content is strong, the writing could be clearer in dense theoretical sections (e.g., Sec. 4), which currently may hinder accessibility to a broader ML audience. Specifically:\n  a. (lines 125-126) The concepts of Gradient Matching and Distribution Matching have not been adequately explained neither here nor in the related works. The authors should elaborate more on how the gradient information and embedding distribution matching is formulated and achieved.\n  b. (line 130) Abbreviations IDC and DREAM are not defined and citations are missing.\n  c. (lines 129-130) How important is the choice of distance metric, and why are these particular metrics better suited for these methods?\n d. (lines 151-153) The fact that bias-aligned samples contribute more to the loss does not necessarily mean that the loss cannot be minimized for bias-conflicting samples. In typical classification tasks, previous work [1] has investigated the loss and gradient spaces with respect to bias-aligned and bias-conflicting samples to demonstrate how bias is introduced. Does this also apply to the Dataset Distillation task?\n e. Considering the previous comment, the authors should elaborate further on the two arguments (in bold) presented in lines 155–158. \n f. It is not clear whether the suggested method can generalize for multiple protected attributes.\ng. The authors should include an algorithm in Section 5 that outlines the proposed method to enhance the reproducibility of their work.\n\n3. While Worst Group Accuracy is a standard evaluation metric in the context of mitigating visual biases, the authors opt for Equalized Odds. It would be helpful if they could elaborate on the rationale behind this choice.\n\n[1] Sarridis, I., Koutlis, C., Papadopoulos, S., & Diou, C. (2024). BAdd: Bias Mitigation through Bias Addition. *arXiv preprint arXiv:2408.11439*.\n\nQUESTIONS:\nNone\n\nLIMITATIONS:\nSee Strengths and Weaknesses field.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work argues that existing dataset distillation methodologies are biased towards majority protected attribute groups and fail to achieve unfairness towards minority protected attribute groups with theoretical evidences. To solve this problem, this work proposes the FairDD framework, which divides a given original dataset according to attributes and aligns each sub-dataset with a learnable small dataset. The authors conduct extensive experiments on a wide range of benchmark datasets and experimentally demonstrate that FairDD simultaneously improves both accuracy and fairness on an unbiased test dataset.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n1. To the best of my knowledge, this research is the first work to discuss the fairness in dataset distillation.\n\n2. I like the analysis of why vanilla DD fails in PA imbalance situations. It is easy for the reader to follow why we should explore dataset distillation methodologies for fairness.\n\n3. Through the extensive experimental results, FairDD has demonstrated high performance gains despite its very simple form.\n\n**Weaknesses**\n1. My major concern is the novelty of the proposed method. FairDD partitions the original dataset into several sub-datasets w.r.t PA to mitigate the domination of the majority group. However, partitioning requires that every instance of the original dataset has a labelled attribute. This may not be realistic and becomes a shortcoming that limits the scope of application of FairDD. In addition, the methodology of dividing the real dataset according to the attribute is a simple but strong baseline, but the contribution is marginal to be called a core methodology. Finally, Attribute-based partitioning has clear drawbacks that make it difficult to apply to bilevel optimization and the trajectory matching framework.\n\n2. Lack of sufficient comparison to a baseline that could be simple but effective. For example, a methodology that applies vanilla DD and uses fairness-aware learning to train the network in the test phase could be a baseline. I also believe that gradient matching for fairness-aware loss is a baseline. Finally, this research should also include whether bias also occurs in bilevel optimization or trajectory matching using fairness-aware learning. As this research is the first to study the possibility of dataset distillation in a new context, it is necessary to make detailed comparisons with various possible baselines.\n\nQUESTIONS:\nPlease refer to the weaknesses also.\n1. I am curious about the derivation of Eqs. 3 and 5.\n2. Is FairDD applicable to datasets where each instance has more than one attribute? I suspect it would be difficult to apply Attribute-aware partitioning naively in this situation.\n\nLIMITATIONS:\nSee weaknesses and questions", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}