M3D: Dataset Condensation by Minimizing Maximum Mean Discrepancy

Training state-of-the-art (SOTA) deep models often requires extensive data, resulting in substantial training and storage costs. To address these challenges, dataset condensation has been developed to learn a small synthetic set that preserves essential information from the original large-scale dataset. Nowadays, optimization-oriented methods have been the primary method in the field of dataset condensation for achieving SOTA results. However, the bi-level optimization process hinders the practical application of such methods to realistic and larger datasets. To enhance condensation efficiency, previous works proposed Distribution-Matching (DM) as an alternative, which significantly reduces the condensation cost. Nonetheless, current DM-based methods have yielded less comparable results to optimization-oriented methods due to their focus on aligning only the first moment of the distributions. In this paper, we present a novel DM-based method named M3D for dataset condensation by Minimizing the Maximum Mean Discrepancy between feature representations of the synthetic and real images. By embedding their distributions in a reproducing kernel Hilbert space, we align all orders of moments of the distributions of real and synthetic images, resulting in a more generalized condensed set. Notably, our method even surpasses the SOTA optimization-oriented method IDC on the high-resolution ImageNet dataset. Extensive analysis is conducted to verify the effectiveness of the proposed method.