# M3D: Dataset Condensation by Minimizing Maximum Mean Discrepancy

arXiv: https://arxiv.org/abs/2312.15927 · HTML: https://mlsanity.com/paper/2312.15927/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 54 references that are in the map.
- First posted on arXiv 26 Dec 2023.

## Builds on (most cited first, 30 of 37)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [BDD100K: A Diverse Driving Dataset for Heterogeneous Multitask Learning](https://mlsanity.com/paper/1805.04687/) (2018)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [NAS-Bench-101: Towards Reproducible Neural Architecture Search](https://mlsanity.com/paper/1902.09635/) (2019)
- [Selection via Proxy: Efficient Data Selection for Deep Learning](https://mlsanity.com/paper/1906.11829/) (2019)
- [Dataset Condensation with Differentiable Siamese Augmentation](https://mlsanity.com/paper/2102.08259/) (2021)
- [Empirical Analysis of the Hessian of Over-Parametrized Neural Networks](https://mlsanity.com/paper/1706.04454/) (2017)
- [Dataset Meta-Learning from Kernel Ridge-Regression](https://mlsanity.com/paper/2011.00050/) (2020)
- [Dataset Distillation with Infinitely Wide Convolutional Networks](https://mlsanity.com/paper/2107.13034/) (2021)
- [Dataset Condensation via Efficient Synthetic-Data Parameterization](https://mlsanity.com/paper/2205.14959/) (2022)
- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [Dataset Pruning: Reducing Training Data by Examining Generalization Influence](https://mlsanity.com/paper/2205.09329/) (2022)
- [Generalizing Dataset Distillation via Deep Generative Prior](https://mlsanity.com/paper/2305.01649/) (2023)
- [Improved Distribution Matching for Dataset Condensation](https://mlsanity.com/paper/2307.09742/) (2023)
- [Coverage-centric Coreset Selection for High Pruning Rates](https://mlsanity.com/paper/2210.15809/) (2022)
- [Efficient Dataset Distillation Using Random Feature Approximation](https://mlsanity.com/paper/2210.12067/) (2022)
- [Generative Teaching Networks: Accelerating Neural Architecture Search by Learning to Generate Synthetic Training Data](https://mlsanity.com/paper/1912.07768/) (2019)
- [Remember the Past: Distilling Datasets into Addressable Memories for Neural Networks](https://mlsanity.com/paper/2206.02916/) (2022)
- [Condensing Graphs via One-Step Gradient Matching](https://mlsanity.com/paper/2206.07746/) (2022)
- [Optimal Continual Learning has Perfect Memory and is NP-hard](https://mlsanity.com/paper/2006.05188/) (2020)
- [FedDM: Iterative Distribution Matching for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2207.09653/) (2022)
- [Accelerating Dataset Distillation via Model Augmentation](https://mlsanity.com/paper/2212.06152/) (2022)
- [Adaptive Second Order Coresets for Data-efficient Machine Learning](https://mlsanity.com/paper/2207.13887/) (2022)
- [Dataset Distillation with Convexified Implicit Gradients](https://mlsanity.com/paper/2302.06755/) (2023)
- [Delving into Effective Gradient Matching for Dataset Condensation](https://mlsanity.com/paper/2208.00311/) (2022)

## Built on by (most cited first, 30 of 49)

- [Dataset Distillation with Neural Characteristic Function: A Minmax Perspective](https://mlsanity.com/paper/2502.20653/) (2025)
- [Elucidating the Design Space of Dataset Condensation](https://mlsanity.com/paper/2404.13733/) (2024)
- [The Evolution of Dataset Distillation: Toward Scalable and Generalizable Solutions](https://mlsanity.com/paper/2502.05673/) (2025)
- [Are Large-scale Soft Labels Necessary for Large-scale Dataset Distillation?](https://mlsanity.com/paper/2410.15919/) (2024)
- [Emphasizing Discriminative Features for Dataset Distillation in Complex Scenarios](https://mlsanity.com/paper/2410.17193/) (2024)
- [Towards Adversarially Robust Dataset Distillation by Curvature Regularization](https://mlsanity.com/paper/2403.10045/) (2024)
- [DANCE: Dual-View Distribution Alignment for Dataset Condensation](https://mlsanity.com/paper/2406.01063/) (2024)
- [Hyperbolic Dataset Distillation](https://mlsanity.com/paper/2505.24623/) (2025)
- [DD-Ranking: Rethinking the Evaluation of Dataset Distillation](https://mlsanity.com/paper/2505.13300/) (2025)
- [Adaptive Dataset Quantization](https://mlsanity.com/paper/2412.16895/) (2024)
- [Enhancing Dataset Distillation via Non-Critical Region Refinement](https://mlsanity.com/paper/2503.18267/) (2025)
- [LearnAlign: Data Selection for LLM Reinforcement Learning with Improved Gradient Alignment](https://mlsanity.com/paper/2506.11480/) (2025)
- [Efficient Multimodal Dataset Distillation via Generative Models](https://mlsanity.com/paper/2509.15472/) (2025)
- [Optimizing Distributional Geometry Alignment with Optimal Transport for Generative Dataset Distillation](https://mlsanity.com/paper/2512.00308/) (2025)
- [Mitigating Bias in Dataset Distillation](https://mlsanity.com/paper/2406.06609/) (2024)
- [FYI: Flip Your Images for Dataset Distillation](https://mlsanity.com/paper/2407.08113/) (2024)
- [Improving Noise Efficiency in Privacy-preserving Dataset Distillation](https://mlsanity.com/paper/2508.01749/) (2025)
- [EVLF: Early Vision-Language Fusion for Generative Dataset Distillation](https://mlsanity.com/paper/2603.07476/) (2026)
- [ATOM: Attention Mixer for Efficient Dataset Distillation](https://mlsanity.com/paper/2405.01373/) (2024)
- [Dataset Distillation from First Principles: Integrating Core Information Extraction and Purposeful Learning](https://mlsanity.com/paper/2409.01410/) (2024)
- [Decomposed Distribution Matching in Dataset Condensation](https://mlsanity.com/paper/2412.04748/) (2024)
- [TGDD: Trajectory Guided Dataset Distillation with Balanced Distribution](https://mlsanity.com/paper/2512.02469/) (2025)
- [GeoDM: Geometry-aware Distribution Matching for Dataset Distillation](https://mlsanity.com/paper/2512.08317/) (2025)
- [Multimodal Distribution Matching for Vision-Language Dataset Distillation](https://mlsanity.com/paper/2605.23482/) (2026)
- [Stationary MMD Points](https://mlsanity.com/paper/2505.20754/) (2025)
- [Learning from Dense Events: Towards Fast Spiking Neural Networks Training via Event Dataset Distillation](https://mlsanity.com/paper/2511.12095/) (2025)
- [A Discrepancy-Based Perspective on Dataset Condensation](https://mlsanity.com/paper/2509.10367/) (2025)
- [Harmonic Dataset Distillation for Time Series Forecasting](https://mlsanity.com/paper/2603.03760/) (2026)
- [Geometry-Aware Dataset Condensation for Diffusion Model Training](https://mlsanity.com/paper/2606.05883/) (2026)
- [Distill Once, Adapt Life-Long: Exploring Dataset Distillation for Continual Test-Time Adaptation](https://mlsanity.com/paper/2606.20196/) (2026)

## Abstract (arXiv)

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 still yield less comparable results to SOTA optimization-oriented methods. In this paper, we argue that existing DM-based methods overlook the higher-order alignment of the distributions, which may lead to sub-optimal matching results. Inspired by this, 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. Source codes are available at https://github.com/Hansong-Zhang/M3D.