# Spectral Gradient Surgery for Domain-Generalizable Dataset Distillation

arXiv: https://arxiv.org/abs/2605.18836 · HTML: https://mlsanity.com/paper/2605.18836/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 27 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 22 of 22)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [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)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [Learning to Generate Novel Domains for Domain Generalization](https://mlsanity.com/paper/2007.03304/) (2020)
- [Dataset Condensation with Differentiable Siamese Augmentation](https://mlsanity.com/paper/2102.08259/) (2021)
- [A Fourier-based Framework for Domain Generalization](https://mlsanity.com/paper/2105.11120/) (2021)
- [CORe50: a New Dataset and Benchmark for Continuous Object Recognition](https://mlsanity.com/paper/1705.03550/) (2017)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Scaling Up Dataset Distillation to ImageNet-1K with Constant Memory](https://mlsanity.com/paper/2211.10586/) (2022)
- [DataDAM: Efficient Dataset Distillation with Attention Matching](https://mlsanity.com/paper/2310.00093/) (2023)
- [M3D: Dataset Condensation by Minimizing Maximum Mean Discrepancy](https://mlsanity.com/paper/2312.15927/) (2023)
- [Dataset Distillation with Neural Characteristic Function: A Minmax Perspective](https://mlsanity.com/paper/2502.20653/) (2025)
- [AdvST: Revisiting Data Augmentations for Single Domain Generalization](https://mlsanity.com/paper/2312.12720/) (2023)
- [Hyperbolic Dataset Distillation](https://mlsanity.com/paper/2505.24623/) (2025)
- [Towards Combating Frequency Simplicity-biased Learning for Domain Generalization](https://mlsanity.com/paper/2410.16146/) (2024)
- [DAM: Domain-Aware Module for Multi-Domain Dataset Condensation](https://mlsanity.com/paper/2505.22387/) (2025)

## Abstract (arXiv)

Dataset Distillation (DD) synthesizes a compact synthetic dataset that preserves the training utility of a full dataset. However, its standard formulation assumes that test data follow the same distribution as training data, an assumption that rarely holds in practice. A straightforward extension-applying post-hoc Domain Generalization (DG) techniques to distilled data-is ill-suited because existing DG methods rely on the natural diversity of real datasets, which compact synthetic sets inherently lack, while also incurring substantial augmentation overhead that conflicts with the efficiency objective of dataset distillation. To address this limitation, we introduce Domain Generalizable Dataset Distillation (DGDD), a new problem setting that explicitly targets out-of-distribution (OOD) generalization of distilled datasets. We study this problem through a widely adopted DD baseline of Distribution Matching (DM). We attribute the OOD vulnerability of DM to the entanglement of class-discriminative and domain-specific information within the compressed synthetic set, and propose Spectral Gradient Surgery (SGS) to disentangle the two. The key insight of SGS is that cross-domain agreement among domain-wise gradients in the spectral domain reveals which gradient components are shared across source domains-and are therefore class-discriminative-and which are domain-specific. Based on this observation, SGS augments the standard DM update with two complementary gradients: one that reinforces cross-domain shared components and another that explicitly promotes diversity within the distilled dataset. Extensive experiments on diverse-scale benchmarks demonstrate that SGS substantially improves OOD generalization while remaining plug-and-play compatible with existing DM methods.