D-GAP: Improving Out-of-Domain Robustness via Dataset-Agnostic and Gradient-Guided Augmentation in Frequency and Pixel Spaces

Domain generalization (DG) and neural network pruning are conventionally treated as distinct objectives, targeting out-of-distribution (OOD) robustness and model efficiency, respectively. In this work, we bridge this gap by introducing Domain-Aware Pruning (DAP), a framework that leverages network sparsity as a mechanism to implicitly enhance generalization to unseen domains. Diverging from standard binary mask optimization, DAP learns a continuous parameter retention probability $p \in [0, 1]$, framing network compression as a continuous probabilistic masking problem. By introducing a regularization objective that actively penalizes the retention of domain-sensitive weights during the mask training, DAP identifies a domain-invariant subnetwork. Empirical results across five DG benchmark datasets demonstrate that DAP achieves significant sparsity while consistently matching or exceeding the OOD performance of its dense counterparts. Crucially, DAP is an algorithm-agnostic framework that integrates seamlessly with existing DG pipelines without necessitating post-hoc fine-tuning. Beyond efficiency and generalization, we show that DAP natively provides increased robustness to adversarial perturbations and yields highly interpretable models, where the retained weights reliably encapsulate the most domain-invariant and task-critical representations.

Domain Generalization (DG) aims to learn representations that remain robust under out-of-distribution (OOD) shifts and generalize effectively to unseen target domains. While recent invariant learning strategies and architectural advances have achieved strong performance, explicitly discovering a structured domain-invariant subspace through second-order statistics remains underexplored. In this work, we propose CPCANet, a novel framework grounded in Common Principal Component Analysis (CPCA), which unrolls the iterative Flury-Gautschi (FG) algorithm into fully differentiable neural layers. This approach integrates the statistical properties of CPCA into an end-to-end trainable framework, enforcing the discovery of a shared subspace across diverse domains while preserving interpretability. Experiments on four standard DG benchmarks demonstrate that CPCANet achieves state-of-the-art (SOTA) performance in zero-shot transfer. Moreover, CPCANet is architecture-agnostic and requires no dataset-specific tuning, providing a simple and efficient approach to learning robust representations under distribution shift. Code is available at https://github.com/wish44165/CPCANet.

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.