Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs but is challenged by complex, multi-faceted distributional shifts. Existing methods attempt to reduce distributional shifts by aligning manually selected graph elements (e.g., node attributes or structural statistics), which typically require manually designed graph filters to extract relevant features before alignment. However, such approaches are inflexible: they rely on scenario-specific heuristics, and struggle when dominant discrepancies vary across transfer scenarios. To address these limitations, we propose \textbf{ADAlign}, an Adaptive Distribution Alignment framework for GDA. Unlike heuristic methods, ADAlign requires no manual specification of alignment criteria. It automatically identifies the most relevant discrepancies in each transfer and aligns them jointly, capturing the interplay between attributes, structures, and their dependencies. This makes ADAlign flexible, scenario-aware, and robust to diverse and dynamically evolving shifts. To enable this adaptivity, we introduce the Neural Spectral Discrepancy (NSD), a theoretically principled parametric distance that provides a unified view of cross-graph shifts. NSD leverages neural characteristic function in the spectral domain to encode feature-structure dependencies of all orders, while a learnable frequency sampler adaptively emphasizes the most informative spectral components for each task via minimax paradigm. Extensive experiments on 10 datasets and 16 transfer tasks show that ADAlign not only outperforms state-of-the-art baselines but also achieves efficiency gains with lower memory usage and faster training.

翻译：图域适应（GDA）旨在将知识从带标签的源图迁移至无标签的目标图，但面临复杂、多层面的分布偏移挑战。现有方法试图通过对齐人工选择的图元素（如节点属性或结构统计量）来减少分布偏移，这通常需要人工设计图滤波器以在对齐前提取相关特征。然而，此类方法缺乏灵活性：它们依赖于特定场景的启发式策略，且在迁移场景中主导性差异发生变化时难以有效应对。为克服这些局限，我们提出了\textbf{ADAlign}——一种用于GDA的自适应分布对齐框架。与启发式方法不同，ADAlign无需人工指定对齐准则。它能自动识别每次迁移中最相关的差异并对其进行联合对齐，从而捕捉属性、结构及其依赖关系之间的相互作用。这使得ADAlign具有灵活性、场景感知能力，并能适应多样且动态演变的分布偏移。为实现这种自适应性，我们提出了神经谱差异（NSD），这是一种理论上有依据的参数化距离度量，为跨图偏移提供了统一视角。NSD在谱域中利用神经特征函数编码所有阶数的特征-结构依赖关系，同时通过极小极大范式，可学习的频率采样器能自适应地强调每个任务中最具信息量的谱分量。在10个数据集和16个迁移任务上的大量实验表明，ADAlign不仅优于现有最先进的基线方法，还通过更低的内存占用和更快的训练实现了效率提升。