Learning Adaptive Distribution Alignment with Neural Characteristic Function for Graph Domain Adaptation

TL;DR

This paper introduces ADAlign, a flexible and adaptive framework for graph domain adaptation that automatically identifies and aligns the most relevant distribution discrepancies using neural characteristic functions, improving transfer performance.

Contribution

The paper proposes ADAlign, a novel adaptive distribution alignment method that automatically detects and aligns key discrepancies in graph domain adaptation without manual heuristics.

Findings

Outperforms state-of-the-art methods on 10 datasets and 16 transfer tasks.

Achieves lower memory usage and faster training.

Effectively captures complex attribute-structure dependencies.

Abstract

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.