DSBD: Dual-Aligned Structural Basis Distillation for Graph Domain Adaptation

2026-04-03

AI Summary

This work addresses the challenge of unreliable knowledge transfer in graph domain adaptation caused by drastic topological shifts. To this end, we propose a novel framework that achieves cross-domain structural alignment by constructing a differentiable structural basis and jointly optimizing geometric and spectral consistency. Specifically, we introduce a unified approach that, for the first time, combines permutation-invariant topological moment matching for geometric alignment with Dirichlet energy calibration for spectral alignment, explicitly modeling structural discrepancies. Furthermore, a decoupled inference paradigm is incorporated to eliminate structural bias inherited from the source domain. Extensive experiments on multiple graph and image benchmarks demonstrate that our method significantly outperforms state-of-the-art approaches, confirming its robustness and effectiveness under severe topological distribution shifts.

Abstract

Graph domain adaptation (GDA) aims to transfer knowledge from a labeled source graph to an unlabeled target graph under distribution shifts. However, existing methods are largely feature-centric and overlook structural discrepancies, which become particularly detrimental under significant topology shifts. Such discrepancies alter both geometric relationships and spectral properties, leading to unreliable transfer of graph neural networks (GNNs). To address this limitation, we propose Dual-Aligned Structural Basis Distillation (DSBD) for GDA, a novel framework that explicitly models and adapts cross-domain structural variation. DSBD constructs a differentiable structural basis by synthesizing continuous probabilistic prototype graphs, enabling gradient-based optimization over graph topology. The basis is learned under source-domain supervision to preserve semantic discriminability, while being explicitly aligned to the target domain through a dual-alignment objective. Specifically, geometric consistency is enforced via permutation-invariant topological moment matching, and spectral consistency is achieved through Dirichlet energy calibration, jointly capturing structural characteristics across domains. Furthermore, we introduce a decoupled inference paradigm that mitigates source-specific structural bias by training a new GNN on the distilled structural basis. Extensive experiments on graph and image benchmarks demonstrate that DSBD consistently outperforms state-of-the-art methods.

Problem

• Graph Domain Adaptation
• Structural Discrepancy
• Topology Shift
• Graph Neural Networks
• Distribution Shift

Innovation

• graph domain adaptation
• structural basis distillation
• dual-alignment
• topological moment matching
• Dirichlet energy calibration