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

TL;DR

ADAlign addresses graph domain adaptation under complex distribution shifts by introducing Neural Spectral Discrepancy ($NSD$), a spectral-domain distance between source and target embeddings defined via characteristic functions of the embeddings. An adaptive frequency sampler learns which spectral components to emphasize, and a minimax training framework jointly optimizes source discrimination and spectral alignment, balancing amplitude and phase differences with a tunable $κ$. Theoretical guarantees connect $NSD$-based alignment to generalization bounds via a PAC-Bayesian analysis, and empirical results on 10 datasets with 16 transfer tasks demonstrate state-of-the-art performance with notable efficiency gains. Overall, ADAlign provides a scalable, scenario-aware approach for robust cross-graph transfer learning by seamlessly combining CF-based distribution matching with adaptive spectral prioritization.

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.

Figures (13)

• Figure 1: Distributional disparities across different scenarios. Each dimension (e.g., 1, 2) corresponds to a PCA-reduced feature, and the value represents the KL divergence between pairs of the top 5 features, computed for each transfer task, e.g., KL(B1$||$U1).
• Figure 2: Overall architecture of our proposed ADAlign Framework. The model consists of a source and target branch, each processed by a GNN. A frequency sampler adaptively selects spectral components via a learnable parameter $\bm{\phi}$, while the classifier is optimized with source labels. The alignment objective $\mathcal{L}_{\text{align}}$ is adversarially maximized with respect to $\bm{\phi}$ and minimized with respect to the model parameters $\bm{\delta}$, enabling dynamic and efficient distribution matching in the spectral domain.
• Figure 2: Per-iteration runtime and memory consumption comparison on two transfer tasks. Values in parentheses show relative improvement: "$\uparrow$” speedup, "$\downarrow$” memory reduction.
• Figure 3: The comparative training curves of Micro-F1 scores are illustrated for four representative baselines across two distinct transfer scenarios over 200 epochs of iterative learning.
• Figure 4: Classification Micro-F1 comparisons between ADA variants on four cross-domain tasks.

Theorems & Definitions (6)

• Theorem 1: Convergence
• Theorem 2: Uniqueness
• Theorem 3: GDA Bound for Deterministic Classifiers
• Definition 1
• Theorem 4
• proof