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

arXiv: https://arxiv.org/abs/2602.10489 · HTML: https://mlsanity.com/paper/2602.10489/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 62 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Builds on (most cited first, 30 of 33)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [OOD-GNN: Out-of-Distribution Generalized Graph Neural Network](https://mlsanity.com/paper/2112.03806/) (2021)
- [Amplitude-Phase Recombination: Rethinking Robustness of Convolutional Neural Networks in Frequency Domain](https://mlsanity.com/paper/2108.08487/) (2021)
- [Subgroup Generalization and Fairness of Graph Neural Networks](https://mlsanity.com/paper/2106.15535/) (2021)
- [Graph Transfer Learning via Adversarial Domain Adaptation with Graph Convolution](https://mlsanity.com/paper/1909.01541/) (2019)
- [Joint Distribution Matters: Deep Brownian Distance Covariance for Few-Shot Classification](https://mlsanity.com/paper/2204.04567/) (2022)
- [Structural Re-weighting Improves Graph Domain Adaptation](https://mlsanity.com/paper/2306.03221/) (2023)
- [Dataset Distillation with Neural Characteristic Function: A Minmax Perspective](https://mlsanity.com/paper/2502.20653/) (2025)
- [DANE: Domain Adaptive Network Embedding](https://mlsanity.com/paper/1906.00684/) (2019)
- [Non-IID Transfer Learning on Graphs](https://mlsanity.com/paper/2212.08174/) (2022)
- [Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?](https://mlsanity.com/paper/2306.01323/) (2023)
- [Distributed Graph Neural Network Training: A Survey](https://mlsanity.com/paper/2211.00216/) (2022)
- [Rethinking Propagation for Unsupervised Graph Domain Adaptation](https://mlsanity.com/paper/2402.05660/) (2024)
- [A Characteristic Function Approach to Deep Implicit Generative Modeling](https://mlsanity.com/paper/1909.07425/) (2019)
- [Pairwise Alignment Improves Graph Domain Adaptation](https://mlsanity.com/paper/2403.01092/) (2024)
- [On the Benefits of Attribute-Driven Graph Domain Adaptation](https://mlsanity.com/paper/2502.06808/) (2025)
- [SA-GDA: Spectral Augmentation for Graph Domain Adaptation](https://mlsanity.com/paper/2408.09189/) (2024)
- [PCF-GAN: generating sequential data via the characteristic function of measures on the path space](https://mlsanity.com/paper/2305.12511/) (2023)
- [Smoothness Really Matters: A Simple Yet Effective Approach for Unsupervised Graph Domain Adaptation](https://mlsanity.com/paper/2412.11654/) (2024)
- [Can Modifying Data Address Graph Domain Adaptation?](https://mlsanity.com/paper/2407.19311/) (2024)
- [Hyperbolic Diffusion Recommender Model](https://mlsanity.com/paper/2504.01541/) (2025)
- [Homophily Enhanced Graph Domain Adaptation](https://mlsanity.com/paper/2505.20089/) (2025)

## Built on by (most cited first, 1 of 1)

- [Graph Domain Adaptation Does Not End with Representation Learning](https://mlsanity.com/paper/2609.25692/) (2026)

## Abstract (arXiv)

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 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.