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1. Pave Your Own Path: Graph Gradual Domain Adaptation on Fused Gromov-Wasserstein Geodesics

   Zeng, Zhichen; Qiu, Ruizhong; Bao, Wenxuan; Wei, Tianxin; Lin, Xiao; Yan, Yuchen; Abdelzaher, Tarek F; Han, Jiawei; Tong, Hanghang (March 2026, Transactions on machine learning research)

   Graph neural networks, despite their impressive performance, are highly vulnerable to distribution shifts on graphs. Existing graph domain adaptation (graph DA) methods often implicitly assume a mild shift between source and target graphs, limiting their applicability to real-world scenarios with large shifts. Gradual domain adaptation (GDA) has emerged as a promising approach for addressing large shifts by gradually adapting the source model to the target domain via a path of unlabeled intermediate domains. Existing GDA methods exclusively focus on independent and identically distributed (IID) data with a predefined path, leaving their extension to non-IID graphs without a given path an open challenge. To bridge this gap, we present Gadget, the first GDA framework for non-IID graph data. First (theoretical foundation), the Fused Gromov-Wasserstein (FGW) distance is adopted as the domain discrepancy for non-IID graphs, based on which, we derive an error bound on node, edge and graph-level tasks, showing that the target domain error is proportional to the length of the path. Second (optimal path), guided by the error bound, we identify the FGW geodesic as the optimal path, which can be efficiently generated by our proposed algorithm. The generated path can be seamlessly integrated with existing graph DA methods to handle large shifts on graphs, improving state-of-the-art graph DA methods by up to 6.8% in accuracy on real-world datasets. 

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2. Graph Domain Adaptation via Theory-Grounded Spectral Regularization

   You, Y.; Chen, T.; Wang, Z.; Shen, Y. (February 2023, The Eleventh International Conference on Learning Representations)

   Transfer learning on graphs drawn from varied distributions (domains) is in great demand across many applications. Emerging methods attempt to learn domain-invariant representations using graph neural networks (GNNs), yet the empirical performances vary and the theoretical foundation is limited. This paper aims at designing theory-grounded algorithms for graph domain adaptation (GDA). (i) As the first attempt, we derive a model-based GDA bound closely related to two GNN spectral properties: spectral smoothness (SS) and maximum frequency response (MFR). This is achieved by cross-pollinating between the OT-based (optimal transport) DA and graph filter theories. (ii) Inspired by the theoretical results, we propose algorithms regularizing spectral properties of SS and MFR to improve GNN transferability. We further extend the GDA theory into the more challenging scenario of conditional shift, where spectral regularization still applies. (iii) More importantly, our analyses of the theory reveal which regularization would improve performance of what transfer learning scenario, (iv) with numerical agreement with extensive real-world experiments: SS and MFR regularizations bring more benefits to the scenarios of node transfer and link transfer, respectively. In a nutshell, our study paves the way toward explicitly constructing and training GNNs that can capture more transferable representations across graph domains. Codes are released at https://github.com/Shen-Lab/GDA-SpecReg. 

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3. Avoiding Structural Pitfalls: Self-Supervised Low-Rank Feature Tuning for Graph Test-Time Adaptation

   Zhang, Haoxiang; Li, Zhuofeng; Zhang, Qiannan; Kou, Ziyi; Li, Juncheng; Pei, Shichao (November 2025, Transactions on machine learning research)

   Pre-trained graph neural networks (GNNs) have demonstrated significant success in leveraging large-scale graph data to learn transferable representations. However, their performance often degrades under distribution shifts, particularly in real-world scenarios where test labels are unavailable. To address this challenge, we propose Graph Optimization via Augmented Transformations (GOAT), a novel self-supervised test-time tuning paradigm that adapts pre-trained GNNs to distribution-shifted test data by focusing exclusively on node feature transformations. By avoiding complex and often suboptimal graph structure transformations, GOAT overcomes the limitations of existing data-centric methods. To further address the issue of transformation collapse, where feature transformations converge to trivial solutions—such as when the test-time learned data-centric transformation degenerates into a constant or identity mapping across different inputs, we introduce a parameter-efficient low-rank adapter that generates diverse transformations tailored to individual input graphs. This design not only enhances adaptation performance but also improves interpretability by avoiding modifications to the graph structure. Through extensive experiments on six real-world datasets with diverse distribution shifts, we demonstrate that GOAT achieves consistent performance improvements across different pre-trained GNN backbones, outperforming state-of-the-art test-time adaptation methods. 

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4. Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?

   Mao, Haitao; Chen, Zhikai; Jin, Wei; Han, Haoyu; Ma, Yao; Zhao, Tong; Shah, Neil; Tang, Jiliang (December 2023, NeurIPS)

   Recent studies on Graph Neural Networks(GNNs) provide both empirical and theoretical evidence supporting their effectiveness in capturing structural patterns on both homophilic and certain heterophilic graphs. Notably, most real-world homophilic and heterophilic graphs are comprised of a mixture of nodes in both homophilic and heterophilic structural patterns, exhibiting a structural disparity. However, the analysis of GNN performance with respect to nodes exhibiting different structural patterns, e.g., homophilic nodes in heterophilic graphs, remains rather limited. In the present study, we provide evidence that Graph Neural Networks(GNNs) on node classification typically perform admirably on homophilic nodes within homophilic graphs and heterophilic nodes within heterophilic graphs while struggling on the opposite node set, exhibiting a performance disparity. We theoretically and empirically identify effects of GNNs on testing nodes exhibiting distinct structural patterns. We then propose a rigorous, non-i.i.d PAC-Bayesian generalization bound for GNNs, revealing reasons for the performance disparity, namely the aggregated feature distance and homophily ratio difference between training and testing nodes. Furthermore, we demonstrate the practical implications of our new findings via (1) elucidating the effectiveness of deeper GNNs; and (2) revealing an over-looked distribution shift factor on graph out-of-distribution problem and proposing a new scenario accordingly. 

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5. Gradual Domain Adaptation without Indexed Intermediate Domains

   Chen, Hong-You; Chao, Wei-Lun (January 2021, Advances in neural information processing systems)

   The effectiveness of unsupervised domain adaptation degrades when there is a large discrepancy between the source and target domains. Gradual domain adaption (GDA) is one promising way to mitigate such an issue, by leveraging additional un- labeled data that gradually shift from the source to the target. Through sequentially adapting the model along the “indexed” intermediate domains, GDA substantially improves the overall adaptation performance. In practice, however, the extra unla- beled data may not be separated into intermediate domains and indexed properly, limiting the applicability of GDA. In this paper, we investigate how to discover the sequence of intermediate domains when it is not already available. Concretely, we propose a coarse-to-fine framework, which starts with a coarse domain dis- covery step via progressive domain discriminator training. This coarse domain sequence then undergoes a fine indexing step via a novel cycle-consistency loss, which encourages the next intermediate domain to preserve sufficient discriminative knowledge of the current intermediate domain. The resulting domain sequence can then be used by a GDA algorithm. On benchmark data sets of GDA, we show that our approach, which we name Intermediate DOmain Labeler (IDOL), can lead to comparable or even better adaptation performance compared to the pre-defined do- main sequence, making GDA more applicable and robust to the quality of domain sequences. Codes are available at https://github.com/hongyouc/IDOL. 

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