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

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.

💡 Research Summary

The paper tackles the problem of large distribution shifts in graph neural networks (GNNs), which severely degrade performance when source and target graphs differ substantially in node attributes and structure. Existing graph domain adaptation (DA) methods assume only mild shifts and thus fail under realistic, large‑scale changes. While gradual domain adaptation (GDA) has been successful for i.i.d. data by interpolating through a sequence of unlabeled intermediate domains, extending GDA to non‑i.i.d. graph data—where nodes are dependent—has remained an open challenge.

To fill this gap, the authors propose Gadget, the first GDA framework designed for graph data. The core of Gadget is the Fused Gromov‑Wasserstein (FGW) distance, a metric that simultaneously accounts for node feature discrepancies and graph topology differences. By treating each graph as a probability measure over node‑feature pairs and using a coupling matrix to align nodes across graphs, FGW provides a principled way to quantify domain discrepancy in a non‑IID setting.

The theoretical contribution begins with a set of regularity assumptions: (i) graph convolution layers are Lipschitz‑continuous with respect to a Wasserstein‑type distance between local neighborhoods, (ii) linear layers have bounded operator norm, and (iii) task‑specific loss functions (node‑level, edge‑level, graph‑level) are Lipschitz. Under these conditions, the authors derive an error bound for any gradual adaptation path (H = (H_0,\dots,H_T)) connecting source (G_0) to target (G_T): \