EdgeMask-DG*: Learning Domain-Invariant Graph Structures via Adversarial Edge Masking

Structural shifts pose a significant challenge for graph neural networks, as graph topology acts as a covariate that can vary across domains. Existing domain generalization methods rely on fixed structural augmentations or training on globally perturbed graphs, mechanisms that do not pinpoint which specific edges encode domain-invariant information. We argue that domain-invariant structural information is not rigidly tied to a single topology but resides in the consensus across multiple graph structures derived from topology and feature similarity. To capture this, we first propose EdgeMask-DG, a novel min-max algorithm where an edge masker learns to find worst-case continuous masks subject to a sparsity constraint, compelling a task GNN to perform effectively under these adversarial structural perturbations. Building upon this, we introduce EdgeMask-DG*, an extension that applies this adversarial masking principle to an enriched graph. This enriched graph combines the original topology with feature-derived edges, allowing the model to discover invariances even when the original topology is noisy or domain-specific. EdgeMask-DG* is the first to systematically combine adaptive adversarial topology search with feature-enriched graphs. We provide a formal justification for our approach from a robust optimization perspective. We demonstrate that EdgeMask-DG* achieves new state-of-the-art performance on diverse graph domain generalization benchmarks, including citation networks, social networks, and temporal graphs. Notably, on the Cora OOD benchmark, EdgeMask-DG* lifts the worst-case domain accuracy to 78.0%, a +3.8 pp improvement over the prior state of the art (74.2%). The source code for our experiments can be found here: https://anonymous.4open.science/r/TMLR-EAEF/

💡 Research Summary

EdgeMask‑DG* addresses the challenging problem of graph domain generalization (Graph‑DG) under structural distribution shifts. Traditional GNNs assume identical training and test distributions; when the underlying graph topology varies across domains, models trained by empirical risk minimization overfit to source‑specific structures and fail on unseen targets. Existing Graph‑DG methods either design invariant architectures, employ robust loss functions, or apply fixed structural augmentations such as GraphAug. However, these approaches do not explicitly identify which edges carry domain‑invariant information, limiting their effectiveness.

The authors propose a two‑stage solution. The first stage, EdgeMask‑DG, formulates a min‑max game between a “TaskNet” (the primary GNN) and a lightweight “MaskNet”. MaskNet generates a continuous mask s_uv∈