Geometry-aware Test-Time Adaptation on Graphs

Test-time adaptation (TTA) has been a widely-studied paradigm for adapting well-trained models to distributionally shifted test data. Recent works extend TTA to graphs using graph augmentations and self-supervised objectives in Euclidean space. However, graph-structured data often exhibit heterogeneity where semantic similarity and topology-induced variations show different geometric patterns. As a result, relying on a single fixed geometry would distort representations and mislead test-time updates. In this paper, we explore Riemannian geometry as a principled foundation to mitigate the geometric distortion issue in test-time adaptation on graphs. We propose a novel geometry-aware test-time graph adaptation framework (GeoTTA) to explicitly control test-time update directions for more effective adaptation. During testing, GeoTTA decomposes graph representations into hyperspherical and hyperbolic subspaces to respectively capture semantic and structural variations in target samples. Based on this decomposition, a joint geometry-aware adaptation objective is designed to perform prototype alignment and maintain geometric consistency in curvature-matched manifolds. By adaptively measuring distances and updating gradients on the decoupled manifolds, GeoTTA prevents the optimization from being dominated by semantic or structural variants, thereby effectively mitigating the negative impact of distribution shifts at test time. Experiments on ten public benchmarks demonstrate that GeoTTA consistently achieves superior source-free test-time adaptation performance across diverse domains with competitive efficiency.