Radially Dominant Hyperbolic Transport for Graph Domain Adaptation

Leading solutions in graph domain adaptation treat domain shift as distribution alignment, learning domain-invariant representations by reducing the discrepancy between two graphs. Such methods transfer well across visual scenes, where CNN features decouple appearance from semantic structure. In a graph, however, a node's adjacency, neighborhood scale and branch membership are deeply entangled, so learning domain-invariant features by directly aligning distributions is often impractical. To address this, through an in-depth analysis of how nodes behave during transfer, we present Compass, which recasts graph domain adaptation as the fine-grained movement of individual nodes, termed transport, driven by a position-adaptive hyperbolic velocity field. Specifically, the transport has two properties. The first governs how far each node moves: hubs, rescaled strongly by the shift, and peripheral nodes, barely touched, each receive a correction matched to their structural position. The second governs which way it moves: along the radial direction that carries the domain gap and away from the angular direction that carries class, so trajectories of different classes stay apart, transported labels remain valid without target labels, and a few integration steps suffice. Compass reveals that graph adaptation has so far neglected the direction of movement, and the constraint it introduces is flexible, orthogonal to current top solutions and plug-and-play, bringing consistent gains on mainstream benchmarks.