DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation

TL;DR

DisRFM introduces a geometry-aware graph domain adaptation framework using Riemannian representations and flow matching to preserve structure and improve transfer across domains.

Contribution

It proposes a novel Riemannian flow matching approach with topology-aware regularization for structure-preserving graph domain adaptation.

Findings

DisRFM outperforms state-of-the-art methods across diverse domain shifts.

Theoretical analysis links polar discrepancies and flow error to target risk.

Polar flow matching effectively couples class-compatible samples for better adaptation.

Abstract

Graph Domain Adaptation (GDA) aims to transfer graph classifiers across domains with both semantic and topological shifts. Existing Euclidean adversarial methods face two challenges: Structural Degeneration, where domain confusion entangles and suppresses label-relevant topology, and Optimization Instability, where minimax training induces oscillatory gradients under large structural shifts. We propose DisRFM, a geometry-aware GDA framework that addresses these challenges with Riemannian representation learning and flow-based transport. DisRFM embeds graph representations on a constant-curvature manifold and expresses them in geodesic polar coordinates. Polar endpoint regularization calibrates topologysensitive radial scales via univariate Wasserstein alignment and preserves scalenormalized class semantics through confidence-filtered angular alignment, with radial magnitude modulating pseudo-label reliability. DisRFM introduces topologyconditioned polar flow matching, which couples class-compatible source and target samples by a normalized polar transport cost and learns a metric-corrected vector field along geodesic interpolants. Theoretical analysis characterizes the structural risk of unconditional domain confusion and relates polar discrepancies and flow error to target risk. Extensive experiments under diverse domain shifts demonstrate that DisRFM consistently outperforms state-of-the-art methods.