Riemannian Flow Matching for Disentangled Graph Domain Adaptation

2026-01-31

AI Summary

This work addresses the entanglement of structural and semantic information and training instability in graph domain adaptation caused by adversarial alignment in Euclidean space. To resolve these issues, the authors propose a novel approach grounded in Riemannian geometry, embedding graphs into hyperbolic space using polar coordinates to explicitly disentangle structure (radius) from semantics (angle). The method integrates radial Wasserstein alignment, angular clustering, and Riemannian flow matching to enable smooth feature transfer along geodesics. This is the first study to incorporate Riemannian geometry and flow matching into graph domain adaptation, achieving disentangled representations, asymptotically stable training dynamics, and a tighter bound on target risk. Extensive experiments demonstrate significant performance gains over existing methods across multiple benchmarks.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

Graph Domain Adaptation (GDA) typically uses adversarial learning to align graph embeddings in Euclidean space. However, this paradigm suffers from two critical challenges: Structural Degeneration, where hierarchical and semantic representations are entangled, and Optimization Instability, which arises from oscillatory dynamics of minimax adversarial training. To tackle these issues, we propose DisRFM, a geometry-aware GDA framework that unifies Riemannian embedding and flow-based transport. First, to overcome structural degeneration, we embed graphs into a Riemannian manifold. By adopting polar coordinates, we explicitly disentangle structure (radius) from semantics (angle). Then, we enforce topology preservation through radial Wasserstein alignment and semantic discrimination via angular clustering, thereby preventing feature entanglement and collapse. Second, we address the instability of adversarial alignment by using Riemannian flow matching. This method learns a smooth vector field to guide source features toward the target along geodesic paths, guaranteeing stable convergence. The geometric constraints further guide the flow to maintain the disentangled structure during transport. Theoretically, we prove the asymptotic stability of the flow matching and derive a tighter bound for the target risk. Extensive experiments demonstrate that DisRFM consistently outperforms state-of-the-art methods.

Problem

• Graph Domain Adaptation
• Structural Degeneration
• Optimization Instability
• Feature Disentanglement
• Adversarial Learning

Innovation

• Riemannian manifold
• disentangled representation
• flow matching
• graph domain adaptation
• geodesic transport