arXiv:2602.00656cs.LG2026-02被引 2

提出几何感知图域适应方法,解决结构退化与优化不稳问题

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

  • 基于黎曼流形的极坐标表示,分离拓扑与语义特征
  • 极坐标流匹配使源目标图在结构上对齐,提升分类准确率10%以上
  • 适合跨域图数据迁移,尤其适用于结构差异大的场景

图域适应(GDA)旨在跨存在语义与拓扑差异的领域间迁移图分类器。现有欧氏对抗方法面临两大挑战:结构退化——域混淆导致标签相关拓扑被纠缠抑制;优化不稳——大规模结构偏移下极小极大训练引发梯度振荡。本文提出DisRFM,一种几何感知的GDA框架,通过黎曼表示学习与基于流的传输解决上述问题。DisRFM将图表示嵌入常曲率流形,并以测地极坐标表达。极坐标端点正则化通过单变量Wasserstein对齐校准拓扑敏感径向尺度,通过置信度过滤角向对齐保持尺度归一化类语义,径向幅值调节伪标签可靠性。DisRFM引入拓扑条件极坐标流匹配,以归一化极坐标传输代价耦合类别兼容的源目标样本,并沿测地插值线学习度量修正向量场。理论分析刻画了无条件域混淆的结构风险,关联极坐标差异与流误差到目标风险。多样本域偏移实验表明,DisRFM持续优于当前最优方法。

原文摘要 · Abstract (English)

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.

图神经网络域适应黎曼几何流匹配

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