通过混合黎曼专家模型,实现图嵌入中拓扑异质性的精准建模。
GraphMoRE: Mitigating Topological Heterogeneity via Mixture of Riemannian Experts
- 基于拓扑感知门控机制,为每个节点动态选择最优黎曼空间。
- 在真实与合成数据集上,嵌入失真显著降低,性能全面领先。
- 适合构建能处理多样化图数据的图基础模型,尤其关注复杂拓扑建模。
现实世界图具有固有的复杂多样的拓扑模式,称为拓扑异质性。现有方法通常在单一常曲率空间中学习图表示,难以匹配复杂的几何形状,导致嵌入质量低且失真大,这对图基础模型构成挑战。尽管乘积流形具备解决异质性的潜力,但其本身仍具同质性,无法灵活表达混合异质拓扑。本文提出新型图混合黎曼专家(GraphMoRE)框架,通过个性化细粒度拓扑几何模式保留来有效应对拓扑异质性。具体地,设计拓扑感知门控机制,为每个节点选择最优嵌入空间;通过学习门控权重融合多个黎曼专家输出,构建节点级个性化混合曲率空间,将图嵌入到不同位置曲率各异的异质流形中。此外,提出简洁有效的对齐策略,公平衡量不同嵌入空间间的成对距离。在真实与合成数据集上的大量实验表明,本方法在更低失真下取得更优性能,凸显其对复杂拓扑异质图的建模潜力,并为图基础模型提供新颖架构视角。
原文摘要 · Abstract (English)
Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex geometric shapes, resulting in low-quality embeddings with high distortion. This also constitutes a critical challenge for graph foundation models, which are expected to uniformly handle a wide variety of diverse graph data. Recent studies have indicated that product manifold gains the possibility to address topological heterogeneity. However, the product manifold is still homogeneous, which is inadequate and inflexible for representing the mixed heterogeneous topology. In this paper, we propose a novel Graph Mixture of Riemannian Experts (GraphMoRE) framework to effectively tackle topological heterogeneity by personalized fine-grained topology geometry pattern preservation. Specifically, to minimize the embedding distortion, we propose a topology-aware gating mechanism to select the optimal embedding space for each node. By fusing the outputs of diverse Riemannian experts with learned gating weights, we construct personalized mixed curvature spaces for nodes, effectively embedding the graph into a heterogeneous manifold with varying curvatures at different points. Furthermore, to fairly measure pairwise distances between different embedding spaces, we present a concise and effective alignment strategy. Extensive experiments on real-world and synthetic datasets demonstrate that our method achieves superior performance with lower distortion, highlighting its potential for modeling complex graphs with topological heterogeneity, and providing a novel architectural perspective for graph foundation models.
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