具有曲率引导自适应路由的几何混合专家用于图表示学习
Geometric Mixture-of-Experts with Curvature-Guided Adaptive Routing for Graph Representation Learning
AI总结：
本文提出GeoMoE框架，通过Ollivier-Ricci曲率指导的自适应路由融合不同黎曼空间的节点表示，提升多尺度拓扑结构的建模能力。
摘要：
图结构数据通常表现出复杂的拓扑异质性，难以在单一黎曼流形中准确建模。尽管新兴的混合曲率方法试图捕捉这种多样性，但它们通常依赖于隐式的、任务驱动的路由，缺乏根本的几何基础。为此，我们提出了一个几何混合专家框架（GeoMoE），能够自适应地融合不同黎曼空间的节点表示，以更好地适应多尺度拓扑结构。核心在于GeoMoE利用Ollivier-Ricci曲率（ORC）作为内在几何先验，协调专门专家的合作。具体而言，我们设计了一个图感知的门控网络，分配节点特定的融合权重，通过曲率引导的对齐损失进行正则化，以确保可解释且几何一致的路由。此外，我们引入了曲率感知的对比目标，通过根据曲率一致性构建正负样本对，促进几何可区分性。在六个基准数据集上的广泛实验表明，GeoMoE在各种图类型上均优于最先进的基线方法。
英文摘要：
Graph-structured data typically exhibits complex topological heterogeneity, making it difficult to model accurately within a single Riemannian manifold. While emerging mixed-curvature methods attempt to capture such diversity, they often rely on implicit, task-driven routing that lacks fundamental geometric grounding. To address this challenge, we propose a Geometric Mixture-of-Experts framework (GeoMoE) that adaptively fuses node representations across diverse Riemannian spaces to better accommodate multi-scale topological structures. At its core, GeoMoE leverages Ollivier-Ricci Curvature (ORC) as an intrinsic geometric prior to orchestrate the collaboration of specialized experts. Specifically, we design a graph-aware gating network that assigns node-specific fusion weights, regularized by a curvature-guided alignment loss to ensure interpretable and geometry-consistent routing. Additionally, we introduce a curvature-aware contrastive objective that promotes geometric discriminability by constructing positive and negative pairs according to curvature consistency. Extensive experiments on six benchmark datasets demonstrate that GeoMoE outperforms state-of-the-art baselines across diverse graph types.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
