arXiv:2603.22317cs.LGcs.AI2026-03

用曲率引导路由,让专家协作更好建模复杂图结构。

Geometric Mixture-of-Experts with Curvature-Guided Adaptive Routing for Graph Representation Learning

  • 基于曲率设计自适应路由机制,融合多个黎曼空间表示。
  • 在6个数据集上超越现有方法,最高提升2.3%准确率。
  • 适合需要精准建模异构图结构的研究者使用。

图结构数据通常具有复杂的拓扑异质性,难以在单一黎曼流形中准确建模。尽管新兴的多曲率方法试图捕捉这种多样性,但往往依赖隐式、任务驱动的路由机制,缺乏根本的几何基础。为此,我们提出几何混合专家框架(GeoMoE),通过在多种黎曼空间中自适应融合节点表示,更好地适应多尺度拓扑结构。核心在于利用奥利维耶-里奇曲率(ORC)作为内在几何先验,协调专用专家间的协作。具体而言,设计了图感知门控网络,为每个节点分配特定融合权重,并引入曲率引导对齐损失以确保可解释且几何一致的路由。此外,提出曲率感知对比目标,根据曲率一致性构建正负样本对,增强几何可区分性。在六个基准数据集上的大量实验表明,GeoMoE 在多种图类型上均优于当前最优基线。

原文摘要 · Abstract (English)

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.

图神经网络曲率建模专家模型几何学习

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