Geometric deep learning has demonstrated a great potential in non-Euclidean data analysis. The incorporation of geometric insights into learning architecture is vital to its success. Here we propose a curvature-enhanced graph convolutional network (CGCN) for biomolecular interaction prediction. Our CGCN employs Ollivier-Ricci curvature (ORC) to characterize network local geometric properties and enhance the learning capability of GCNs. More specifically, ORCs are evaluated based on the local topology from node neighborhoods, and further incorporated into the weight function for the feature aggregation in message-passing procedure. Our CGCN model is extensively validated on fourteen real-world bimolecular interaction networks and analyzed in details using a series of well-designed simulated data. It has been found that our CGCN can achieve the state-of-the-art results. It outperforms all existing models, as far as we know, in thirteen out of the fourteen real-world datasets and ranks as the second in the rest one. The results from the simulated data show that our CGCN model is superior to the traditional GCN models regardless of the positive-to-negative-curvature ratios, network densities, and network sizes (when larger than 500).

中文翻译：

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用于生物分子相互作用预测的曲率增强图卷积网络

几何深度学习在非欧几里得数据分析中展现出了巨大的潜力。将几何见解融入学习建筑对于其成功至关重要。在这里，我们提出了一种用于生物分子相互作用预测的曲率增强图卷积网络（CGCN）。我们的 CGCN 采用 Olivier-Ricci 曲率（ORC）来表征网络局部几何特性并增强 GCN 的学习能力。更具体地说，ORC 基于节点邻域的局部拓扑进行评估，并进一步纳入消息传递过程中特征聚合的权重函数中。我们的 CGCN 模型在 14 个现实世界的双分子相互作用网络上进行了广泛验证，并使用一系列精心设计的模拟数据进行了详细分析。已经发现我们的CGCN可以达到state-of-the-art的结果。据我们所知，它在 14 个现实世界数据集中的 13 个中优于所有现有模型，并在其余数据集中排名第二。模拟数据的结果表明，无论正负曲率比、网络密度和网络规模（大于 500 时），我们的 CGCN 模型都优于传统的 GCN 模型。