Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds to graph evolution. We propose a smooth parameterization of the GNN predicted distributions using axiomatic attribution, where the distributions are on a low-dimensional manifold within a high-dimensional embedding space. We exploit the differential geometric viewpoint to model distributional evolution as smooth curves on the manifold. We reparameterize families of curves on the manifold and design a convex optimization problem to find a unique curve that concisely approximates the distributional evolution for human interpretation. Extensive experiments on node classification, link prediction, and graph classification tasks with evolving graphs demonstrate the better sparsity, faithfulness, and intuitiveness of the proposed method over the state-of-the-art methods.

翻译：图结构在社交网络和生物化学中普遍存在，图神经网络（GNN）是目前最先进的预测模型。图可能随时间演化，因此形式化建模并理解训练后的GNN如何响应图的演化至关重要。我们提出了一种基于公理归因的GNN预测分布的平滑参数化方法，其中分布位于高维嵌入空间内的低维流形上。利用微分几何视角，我们将分布演化建模为流形上的平滑曲线。通过重新参数化流形上的曲线族，我们设计了一个凸优化问题，以寻找唯一能够简洁近似分布演化、便于人类解读的曲线。在节点分类、链接预测和图分类任务中针对演化图的广泛实验表明，所提出方法在稀疏性、忠实性和直观性上均优于现有最先进方法。