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.

通过使用公理化归因，我们提出了一种平滑参数化的图神经网络（GNN）预测分布，在一个高维嵌入空间中的低维流形上进行。我们利用微分几何观点在流形上建模分布演化，通过重新参数化流形上的曲线族并设计一个凸优化问题，找到一个独特的曲线，以简洁地近似分布演化，以供人类解释。对于具有演化图的节点分类、链路预测和图分类任务的大量实验证明了所提方法相对于现有技术方法的更好的稀疏性、忠实性和直观性。

演化图上 GNN 的微分几何视角与可解释性

A Differential Geometric View and Explainability of GNN on Evolving  Graphs

An emerging problem in trustworthy machine learning is to train models that
produce robust interpretations for their predictions. We take a step towards
solving this problem through the lens of axiomatic attribution of neural
networks. Our theory is grounded in the recent work, Integrated Gradients (IG),
in axiomatically attributing a neural network's output change to its input
change. We propose training objectives in classic robust optimization models to
achieve robust IG attributions. Our objectives give principled generalizations
of previous objectives designed for robust predictions, and they naturally
degenerate to classic soft-margin training for one-layer neural networks. We
also generalize previous theory and prove that the objectives for different
robust optimization models are closely related. Experiments demonstrate the
effectiveness of our method, and also point to intriguing problems which hint
at the need for better optimization techniques or better neural network
architectures for robust attribution training.

通过公理归因神经网络的视角，我们提出了经典鲁棒优化模型的训练目标，旨在实现鲁棒的集成梯度归因。实验结果表明了我们方法的有效性，并表明需要更好的优化技术或更好的神经网络架构来进行鲁棒的归因训练。