论文标题
树木动物的距离：图形神经网络的桥接图指标和稳定性
Tree Mover's Distance: Bridging Graph Metrics and Stability of Graph Neural Networks
论文作者
论文摘要
理解机器学习模型的概括和鲁棒性从根本上依赖于在数据空间上假设适当的指标。对于非欧国人数据（例如图形），识别这种度量特别具有挑战性。在这里，我们提出了归因图，树搬运工（TMD）的伪计，并研究了其与概括的关系。通过层次最佳传输问题，TMD反映了节点属性的局部分布以及局部计算树的分布，众所周知，这对于图形神经网络（GNNS）的学习行为是决定性的。首先，我们表明TMD捕获了与图形分类相关的属性：简单的TMD-SVM与标准GNN竞争性能。其次，我们将TMD与分布偏移的GNN的概括相关联，并表明它与此类偏移下的性能下降良好相关。
Understanding generalization and robustness of machine learning models fundamentally relies on assuming an appropriate metric on the data space. Identifying such a metric is particularly challenging for non-Euclidean data such as graphs. Here, we propose a pseudometric for attributed graphs, the Tree Mover's Distance (TMD), and study its relation to generalization. Via a hierarchical optimal transport problem, TMD reflects the local distribution of node attributes as well as the distribution of local computation trees, which are known to be decisive for the learning behavior of graph neural networks (GNNs). First, we show that TMD captures properties relevant to graph classification: a simple TMD-SVM performs competitively with standard GNNs. Second, we relate TMD to generalization of GNNs under distribution shifts, and show that it correlates well with performance drop under such shifts.
