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Title: Tree Mover's Distance: Bridging Graph Metrics and Stability of Graph Neural Networks
Understanding generalization and robustness of machine learning models funda- mentally 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 distri- bution 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 competi- tively 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.  more » « less
Award ID(s):
1741341 1553284
NSF-PAR ID:
10412974
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Neural Information Processing Systems (NeurIPS)
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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