Understanding over-squashing and bottlenecks on graphs via curvature

Conference item

Most graph neural networks (GNNs) use the message passing paradigm, in which node features are propagated on the input graph. Recent works pointed to the distortion of information flowing from distant nodes as a factor limiting the efficiency of message passing for tasks relying on long-distance interactions. This phenomenon, referred to as 'over-squashing', has been heuristically attributed to graph bottlenecks where the number of k-hop neighbors grows rapidly with k. We provide a precise description of the over-squashing phenomenon in GNNs and analyze how it arises from bottlenecks in the graph. For this purpose, we introduce a new edge-based combinatorial curvature and prove that negatively curved edges are responsible for the over-squashing issue. We also propose and experimentally test a curvature-based graph rewiring method to alleviate the over-squashing.

Authors: Topping, J; Di Giovanni, F; Chamberlain, BP; Dong, X; Bronstein, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: OpenReview
• Host title: ICLR 2022 - 10th International Conference on Learning Representations
• Article number: 1302
• Series: International Conference on Learning Representations
• Publication date: 2022-01-28
• Acceptance date: 2022-01-20
• Event title: Tenth International Conference on Learning Representations (ICLR 2022)
• Event location: Virtual event
• Event website: https://iclr.cc/Conferences/2022/
• Event start date: 2022-04-25
• Event end date: 2022-04-29
• Language: English
• Keywords: graph neural networks; FFR; Ricci curvature; geometric deep learning; differential geometry