## Understanding over-squashing and bottlenecks on graphs via curvature

### Jake Topping · Francesco Di Giovanni · Benjamin Chamberlain · Xiaowen Dong · Michael Bronstein

Keywords: [ geometric deep learning ] [ graph neural networks ] [ Differential Geometry ]

 Honorable Mention
[ Abstract ]
Wed 27 Apr 10:30 a.m. PDT — 12:30 p.m. PDT

Oral presentation: Oral 2: Structured learning
Tue 26 Apr 1 a.m. PDT — 2:30 a.m. PDT

Abstract: 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.

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