Papers › Understanding over-squashing and bottlenecks on graphs via curvature

Understanding over-squashing and bottlenecks on graphs via curvature

29 Nov 2021ICLR 2022 4arXiv:2111.14522archive 2025-07-28

Jake Topping, Francesco Di Giovanni, Benjamin Paul Chamberlain, Xiaowen Dong, Michael M. Bronstein

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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jctops/understanding-oversquashing officialmentioned on GitHubpytorchMIT report
harel147/REFine mentioned on GitHubpytorchMIT report
josephjwilson/cayley_graph_propagation mentioned on GitHubpytorchMIT report
gitlab.com/cedric_sanders/masterarbeit mentioned on GitHubpytorch report

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balanced_forman_curvature jctops/understanding-oversquashing/gdl/src/gdl/curvature/numba.py official repository unverified MIT (permissive) · 01dafd45036549e9 · report
balanced_forman_post_delta jctops/understanding-oversquashing/gdl/src/gdl/curvature/numba.py official repository unverified MIT (permissive) · 6fc07452a6ae5e40 · report
evaluate jctops/understanding-oversquashing/gdl/src/gdl/experiment/node_classification.py official repository unverified MIT (permissive) · 8e261bcbef0de223 · report
get_optimizer jctops/understanding-oversquashing/gdl/src/gdl/experiment/optimizer.py official repository unverified MIT (permissive) · b335bd8cd24e345b · report
train jctops/understanding-oversquashing/gdl/src/gdl/experiment/node_classification.py official repository unverified MIT (permissive) · 9d0aa5bc590c31b7 · report

Tasks

Node Classification

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Node Classification Actor SDRF Accuracy 28.42 ± 0.75 #62 of 62 Archive leaderboard report
Node Classification Chameleon SDRF Accuracy 42.73±0.15 #61 of 61 Archive leaderboard report
Node Classification Citeseer SDRF Accuracy 72.58±0.20 #41 of 71 Archive leaderboard report
Node Classification Cora SDRF Accuracy 82.76±0.23% #49 of 73 Archive leaderboard report
Node Classification Cornell SDRF Accuracy 54.60±0.39 #59 of 60 Archive leaderboard report
Node Classification Pubmed SDRF Accuracy 79.10±0.11 #52 of 70 Archive leaderboard report
Node Classification Squirrel SDRF Accuracy 37.05±0.17 #53 of 59 Archive leaderboard report
Node Classification Texas SDRF Accuracy 64.46±0.38 #58 of 62 Archive leaderboard report
Node Classification Wisconsin SDRF Accuracy 55.51±0.27 #63 of 63 Archive leaderboard report

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