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Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature
Khang Nguyen · Nong Hieu · Vinh NGUYEN · Nhat Ho · Stanley Osher · TAN NGUYEN

Thu Jul 27 01:30 PM -- 03:00 PM (PDT) @ Exhibit Hall 1 #616
Event URL: https://github.com/hieubkvn123/revisiting-gnn-curvature »

Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limiting their effectiveness in taking into account distant information. Our study reveals the key connection between the local graph geometry and the occurrence of both of these issues, thereby providing a unified framework for studying them at a local scale using the Ollivier-Ricci curvature. Specifically, we demonstrate that over-smoothing is linked to positive graph curvature while over-squashing is linked to negative graph curvature. Based on our theory, we propose the Batch Ollivier-Ricci Flow, a novel rewiring algorithm capable of simultaneously addressing both over-smoothing and over-squashing.

Author Information

Khang Nguyen (FPT Software)
Nong Hieu (University of Wollongong)
Vinh NGUYEN (Fpt software, Vietnam)
Nhat Ho (University of Texas at Austin)
Stanley Osher (UCLA)

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