Thread by @mmbronstein

Over-squashing is a common plight of GNNs occurring when message passing fails to propagate information efficiently on the graph. In a new post, we discuss how this phenomenon can be understood and remedied through the concept of Ricci curvature

michael-bronstein.medium.com/over-squashing…

Collaboration between @TwitterEng #Cortex and @UniofOxford Jake Topping Francesco Di Giovanni @b_p_chamberlain Xiaowen Dong

Details in the paper: arxiv.org/pdf/2111.14522…

This is part of a new series on "GNNs through the lens of Differential Geometry and Algebraic Topology"

towardsdatascience.com/graph-neural-n…

(though in a different order I have initially promised :-)

The second installment of this post will discuss whether (and when) diffusion improves graph learning, analysing the popular DIGL rewiring method of @klicperajo @guennemann Weissenberger from a geometric perspective

Our work was inspired by the influential paper of @urialon1 that studied over-squashing in graphs

Ricci curvature is a fundamental object in differential geometry of manifolds. It has gained visibility outside this field thanks to Ricci flow, a geometric PDE used by Grigori Perelman to prove the famous Poincaré Conjecture