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SUMMARY:Neural Sheaf Diffusion: A Topological Perspective on Heterophily a
 nd Oversmoothing in GNNs - Cris Bodnar
DTSTART:20220215T131500Z
DTEND:20220215T141500Z
UID:TALK170411@talks.cam.ac.uk
CONTACT:Mateja Jamnik
DESCRIPTION:"Join us on Zoom":https://zoom.us/j/99166955895?pwd=SzI0M3pMVE
 kvNmw3Q0dqNDVRalZvdz09\n\nCellular sheaves equip graphs with "geometrical"
  structure by assigning vector spaces and linear maps to nodes and edges. 
 Graph Neural Networks (GNNs) implicitly assume a graph with a trivial unde
 rlying sheaf. This choice is reflected in the structure of the graph Lapla
 cian operator\, the properties of the associated diffusion equation\, and 
 the characteristics of the convolutional models that discretise this equat
 ion. In this paper\, we use cellular sheaf theory to show that the underly
 ing geometry of the graph is deeply linked with the performance of GNNs in
  heterophilic settings and their oversmoothing behaviour. By considering a
  hierarchy of increasingly general sheaves\, we study how the ability of t
 he sheaf diffusion process to achieve linear separation of the classes in 
 the infinite time limit expands. At the same time\, we prove that when the
  sheaf is non-trivial\, discretised parametric diffusion processes have gr
 eater control than GNNs over their asymptotic behaviour. On the practical 
 side\, we study how sheaves can be learned from data. The resulting sheaf 
 diffusion models have many desirable properties that address the limitatio
 ns of classical graph diffusion equations (and corresponding GNN models) a
 nd obtain state-of-the-art results in heterophilic settings. Overall\, our
  work provides new connections between GNNs and algebraic topology and wou
 ld be of interest to both fields.
LOCATION:Zoom
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