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SUMMARY:Opinion dynamics inspired sheaf neural networks. - Ferran Hernande
 z Caralt
DTSTART:20240216T170000Z
DTEND:20240216T180000Z
UID:TALK212347@talks.cam.ac.uk
CONTACT:Pietro Lio
DESCRIPTION:Link to google meet: https://meet.google.com/wtz-cxne-shb to w
 atch online.\n\nGraph Neural Networks are becoming very popular as a way t
 o model relational data with\nmany applications. Nonetheless\, there are t
 wo problems that frequently appear when\ndealing with GNNs: they perform p
 oorly on heterophilic data and they exhibit over-\nsmoothing behaviour. Th
 e first problem emerges because most models assume homophily\n(similar nod
 es tend to be connected) and the second one arises from deep GNNs tending\
 nto produce features too smooth in order to be useful.\n\nSheaf Neural Net
 works were proposed to address the problems described above. These\nequip 
 each node and edge with a vector space and a linear application between th
 ese\nspaces for each incident edge-node pair. This gives the graph a non-t
 rivial diffusion\noperator that may not have the aforementioned issues. No
 netheless\, the way this extra\nstructure is computed leaves little room f
 or interpretation of the overall model.\n\nConsequently\, in this talk we 
 will explore sheaf neural networks and other GNN’s through\nthe lens of 
 opinion dynamics\, namely the study of the evolution of opinions through\n
 (mostly) ODEs. This theoretical framework will allow us to interpret the s
 heaf in a very\nnatural way. We will also explore the direct incorporation
  of the opinion dynamics diffusion\nprocesses into new neural network arch
 itectures such as Joint diffusion Sheaf Neural\nNetworks and Rotation inva
 riant Sheaf Neural Networks. On top of that\, new data\ngeneration methods
  to evaluate sheaf based models will be proposed. Overall we show\nthat ou
 r new SNN variants may have a more fitting inductive bias towards heteroph
 ilic data\nas well as the ability to detect and account for long range cor
 relations between nodes
LOCATION:Lecture Theatre 2\, Computer Laboratory\, William Gates Building
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