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SUMMARY:Weisfeiler and Lehman Go Topological: Message Passing Simplicial N
 etworks - Fabrizio Frasca\, Yu Guang and Cris Bodnar
DTSTART:20210511T121500Z
DTEND:20210511T131500Z
UID:TALK159697@talks.cam.ac.uk
CONTACT:Mateja Jamnik
DESCRIPTION:"Join us on Zoom":https://zoom.us/j/99166955895?pwd=SzI0M3pMVE
 kvNmw3Q0dqNDVRalZvdz09\n\nThe pairwise interaction paradigm of graph machi
 ne learning has predominantly governed the modelling of relational systems
 . However\, graphs alone cannot capture the multi-level interactions prese
 nt in many complex systems and the expressive power of such schemes was pr
 oven to be limited. To overcome these limitations\, we propose Message Pas
 sing Simplicial Networks (MPSNs)\, a class of models that perform message 
 passing on simplicial complexes (SCs) - topological objects generalising g
 raphs to higher dimensions. To theoretically analyse the expressivity of o
 ur model we introduce a Simplicial Weisfeiler-Lehman (SWL) colouring proce
 dure for distinguishing non-isomorphic SCs. We relate the power of SWL to 
 the problem of distinguishing non-isomorphic graphs and show that SWL and 
 MPSNs are strictly more powerful than the WL test and not less powerful th
 an the 3-WL test. We deepen the analysis by comparing our model with tradi
 tional graph neural networks with ReLU activations in terms of the number 
 of linear regions of the functions they can represent. We empirically supp
 ort our theoretical claims by showing that MPSNs can distinguish challengi
 ng strongly regular graphs for which GNNs fail and\, when equipped with or
 ientation equivariant layers\, they can improve classification accuracy in
  oriented SCs compared to a GNN baseline. Additionally\, we implement a li
 brary for message passing on simplicial complexes that we envision to rele
 ase in due course.
LOCATION:Zoom
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