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CATEGORIES:Artificial Intelligence Research Group Talks (Comp
uter Laboratory)
SUMMARY:Neural Sheaf Diffusion: A Topological Perspective
on Heterophily and Oversmoothing in GNNs - Cris Bo
dnar
DTSTART;TZID=Europe/London:20220215T131500
DTEND;TZID=Europe/London:20220215T141500
UID:TALK170411AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/170411
DESCRIPTION:"Join us on Zoom":https://zoom.us/j/99166955895?pw
d=SzI0M3pMVEkvNmw3Q0dqNDVRalZvdz09\n\nCellular she
aves equip graphs with "geometrical" structure by
assigning vector spaces and linear maps to nodes a
nd edges. Graph Neural Networks (GNNs) implicitly
assume a graph with a trivial underlying sheaf. Th
is choice is reflected in the structure of the gra
ph Laplacian operator\, the properties of the asso
ciated diffusion equation\, and the characteristic
s of the convolutional models that discretise this
equation. In this paper\, we use cellular sheaf t
heory to show that the underlying geometry of the
graph is deeply linked with the performance of GNN
s in heterophilic settings and their oversmoothing
behaviour. By considering a hierarchy of increasi
ngly general sheaves\, we study how the ability of
the sheaf diffusion process to achieve linear sep
aration of the classes in the infinite time limit
expands. At the same time\, we prove that when the
sheaf is non-trivial\, discretised parametric dif
fusion processes have greater control than GNNs ov
er their asymptotic behaviour. On the practical si
de\, we study how sheaves can be learned from data
. The resulting sheaf diffusion models have many d
esirable properties that address the limitations o
f classical graph diffusion equations (and corresp
onding GNN models) and obtain state-of-the-art res
ults in heterophilic settings. Overall\, our work
provides new connections between GNNs and algebrai
c topology and would be of interest to both fields
.
LOCATION:Zoom
CONTACT:Mateja Jamnik
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