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SUMMARY:Gauge Fields in Deep Learning
DTSTART;VALUE=DATE-TIME:20190416T143000Z
DTEND;VALUE=DATE-TIME:20190416T153000Z
DTSTAMP;VALUE=DATE-TIME:20190822T173820Z
UID:indico-event-812801@indico.cern.ch
DESCRIPTION:Joint work with Taco Cohen\, Maurice Weiler and Berkay Kicanao
glu\n\nGauge field theory is the foundation of modern physics\, including
general relativity and the standard model of physics. It describes how a t
heory of physics should transform under symmetry transformations. For inst
ance\, in electrodynamics\, electric forces may transform into magnetic fo
rces if we transform a static observer to one that moves at constant speed
. Similarly\, in general relativity acceleration and gravity are equated t
o each other under symmetry transformations. Gauge fields also play a cruc
ial role in modern quantum field theory and the standard model of physics\
, where they describe the forces between particles that transform into eac
h other under (abstract) symmetry transformations. \n\nIn this work we
describe how the mathematics of gauge groups becomes inevitable when you a
re interested in deep learning on manifolds. Defining a convolution on a m
anifold involves transporting geometric objects such as feature vectors an
d kernels across the manifold\, which due to curvature become path depende
nt. As such it becomes impossible to represent these objects in a global r
eference frame and one is forced to consider local frames. These reference
frames are arbitrary and changing between them is called a (local) gauge
transformation. Since we do not want our computations to depend on the spe
cific choice of frames we are forced to consider equivariance of our convo
lutions under gauge transformations. These considerations result in the fi
rst fully general theory of deep learning on manifolds\, with gauge equiva
riant convolutions as the necessary key ingredient. \n\n \n\nhttps://
indico.cern.ch/event/812801/
LOCATION:CERN 500/1-001 - Main Auditorium
URL:https://indico.cern.ch/event/812801/
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