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SUMMARY: Harmonic Exponential Families and Group-Equivariant Convolution N
 etworks - Taco Cohen (University of Amsterdam)
DTSTART:20150916T100000Z
DTEND:20150916T110000Z
UID:TALK60265@talks.cam.ac.uk
CONTACT:Dr Jes Frellsen
DESCRIPTION:In a range of fields including the geosciences\, molecular bio
 logy\, robotics and computer vision\, one encounters problems that involve
  random variables on manifolds. Currently\, there is a lack of flexible pr
 obabilistic models on manifolds that are fast and easy to train. We define
  an extremely flexible class of exponential family distributions on manifo
 lds such as the torus\, sphere\, and rotation groups\, and show that for t
 hese distributions the gradient of the log-likelihood can be computed effi
 ciently using generalized Fast Fourier Transforms. We discuss applications
  to Bayesian transformation estimation (where harmonic exponential familie
 s appear as conjugate priors to a special parameterization of the normal d
 istribution)\, and modelling of the spatial distribution of earthquakes on
  the surface of the earth.\n\nThe second part of this talk is about ongoin
 g work on Group-equivariant Convolutional Neural Networks (G-CNNs)\, a nat
 ural generalization of convnets that can deal with geometrical variability
  due to Lie groups. By convolving over groups G larger than the translatio
 n group\, G-CNNs build representations that are equivariant to these group
 s\, which allows for a much greater degree of parameter sharing. Implement
 ed naively\, the group convolutions employed by G-CNNs are very slow\, so 
 we introduce a fast method based on the Fast Fourier Transform on G that c
 omputes both the forward and backward propagation through a G-CNN efficien
 tly.
LOCATION:Engineering Department\, CBL Room BE-438
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