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SUMMARY:Don't go with the Flow - A new tensor algebra for Neural Networks 
 - Lior Horesh (IBM\, Columbia University)
DTSTART:20180510T140000Z
DTEND:20180510T150000Z
UID:TALK105589@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:Multi-dimensional information often involves multi-dimensional
  correlations that may remain latent by virtue of traditional matrix-based
  learning algorithms. In this study\, we propose a tensor neural network f
 ramework that offers an exciting new paradigm for supervised machine learn
 ing. The tensor neural network structure is based upon the t-product (Kilm
 er and Martin\, 2011)\, an algebraic formulation to multiply tensors via c
 irculant convolution which inherits mimetic matrix properties. \nWe demons
 trate that our tensor neural network architecture is a natural high-dimens
 ional extension to conventional neural networks. Then\, we expand upon (Ha
 ber and Ruthotto\, 2017) interpretation of deep neural networks as discret
 izations of nonlinear differential equations\, to construct intrinsically 
 stable tensor neural network architectures. We illustrate the advantages o
 f stability and demonstrate the potential of tensor neural networks with n
 umerical experiments on the MNIST dataset.
LOCATION:MR14\, Centre for Mathematical Sciences
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