Wednesday, October 21, 2020

Tensors

-- https://www.youtube.com/watch?v=VL4NC4f6m0w


  • Tensors are Multi-Dimensional
  • Tensors are higher extensions of matrices.
  • Tensors to encode multi-dimensional data.  Images - 3 dimensions Vidoes - 4 dimensions
  • Tensors to encode higher order relationships  and modalities.
  • Tensor algebra is richer than matrix algebra. Richer neural network architectures. 
  • More compact networks/better accuracy.

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  • Tensorly: Framework for Tensor Algebra

  • Tensors contractions are a core primitive of multilinear algebra.

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Why Tensors

  • Statistical reasons 

                  Incorporate higher order relationships in data.

                  Discover hidden topics (not possible with matrix methods)

  • Computational reasons:

              Tensor algebra is parallellizable like linear algebra

              Faster than other algorithms for LDA.

              Flexible: Training and inference decoupled

              Guaranteed in theory to converge to global optimum.

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