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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