“Tensors” used in deep learning or machine learning are defined as N-dimensional arrays of data that can take any value and be operated on by in any way.

This differs from the tensor definition used in Physics or differential geometry. Deep learning tensors don’t need to conform in the same way. For example, there is no distinction between covariant and contravariant indices, and the same tensor transformation rules don’t apply.

What is the best way of describing tensors in deep learning? Would it be right to say they are N-dimensional Cartesian tensors?

  • $\begingroup$ Yes since under the metric of a Cartesian inner product space $x_i=\delta_{ij}x^j $. This means that one can use tensor notation as a way to simplify expressions without having to worry about the transformation properties of the quantities in question. $\endgroup$
    – Ted Black
    May 15 at 20:35
  • $\begingroup$ @TedBlack Ok thanks. If you want to submit that as an answer, I would be happy to accept it :) $\endgroup$
    – joshlk
    May 16 at 13:37


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