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From this (and many other) tutorial it is not clear if tensors in tensorflow are true mathematical tensors (that is, having covariant and contravariant indices)

From this (and many other) tutorial it is not clear if tensors in tensorflow are true mathematical tensors (that is, having covariant and contravariant indices) or they are multidimensional arrays. The name Tensorflow and terminology suggests that Tensorflow manipulates mathematical tensors, for example: Scalars -> Vectors -> Matrices -> Tensors (really tensors?) but what you see are multidimensional arrays. It is of course not a big problem but probably could be clarified somewhere at least in small font to avoid ambiguity. Or Tensorflow objects are true tensors indeed?

dragandj 9y ago
Even if they were (I doubt), I haven't found a clear and informed description how they relate exactly to tensors found in math/physics literature. I agree with your view that they look more like nd-arrays.
- zazen 9y ago
  I was surprised when I first saw the word "tensor" being thrown around by computer scientists to apparently mean just multi-dimensional array. But then I thought, well, "vector" is very widely used - including by mathematicians - to mean simply an nx1 or 1xn array, rather than an object which transforms a certain way under coordinate tranformations. So in the same way, I suppose we really might as well use "tensor" to mean "just" a multi-dimensional array of numbers, in contexts where coordinate transformations aren't important. Mathematical physics can continue to use the other definition where necessary, just as it does for vectors.
  - dragandj 9y ago
    The trouble with that approach is that in CS, tensors are mostly used in machine learning, which is very math-dependent. So, you read in a textbook or a paper that something can be done elegantly by using some linear algebra operation, or some transformation on a tensor, and are delighted, because your library says to be tensor-based, but, then, when you try to code it, whoops; you meant you had tensor support, but all you've got is a multidimensional array memory layout...

dragandj 9y ago

Even if they were (I doubt), I haven't found a clear and informed description how they relate exactly to tensors found in math/physics literature. I agree with your view that they look more like nd-arrays.

zazen 9y ago
I was surprised when I first saw the word "tensor" being thrown around by computer scientists to apparently mean just multi-dimensional array. But then I thought, well, "vector" is very widely used - including by mathematicians - to mean simply an nx1 or 1xn array, rather than an object which transforms a certain way under coordinate tranformations. So in the same way, I suppose we really might as well use "tensor" to mean "just" a multi-dimensional array of numbers, in contexts where coordinate transformations aren't important. Mathematical physics can continue to use the other definition where necessary, just as it does for vectors.
- dragandj 9y ago
  The trouble with that approach is that in CS, tensors are mostly used in machine learning, which is very math-dependent. So, you read in a textbook or a paper that something can be done elegantly by using some linear algebra operation, or some transformation on a tensor, and are delighted, because your library says to be tensor-based, but, then, when you try to code it, whoops; you meant you had tensor support, but all you've got is a multidimensional array memory layout...