Tensor Is the Might

I just recently watched some (not all) of this video "coding a machine learning library in c from scratch" and seems like he's going through a similar process in this blog as this video. I would recommend watching the video to get an idea of what the fundamentals of a ML library look like. From someone who has recently been getting interested in actually writing ML code and trying to make sense of it myself (from the perspective of just a typical backend engineer) it was very interesting to see. Previously my experience with ML libs (PyTorch specific) was writing my own Mini-GPT and training it on a small dataset using my own GPU (5090). Cool to see the behind the scenes and took away some o the handwaveyness... https://www.youtube.com/watch?v=hL_n_GljC0I

If one wants to add the capability to reason about shape and shape compatibility, Barry Jay's FiSh would be an interesting detour.

https://web.archive.org/web/20111015133833/http://www-staff....

This was used in his shape aware language FiSh, for dealing with multidimensional arrays. Shape compatibilities were statically type checked, if I recall correctly. Shapes were also used to optimize the loops.

[Programming in FISh] https://link.springer.com/article/10.1007/s100090050037

[Towards Dynamic Shaping] https://www.researchgate.net/publication/265975794_Towards_D...

> A tensor is nothing but a flat array of numbers, plus some metadata telling you how to interpret those numbers as a multi-dimensional object.

Erm... many would disagree. I think what he means is just a multidimensional array.

Cool, but I find rather than just shapes and indexes, tensors with labels are much easier to use and reason about. E.g.:

  {
      {user:bob, movie:"Heat"}:0.1,
      {user:alice, movie:"Frozen"}:0.9,
      {user:carol, movie:"Top Gun"}:0.3,
  }

> A tensor is nothing but a flat array of numbers, plus some metadata telling you how to interpret those numbers as a multi-dimensional object.

Yikes! No.

I mean even for the intents and purposes of using this definition in ML, this might not be right.

I am trying not to be pedantic, so I will not go with the official/mathematical definition of a tensor as that could be incredibly confusing (look it up!!!).

But a tensor is a LOT more than that. Essentially it's a multilinear map that transforms a set of basis vectors in a certain way, and is coordinate agnostic.

This is not even half its definition so you can see how much the author left out.

Having said that, this is still a good way to start getting intuition into it and I urge the author to continue refining the definition as he/she learns more.

Disclaimer: MS in Math with concentration of GR.

EDIT: Also tensor aren't simply "flat" array of numbers. They are multidimensional. A grounded example, a rank 3 tensor is a collection of 2d matrices. Think of it as a bunch of 2d matrices stacked on top of each other. You need 3 indices to keep track of numbers --- sure in a programming language, it can be represented as a 1d array as well with 0s filling up empty spaces, but you get the idea.

I know there are different contexts, but a tensor is not a collection of numbers, in a mathematical sense. A vector is not a list of numbers. Such collections of numbers are representations of objects with very specific kinds of properties under coordinate transformations.

I think it genuinely damages people's ability to digest the mathematics to tell them first and foremost that these objects are collections of numbers.

Why does does the diagram say tensors are 3D?

> A tensor is nothing but a flat array of numbers

I'm so very, very tired of tech coopting rigorous mathematical terms.