[ghj]

I can give another example use case.

Say I know math but don't know tf api. I already know how to matrix multiply with `@` but don't know the function for matrix power.

Then in theory it should be fairly quick for me to create a random matrix and feed it `mat @ mat`, `mat @ mat @ mat`, `mat @ mat @ mat @ mat`, etc until it spits out the correct tf function I should call for matrix_power.

This is even better than googling since it guarantees that the function it found is correct for your example (googling returns tf.pow tf.exp tf.expm, none of which are actually what you want!)

[YeGoblynQueenne]

Thanks, I see what you two mean. It didn't occur to me that programming with tensors can be so challenging and I thought the authors just big it up a little to motivate the work - as one does :)

[ghj]

It's more that programming with math is hard.

When communicating in mathematics you often assume the reader can understand precisely which mathematical object you're talking by extrapolating from ellipses "...". For example "the naturals are 1,2,3,4,..." or "the evens are 2,4,6,8,..."

Or I might tell you a shift matrix is something that looks like:

  [0 1 0 0 0]
  [0 0 1 0 0]
  [0 0 0 1 0]
  [0 0 0 0 1]
  [0 0 0 0 0]

And that single example with the suggestive naming should be enough for most people to understand what a shift matrix is for arbitrary size.

But if you want to explain what a shift matrix is to a computer, you must use a formal definition (and to do it idiomatically you need to know esoteric details like that numpy.diagonal takes in an offset parameter so you can do something like https://stackoverflow.com/a/30230801).

It would be nice if we can talk math with a computer in the same intuitive language we use with humans, just give it a few examples and it will generate the the rest and let you double check the formula is correct.

So I see stuff like tf-coder as a great step, not for synthesizing programs we don't know how to solve, but for language translation: between math notation and programming notation.

[YeGoblynQueenne]

I wonder whether the same effect could be achieved with a better designed programming language, though. If the problem is ambiguity- there's nothing stopping a programming language from accepting ambiguous statements, which of course it would then interpret unambigously, according to context. It's just that this takes a lot of work and it's really not the done thing in terms of programming languages as far as I can tell- for reasons of eficiency of parsing also, I think.

Anyway I guess I'm turnning into the typical stuffy academic who can't even begin to think of real-world applications, hah. Thanks for pointing out the practical uses of the work described in the article.

[im3w1l]

And the reason it's hard is because of how heavily tensorflow discourages flow control and reusable general purpose constructs for efficiency and differentiability reasons. Instead you have to use the list of blessed special purpose things.