tensor_annotations VS miniF2F

Not really an answer to your question, but there are Python packages that try to solve the problem of tensor shapes that you mentioned, e.g. https://github.com/patrick-kidger/torchtyping or https://github.com/deepmind/tensor_annotations

I've explored this space quite a bit. In my view, static checking should be the goal.

https://github.com/deepmind/tensor_annotations and tsastanley seem to be the most far along. I've developed a mypy plugin that does similarly off of the "Named Tensor" dynamic feature (which isn't well supported yet), but haven't released it yet.

That said, you *can* write down a desired type and have a system write down a ton of type annotations or generate a bunch of code to prove that the type you wrote down is satisfied by your program. There's been recent work on this in deep learning for theorem proving, such as this work which uses GPT for proving theorems in Lean, a dependently type programming language and theorem prover. A better approach though would be to combine this with an actual tree search algorithm to allow a more structured search over the space of proofs, instead of trying to generate full correct proofs in one shot. Hypertree Proof Search does this, using a variant of AlphaZero to search and fine-tune the neural net. Unfortunately it hasn't been open-sourced though, and it's pretty compute intensive, so we can't use this for actual type inference yet. But yeah there's active interest in doing this kind of thing, both as a proving ground for using RL for reasoning tasks and from mathematicians for theorem-proving.