> All non-trivial properties of neural networks are undecidable.

hey, I don't know how to say this less directly, but: you're talking a lot about Rice's theorem in your comments, and I think you're using it way too broadly (look, I get it. It's a wild, mindblowing theorem). But it only applies when you take the claim in the piece to be much more general than it has to be, and when you take the narrow claim of the paper (current specific LLMs can be fruitfully analyzed with the tools we have), Rice's theorem just isn't at play.

The math analog is: you're right that the Halting problem says there are many unprovable things, but Lean + mathlib are still incredibly useful, and the halting theorem doesn't actually stop that.

> neural networks are algorithms

Again, that invites an interpretation that is too broad. Very concretely: any one neural network is a _single finite network that you can write as a single formula_. (Another analogy: we can't have an algorithm that solves the general quintic, but we can prove useful things about many specific quintics.)