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.)
... are they?
Algorithms are predictable:
1. it's really difficult to produce true randomness in an algorithm, which is why there's a whole area of study surrounding the qualities of pseudo-randomness, specifically with regards to the generation of cryptographic material with most conclusions being that we should draw entropy from the environment (e.g. electrical noise as cloudflare does - the lava lamp is a distraction)
2. when algorithms are not predictable despite being mathematically sound, this is indicative of a problem nowadays called "numerical stability" which again spawned its own area of study.
CGoL shows how really simple rules (couple of bytes of data) can lead to extremely complex outcomes and you have the BB turing-golf aspect as proof of the worst case scenario.
And with current models being measured in hundreds of gigabytes, with frontier labs deprecating then removing the "temperature" parameter (which never worked to begin with, temp=0 did not result in reproducible results), where exactly is the confidence of this 10^10 prediction coming from?
You probably know that non-determinism in real-world inference comes from deliberately stochastic features like temperature, from implementation choices like distributed and parallel computation, and numerical effects like floating point precision.
The fact that a neural network's execution can be nondeterministic doesn't mean that the network stops being an algorithm.
The point you're making boils down to speculation that the accidental non-determinism involved in real-world inference is significant enough to undermine or negate interpretability findings based on the algorithms. That would need to be demonstrated.
The CGoL and BB examples demonstrate what might be possible in a worst-case scenario, but they're only analogies in this context. It's far from clear that real models suffer from such effects to a significant degree. You might actually be better off talking about the butterfly effect!
Someone call the FCC, they've been doing it wrong all these years!