The big questions I’m taking away are:

(1) they are claiming to produce apparently bijective closed-form symbolic representations/approximations of, among other things, LLMs. Is evaluating these closed-form representations more computationally efficient? The implications of that are potentially huge. It would be essentially analytic distillation. Fable on a chip and not a data center would be important — and disruptive - in many ways.

(2) Unsupervised, and even supervised, symbolic approaches to problem solving break down due to combinatorial explosion, among other things. This could potentially allow us to treat LLM training and inference as a search algorithm for novel symbolic approaches to solving new classes of complex problems hitherto unreachable through other approaches. If that works, I suspect it’s a feedback loop, too - the learnings from one representation push advances in the other. This would also increase the economic value of large training runs, since the model itself is now valuable, not just its inference.

(3) Per the above, can this push LLM design to greater capabilities?

The relationship between this and Anthropic’s J-space observation is also interesting. This is much, much deeper and more directly actionable, though.

EDIT: I ran my questions through Sonnet — yes, I appreciate the irony — and it was none too sanguine about questions (1) and (2), but thought (3) was reasonable. In any case, this is quite the paper. On reflection, I do think that the apparent reliance on very simple symbolic representations and tasks is underwhelming. But the approach is impressive. And obviously this is still early days, and the value of building a bridge between the very fuzzy LLM models and the rigorous, mechanically provable models would be enormous.

Inference is just tokens transformed through a fixed crystalline structure, no? You already could put that on a chip. There's no particular reason it couldn't be represented as some set of symbolic equations instead of a layered process... it's just another kind of quantization.

When symbolic algorithms are that large, they're equally hard to reason with most of the time. The upshot would be a lot more storage required in exchange for more generalized computing, lessening the need for so much GPU in a lot of cases.

I don't see why a model couldn't be represented that way. After all, if you just polled the output of a model, you could evolve genetic algorithms to predict it with fairly high accuracy in a limited domain. Take that out to the Nth degree and you're basically just unspooling the model into a giant set of equations.