The Emergent Symbolic Structure of Artificial Neural Networks

(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.

Just going from 2D to 3D creates massive new positional potential (e.g. surface of the earth, vs. the atmosphere above earth...).

Now imagine 1,000 dimensions.

That's pretty cool. I hope I've got that kinda-right.

They say this holds in... Some examples they found?

I don't enough about this area