It doesn't.

In a nearby comment: https://news.ycombinator.com/item?id=48983413

> In mathematics (including information science, CS) there are all sorts of problems that are essentially searches for a solution, and many have the property that the search is computationally difficult, but verifying the solution is relatively cheap. E.g. finding integers such that a^2 + b^2 = c^2 isn't easy, but given a claim that some proposed <a, b, c> satisfies this equation is easy to check. The LLM is like that: it solves a search problem that can be fairly hard.

Funnily enough, one of the attempted solves in the litterature is exploring the problem space in two-dimensional space; the LLM found one in three-dimensional space.

So far we know very little as to why and how it found the solution.

It may very well have been directed to brute force 3D space, or even "elected" to" by expanding the known-failed 2D approach to 3D as pure mimicry.

> It does so unreliably, but if you can cheaply verify the solution, there is a win there.

This circles back to what the LLM advocates are pushing for: build the harness that keeps the agent in check, guardrails all the way because it's driving like a demolition derby.