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Sharing AI Progress in Mathematics
- > The cost is measured in an exact complex-register model that assigns unit cost to exact complex field operations. The algorithm accepts every x ∈ Cn, with no bound on its entries or on intermediate complex magnitudes. Its computation on the input uses only addition, subtraction, and multiplication by prepared input-independent scalars. The magnitudes of those scalar coefficients are unrestricted as well.
I'm not very familiar with this kind of low-level theoretical computer science, so please forgive my possibly stupid question: is it common to use a model of computation like this, with registers which can store exact complex numbers? Since no computers like that really exist, would that limit the practical application of this finding?
- this is perfect for when i have an array of at LEAST 2^118000 items
i will NEVER care about proposed multiplication speedups unless they are truly generalized
by 12390asdjkas - There are several of these "exponent used to be 1.0, we reduced it to 0.9999999" results in the "catalog".
There are also a bunch of other stinkers, like building a Turing machine out of Navier-Stokes fluids -- except that it only works if you can encode literally infinite amounts of data in the relative positions of two particles. I.e. assuming physics is based on set-theoretic real numbers, something we've known is wildly false for over a century: https://en.wikipedia.org/wiki/Banach-Tarski_paradox
Just like vuln reporting, the AI industry has put zero effort into triage here, and the models are really good at making their findings sound more important than they really are.
The cynic in me suspects this is a smokescreen for the Navier-Stokes tokenstream plagarism fiasco.
- For the uninitiated, why is this interesting given it doesn't seem to be so much below the threshold?
- I laughed out loud at the n lg n ^ (1 - 2^{-182}). It is so funny.by shmoil
- Is there an associated machine-checked proof of this?
We're in full vibe-code mode at work, so I understand both how powerful frontier models can be and how often they can over-confidently state subtly (or not so subtly) wrong things, even when you're taking great efforts to try to keep that from happening.
So without a Lean development or extensive human verification, I guess I'm a little bit skeptical, and even sort of hoping this is wrong - not just because of my not so positive feelings about AI, but by my disposition towards beauty in math. n log n is an awful lot nicer than what we have here.
by wk_end - We shaved a whole: 1/6129982163463555433433388108601236734474956488734408704 off the nlognby TGower