This also reaffirms my (wishful) thinking that if there’s a way to do FTL communication it’ll be something with an absurdly tiny factor like 2^-182 with a slight asymmetry in a probability somewhere.
Then you’re not violating FTL, just gaining a very slight chance that you might know something FTL – probably.
From that angle, beating light speed by some absurdly tiny factor would probably correspond to a means of predicting the future at some almost absurdly tiny factor better than random guessing.
i will NEVER care about proposed multiplication speedups unless they are truly generalized
It's most interesting when the lower bound can actually be proven. In lack of that, we have to guess what the best possible algorithm might yield (generalized or not). This tells us that need not be O(n log n) and we have the opportunity to still find better algorithms than we typically thought would be possible. This does the latter, which is interesting, but it just leaves us to hunger more for what the real limit must be :).
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-confidentially 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.
infocollector•53m ago
saagarjha•45m ago
cr4zy•37m ago
OpenAI. An explicit power saving for the exact discrete Fourier transform.
Here's a random excerpt:
8.3 The middle transform and the final permutation The factor QFt in (35) can be computed from a cyclic convolution and two pointwise phase multiplications. The chirp identity below performs the frequency change in Q without applying Q as a separate permutation of the array. The second identity shows how the retained source permutation R cancels when computing a convolution. Here ∗ denotes cyclic convolution on the product of the coordinate groups and a dot denotes coordinatewise multiplication.
saagarjha•10m ago