A look at the math that OpenAI claims computes faster Fourier transforms

A recent article examines OpenAI's claim of faster Fourier transforms, delving into the underlying mathematics. The author notes that for a given 'n', the speedup can be substantial; for instance, when n is 1,000, a 20-fold speedup is observed, and for n equal to 1,000,000, the speedup reaches 10,000-fold. This acceleration is crucial for signal processing applications, potentially making previously uncomputable transforms feasible. The article also mentions a formula T(n) <= n^(2.25 +epsilon + C/log(n)) related to the computational complexity.

This analysis details the specific mathematical claims and speedup factors, such as 20-fold for n=1,000, unlike general discussions of Fourier transform improvements.