A look at OpenAI’s math that’s claimed computes faster Fourier transforms

The mathematical shortcut claimed by OpenAI does not offer a real-world speedup for computing Fourier transforms.

OpenAI has published a set of mathematical papers, one of which claims a faster Fourier Transform (FFT) algorithm. The author, Ben Recht, analyzed this claim and found it to be a theoretical construct rather than a practical advancement. The claimed FFT algorithm is described as a "galactic algorithm," meaning it has an astronomically large hidden constant factor in its Big-O notation. This makes the algorithm perform faster than the standard FFT only for impossibly large input sizes, rendering it impractical for real-world applications. The algorithm also relies on exact complex arithmetic and assumes the ability to multiply arbitrarily large complex numbers in a single operation, which is not supported by current computing hardware. Recht criticizes the paper for leveraging theoretical loopholes and a detached model of computation, suggesting it highlights a broader issue of theoretical computer science becoming disconnected from practical computing.

The core issue with OpenAI's claimed FFT is its reliance on "galactic algorithms," where the theoretical speedup is only achieved at input sizes so large they are practically impossible to encounter. This highlights a divergence between abstract mathematical efficiency and tangible computational performance, where an algorithm's theoretical Big-O notation can obscure vastly impractical execution requirements due to enormous hidden constants.

This situation underscores a growing concern in AI research where models can generate technically valid, yet practically useless, theoretical artifacts by exploiting the nuances of mathematical formalisms. The analysis suggests that while AI might automate the process of generating such theoretical papers, it also amplifies existing tendencies within fields like theoretical computer science to prioritize asymptotic analysis over real-world implementability and measurable performance gains on actual hardware.