OpenAI's Faster FFT Faces a 'Galactic Algorithm' Critique
Ben Recht says the preprint's better theoretical bound hides arithmetic costs that keep it far from a useful faster transform.
A theoretical speed claim meets a practical objection
Researcher Ben Recht has challenged the practical value of OpenAI’s proposed faster Fourier transform. OpenAI’s preprint, dated September 25, claims a slight improvement in the asymptotic operation count for an exact discrete Fourier transform. Scientific American highlighted that claim on October 8 as a break with a longstanding theoretical barrier, while describing the improvement as extremely small. Recht’s October 12 English essay argues that the result is a “galactic” algorithm: a better formula for sufficiently vast inputs whose hidden costs would make it unusable for realistic ones. The fresh essay, rather than a new OpenAI release, is the development drawing discussion now.
What remains in dispute
Recht’s central objection is that the paper counts exact operations on complex numbers as single steps even as, he says, the numbers involved grow too large to represent and multiply cheaply on real hardware. He also argues that large constants hidden by the asymptotic notation overwhelm the tiny improvement. These are Recht’s assessments; they do not prove that OpenAI’s mathematical result is invalid. In the October 13 Hacker News discussion, some readers endorse the practical concern, while others note that a theoretical result can inspire later, usable algorithms even when its first construction is impractical. There is no verified faster implementation or independent adjudication of this particular proof in these sources.