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OpenAI’s mathematics repository includes a paper claiming an asymptotically faster Fourier transform, but an analysis by arg min says the result would not outperform the standard Cooley-Tukey FFT at any realistic input size. The critique centers on enormous hidden constants in the paper’s big-O bound; OpenAI’s claim is theoretical, not evidence of a practical speedup.
A paper in OpenAI’s mathematics repository claims an asymptotically faster way to compute Fourier transforms, but an analysis published by arg min says the algorithm would not beat the standard Fast Fourier Transform at any practical input size. The dispute matters because the claimed improvement is expressed through big-O notation, which describes long-run growth while concealing constants that can determine whether an algorithm is usable.
The arg min report examines a paper OpenAI included in what it describes as a recent, large mathematics-repository release. The report says the paper’s central result gives a Fourier-transform algorithm with a slightly smaller logarithmic term than the conventional FFT. That is an asymptotic claim: it concerns how operation counts grow as input size tends toward infinity, not demonstrated performance on ordinary computers or signal-processing workloads.
The report’s author says estimated constants in the claimed bound are extraordinarily large. In the author’s account, the estimate is about 10100 at a stated threshold of 1012. The report concludes that the new method would become faster only at input sizes far beyond any feasible computation. It estimates that even at an input size of 10100, the traditional Cooley-Tukey-Gauss FFT would be about 1099 times faster. These are the report’s interpretations and estimates, not practical benchmark results.
The report says its author did not read the paper in full and instead used a chatbot interface to retrieve and summarize information from it. That limits how independently the piece verifies the proof or its assumptions. The source material does not include a response from OpenAI, a detailed independent review of the paper, or experimental measurements comparing implementations.
For engineers, a smaller asymptotic growth rate does not by itself mean a faster program. An algorithm may have a better theoretical rate but require so much setup work—or carry such a large constant in its operation count—that it loses to an older method for every input size that can actually be processed. The arg min analysis says that is the situation here: the paper’s bound may be mathematically faster in the limit, while offering no practical speed advantage.
The distinction matters because Fourier transforms underpin work in signal processing and other computations that analyze frequency content. In applications, available time and hardware capacity set real limits. A theoretical result can still be mathematically meaningful, but it should not be read as evidence that existing transform workloads will run faster or that users can replace established FFT software.
The criticism also illustrates a broader issue in reporting algorithmic results: a complexity class is only part of the performance picture. Big-O notation suppresses constant factors and lower-order terms. Readers need the full bound, its assumptions, and a realistic account of the input sizes at which an advantage could appear. The arg min author’s conclusion is that the OpenAI result’s formal asymptotic improvement does not translate into a usable speedup under feasible conditions.
Fast Fourier Transform (FFT) software
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From the FFT to the New Bound
The discrete Fourier transform maps a sequence of samples into its frequency components. Calculating each output directly requires comparing the input against each frequency, producing a straightforward operation count that grows roughly as n² for an input of length n. The FFT is a family of methods that reduces this work by exploiting structure in the transform.
The familiar Cooley-Tukey approach, published by James Cooley and John Tukey in 1965, recursively divides a transform into smaller ones and combines their results. The arg min report gives a bound of fewer than roughly 5n log₂ n arithmetic operations for this method. Compared with a direct calculation, that reduction can be substantial as n grows. The report uses a length of 1,000 as an illustration: its stated operation-count comparison is about one million for the direct method versus about 50,000 for the FFT.
Researchers have continued to seek faster transform algorithms, including improvements to the factors in the operation count. The OpenAI paper, as described by arg min, addresses that theoretical question. The report’s central objection is not that asymptotic analysis is irrelevant, but that its conclusion can be misleading if the constants and thresholds needed for an actual crossover are not made clear.
““The OpenAI FFT algorithm is definitely galactic.””
— The arg min report
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Proof, Assumptions and Benchmarks
The source material does not establish whether the paper’s proof has been independently checked, whether OpenAI has published a response to the critique, or how the result’s stated bounds were derived in detail. The arg min author acknowledges not reading the paper in full and describes using a chatbot to retrieve salient information. Readers should treat the report’s account of the paper and its constants as an attributed analysis, not as a substitute for a full technical review.
No implementation, hardware comparison, or benchmark is provided in the supplied material. It also does not set out the exact crossover calculation in a form that can be independently assessed here. What is supported by the report is narrower: it says the algorithm’s asymptotic bound has extremely large constants and argues that the resulting method cannot outperform the established FFT at feasible input sizes. Whether the paper has other mathematical contributions beyond this running-time claim is not addressed.
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Independent Review and Practical Tests
The next useful step would be a direct examination of the paper’s proof, definitions, and operation-count bound, followed by independent expert assessment of the assumptions behind the constants. Any claim of practical value would also require a working implementation and comparisons against established FFT methods across realistic input sizes and computing platforms.
The supplied source does not identify a planned response from OpenAI, a peer-review process, or a timeline for further evaluation. Until those details emerge, the result is best described as a theoretical asymptotic claim challenged by arg min on practical grounds—not as a faster FFT available to users.
scientific computing Fourier transform
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Key Questions
What does OpenAI’s paper claim?
As described by arg min, the paper claims an asymptotically faster Fourier-transform algorithm, with a slightly smaller logarithmic term than the standard FFT. The supplied material does not provide the full paper or independently establish its proof.
Does the claimed algorithm run faster in practice?
The arg min report says no. It argues that the constants in the paper’s bound are so large that the algorithm would become faster only at impossible input sizes. No practical benchmark is included in the supplied material.
Why do hidden constants matter?
Big-O notation describes how an operation count grows for large inputs, but it suppresses constant factors and lower-order costs. Those omitted terms can make an algorithm with a theoretically better growth rate slower at every feasible size.
What is the standard FFT method being compared?
The report compares the claim with the Cooley-Tukey FFT, a recursive method published by James Cooley and John Tukey in 1965. The report gives its operation count as fewer than roughly 5n log₂ n arithmetic operations.
Has OpenAI responded to the critique?
The supplied source material does not include a response from OpenAI or say whether the paper has undergone independent review.
Source: hn
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