Math researcher debunks OpenAI's faster Fourier transform as flawed
Argmin analysis finds the claimed breakthrough lacks rigor; competing researchers question the result's theoretical validity.
What to know
- OpenAI claimed to have discovered a sub-n-log-n algorithm for computing discrete Fourier transforms, potentially breaking a long-standing computational limit.
- A detailed technical critique argues the work lacks rigor and does not constitute a genuine breakthrough, comparing the research process to low-quality AI-generated mathematics.
- Competing researchers have published alternative approaches to sub-n-log-n Fourier transforms, with one proposing δ = 7.3×10⁻⁵ exponent savings.
OpenAI Research organizationArgmin author Mathematics researcher and technical criticRyan Shea Independent researcherJohn D. Cook Mathematics blogger
How it unfolded 5 developments, newest first · click a bar or a number to jump articlesposts
-
5
Hacker News surfaces critique framing OpenAI result as 'malicious exploit'
The Argmin critique gains traction on Hacker News with a headline characterizing the OpenAI algorithm as less a breakthrough and more a malicious exploit, drawing 43 points and 15 comments.
“OpenAI algorithm for the FFT is less a breakthrough and more a malicious exploit…”
— mochomocha, Hacker News commenter · source -
first by HN Frontpage, 2d ago
-
The author is attacking the field of theoretical algorithm design broadly as being useless. If we take the author's logic to its conclusion, many algorithms we learn about in a standard Algorithm Design course such as "median of medians" (finding the median in a list in O(n) worst-case time) is useless because it is not used in practice. Even the…
2 more of the top 3 · 22 posts in this stretch
-
W
A very readable (as long as you can stomach multiplication, the log function, and powers) discussion of the OpenAI dump of pseudo-proofs*. Calling them pseudo bc they fail to carry out the second function of proofs: to make the result comprehensible and worth examining to *some* mathematician. https://www. argmin.net/p/faster-fourier-tr…
-
> The theory of computer science has become a form of mathematics that doesn’t concern itself with computersPerfectly summarizes the post, which I'd qualify as a rant (the author's main gripe seems to be that it's a galactic algorithm that assumes exact complex multiplication). The theory of computer science literally started with a mathematical…
-
-
4
Argmin technical critique questions OpenAI's mathematical rigor
A detailed mathematical analysis published on Argmin argues that OpenAI's claimed faster Fourier transform is not a genuine breakthrough. The author notes the paper was not carefully reviewed and compares the research process to 'AI slop'—using AI to analyze AI-generated mathematics.
“Did I read this paper? Of course not. No one at OpenAI read this paper either, so why should I? I did what every other mathematician in the world does with AI slop mathematics: I fed it back into the slop machine.”
— Argmin author -
OpenAI’s faster Fourier transform is less a mathematical breakthrough and more a malicious exploit of mathematical traditions.
1 more of the top 2 · 2 posts in this stretch
-
Is the @OpenAI Faster Fourier Transform merely a theory hack that cheats by relying on arbitrary precision real arithmetic? The answer is no: the savings are preserved when the algorithm is transferred to the finite odd characteristic setting, where no o(n log n) algorithm was
-
- 3 days quiet
-
3
Ryan Shea publishes competing sub-n-log-n Fourier transform bound
Independent researcher publishes a draft claiming an alternative bound of O(n(log n)^(1−δ)) with δ = 7.3×10⁻⁵, offering a competing approach to the same problem.
“We're publishing a research draft on OpenAI Problem #130: computing the exact discrete Fourier transform below n log n. Our draft proposes an all-length bound of T(n) = O(n(log n)^(1−δ)), with δ = 7.3×10⁻⁵.”
— @ryaneshea, Independent researcher · source -
We’re publishing a research draft on OpenAI Problem #130: computing the exact discrete Fourier transform below n log n. Our draft proposes an all-length bound of T(n) = O(n(log n)^(1−δ)), with δ = 7.3×10⁻⁵. That’s a 730-million-fold increase in the exponent saving over
-
-
2
Cook reports result is theoretically surprising but practically useless
A mathematics blog post notes the result challenges assumptions about algorithmic limits but emphasizes it has no practical value yet.
“The result is amazing. It seemed that O(n log n) was as good as you could do… But since the theorem shows that our assumptions were wrong, however slightly, about what is possible, maybe we're in for further surprises.”
— John D. Cook -
1
OpenAI releases papers on faster Fourier transform
OpenAI published research claiming an algorithm to compute the discrete Fourier transform faster than the long-standing O(n log n) bound, proposing a sub-n-log-n approach.
-
first by HN Best, 2d ago
-
What people are saying 18 voices from 2 sites · best of 25 · verbatim
- Yesterday
-
> I can have this view while simultaneously thinking that Ben is a badassYeah? Seems more like an ass.
- Oct 13
-
> If you want that, you go to ESA, ALENEX, or VLDB/SIGMOD, or any of the other more applied venues featuring this workWell, I want openAI to focus on these things instead, so it is not a totally unreasonable thing to advocate against their current focus
-
great article, and when i read that:"I found the rot that develops inside applied mathematical theory when formalism becomes so detached from reality that a “breakthrough” is nothing more than an artifact of mathematicians not being able to properly specify the rules of their games in natural language."it's like in my company, where some software…
-
>malice >shit on I don't think this is a productive or interesting way to discuss mathematics.
-
I'm confused by some of the reactions here. Isn't this the first step toward taking theory into reality? So, FT could be faster if we could multiply larger numbers. The problem has now moved from is it possible to "do we have the hardware to do it?" Not my area, so maybe someone could explain to me why this isn't a question of how large the…
-
If you read the entire argument, it makes perfect sense. It’s simultaneously mocking the poorly established ways of measuring asymptotic complexity of algorithms.TL;DR - time complexity calculations ignore constant values. So if algorithm A takes 10^10 + n number of iterations to do something, and B does n^2, in theory B is worse, because n < n^2…
-
So, the pseudo-FFT exploits algorithmic similarity between DFT and multiplication to translate part of the DFT work into multiplication work, which is O(1) in the exact arithmetic model.Thus, the magnitudes of the numbers being multiplied grow superpolynomially with n (the DFT problem size): because the robot's stuffing its work in there and using…
-
This made me chortle:> Did I read this paper? Of course not. No one at OpenAI read this paper either, so why should I? I did what every other mathematician in the world does with AI slop mathematics: I fed it back into the slop machine and ran an information retrieval session with a chatbot interface to extract salient facts. Anthropomorphically…
-
H
A look at OpenAI’s math that’s claimed computes faster Fourier transforms Link: https://www. argmin.net/p/faster-fourier-tr ansforms Discussion: https:// news.ycombinator.com/item?id=5 0065932
-
The author could have left AI entirely out of the essay and come to the same conclusions. He just really doesn't like TCS. That's fine, it's really a part of mathematics not science, but it's silly to dismiss a field with "theoretical" in its name for being impractical.
-
As a theorist, it's sort of true that I "don't care" about galactic constants. I'm interested in the structure of computation for philosophical reasons. But I really do care about the model of computation.To put it another way, the constants inside a big-O are not really constant: they depend on what you assume is a constant-time operation.
-
"Malicious" is an overstatement, but "exploit" is completely fair in my view. Theory with no possible practical relevance is useless, and I think a computational complexity result requiring arbitrary-precision arithmetic that is impossible to implement using any physical system qualifies.
-
I’ve made some half hearted attempts to try and understand even the framing of some of these problems that were solved, and my god theoretical math is hard. It’s completely impenetrable with unknown symbols and hard to comprehend bounds and several orders of derivatives. It’s all unintuitive to me.
- Oct 12
-
There is currently an effort underway to improve the bound. They have reached at a much larger kappa around 0.001635527380375392
-
> the algorithm requires you to multiply complex numbers whose magnitudes grow superpolynomially with n.Err... doesn't that completely invalidate the big-O analysis!?I suspected that these Open AI "proofs" of sub-nlogn times were cheating somehow, by sweeping something under a rug. This seems to be it!
-
Did not realize that the model of computation for all of the banner computational complexity results from last week was "exact complex arithmetic." Is this and/or "exact real arithmetic" a common premise for papers in this field? My assumption as an outsider was that people mostly care about things equivalent to Turing machines.edit: by "things…
-
If algorithmic theorists don't care about practical performance then why should we care about what they're doing? It's just a strange game they're playing, of no interest to anyone else.It seems like rather than coming up with more "galactic" algorithms, a more useful thing to do might be to come up with a replacement for big-O that's not so…
-
This is a bad take. I will happily acknowledge the new term "slopository" which I had not heard before, while taking the author to task for malice towards theorists. STOC/FOCS/SODA, etc are not about "doing practical algorithms". If you want that, you go to ESA, ALENEX, or VLDB/SIGMOD, or any of the other more applied venues featuring this work. I…