Huh? The newly minted Fields Medalist, Hong Wang, once dabbled in AI?
With NeurIPS 2026 reviews imminent, netizens dug up that Professor Hong Wang once co-authored a NeurIPS 2019 paper.
And it wasn't just a nominal credit; she was a veritable co-first author.
So here's the question: why would a top mathematician in pure mathematics publish a paper in an AI top-tier conference?
After reading through, our conclusion is that this is an excellent example of mathematical theory + machine learning.
Interestingly though, on Hong Wang's personal homepage, nearly all of the 40+ listed papers and preprints have complete links attached.
Except for this one, which is an exception.
Hong Wang's Crossover into AI
This paper studied a fundamental task in machine learning and data analysis: low-rank matrix approximation.
In simple terms, real-world data can often be organized into a matrix, but these matrices are usually very large, making direct storage and processing extremely costly.
Low-rank approximation aims to reconstruct the original matrix as accurately as possible using a simpler, lower-rank matrix.
A commonly used approximation algorithm recently is Column Subset Selection (CSS).
Its concept is actually quite intuitive.
When faced with a data matrix containing a large number of columns, instead of directly computing a brand-new low-rank matrix, it selects a few representative columns from the original matrix and uses the space they span to approximate the entire matrix.
Since the columns selected by CSS come directly from the original data, they are easier to interpret than the abstract vectors obtained from general matrix decomposition. At the same time, it can also reduce storage and computational costs, making it suitable for processing large-scale data.
Previous research proved that for general low-rank approximation, the upper bound of the CSS algorithm's approximation ratio is approximately O(k+1).
Here, k refers to the rank of the target matrix; the larger k is, the larger the theoretically permissible worst-case error.
The work by Hong Wang and others further advanced this bound:
When 1≤p≤2, the approximation ratio is (k+1)^(1/p);
When p≥2, the approximation ratio is (k+1)^(1−1/p).
Compared to the previous unified O(k+1) result, this bound is significantly tighter. The algorithm can be strictly limited, and the worst outcome will only be slightly worse than the optimal solution.
Additionally, for the case p≥2, the paper also constructed a corresponding lower bound, proving the result is precise up to a constant of 1.
In other words, this paper provides a nearly definitive theoretical answer.
The most critical part of this paper, and the part that best reflects Hong Wang's mathematical background, is their use of the classic tool from harmonic analysis: the Riesz–Thorin interpolation theorem.
Typically, to prove that an algorithm holds for all p values, one needs to conduct complex analyses separately for different p values.
For certain endpoint cases, such as p=1, p=2, and p=∞, it is relatively easier to handle.
Then, the Riesz–Thorin interpolation theorem can "interpolate" the conclusion to all intermediate p values after mastering these endpoint results.
Specifically, the paper first proved the three special cases of p=1, 2, ∞, then derived the approximation bounds for the entire range through interpolation theory.
In fact, this tool is a classic method in harmonic analysis and operator theory, but it was not the most commonly used technique among theoretical computer science researchers at the time.
The NeurIPS reviewers of that year also noticed this point.
The reviewers ultimately recognized that the primary technical innovation of this paper was introducing the Riesz–Thorin theorem into the computer science field. The final Meta Review rated it as a paper with quite solid argumentation.
Looking at it today, this paper also provides a very typical interdisciplinary case: the difficult problems in machine learning might find breakthroughs in pure mathematics.
NeurIPS 2026 Reviews Are Imminent
Back to the present, NeurIPS' review mechanism is undergoing a noticeable adjustment.
NeurIPS 2026 requires authors to select the most suitable contribution type from five categories at the time of submission: General, Theory, Use-Inspired, Concept & Feasibility, and Negative Results.
Undoubtedly, Hong Wang's 2019 paper belongs to the Theory category.
According to the latest NeurIPS 2026 review guidelines, theoretical papers are first evaluated on mathematical rigor and correctness. Proofs, lemmas, and overall logic must be sound, so theoretical papers should not be overlooked due to a lack of experiments.
At the same time, NeurIPS 2026 explicitly states that theoretical contributions can stand independently, and the purpose of designing new algorithms is not necessarily to beat the SOTA on the latest application models or largest datasets.
Regarding originality, it can also introduce new proof tools from other disciplines or innovatively synthesize existing tools.
And this is almost a precise description of Hong Wang's paper.
They did not propose a neural network architecture in today's sense, nor did they train models with enormous parameters. Instead, they introduced the interpolation theorem from harmonic analysis into low-rank approximation to solve the approximation algorithm bound problem.
Placed within the 2026 review framework, it remains a very standard NeurIPS theoretical paper.
It also illustrates in reverse that NeurIPS is not equivalent to a neural network model release conference. Providing new understanding of existing methods, discovering new properties, and establishing tighter theoretical bounds are also valuable original contributions.
As for the boundary between mathematics and AI, it has never been as clear as imagined.
A Fields Medalist can publish in NeurIPS, and mathematical language can also find its true general solution for AI.
Reference links:
[1]https://proceedings.neurips.cc/paper_files/paper/2019/file/80a8155eb153025ea1d513d0b2c4b675-Paper.pdf
[2]https://neurips.cc/Conferences/2026/ReviewerGuidelines
[3]https://sites.google.com/view/hongwang/home
[4]http://xhslink.cn/o/8oQ3gm7qaxu
This article is from the WeChat public account "QbitAI", author: Lu Yu
