How did the winners of the Fields Medal send the AI Summit?
Author: qubit
Original title: Fields Medal winner Wang Hong also sent NeurIPS
huh? New Fields Medal WinnersWang HongHave you also done AI across borders?
NeurIPS 2026 is about to be released. Some netizens picked it out. Professor Wang Hong posted an articleNeurIPS 2019。
Also, it's not a public name; it's actually a joint work.
So the question is, why would a top mathematician in the field of pure numbers publish a paper at the AI Summit?
After reading through, our conclusion is that this is an articleMathematical theories+machine learningThe best example.
What's interesting, though, is that of the nearly 40 papers and preprints listed on Wang Hong's personal website, almost every article has a full link.
This one is the only exception.
Wang Hong challenges AI across borders
This paper studies a basic task in machine learning and data analysis:low-rank matrix approximation。
Simply put, actual data can usually be organized into a matrix, but these matrices are often very large, and direct storage and processing costs are extremely high.
Low-rank approximation is to use a matrix with a simpler structure and lower rank to restore the original matrix as accurately as possible.
Recently, commonly used approximation algorithms arecolumn subset selection(Column Subset Selection, CSS).
The idea is actually pretty intuitive.
Facing a data matrix with a large number of columns, no longer directly calculate a new low-rank matrix, but select from the original matrixA few representative columns, and then use the space formed by them to approximate the entire matrix.
Since the columns selected by CSS come directly from the original data, they are easier to explain than abstract vectors obtained by ordinary matrix factorization. At the same time, it can also reduce storage and calculation costs, and is suitable for processing large-scale data.
Previous research has proven that for general low-rank approximations, the approximate ratio of CSS algorithms is about the upper boundO (k+1)。
Here k refers to the rank of the target matrix. The larger k, the greater the worst error allowed in theory.
The work of Wang Hong and others isPushing this field further：
· When 1≤p≤2, the approximate ratio is (k+1) ^ (1/p);
· When p≥2, the approximate ratio is (k+1) ^ (1−1/p).
Compared to the previous unified O (k+1) results, this boundary is clearly tighter. The algorithm can be strictly limited, and the worst results are only slightly worse than the optimal solution.
In addition, for the case of p≥2, the paper also constructed a corresponding lower bound to prove that the results were accurateconstant 1。
In other words, the paper gave a nearly capped theoretical answer.
And the most critical part of this paper, and one that best reflects Wang Hong's mathematical background, is that they used classic tools from harmonic analysisRiesz—Thorin interpolation theorem。
Normally, to prove that an algorithm works at all p-values, it is necessary to carry out complex analyses for different p values separately.
Some endpoint situations, such as p=1, p=2, and p=∞, are relatively easy to handle.
Next, the Riesz—Thorin interpolation theorem can be concluded after grasping the results of these endpoints“interpolation”All p-values to the middle.
Specifically, the paper first proved the three special cases of p=1, 2, and ∞, and then introduced an approximation boundary for the entire range through interpolation theory.
In fact, this set of tools is a classic method in harmonic analysis and operator theory, but it was not the most commonly used technology by theoretical computer science researchers at the time.
NeurIPS's reviewers back then also noticed this.
The reviewers finally approved the paperThe most important technological innovationThat is, the Riesz—Thorin theorem was introduced into the computer field, and the final Meta Review evaluated it as a paper with quite solid arguments.
Looking at it today, this paper actually also provides a very typical interdisciplinary case. The problem of machine learning may be able to find a breakthrough in pure mathematics.
NeurIPS 2026 is about to be released
Time is set back to the present,NeurIPS review mechanismA significant adjustment is taking place.
NeurIPS 2026 requires authors to select the one that best matches the paper's positioning from five contribution types: General, Theory, Use-Inspired, Concept & Feasibility, and Negative Results.
Undoubtedly, Wang Hong's 2019 paper is one of themTheorytype.
According to the latest review guidelines for NeurIPS 2026, theoretical papers first examine mathematical rigor and correctness. Proof, reasoning, and overall logic must be established, so theoretical papers need not be ignored due to lack of experiments.
Meanwhile, NeurIPS 2026 clearly states that theoretical contributions canIndependently establishedNor is the purpose of designing a new algorithm to beat SOTA on the latest application models or largest data sets.
And this is almost an accurate description of Wang Hong's paper.
They did not propose a neural network architecture in today's sense, nor did they have a model with a huge number of training parameters. Instead, they introduced the interpolation theorem in harmonic analysis into low-rank approximation to solve the problem of approximate algorithm boundaries.
In the 2026 review framework, it is still a very standard NeurIPS theoretical paper.
It also explains the opposite,NeurIPS is not the same as a neural network model press conferenceGiving new understanding to existing methods, discovering new properties, and establishing tighter theoretical boundaries are also valuable original contributions.
As for the boundary between math and AI, it's never been as clear as you might think.
Fields Medal winners can send NeurIPS, and mathematical language can also find true solutions 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
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