Author: Quantum Bit
Fields medalist Wang Hong also presented at NeurIPS.
Huh? Did Wang Hong, a new field medalist, also try AI?
NeurIPS 2026 results will be announced soon, but netizens have discovered that Professor Wang Hon has presented a paper at NeurIPS 2019.
And this is not just an honorary award, but a true co-lead authorship.
That begs the question. Why would a leading mathematician specializing in pure mathematics present a paper at an AI conference?
After reading through it, I came to the conclusion that this is a classic case of combining mathematical theory and machine learning.
Interestingly, nearly all of the more than 40 papers and preprints listed on Wang Hon’s personal homepage include full links.
This is an exception.
Wang Hon takes on cross-domain challenges in AI
In this paper, we study low-rank matrix approximation, a fundamental task in machine learning and data analysis.
Simply put, real-world data is often organized into matrices, and these matrices are often very large and very expensive to store and process directly.
A low-rank approximation uses a simpler, lower-rank matrix to exactly reconstruct the original matrix.
A popular approximation algorithm these days is column subset selection (CSS).
The concept is actually very simple.
Instead of directly computing a new low-rank matrix from a data matrix containing many columns, we select a representative subset of columns from the original matrix and use the space over which they span to approximate the entire matrix.
Because the columns selected by CSS are taken directly from the original data, they are easier to interpret than the abstract vectors obtained from standard matrix decomposition, and they also reduce storage and computational costs, making them suitable for large-scale data processing.
Previous work has shown that for general low-rank approximations, the upper bound on the approximation ratio for CSS algorithms is approximately O(k+1).
Here, k refers to the rank of the target matrix. The larger k is, the larger the theoretically acceptable worst-case error is.
The work of Wang Hon et al. pushes this boundary even further.
・If 1≦p≦2, the approximate ratio is (k+1)^(1/p).
・If p≧2, the approximate ratio is (k+1)^(1−1/p).
Compared to the previous uniform O(k+1) result, this bound is much tighter and allows us to tightly constrain the algorithm, making the worst-case result only slightly worse than the optimal solution.
Furthermore, for p≥2, the paper constructs a corresponding lower bound and proves that the result is accurate up to a constant 1.
In other words, this paper provides an answer that is close to the theoretical maximum.
The most important part of this paper, and the part that best reflects Wang Hong’s mathematical background, is the use of the Ries-Thorin interpolation theorem, a classic tool in harmonic analysis.
Proving that an algorithm holds for all values of p typically requires complex analysis tailored to different values of p.
For certain endpoints, such as p=1, p=2, p=∞, the process is relatively simple.
The Ries-Tolin interpolation theorem allows us to “interpolate” our conclusions to all intermediate values of p after establishing these endpoint results.
Specifically, this paper first proves three special cases of p = 1, 2, and ∞, and then uses interpolation theory to derive approximation limits over the entire range.
In fact, although this tool set is a classic approach in harmonic analysis and operator theory, it was not the most commonly used technique among theoretical computer scientists at the time.
NeurIPS reviewers from the same year also noticed this.
The reviewers ultimately identified the paper’s main innovation as introducing the Rhys-Thorin theorem to computer science, and the final meta-review called it a well-argued paper.
Viewed today, the paper also provides a very typical interdisciplinary case study. Perhaps a machine learning challenge could find a breakthrough in pure mathematics.
NeurIPS 2026 results coming soon
The NeurIPS review process is currently undergoing significant adjustments.
In NeurIPS 2026, authors must choose one of five submission types when submitting a paper: General, Theory, Application-inspired, Concept and Feasibility, and Negative Results.
Without a doubt, Wang Hon’s 2019 paper falls into the category of theory.
According to the latest NeurIPS 2026 review guidelines, theoretical papers will first be evaluated for mathematical rigor and accuracy. Proofs, lemmas, and overall logic must be sound, so theoretical papers should not be overlooked due to lack of experiments.
On the other hand, NeurIPS 2026 clearly states that theoretical contributions work independently and that the goal of designing new algorithms is not necessarily to outperform state-of-the-art application models or SOTA on the largest datasets.
And this is almost an accurate description of Wang Hong’s paper.
They did not propose neural network architectures in today’s sense, nor did they train models with huge numbers of parameters. Instead, we introduced the interpolation theorem from harmonic analysis to the low-rank approximation to address the limitations of the approximation algorithm.
It is still a very standard NeurIPS theoretical paper in the 2026 review framework.
It also means that NeurIPS is more than just a platform for launching neural network models. New insights into existing methods, the discovery of new properties, and the establishment of more rigorous theoretical limits are equally valuable original contributions.
The boundaries between mathematics and AI are not as clear-cut as one might imagine.
Fields medalists can be published on NeurIPS. Mathematical language also helps AI find true general solutions.
Reference link:
[1]https://proceedings.neurips.cc/paper_files/paper/2019/file/80a8155eb153025ea1d513d0b2c4b675-Paper.pdf
https://neurips.cc/Conferences/2026/Reviewerguidelines
[3]https://sites.google.com/view/hongwang/home
[4]http://xhslink.cn/o/8oQ3gm7qaxu
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