Author: Quantum Bit
Fields Medalist Wang Hong has also published at NeurIPS.
Huh? The newly awarded Fields Medalist Wang Hong also ventured into AI?
The NeurIPS 2026 results are coming soon, and netizens have found that Professor Wang Hong published a paper at NeurIPS 2019.
And it’s not just an honorary mention—it’s a true co-first authorship.
So the question arises: why would a top mathematician specializing in pure mathematics publish papers at AI conferences?
After reading through it, our conclusion is that this is an exemplary case of mathematical theory combined with machine learning.
Interestingly, nearly all of the more than 40 papers and preprints listed on Wang Hong’s personal homepage include complete links.
This one is the exception.
Wang Hong takes on a cross-domain challenge in AI
This paper studies a fundamental task in machine learning and data analysis: low-rank matrix approximation.
In simple terms, real-world data is often organized into matrices, but these matrices are frequently very large, making direct storage and processing extremely costly.
Low-rank approximation uses a simpler, lower-rank matrix to accurately reconstruct the original matrix.
A commonly used approximate algorithm recently is Column Subset Selection (CSS).
Its concept is actually very straightforward.
Instead of directly computing a brand-new low-rank matrix from a data matrix with many columns, select a representative subset of columns from the original matrix and use the space spanned by them to approximate the entire matrix.
Since the columns selected by CSS come directly from the original data, they are easier to interpret than abstract vectors obtained from standard matrix factorization, while also reducing storage and computational costs, making them well-suited for large-scale data processing.
Previous research has shown that for general low-rank approximation, the approximation ratio upper bound of the CSS algorithm is approximately O(k+1).
Here, k refers to the rank of the target matrix; the larger k is, the greater the worst-case error allowed in theory.
The work of Wang Hong and others further pushes this boundary:
· 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 uniform O(k+1) result, this bound is significantly tighter, allowing the algorithm to be strictly constrained, with the worst-case outcome being only slightly worse than the optimal solution.
Additionally, for the case p≥2, the paper constructs a corresponding lower bound, proving that the result is accurate up to a constant factor of 1.
In other words, this paper provides a near-maximum theoretical answer.
The most critical part of the paper, and the one that best reflects Wang Hong’s mathematical background, is their use of the Riesz–Thorin interpolation theorem, a classical tool from harmonic analysis.
Typically, proving that an algorithm holds for all values of p requires complex analyses tailored to different values of p.
For certain endpoint cases, such as p=1, p=2, and p=∞, the handling is relatively straightforward.
The Riesz–Thorin interpolation theorem allows the conclusion to be "interpolated" to all intermediate values of p after establishing these endpoint results.
Specifically, the paper first proves the three special cases of p = 1, 2, and ∞, then derives the approximation bound over the entire range using interpolation theory.
In fact, this set of tools is a classical approach in harmonic analysis and operator theory, but it was not the most commonly used technique among theoretical computer scientists at the time.
The reviewers at NeurIPS that year also noticed this.
The reviewers ultimately recognized the paper's primary technical innovation as introducing the Riesz–Thorin theorem into computer science, and the final Meta Review described it as a well-argued paper.
Looking at it today, this paper also provides a very typical interdisciplinary case study—perhaps the challenges in machine learning can find breakthroughs in pure mathematics.
NeurIPS 2026 results are coming soon
Now, the review process at NeurIPS is undergoing a noticeable adjustment.
NeurIPS 2026 requires authors to select one of five contribution types that best fits their paper when submitting: General, Theory, Use-Inspired, Concept & Feasibility, or Negative Results.
Without a doubt, Wang Hong's 2019 paper falls into the Theory category.
According to the latest review guidelines for NeurIPS 2026, theoretical papers are first evaluated for mathematical rigor and correctness. Proofs, lemmas, and overall logic must be sound, so theoretical papers should not be overlooked due to the absence of experiments.
Meanwhile, NeurIPS 2026 explicitly states that theoretical contributions can stand on their own, and the purpose of designing new algorithms is not necessarily to outperform the latest application models or SOTA on the largest datasets.
And this is almost an exact description of Wang Hong’s paper.
They did not propose a neural network architecture in today’s sense or train models with massive parameters; instead, they introduced interpolation theorems from harmonic analysis into low-rank approximation to address the bounds of approximation algorithms.
Even within the 2026 review framework, it remains a highly standard NeurIPS theoretical paper.
It also implies that NeurIPS is not merely a platform for launching neural network models; new insights into existing methods, discovery of novel properties, and the establishment of tighter theoretical bounds are equally valuable original contributions.
As for the boundary between mathematics and AI, it has never been as clear as imagined.
Fields Medalists can publish at NeurIPS; mathematical language can also help AI find its true general solution.
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
Twitter: https://twitter.com/BitpushNewsCN
BitPush Telegram community: https://t.me/BitPushCommunity
BitPush TG subscription: https://t.me/bitpush