Huh? The newly crowned Fields Medalist Wang Hong has also dabbled in AI?
With NeurIPS 2026 scores about to be released, netizens have uncovered that Professor Wang Hong has published a paper at NeurIPS 2019.
And it was not just in name only; it was a genuine co-first authorship.
So, the question arises: why would a pure mathematician publish a paper at a top AI conference?
After reading through it, our conclusion is that this is the perfect example of mathematical theory + machine learning.
However, what's interesting is that among the nearly 40 papers and preprints listed on Wang Hong's personal webpage, almost every one has a full link attached.
Except for this one, which is an exception.
Wang Hong's Cross-domain Challenge in AI
This paper explores 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 often very large, with direct storage and processing costs being extremely high.
Low-rank approximation involves using a structurally simpler matrix with a lower rank to accurately reconstruct the original matrix.
The commonly used approximation algorithm nowadays is Column Subset Selection (CSS).
The concept behind it is actually quite intuitive.
Faced with a data matrix containing numerous columns, instead of directly computing an entirely new low-rank matrix, the idea is to select a representative subset of columns from the original matrix and then use 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 a regular matrix decomposition. At the same time, it can reduce storage and computational costs, making it suitable for handling large-scale data.
Prior research has shown that for a general low-rank approximation, the approximation ratio bound of the CSS algorithm is approximately O(k+1).
Here, k refers to the rank of the target matrix, where a larger k allows for a greater worst-case error theoretically.
Wang Hong et al.'s work further advances 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 new bound is significantly tighter, as the algorithm can be strictly constrained, and the worst-case result will only deviate slightly from the optimal solution.
Additionally, for the case of p≥2, the paper also constructs the corresponding lower bound, proving their results are exact within a constant factor of 1.
In other words, this paper provides an almost optimal theoretical answer.
The most crucial part of this paper, which also best showcases Wang Hong's mathematical background, is their use of the classic tool from harmonic analysis, Riesz–Thorin Interpolation Theorem.
Usually, to prove a set of algorithms holds for all p values, complex analyses need to be conducted for different p values.
For certain endpoint cases, such as p=1, p=2, and p=∞, they are relatively easier to handle.
Then, after mastering these endpoint results, the Riesz–Thorin Interpolation Theorem can interpolate the conclusions to all intermediate p values.
Specifically, the paper first proves the three special cases of p=1, 2, ∞, then uses interpolation theory to derive the entire range of approximation bounds.
Indeed, this tool belongs to the classic methods in harmonic analysis and operator theory, yet it is not the most commonly used technique by theoretical computer science researchers at that time.
The NeurIPS reviewers that year also took note of this.
The reviewers ultimately recognized the key technical innovation of this paper, which is introducing the Riesz–Thorin Theorem to the field of computing. The final Meta Review evaluated it as a thoroughly argued paper.
Looking back today, this paper actually provides a very typical interdisciplinary case. The challenge of machine learning may find a breakthrough in pure mathematics.
NeurIPS 2026 Scores Coming Soon
Fast forward to the present, the NeurIPS review mechanism is undergoing a significant adjustment.
NeurIPS 2026 requires authors to choose one of five contribution types that best aligns with the paper's focus when submitting: General, Theory, Use-Inspired, Concept & Feasibility, and Negative Results.
Undoubtedly, Wang Hong's 2019 paper falls under the Theory category.
According to the latest NeurIPS 2026 review guidelines, theoretical papers are first evaluated for mathematical rigor and correctness. Proofs, lemmas, and overall logic must hold, so theoretical papers do not need to be overlooked for lack of experiments.
At the same time, NeurIPS 2026 explicitly points out that theoretical contributions can stand independently, and the purpose of designing new algorithms is not necessarily to outperform the latest application models or SOTA on the largest datasets.
In terms of originality, one can also introduce new proof tools from other disciplines or innovatively synthesize existing tools.
And this is almost a precise description of Wang Hong's paper.
They did not propose a neural network architecture in today's sense, nor did they train models with a huge number of parameters; instead, they introduced the interpolation theorem from harmonic analysis into low-rank approximation to address the boundary problem of approximation algorithms.
In the 2026 review framework, it remains a very standard NeurIPS theoretical paper.
It also highlights that NeurIPS is not synonymous with a neural network model release conference. Providing new understandings of existing methods, discovering new properties, and establishing tighter theoretical bounds are equally valuable original contributions.
As for the boundary between mathematics and AI, it has never been as clear-cut as imagined.
Fields Medalist Can Publish at NeurIPS, Math Language Can Also Find AI's True Universal Solution.
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