New Fields Medalist Hong Wang Also Dabbled in AI?

Original title: "Fields Medalist Hong Wang Also Published at NeurIPS"
Original source: Quantum Bit

Huh? Newly minted Fields Medalist Hong Wang also dabbled in AI?

With NeurIPS 2026 results just around the corner, some netizens have dug up that Professor Hong Wang published a paper at NeurIPS 2019.

And it’s not just a name on the paper; he was a genuine co-author.

So the question arises: why would a top mathematician focused purely on numerical theory publish a paper at a leading AI conference?

After reading through it, our conclusion is that this is a prime example of mathematical theory + machine learning.

Interestingly, among the nearly 40 papers and preprints listed on Hong Wang's personal homepage, almost every one has a complete link.

Except for this one, which is an exception.

Hong Wang's Cross-Disciplinary 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 can usually be organized into a matrix, but these matrices are often very large, making direct storage and processing extremely costly.

Low-rank approximation uses a structurally simpler, lower-rank matrix to accurately reconstruct the original matrix as much as possible.

A commonly used approximation algorithm is Column Subset Selection (CSS).

The idea is quite intuitive.

When faced with a data matrix containing a large number of columns, instead of directly calculating a brand new low-rank matrix, you select a few representative columns from the original matrix and 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 ordinary matrix decomposition, and they also reduce storage and computational costs, making them suitable for handling large-scale data.

Previous research has shown that for general low-rank approximation, the approximation ratio of the CSS algorithm is about O(k+1).

Here, k refers to the rank of the target matrix; the larger k is, the greater the theoretically allowed worst-case error.

The work of Hong Wang and others has pushed this boundary further:

· 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 boundary is significantly tighter, allowing the algorithm to be strictly constrained, with the worst-case result only slightly worse than the optimal solution.

Additionally, for the case of p≥2, the paper also constructs a corresponding lower bound, proving that its result is precise to constant 1.

In other words, this paper provides an almost capped theoretical answer.

The most critical part of this paper, which also 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 a set of algorithms holds for all p values, one needs to conduct complex analysis for different p values separately.

For certain endpoint cases, such as p=1, p=2, and p=∞, it is relatively easy 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 proves the three special cases of p=1, 2, and ∞, and then uses interpolation theory to derive the approximation bounds across the entire range.

In fact, this tool is a classic method in harmonic analysis and operator theory, but it is not the most commonly used technique among theoretical computer science researchers at that time.

The reviewers at NeurIPS that year also noticed this.

The reviewers ultimately recognized the main technical innovation of this paper as introducing the Riesz-Thorin theorem into the field of computer science, and the final Meta Review rated it as a paper with solid arguments.

Looking at it today, this paper also provides a very typical interdisciplinary case, suggesting that challenges in machine learning may find breakthroughs in pure mathematics.

NeurIPS 2026 Results Are Coming Soon

Fast forward to now, the NeurIPS review mechanism is undergoing a noticeable adjustment.

NeurIPS 2026 requires authors to select the most fitting contribution type from five categories when submitting: General, Theory, Use-Inspired, Concept & Feasibility, and Negative Results.

Without a doubt, Hong Wang's 2019 paper falls under the Theory category.

According to the latest NeurIPS 2026 review guidelines, theoretical papers first examine mathematical rigor and correctness. Proofs, lemmas, and overall logic must hold, so theoretical papers should not be overlooked due to a lack of experiments.

At the same time, NeurIPS 2026 clearly states that theoretical contributions can stand independently, and the purpose of designing new algorithms does not necessarily have to be to outperform the latest application models or achieve SOTA on the largest datasets.

In terms of originality, new proof tools can also be introduced from other disciplines, or existing tools can be innovatively synthesized.

And this almost perfectly describes Hong Wang's paper.

They did not propose a neural network architecture in today's sense, nor did they train a model with a massive number of parameters; instead, they introduced the interpolation theorem from harmonic analysis into low-rank approximation, addressing the boundary issues of approximation algorithms.

Within the 2026 review framework, it remains a very standard NeurIPS theoretical paper.

It also indicates that NeurIPS is not merely a neural network model showcase; providing new understandings of existing methods, discovering new properties, and establishing tighter theoretical boundaries are equally valuable original contributions.

As for the boundary between mathematics and AI, it has never been as clear-cut as imagined.

Fields Medalists can publish at NeurIPS, and mathematical language can indeed find the 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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