Qiu Cheng-Tung's team enters quantitative trading! Can YAND trigger a "paradigm shift" in the investment world?

By: Random Thoughts on Transmission and Practice Records

Can the mathematical weapon of a Fields Medal winner change the core algorithms of the trillion-dollar asset management market?

1 Introduction

In the spring of 2026, a piece of news quietly exploded within the quantitative investment community—Qiu Chengtong (Shing-Tung Yau), a mathematical world authority and a Fields Medal laureate, officially entered the quantitative field. A new optimization method, YAND (Yau‘s Affine-Normal Descent, Qiu’s Affine-Normal Descent method), jointly developed by Qiu Chengtong and his collaborators, has been dubbed by some insiders as a “dimensionality-reduction strike,” and is even believed to potentially break a technical paradigm that has lasted nearly 70 years in quantitative investment.

Why would a world-class mathematician who has long immersed himself in pure mathematical theories such as differential geometry and the Calabi conjecture suddenly intersect with stock investing? What exactly has YAND done to cause such a stir? Today, we will explore this question in depth through a long-form article.

2 Event Background: The High-Dimensional Disaster of Building Investment Portfolios

First, let’s go back to the very beginning. In the world of quantitative investing, the vast majority of strategy models are based on the “mean-variance” framework. Modern Portfolio Theory proposed by Harry Markowitz in 1952 has long held mainstream dominance. In simple terms, it treats asset returns as “mean,” and risk (volatility) as “variance,” with the main goal of maximizing returns under a fixed risk level, or minimizing risk under a fixed return level.

This theory has indeed remained a foundation for a long time within the industry, but it has a fatal shortcoming: it focuses only on returns and price fluctuations (first moment and second moment), while ignoring the widely observed “spikes and fat tails” phenomenon in financial markets. In plain language, real-world stock price movements often involve extreme risks and black swan events (third-moment skewness and fourth-moment kurtosis). The mean-variance model often responds sluggishly to sudden crashes or surges, as seen in the 2008 financial crisis and the 2015 A-share stock market crash, when many investment strategies failed collectively.

This is also a long-standing pain point in the quantitative industry: theoretically, if you want to capture extreme risk more accurately, you need to introduce “higher moments” (skewness and kurtosis). But in real practice, once you face a massive scale of thousands of stocks, traditional computation encounters the “curse of dimensionality.” The calculations require extremely large high-order tensors (co-skewness and co-kurtosis), with computational requirements increasing geometrically. Ordinary institutions—even large computers—cannot efficiently complete these calculations in a short time. The emergence of YAND is precisely aimed at solving this unresolved pain point that has persisted for 70 years.

3 Paper Source

The latest high-quality academic research released by Qiu Chengtong’s team points toward optimization of quantitative investment portfolios.

On April 28, 2026, Qiu Chengtong’s team published a paper titled “Yau‘s Affine-Normal Descent for Large-Scale Unrestricted Higher-Moment Portfolio Optimization.” The paper number is arXiv:2604.25378, and it is categorized under finance quantification (q-fin). There are four authors: Ya-Juan Wang, Yi-Shuai Niu, Artan Sheshmani, and the most heavyweight Shing-Tung Yau (Qiu Chengtong) himself. This is the most core foundation for studying this event. Meanwhile, Qiu Chengtong and his collaborators have also in effect released a framework paper for YAND, titled “Yau’s Affine Normal Descent： Algorithmic Framework and Convergence Analysis,” with the number arXiv：2603.28448. This paper is not limited to investment scenarios; from the perspective of pure mathematics and algorithmic optimization, it derives and analyzes various properties of YAND. In terms of peer-reviewed media, academic indexing platforms at various universities, such as Semantic Scholar, have also included another related paper by Qiu Chengtong’s team—“Affine Normal Directions via Log-Determinant Geometry： Scalable Computation under Sparse Polynomial Structure”—and provided Corpus ID: 287023415.

So what is the real secret behind YAND?

4 The Technical Essence of YAND: The Power of Geometry

To understand YAND deeply, we may need to temporarily put aside stock-market terminology and step into a concept at the pure-mathematics level—a ffine-normal direction. I will do my best to explain this concept, which is extremely high-threshold, in a more accessible way. Let’s start with a vivid analogy:

You are climbing in a forest, with thick fog everywhere and you cannot see the summit. You want to step out the fastest route. In the past, traditional methods (such as steepest descent) only care about “the direction with the steepest slope right in front,” and dash forward blindly. But when encountering an irregular-shaped terrain, or a distorted mountain body (mathematically called a “pathological condition number”), this approach often makes you wander far off and be inefficient. YAND, by contrast, is like moving directly toward the mountain’s “affine-normal” direction while keeping the volume unchanged within the correct geometric framework—so climbing is no longer hindered by irregular terrain.

This is exactly YAND’s most mathematically worth-noting advantage: the affine-normal direction has an important geometric property—its invariance under volume-preserving affine transformations. In other words, no matter how you stretch or squeeze the coordinate system, the YAND algorithm will not lose its sense of direction; it can always maintain a stable approximation to the optimal solution. And precisely because of this global geometric property, YAND miraculously sidesteps the ultimate obstacle of “high-order moment computation is difficult.” The paper points out: “The algorithm follows the affine-normal direction of the current level set, while directly handling the return matrix. This method avoids explicit high-order tensors and uses quartic structure for precise sample prediction, derivative evaluation, and exact line search.” What used to require “simultaneously handling tens of thousands of dimensional cubic-shaped third-order tensors” is simplified into “directly and efficiently solving low-order, manageable matrices.”

5 Empirical Backtesting: Numbers Don’t Lie

For all investors and quantitative practitioners, no matter how beautiful the theory looks, real economic value matters more. In this regard, the YAND team provides very specific backtesting data. The paper uses a very strong experimental environment to support it:

The sample covers 5,440 A-share stocks, and the data uses 5-minute high-frequency K-line panels.

This coverage is astonishing. From an investment-industry perspective, the total number of stocks in the real A-share market is just over 5,000. The YAND paper essentially conducts a comprehensive portfolio optimization for the entire A-share market as a whole—something many previous algorithms have never even dared to attempt in theoretical modeling. The backtest conclusions are clear:

This method can directly conduct a complete whole-market comparison with the exact mean-variance investment portfolio, and in the baseline period, it shows that the incremental value of higher moments is strongest under moderate return targets.

Translated into investment language, this means YAND not only can produce optimal solutions for the whole market, but more importantly, traditional models often fail to realize the advantage of higher moments in low-risk, conservative asset pools (for example, large-cap stocks). Under moderate return target conditions, however, YAND instead excavates the potential for excess returns brought by skewness and kurtosis.

6 Industry Shock: A Paradigm Revolution or Media Overhyping?

Within 24 hours of the arXiv paper going live across the ocean, a large number of quantitative practitioners and enthusiasts began discussing the true significance of YAND. Some even shouted that “Qiu Chengtong’s team overturned the 70-year-old model.” But behind the cheering, there has also been rational reflection and even criticism. A highly upvoted Zhihu article titled “There are no higher moments in YAND-MVSK, just like there’s no memory in Engram” raises three strong doubts:

Stability of higher moments: “Mean-variance optimization has been jokingly called the error maximizer in the industry. Yet this paper still wants to fit third and fourth moments? … In the peaks you compute from historical data, 90% are random noise.”

Signal and holding period mismatch: “The paper uses 5-minute high-frequency data to capture price skewness, yet uses such highly sensitive features in backtests where you do not rebalance for one and a half years. It’s like using radar to detect a pit 10 meters ahead, then closing your eyes and stepping on the accelerator to drive 100 kilometers per hour.”

Benchmark problems in the empirical comparison: Some voices point out that what YAND beats is only the “exact mean-variance (Exact MV)” benchmark, but that benchmark itself does not represent a strong baseline in the industry. In practice, the industry’s core models—such as Bridgewater risk parity (Risk Parity)—are the real tough nuts.

At least for now, all of this is still far from large-scale deployment in real-world trading. YAND’s method was uploaded to arXiv only in April 2026. Although the surface-level academic empirical results look promising, large-scale live quantitative trading still needs to address issues such as transaction costs, liquidity impact, and robustness under extreme market regime shifts. At present, truly active trading teams in the industry may remain cautiously watching rather than immediately replacing all core code.

7 The Crossroads of Mathematics and Asset Management

Leaving the controversy aside, this event carries a more far-reaching meaning—global top mathematical minds are officially moving into the core algorithm field of financial asset management. The academic identity of Qiu Chengtong himself determines the special significance of this event. Born in 1949 in Shantou, Guangdong, and now a professor in the Department of Mathematics at Harvard University, Qiu Chengtong is not only a member of the U.S. National Academy of Sciences, but also the 1982 Fields Medal laureate. He completed a series of pioneering contributions in differential geometry, such as the proof of the Calabi conjecture and the positive mass conjecture.

Such a scientific giant could, in theory, spend his entire life within the realm of abstract pure mathematics. But in recent decades, he has increasingly emphasized the application of mathematics in other fields. He has stated publicly: “One of the amazing applications of the mathematics discipline is to take pure mathematical theories—such as geometric analysis—and use them in the core quantitative trading of modern financial markets.” This shows that Qiu Chengtong’s personal entry into the field is not a sudden cross-industry performance; rather, it is an exploration by a top-level scientist to push new mathematical tools into the real world.

Another key point noticed by the author is that the second and third authors of the YAND paper also represent a new force in applied mathematics in China. For example, Artan Sheshmani is a professor at Harvard University’s CMSA, as well as a professor and chief science officer at the Beijing Yanqi Lake Institute of Applied Mathematics. His research directions include algebraic geometry, string theory, and enumerative geometry. Yi-Shuai Niu (Niu Yishuai) is a deputy professor at the Beijing Yanqi Lake Institute of Applied Mathematics (BIMSA), specializing in optimization, high-performance computing, and machine learning. Their involvement implies that applied mathematics has achieved a seamless connection with the needs of fund investing.

8 Future Revelation

So what impacts might YAND bring to the future of the quantitative investment industry? The author tends to answer this question with a steady analytical framework: calm in the short term, far-reaching in the long term. In the short term, YAND cannot overturn an entire hedge fund or public quant team overnight. This is not only because of “high theoretical barriers.” The success of quantitative strategies depends on three things: data acquisition capability, computation accuracy, and cost/risk control. YAND is only one part of this. In addition, the paper and some technical media admit that YAND’s computational optimization is more reflected in large-scale computations involving higher moments. But in real strategy scenarios where you must run thousands of product iterations within only a few minutes after the close of each trading day, whether it can continuously and stably beat the existing core libraries in the secondary industry still needs to be independently verified by third parties.

But in the long run, YAND opens the door to a new generation of optimization paradigms. Because the robustness of the affine-normal direction—under constraints such as extremely small-valued local minima irrelevant saddle-like fixed points and pathological transformations—is a core technology that the mathematical community had never previously explored systematically and transplanted into investment fields. Several research institutions have already seen the potential application space for YAND—for example, risk control and tail hedging in high-frequency trading, improvements in stability for large-scale index-enhanced funds when rotating across industries, and effective allocation for multi-asset macro hedging under non-normal distributions.

Also, the author believes that the significance of YAND may not be limited to a single “quant track.” The way of thinking demonstrated by the paper—“applying pure differential geometry to optimal control problems”—can be extended to multiple disciplines such as machine learning, autonomous driving decision systems, and bioinformatics, thereby triggering broader cross-disciplinary innovations.

9 Rationally View This “Dimensionality-Reduction Strike” Attempting to Solve High-Dimensional Problems

Perhaps we do not need to view Qiu Chengtong’s team’s results through polarized lenses of either “total worship” or “total denial.” A more rational attitude is: YAND is an elegant spear bestowed by the mathematics community to quantitative finance, but quantitative trading is ultimately a multi-dimensional survival war. Pure academic empirical findings are indeed astonishing, but real live markets contain countless interference factors—transaction costs, market impact costs, slippage, market microstructure, and dark-pool liquidity, among many others. Moreover, backtest returns do not equal actual investment returns. This is also why many professionals have already stated clearly: “The YAND method was only uploaded to arXiv in April 2026. Although the paper’s empirical results are very good, large-scale live validation and long-term robustness testing still require time. After all, the core of the quantitative industry is execution capability.”

Another useful reference is the typical example of the integration of U.S. mathematics and finance: James Simons. Simons himself is also an outstanding mathematician, but after he switched fields and founded Renaissance Technologies, he used quantitative strategies to generate profits for 30 consecutive years, and he is often told as a classic allegory of “turning mathematics into money.” So whether Qiu Chengtong’s entry into quantitative finance is drama or epic may only be concluded five or ten years from now. However, one thing is undeniable: every time a top mind crosses into a new field, it advances the boundary of human knowledge by a little, often imperceptibly.

10 Reference Information Summary

The main references and sources are listed below. Readers who are interested can look them up for expansion:

Cited Paper 1 (Quantitative Investment Direction):

Title: Yau’s Affine-Normal Descent for Large-Scale Unrestricted Higher-Moment Portfolio Optimization

Authors: Ya-Juan Wang, Yi-Shuai Niu, Artan Sheshmani, Shing-Tung Yau

Number: arXiv:2604.25378 (q-fin, published 2026-04-28)

DOI/EPRINT: https：//arxiv.org/abs/2604.25378

Cited Paper 2 (Geometric Optimization Framework Direction):

Title: Yau’s Affine Normal Descent： Algorithmic Framework and Convergence Analysis

Authors: Yi-Shuai Niu, Artan Sheshmani, Shing-Tung Yau

Number: arXiv：2603.28448

Source: arxiv.org/abs/2603.28448

Other related papers:

Semantic Scholar includes “Affine Normal Directions via Log-Determinant Geometry： Scalable Computation under Sparse Polynomial Structure,” by Yi-Shuai Niu, Artan Sheshmani, S.-T Yau, Corpus ID: 287023415, 2026.

Chinese background and interpretation:

Zhihu column “Qiu Chengtong enters the field: Will traditional quant face a dimensionality-reduction strike?” 2026-04-30

Zhihu column “There are no higher moments in YAND-MVSK, just like there’s no memory in Engram,” 2026-05-01

PS: Financial markets carry risks, and investments must be made with extreme caution. The YAND method discussed in this article is currently still at the academic empirical stage and does not constitute any investment advice.