At the top floor of Shanghai Center Tower, Mozi's trading room resembled the bridge of a spacecraft, suspended above the city's neon lights. The massive curved screen wall no longer displayed waterfall-like streams of market data; instead, it showed countless winding and twisting, colorful lines and complex abstract geometric patterns. The air carried an atmosphere different from the usual tension of battle—more like a scientist's focused contemplation in a late-night laboratory facing unknown phenomena.
Mozi leaned back in his ergonomic chair, fingertips unconsciously tapping the armrests. His gaze penetrated the screen, seeming to land somewhere far more distant. The video of Yue'er's speech at the Fields Medal awards ceremony had been replayed countless times by him, especially the parts about "Stringlight Code" and "mathematical invariants." Those once overly abstract, almost ethereal mathematical concepts now circled like ghosts in his mind, producing strange resonances with the chaotic landscape of financial markets.
His "Adaptive Dual-Core Model"—the fusion of an oscillation model and a trend model—had achieved enormous success over the past few years. Gradient descent algorithms searched for tiny profit depressions in the market's noise swamp, while relative strength algorithms rode the waves of trend formation. The model switching logic grew increasingly refined, like an experienced helmsman keenly sensing shifts in wind direction.
But Mozi knew deeply that this was far from the endpoint. The model still failed—at nodes of market structural transformation, in the shadows where "black swans" swept past—it could appear slow-witted, even foolish. The root of the problem lay in that, whether the oscillation model or trend model, both were merely fitting and switching at the "phenomenon" level; they couldn't comprehend fundamental changes in the market's underlying "dynamical system." Like a doctor who only knows to prescribe medicine based on fever or cough, yet cannot determine whether the patient has a cold or pneumonia—their pathological mechanisms are entirely different.
The "topological invariant" Yue'er mentioned struck like lightning piercing darkness. In the mathematical world she described, those seemingly ever-changing complex structures often harbored some deep-seated properties that didn't change with continuous deformation—like the number of "holes." A coffee cup and a donut were equivalent in the eyes of a topologist, because both had only one "hole." This idea of grasping essence while ignoring details made Mozi's heart pound.
Did financial markets also possess such "topological invariants"? Was there some deep, intrinsic structure determining market operating modes that could be quantified and identified? If he could construct a model that no longer merely focused on surface features like price and volume, but could directly perceive the "essence" of the market state, and judge its inherent "complexity level", then model selection would no longer be based on probabilistic inference from historical data, but on profound understanding of the current market's "nature."
This thought excited him to a slight tremble. He would introduce Yue'er's mathematical ideas—those treasures from the halls of pure reason—into his capital battlefield filled with desire and gunpowder smoke. He would build a **meta-model**—a model about models.
**Meta-learning**, or "learning to learn," was precisely the framework to realize this ambition. Traditional machine learning models, whether oscillation strategies or trend strategies, were fixed mapping functions trained through vast amounts of data for given tasks (market states). The goal of meta-learning was to endow models with the ability to rapidly adapt and switch between different tasks. What it learned wasn't specific prediction outcomes, but the capability of "how to choose or adjust the best prediction strategy based on new environments."
The core task of the meta-model Mozi envisioned was to act as a "market state diagnostic expert." It needed to continuously monitor massive, multidimensional high-frequency data streams—not merely price and volume, but also order book depth, market microstructure, news sentiment analysis, cross-asset correlations, even macro event flows—and extract from these complex information flows features capable of characterizing the market's "intrinsic structure."
These features would no longer be simple technical indicators. He needed to introduce more complex mathematical tools. For example, he attempted to compute the **Hölder exponent** of market data across different time scales, used to characterize market fluctuation's "roughness" or "memory characteristics." Markets in smooth trend versus violent volatility exhibited significantly different Hölder indices in their fluctuation paths. He constructed analysis based on **random matrix theory** using correlation matrices, to monitor whether market participant behavior tended toward consistency (leading to high correlation, system fragility) or differentiation and independence (low correlation, system robustness). He even borrowed **complex network** theory from physics, treating different financial assets as nodes and their dynamic correlations as edges, building and analyzing this financial ecological network's topological properties in real-time—for instance, whether the network's "clustering coefficient" and "average path length" hinted at accumulation of some systemic risk.
All these higher-order features aimed to capture that elusive "market state." Mozi roughly divided it into two ideal types: one was the "**simple predictable**" state, analogous to the **P problems** Yue'er studied (existence of efficient deterministic algorithms). In this state, the market might be in a strong trend or stable oscillation, driving factors relatively singular, noise levels low; his traditional oscillation or trend sub-models could better capture patterns. The meta-model's task was to confidently activate the corresponding sub-model and allocate higher capital weight.
The other was the "**complex requiring exploration**" state, analogous to **NP problems** (verification easy but finding solutions possibly difficult). In this state, the market might be on the eve of a paradigm shift, or pulled by multiple contradictory factors, manifesting as high noise, low correlation, pronounced nonlinear dynamical characteristics. Traditional single models easily failed. Here, the meta-model's task wasn't simply switching to a "complex market model," but needed to initiate an entirely new coping mechanism—an **exploration mode**.
In exploration mode, the meta-model might simultaneously run multiple different, even mutually contradictory weak prediction models (similar to ensemble learning, but more dynamic), granting each model small funds for "live testing," dynamically adjusting weights based on their short-term performance, rapid trial and error, searching for potentially effective "temporary patterns" in the current complex environment. It might also actively reduce trading frequency and position size, shift to higher-frequency statistical arbitrage, capturing temporary pricing deviations in market microstructure. Even, it would activate "reinforcement learning" modules, in real-time interaction with the environment, through rewards (profits) and penalties (losses) to learn and adjust strategies, no longer relying on any predefined model structure.
This undoubtedly was a project so massive it bordered on madness. It demanded the model not only possess powerful computational capabilities and massive amounts of data, but also have a kind of "self-awareness," able to evaluate its own cognitive boundaries and uncertainties in different environments. This already touched the realm of **artificial intelligence agents**.
Mozi immersed himself in this grand construction, often forgetting the passage of time. In the late-night trading room, only the low operating sound of server clusters and his tapping keyboard, the rustling sound of writing formulas remained. On the screen, various mathematical symbols, algorithm flowcharts, and backtesting system performance curves intertwined.
In this process, his connection with Yue'er reached a new dimension. Their video calls no longer were merely emotional solace and daily sharing, but more intense and in-depth academic discussions.
"Mozi, the idea you mentioned about using eigenvalue distribution of correlation matrices to identify market states is quite interesting," Yue'er on the screen said, her background a study piled with books and scratch paper, eyes bright. "This reminds me of the separation of 'signal' from 'noise' in random matrix theory. When the largest few eigenvalues significantly deviate from the predicted distribution of random matrices, perhaps that signals the market entering a relatively 'simple' state driven by a few dominant factors."
"Exactly!" Mozi sat up sharply, as if discovering a new continent. "And when the eigenvalue distribution more closely resembles random matrix predictions, it means no obvious dominant factors exist; the market is in a 'chaotic,' high-entropy state. This likely corresponds to the 'complex requiring exploration' NP-like state you mentioned!"
"You could try computing the **approximate entropy** or **sample entropy** of the market data series," Yue'er continued suggesting, fingers swiftly gliding on the virtual screen, seemingly deducing something. "These nonlinear dynamics indicators can quantify time series complexity and unpredictability. Low values might imply strong regularity (P-like); high values mean high complexity (NP-like)."
"Sample entropy... I need to add it to the feature engineering," Mozi rapidly recorded, an inexpressible excitement welling within him. Yue'er's mathematical intuition always pointed him toward a more essential direction when he got mired in technical details. Her theories were no longer abstract thinking suspended in the clouds, but could be transformed into lines of code, integrated into his meta-model, to interpret that unpredictable market language.
This intellectual symbiosis and resonance brought Mozi a sense of satisfaction that even surpassed the thrill of huge profits. He felt he wasn't merely utilizing Yue'er's wisdom but participating in a great, cross-disciplinary boundary expedition. His financial battlefield became the first, and most challenging, "application scenario" of her mathematical theories. They were jointly verifying whether those deep laws governing the mathematical universe also governed the financial world constructed from human group behavior.
Of course, the construction process was by no means smooth sailing. The meta-model initially performed like a toddler learning to walk, sometimes overly confident, blindly switching models in complex markets causing series of losses; sometimes overly cautious, hesitating to place large bets when trends were clear. Feature engineering choices were like groping in a maze—which mathematical tools could truly capture the market's "topological essence"? Hölder exponent, sample entropy, network topology indicators, eigenvalue distribution... thousands upon thousands of feature dimensions brought severe dimensionality disaster and overfitting risks.
Mozi had to introduce more complex **feature selection** and **dimensionality reduction techniques**, for example, feature importance assessment based on **random forests**, and nonlinear dimensionality reduction methods like **autoencoders**, attempting to distill from the massive features the most core, most robust "state indicators."
The model's training approach was also crucial. He adopted the framework of **meta reinforcement learning**. Treating market environments as a series of different "tasks" (different time periods, different market regimes), the meta-model (or agent) needed, within each task, to maximize cumulative returns (rewards) by choosing and executing different sub-models (actions). Through repeated training on vast historical data (covering various market states), the meta-model gradually learned "experience," knowing what kind of model strategy to tend toward under what market characteristic patterns.
This was an extremely time-consuming process; demands on computational power reached unprecedented heights. Mozi mobilized part of "Stringlight Cloud Brain" resources, constructing a specialized financial simulation environment, letting thousands of meta-model "copies" explore, trial and error, and learn in parallel within it.
In countless cycles of debugging, failure, and re-optimization, Mozi occasionally felt a profound awe. He was creating no longer a passively executing instructions tool, but a complex system with preliminary "cognitive" capabilities. It began displaying some astonishing behaviors.
Once, without any preset rules, the meta-model, on a calm trading day, suddenly significantly reduced all trend-type sub-model weights and initiated an exploration mode for high-frequency market-making strategies. At the time, Mozi's traditional risk control systems didn't issue any alarms. Yet, just half an hour later, rumors of a large hedge fund's collapse began circulating in the market, triggering brief but extremely violent liquidity dry-up and price flash crash. Because the meta-model had already switched to focusing on capturing micro-pricing deviations mode, it instead gained small profits in this unexpected volatility, while traditional trend models generally suffered significant drawdowns.
This incident made Mozi realize that his meta-model might truly have captured some "stress" in the market's deep structure that traditional indicators couldn't detect. It was like a precision instrument capable of sensing subtle movements deep within strata, emitting its unique "warning" before an earthquake.
Another time, the meta-model, for two whole weeks, consistently gave judgments of "highly complex, unpredictable" state and consistently maintained extremely low risk exposure and exploratory trading. During that period, the market looked calm and tranquil, even slightly rising. But Mozi chose to trust his model, maintaining extremely low positions. A week later, the Fed's interest rate meeting released extremely chaotic and contradictory signals, plunging the market into a month of violent fluctuations and disorderly volatility; many strategies relying on historical data suffered heavy losses. Mozi successfully avoided this storm.
These successful cases didn't make Mozi arrogant; instead, they made him more cautious. He knew deeply that the model's "intelligence" was still built on data and algorithms; it might capture some new patterns, but could also be merely overfitting historical coincidences. The true test was always the unknown future.
He often thought of Yue'er's contemplation on "P versus NP." Perhaps, financial markets, under most circumstances, were precisely that "complex requiring exploration" NP world; the so-called "simple predictable" P states were merely brief and precious exceptions. His meta-model, rather than seeking a "holy grail" that could dominate everything, was learning how to survive and explore in this complex NP world more gracefully, more adaptively—knowing when efficient solutions existed, when complexity and uncertainty had to be acknowledged, and adopting more flexible, more robust coping strategies.
Late at night, Mozi's meta-model was undergoing a new round of iterative training in the background. On the screen, cluster centers representing different market states slowly moved in the dimensionality-reduced feature space, like celestial bodies running in the cosmos. He stood up, walking to the huge floor-to-ceiling window, looking down at the sleepless financial city below. Lights glittered; behind each light were countless rational calculations, irrational impulses, greed and fear intertwined, together weaving this extremely complex financial web.
His model was attempting to understand the deep structure of this web. And supporting him in completing this grand conception, were not only cutting-edge computing power and algorithms, but also mathematical thought from another domain of wisdom, shining like the North Star guiding direction.
He picked up his private terminal, sending a brief message to Yue'er: "Sample entropy features performed excellently in identifying market phase transition points. Your mathematics is shining in my world."
Soon, a reply came—only a simple smiling emoji, yet it made Mozi feel an unprecedented, spiritual richness and connection. The codes of capital and the stringlight of mathematics, in this moment, completed yet another profound fusion.