A Deep Dive: Deconstructing and Reconstructing LLM Reasoning: A Theoretical Framework for Advanced Quantitative Investment Strategies

Reference List Stanford Online. (2025, Apr 29). Stanford CS25: V5 | Large Language Model Reasoning, Denny Zhou of Google DeepMind [Video]. YouTube. https://www.youtube.com/watch?v=ebnX5Ur1hBk

Author’s Note:

This article presents a detailed analysis and interpretation of the views expressed by Denny Zhou during a Stanford CS25 lecture published by Stanford Online on YouTube. The analysis herein is based entirely on the publicly available content of that video and is intended for academic, research, and commentary purposes. All interpretations of Dr. Zhou’s statements—and any related quantitative or theoretical analyses—are the author’s own and do not necessarily reflect the views of Stanford University, Stanford Online, Google DeepMind, or YouTube. Readers are strongly encouraged to watch the original lecture to form their own conclusions.

This paper delves into the computational foundations and optimization pathways of Large Language Model (LLM) reasoning capabilities, as well as their potential applications and challenges in advanced quantitative investment strategies—specifically, mean reversion pairs trading (Relative Value Strategy) and momentum trend following (Momentum Trend Following Strategy). We critically analyze Professor Denny Zhou's views on LLM reasoning and attempt to construct a theoretical framework that transcends traditional supervised learning paradigms. The paper first formalizes LLM reasoning as a computable process, leveraging recent advances in circuit complexity theory and mechanistic interpretability to reveal how "Chain of Thought" (CoT) expands the model's computational boundaries. Subsequently, we argue for the limitations of imitating human thought in the financial domain and propose a self-improvement framework based on Direct Preference Optimization (DPO) and risk-sensitive Reinforcement Learning (RL), which utilizes an internal backtesting engine as an objective validator. Furthermore, we explore advanced techniques for enhancing decision robustness through Self-Consistency and Tree-of-Thought, as well as achieving knowledge-intensive reasoning by integrating with Financial Knowledge Graphs (KG-RAG). Finally, we propose a paradigm shift from correlation to causal inference and detail a practical system architecture designed to mitigate backtest overfitting risk (using techniques like DSR and PBO), enable safe deployment, and facilitate scalable oversight. This research aims to lay the theoretical groundwork for developing LLM-driven investment agents capable of discovering non-intuitive Alpha sources and possessing autonomous learning and risk management capabilities.

Part One: The Algorithmic Basis of Thought: Theoretical Exploration of LLM Reasoning

This section aims to establish a solid computational and theoretical foundation for the reasoning capabilities of Large Language Models (LLMs). We will move beyond the popular notion of LLMs as simple pattern matchers, instead formally understanding them as computational systems and rooting their reasoning abilities in the intersecting principles of circuit complexity, learning theory, and cognitive science.

1.1 Reasoning as a Computable Process: From Boolean Circuits to Financial Sequential Computation

According to Professor Denny Zhou, the reasoning process of an LLM can be formally defined as the generation of a series of intermediate computational steps (in the form of tokens), which together constitute a "Chain of Thought" (CoT). This process not only enhances the interpretability of the results but, more fundamentally, expands the model's computational boundaries. Recent research in theoretical computer science provides a solid mathematical basis for this observation, with a key theorem stating that a constant-depth Transformer model, by generating O(T) intermediate CoT tokens, can simulate any Boolean circuit of size T.

Boolean circuits are the fundamental model in computation theory used to describe logical operations. Therefore, the aforementioned theorem builds a direct bridge between LLMs and general-purpose computation. It implies that the length of a CoT is not merely an increase in text length but a direct reflection of the amount of sequential computational resources available to the model during reasoning.

1.1.1 Computational Complexity and the Deep Structure of Financial Markets

The profound significance of this theoretical framework is that it connects the reasoning ability of LLMs with the core concepts of computational complexity theory. The Transformer architecture is inherently highly parallel. Without CoT, its computational depth is limited by the number of layers. In theory, the computational power of a constant-depth Transformer is restricted to the complexity class TC^0 (problems solvable by constant-depth, polynomial-size circuits with "majority" gates), meaning they cannot effectively solve problems that inherently require deep sequential dependencies.

The introduction of CoT cleverly bypasses this limitation. By sequentially writing intermediate results to an autoregressive "scratchpad," the model is effectively trading the time dimension for the space dimension (circuit depth). This mechanism allows a model originally limited by a shallow circuit to simulate circuits of arbitrary depth, thereby theoretically elevating its computational power to the class P (problems solvable in polynomial time).

In the field of quantitative finance, this theory has profound practical implications. The internal logic of a complex investment decision can be abstracted into a computational graph.

Take mean reversion pairs trading as an example. The core of this strategy is to test for a cointegration relationship between two or more asset price series. This usually involves a series of complex statistical tests, such as the Johansen Test. The Johansen test involves calculating the rank of a Vector Error Correction Model (VECM), which is computationally complex and involves the eigenvalue decomposition of a matrix.

The VECM model can be expressed as:

ΔY_t = ΠY_{t-1} + Σ_{i=1}^{p-1} Γ_i ΔY_{t-i} + ε_t

Where Π is the cointegration matrix. Testing for the existence of a cointegration relationship is equivalent to testing the rank r of Π.

This series of steps (data preprocessing, model estimation, rank test, threshold comparison) constitutes a complex computational graph with sequential dependencies. A depth-limited Transformer without CoT might not be able to complete such a complex calculation in a single forward pass.

However, when we guide the model to generate a CoT through a prompt, we are in fact authorizing the model to decompose this complex statistical test into a series of manageable computational steps. For example: "Step one, confirm the asset series is integrated of order one, I(1). Step two, use the Johansen test to estimate the cointegration vector and calculate the trace statistic. Step three, compare the statistic with the critical value. Step four, if a cointegration relationship exists, construct the spread series."

1.1.2 Dynamic Beta and the Sequential Simulation of Kalman Filters

Another example demonstrating the importance of sequential computation is the estimation of time-varying beta in pairs trading. To capture the evolving relationship between assets, we often need to use state-space models and perform real-time estimation with a Kalman Filter. The Kalman Filter is an inherently sequential, iterative computational process, involving two steps: Prediction and Update.

Suppose we have a simple time-varying beta model:

Observation equation: y_t = α_t + β_t x_t + ε_t

State equation: β_t = β_{t-1} + η_t

The iterative process of the Kalman filter involves complex matrix operations, such as calculating the Kalman gain K_t and updating the state covariance P_{t|t}. Through CoT, the model can decompose this iterative process: "Calculate the prior state estimate β_hat_{t|t-1}... Calculate the Kalman gain K_t}... Update the posterior estimate β_hat_{t|t} based on the new observation...". Each step can be efficiently executed within the Transformer's parallel architecture, while the entire sequence simulates the iterative nature of the Kalman filter, thereby achieving a task of high computational depth.

1.1.3 Prompt Engineering as Computational Resource Allocation

Therefore, the linear relationship between the CoT length T and the solvable problem complexity T provides us with a completely new perspective. When we ask the model to "think step by step," we are fundamentally authorizing the model to execute a more extensive computational task. This transforms Prompt Engineering from an "art" into a precise "science of computational resource allocation."

For a proprietary hedge fund, this means that the length of the reasoning chain can be dynamically adjusted according to the complexity of the task. A simple momentum signal generation (e.g., calculating and ranking the past 12 months' returns) might only require a short CoT. In contrast, a complex momentum strategy adjustment involving macroeconomic environment analysis, factor crowding assessment, and micro-market structure analysis (utilizing high-frequency data generated by our proprietary engine) would require a longer reasoning chain to ensure the model has sufficient computational power to integrate all information and arrive at a reliable conclusion.

1.2 Mechanisms of Emergent Reasoning in the Transformer Architecture

To truly harness the reasoning power of LLMs, we must open their "black box" and understand how reasoning physically occurs within the model's internal architecture. Recent research in "Mechanistic Interpretability" has begun to reveal that the model's interior is not chaotic but forms highly specialized functional "circuits."

1.2.1 Internal Circuits and Information Flow

Through causal intervention experiments, such as using Activation Patching, research has identified components that perform specific reasoning sub-tasks. For example, a "rule-locating head" is responsible for locating relevant information in the context, while an "information-moving head" is responsible for transporting key information to subsequent layers for processing.

A particularly crucial discovery is the "Induction Heads." An induction head is a specific attention pattern that can identify and continue patterns appearing in the context, in the form of [...A B... -> A B]. This is the fundamental mechanism for achieving In-context Learning (ICL).

In financial time series analysis, the capability of induction heads is vital. For instance, in a momentum trend-following strategy, market dynamics are highly non-stationary. A successful strategy must be able to quickly adapt to changes in the market regime. When we provide recent market data in a prompt, the induction heads inside the LLM can identify new patterns, such as "a rising VIX is accompanied by an increase in negative correlation with major stock indices." Through induction heads, the model can "learn" a new temporary rule in context: "In a high-VIX environment, the position size of the momentum strategy should be reduced."

1.2.2 In-Context Learning as Implicit Optimization

This micro-mechanism perfectly echoes macro learning theories. Some research suggests that CoT can be understood as the practical embodiment of an efficient ICL algorithm. This theory posits that a Transformer can, during its forward pass, implicitly perform an optimization process similar to gradient descent.

More specifically, the self-attention mechanism of a Transformer can be viewed as performing a form of "Meta-Gradient Descent." During pre-training, the model learns a "meta-optimizer." At inference time, when given a task, the model performs optimization in its activation space (rather than parameter space) to find the "implicit model" needed to solve the current task.

Each step in the reasoning chain is effectively one iteration of optimization being performed by the model. The most important corollary of this theoretical framework is that the performance bottleneck of the entire reasoning process lies in its "most difficult reasoning step."

1.2.3 Guiding Principles for Structured Prompt Design

Combining these two insights provides profound guidance for designing prompts for financial strategies. The success of an effective CoT prompt depends on whether it can decompose a complex financial problem into a series of sub-problems that map well to the Transformer's inherent computational circuits, with a special focus on guiding the model through the "most difficult steps."

Take mean reversion pairs trading as an example. The most difficult step is often determining whether a deviation in the spread is temporary noise or a permanent structural break. A structured prompt designed based on the above theories would look like this:

"Let's analyze the GLD/GDX pairs trading strategy step-by-step, with a special focus on testing the validity of the statistical arbitrage:

Step 1: Retrieve and calculate the historical beta of GDX's daily log returns relative to GLD's over the past 60 trading days.

Step 2: Based on the calculated beta, construct the spread series using the formula: spread = log(GDX) - beta * log(GLD).

Step 3 (Critical Step: Stationarity Test): Perform both the Augmented Dickey-Fuller (ADF) test and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test on the constructed spread series. The null hypothesis of the ADF test is the presence of a unit root (non-stationarity), while the null hypothesis of the KPSS test is stationarity. Report the test statistics and p-values for both tests and make a composite judgment (e.g., require ADF to reject the null and KPSS not to reject the null).

Step 4 (Critical Step: Mean Reversion Speed & Structural Break): If the spread series is stationary, calculate its Hurst exponent H. Confirm that H < 0.5 indicates mean-reverting properties. Concurrently, use a rolling-window Chow test to assess the stability of the cointegration relationship and detect any potential structural breaks.

Step 5: If all conditions are met (stationarity, mean reversion, stable relationship), calculate the z-score of its current value relative to its historical mean."

This structured prompt breaks down the complex analytical task into executable steps. We have specifically introduced more rigorous statistical tests in steps three and four (KPSS test, Hurst exponent, Chow test) that explicitly target the most difficult aspects of pairs trading—confirming the validity and stability of the statistical relationship. This design aligns with the model's underlying computational mechanisms, thereby greatly increasing the probability of obtaining accurate and reliable analytical results.

1.3 Unlocking Latent Capabilities: Advanced Decoding and Bayesian Reasoning

A core view of Professor Denny Zhou is that reasoning ability is an "emergent" property of pre-trained models. These capabilities are stored in a latent form within the model's parameters, constituting a vast, complex, and highly structured probability distribution. Our task is not to "teach" the model to reason, but to "guide" it to discover and follow the correct path within this enormous space of possibilities through effective decoding and prompting strategies.

From a Bayesian inference perspective, the decoding process can be seen as finding the maximum a posteriori (MAP) output sequence y* given an input x and model parameters θ: y* = argmax_y P(y|x; θ).

1.3.1 Beyond Greedy Search: Navigating Complex Probability Spaces

Standard greedy decoding pursues local optima. For problems requiring multi-step complex reasoning, greedy decoding often gets stuck. The correct reasoning path may not consist of the locally most probable choice at every step.

In financial forecasting, this "short-sighted" trap is particularly dangerous. Financial markets are full of non-linearities and sudden changes. A successful trading strategy often needs to capture rare but important signals. Greedy decoding, due to its short-sightedness, will miss such paths, ultimately generating a seemingly plausible but mediocre consensus view.

To overcome this limitation, we need to adopt decoding strategies that can explore a wider output space, such as temperature sampling or nucleus sampling (Top-p). This is equivalent to encouraging the model to engage in "lateral thinking" and explore multiple different possibilities.

1.3.2 Advanced Decoding Strategies: Contrastive Decoding

In recent years, researchers have proposed more advanced decoding strategies. Contrastive Decoding (CD) aims to generate token sequences that are not only high-probability under an expert model but also low-probability under an amateur model. Its objective function is:

CD(x) = argmax_y { (1-α) log P_expert(y|x) - α log P_amateur(y|x) }

In a quantitative investment scenario, we can use an LLM fine-tuned on financial data as the Expert and a general-purpose base LLM as the Amateur. Decoding with CD would tend to generate analyses that contain deep financial insights, rather than just fluent but superficial general language.

1.3.3 Prompting as a Bayesian Prior

Simple prompting techniques, like adding "Let's think step by step," actually act as a powerful Bayesian prior. It effectively adjusts the conditional probability distribution of the model's output, significantly increasing the overall probability of token sequences that have a step-by-step, orderly, and logically coherent structure.

In the application scenario of a momentum trend-following strategy, combining exploratory decoding with guiding prompts is crucial. A model using advanced decoding strategies might explore a less probable but more insightful path:

"The current upward trend in the S&P 500 is primarily driven by a few large-cap tech stocks (declining market breadth). At the same time, the VIX futures curve is in backwardation, which has historically often been a precursor to increased market fragility and a trend reversal for high-beta stocks. Furthermore, high-frequency fund flow data monitored by our proprietary engine shows that institutional buying is weakening. Although the time-series momentum signal is still positive, cross-asset momentum signals show relative strength in defensive assets. Synthesizing these signals, I judge the sustainability of the current momentum trend to be questionable. Decision: Halve the size of momentum long positions and tighten stop-loss levels to control the risk of a potential momentum crash."

This reasoning path integrates multiple key risk signals (market breadth, VIX structure, fund flows, cross-asset signals), ultimately leading to a more prudent and, on a risk-adjusted basis, superior decision. This fully demonstrates that through advanced decoding strategies, we can unearth complex reasoning capabilities that are not obvious but are crucial for alpha generation.

Part Two: Optimizing Reasoning Trajectories: From Supervised Imitation to Autonomous Evolution

After understanding the inherent reasoning capabilities of LLMs, the next core task is how to actively shape and optimize these abilities. This section will argue that for a dynamic, adversarial, and noisy domain like finance, directly imitating the thought patterns of human experts is a fundamentally flawed paradigm. Instead, we propose a framework in which the LLM learns and refines its reasoning processes autonomously through a self-improvement loop, guided by the objective, verifiable performance results provided by the investment firm's internal quantitative backtesting engine.

2.1 The Fragility of the Human Paradigm: Limitations of SFT in Financial Alpha Discovery

Professor Denny Zhou has clearly pointed out the poor generalization ability of Supervised Fine-Tuning (SFT) on general reasoning tasks. In the field of financial investment, this problem is dramatically amplified.

2.1.1 Cognitive Biases from a Behavioral Finance Perspective

The decisions of human analysts are highly susceptible to various cognitive biases. Research in behavioral finance (such as the work of Kahneman and Tversky) has revealed these biases, such as the narrative fallacy, confirmation bias, and the disposition effect, which is specific to finance (selling winning positions too early and holding losing positions too long). If an LLM is trained via SFT using human trading logs, the model will inevitably learn and entrench these systematic, loss-inducing behavioral patterns.

A deeper problem is that the optimal reasoning path for an LLM may be fundamentally different from the thought process of any human expert. Forcing a model via SFT to imitate what is likely a suboptimal, noisy human thought process not only limits the model's potential to discover new, non-intuitive sources of alpha but may even lead it astray. This is known as the "Alignment Tax"—the performance cost paid to align a model's behavior with human intent.

For example, a human trader executing a pairs trade might rely on intuitive judgments about the fundamentals of the two companies. An LLM, on the other hand, might discover more stable and predictive patterns by analyzing higher-dimensional data (such as supply chain network data or textual analysis of geopolitical events) to determine whether a widening spread is temporary noise or a precursor to a structural break.

2.1.2 The Correct Role of SFT: Structure, Not Substance

Therefore, for a hedge fund pursuing excess returns, the value of SFT is limited. Its primary role should not be to teach the model "how to think" (Process Supervision), but rather "how to organize and present its thought process" (Format Supervision).

We can use SFT to train the model to generate well-structured financial analysis reports. For example, ensuring that every proposal for a momentum strategy includes a quantitative assessment of trend strength, an analysis of potential reversal risks, position sizing calculations, and a defined stop-loss strategy. However, the specific content of these sections—the real alpha—should not be learned by imitating humans but through "Outcome Supervision."

In summary, building a quantitative trading system intended to outperform humans is a logical paradox if its core training paradigm is human imitation. The model learns the "grammar" of communication through SFT, but the "semantics" and effectiveness of its decisions must be learned and optimized through a mechanism directly linked to objective profitability (P&L).

2.2 Self-Improvement via Preference Optimization: A Paradigm Shift in Strategy Discovery

To move beyond the limitations of human imitation, we need a mechanism that allows the model to autonomously explore and refine effective reasoning paths. This is the core of Professor Denny Zhou's "Self-Improve" concept. The evolution of this paradigm has gradually converged on a simpler, more stable, and theoretically more elegant method: "Direct Preference Optimization" (DPO).

2.2.1 Mathematical Foundations of DPO

The core idea of DPO is to bypass the challenging step of explicitly building a Reward Model in RLHF. DPO leverages the closed-form analytical relationship between the optimal reward function and the optimal policy in the Bradley-Terry model, reformulating the alignment problem directly as a supervised learning problem. The DPO loss function directly maximizes the log-probability difference between the model generating a "better" response (y_w) and a "worse" response (y_l).

Its mathematical objective function is as follows:

L_DPO(π_θ; π_ref) = -E_{(x, y_w, y_l) ~ D} [ log σ ( β log (π_θ(y_w|x) / π_ref(y_w|x)) - β log (π_θ(y_l|x) / π_ref(y_l|x)) ) ]

Where x is the market state, y_w and y_l are the "winning" and "losing" trading decisions/reasoning paths, π_θ is the policy being optimized, π_ref is the reference policy, and β is a hyperparameter controlling the strength of the KL-divergence penalty.

2.2.2 The Backtesting Engine as an Objective Verifier

For a quantitative hedge fund, the true power of the DPO framework lies in the fact that the required preference labels (y_w, y_l) can be provided completely automatically and objectively by the fund's internal "verifier"—our proprietary backtesting engine. This process forms a powerful self-improvement loop:

1. Generate: For the current market state x, the LLM generates two different strategy proposals, y_1 and y_2. For example, for a pair of stocks with a potential mean-reversion opportunity, y_1 might be a strategy based on a standard OU process, while y_2 might be a more complex strategy that considers macroeconomic factors.

2. Verify: The backtesting engine receives these two strategies and performs a rigorous, high-fidelity backtest on historical data, accounting for transaction costs and market impact.

3. Refine: If the Sharpe ratio of strategy y_1 is significantly higher than that of y_2, then y_1 is labeled as y_w.

4. Optimize: Use these automatically labeled preference data to update the LLM's parameters θ.

2.2.3 Beyond Binary Preferences: IPO and KTO

We can introduce variants of DPO to handle the intensity of preferences. Identity Preference Optimization (IPO) introduces a regularization term to handle preference strength, allowing the model to learn subtle differences between strategies. Its loss function allows for the introduction of a margin proportional to the difference in backtested performance between two strategies (e.g., the difference in Sharpe ratios).

For example, a strategy that successfully avoids a major momentum crash while another suffers a huge loss should correspond to a very large margin, thus providing a much stronger training signal during the model update.

Another emerging method is Kahneman-Tversky Optimization (KTO). KTO does not require paired preference data, only a binary evaluation of "good" or "bad" for each output (e.g., whether the backtested Sharpe ratio is above a certain threshold). This simplifies the data collection process, allowing us to directly use the vast amount of historical strategy evaluation data generated by our backtesting engine.

In this way, DPO and its variants transform the fundamental problem of alpha discovery from a difficult generative task into a relatively easy and more stable discriminative task. The role of the LLM shifts to that of an efficient "hypothesis generator," responsible for producing diverse and creative strategy ideas, while the final screening and validation are handled by the fund's existing mature and rigorous quantitative infrastructure.

2.3 Advanced Reinforcement Learning Frameworks for Financial Agents

Although DPO/KTO provides a powerful optimization framework, financial decisions are often sequential, and actions affect future states. To optimize in this stateful decision-making environment, we need to introduce a more comprehensive reinforcement learning (RL) framework, viewing it as a Markov Decision Process (MDP), and tailor the environment, actions, and reward functions for our mean reversion and momentum strategies.

2.3.1 Risk-Sensitive and Distributional RL

In finance, simply maximizing expected return is dangerous. The design of the reward function must inherently incorporate risk aversion.

Distributional RL goes beyond learning the expected cumulative return Q(s, a) and instead learns the entire probability distribution of future cumulative returns, Z(s, a). This distribution satisfies the distributional Bellman equation:

Z(s, a) D= R(s, a) + γ Z(s', a')

By learning the complete return distribution, the agent can directly optimize for risk-sensitive objectives, such as Conditional Value at Risk (CVaR). CVaR measures the average loss in the worst α% of cases (e.g., α=5%).

CVaR_α(Z) = E[Z | Z ≤ VaR_α(Z)]

In practice, distributional RL can be implemented via Implicit Quantile Networks (IQN). This enables the agent to explicitly budget for risk, choosing an action plan with a slightly lower expected return but a significantly better CVaR (i.e., smaller tail risk).

2.3.2 Application to Mean Reversion Pairs Trading: Navigating Structural Breaks

For a mean reversion strategy, the core risk is that the cointegration relationship may break down, i.e., a structural break occurs. This is precisely where LLM reasoning can play a key role.

• State Space: S includes not only quantitative indicators (spread series, z-score) but also unstructured data (news, financial reports of the relevant companies). The LLM is responsible for encoding this multimodal data into a unified state representation.

• Action Space: The agent's action A is to dynamically adjust trading parameters. If the spread is modeled as an Ornstein-Uhlenbeck (OU) process: dX_t = θ(μ - X_t)dt + σ dW_t, actions could be adjusting the mean reversion speed θ, the long-term mean μ, the volatility σ, and the trading thresholds, or choosing to "pause trading."

• Reasoning Task and Reward: The core task of the LLM agent is to predict the likelihood of a structural break.

When the LLM parses from the news that "Company A announces a major strategic transformation," it can generate the following reasoning chain: "Company A's transformation will cause the historical cointegration vector with Company B to become invalid. I predict a significant increase in the future volatility of the spread. Decision: Immediately close the current position and pause trading on this pair."

The reward function will use the distributional RL framework and directly optimize for CVaR. Holding exposure during a structural break will lead to extreme negative returns. To optimize CVaR, the agent will learn to identify the early signals that lead to these extreme losses and take evasive action.

2.3.3 Application to Momentum Trend Following: Managing Momentum Crash Risk

The primary "Achilles' heel" of momentum strategies is their momentum crashes in specific market environments. These crashes typically occur in "panic states" after the market has experienced a sharp decline and volatility has spiked.

• State Space: S must include macroeconomic indicators describing the overall "health" of the market, such as the VIX index and its term structure, credit spreads, market breadth indicators, and news sentiment indices.

• Action Space: The core of A is to dynamically adjust the strategy's leverage or position size (Volatility Scaling).

• Reasoning Task and Reward: The task of the LLM agent is to identify in real-time whether the market has entered a "panic state."

When the model observes that the VIX futures curve is in severe Backwardation (spot VIX is much higher than futures VIX), this usually signals extreme market stress. The LLM should generate the reasoning: "The current VIX term structure indicates the market is in extreme panic. Although the short-term momentum signal may still be positive, the conditional probability of a sharp reversal (momentum crash) has significantly increased. Historical data shows that in this state, the return distribution of momentum strategies exhibits extreme negative skewness. Decision: Reduce the size of all momentum positions by 75%."

The design of the reward function will leverage distributional RL to learn this negative skewness. We can use Spectral Risk Measures, which allow us to assign extremely high weights to the worst parts of the return distribution. This will force the agent to prioritize capital preservation as its primary objective in specific market regimes.

Part Three: Enhancing Robustness and Knowledge Density in Financial Reasoning

After building an LLM agent capable of learning specific strategies through self-improvement, we face two major challenges to ensure its reliability and effectiveness in the real world: first, how to handle the inherent randomness of the LLM generation process to ensure stable and credible decisions; second, how to overcome the static and limited nature of the LLM's internal knowledge so that it can access and utilize external, dynamic, and structured financial knowledge.

3.1 Aggregation and Self-Consistency: Achieving High-Confidence Decisions

The generation process of an LLM is inherently random (when using non-greedy decoding). To address the challenge of decision certainty, we cannot rely on a single generation result but must adopt an Aggregation strategy.

3.1.1 The Bayesian Interpretation of Self-Consistency

The most powerful and widely studied implementation of the aggregation concept advocated by Professor Denny Zhou is the Self-Consistency (SC) decoding strategy. Its core idea is: if the same answer is reached through multiple different thought paths, our confidence in that answer increases significantly.

From a Bayesian statistics perspective, self-consistency can be interpreted as a process of marginalizing out the latent variable of the reasoning path, r, to find the posterior probability of an answer a given an input x, P(a|x). Its mathematical expression is:

P(a|x) = Σ_r P(a|r, x) P(r|x).

SC approximates this summation process through Monte Carlo sampling. The final majority vote decision can be expressed as:

a_final = argmax_a Σ_{i=1}^{k} 1(a_i = a)

3.1.2 Beyond Linear Thinking: Tree-of-Thought (ToT)

Traditional CoT and self-consistency usually focus on linear reasoning paths. However, complex financial decisions often require a richer reasoning structure. The Tree-of-Thought (ToT) framework provides us with this capability.

ToT models the reasoning process as a tree. Each node represents an intermediate state, and the edges represent reasoning steps. ToT allows the model to generate multiple branches at each step (exploring different possibilities) and use an "evaluator" to assess the prospects of each branch. The model can backtrack to previous nodes and choose more promising branches to continue exploring.

When evaluating a momentum strategy, the application of ToT is as follows:

Root node: Analyze the current momentum signal for SPY.

Branch 1: Assume the current trend will continue. Evaluate the optimal position size and stop-loss point.

Branch 2: Assume the market is about to reverse (based on VIX signals). Evaluate the defensive measures to be taken.

Branch 3: Assume the market is entering a range-bound state. Evaluate the expected performance of the momentum strategy.

The evaluator (which can be the LLM itself or an external value function) assesses the likelihood and expected return of each branch. Finally, the model chooses the optimal path. ToT provides a reasoning strategy that combines Breadth-First Search (BFS) and Depth-First Search (DFS), which can more effectively explore complex decision spaces than linear CoT.

3.1.3 Endogenous Uncertainty Measurement and Human-AI Collaboration

Integrating self-consistency or ToT mechanisms into the quantitative trading workflow can yield an extremely important byproduct: an endogenous, unsupervised measure of model uncertainty. We can define a "Consistency Score" (C-Score):

C-Score = count(most frequent answer) / total samples

This score directly reflects the model's "confidence" in its decision. We can use the C-Score to establish a dynamic, confidence-based human-in-the-loop system:

• High C-Score (e.g., > 0.9): The model is very confident in its decision. These trading signals can be set for automatic execution and allowed a higher capital weight.

• Low C-Score (e.g., < 0.5): The model's multiple reasoning paths lead to several different, competing decisions. For example, when analyzing a new pairs trading opportunity, if different paths generated by the model reach contradictory conclusions about the stability of the cointegration relationship, the C-Score will be low. These signals should be automatically flagged and submitted to a human portfolio manager for review.

3.2 Retrieval-Augmented Reasoning with Financial Knowledge Graphs

A fundamental limitation of LLMs is that their internal knowledge is static and may suffer from "hallucinations." To solve this problem, we need to connect them with an external, dynamically updated source of knowledge, which is Retrieval-Augmented Generation (RAG). For the financial domain, using a Financial Knowledge Graph (KG) as the external knowledge base for RAG is a superior choice.

3.2.1 Financial KGs and Structured Reasoning

A Financial Knowledge Graph represents entities (companies, macroeconomic indicators, events) as nodes and their relationships (supplier, competitor, affected by...) as edges. This graph-structured data allows us to perform multi-hop, structured, complex queries.

To fully leverage the structured information in a knowledge graph, we can introduce Graph Neural Networks (GNNs). GNNs can learn node and edge embeddings by passing messages on the graph, and these embeddings capture the features of the entities and the relationships between them.

3.2.2 Deep Risk Mining in Pairs Trading with KG-RAG

In mean reversion pairs trading, KG-RAG can reveal hidden risks that might break the cointegration relationship, especially supply chain and cross-holding risks.

Suppose we are trading a pair of consumer goods companies, A and B. A hidden risk is their dependence on a common supplier. With KG-RAG, we can execute the following multi-hop query (in Cypher pseudocode):

Cypher

MATCH (A:Company)-[:SUPPLIED_BY]->(S:Supplier)<-[:SUPPLIED_BY]-(B:Company)
WHERE A.name = 'Company A' AND B.name = 'Company B'
RETURN S.name, S.financial_health_score

If the query result shows that both A and B are heavily dependent on the same financially unhealthy supplier S, then any operational issues at S will affect both A and B simultaneously, potentially causing their stock prices to move sharply in the same direction, thus breaking the original mean-reverting property of the spread. When generating a trading decision, the LLM must incorporate this structured risk information retrieved from the KG into its reasoning process.

3.2.3 Fundamental Grounding of Momentum Strategies with KG-RAG

For momentum trend following, KG-RAG can help us build more fundamentally supported and robust investment portfolios, going beyond momentum signals based purely on price.

Suppose we are building a thematic momentum portfolio on "Artificial Intelligence Infrastructure." With KG-RAG, we can query:

Cypher

MATCH (C:Company)-[:DEVELOPS]->(T:Technology)
WHERE T.name IN ['Silicon Photonics', 'HBM3', 'Chip-on-Wafer-Substrate']
MATCH (C)-[:HAS_PARTNER]->(P:Company)
WHERE P.name IN ['NVIDIA', 'TSMC']
RETURN C.name, C.recent_patent_filings, C.momentum_score

This query identifies companies that have a presence in key emerging technology areas and have partnerships with industry leaders. The LLM can use this information to enhance its interpretation of the momentum signal: "The stock price momentum of Company C is strong. A KG retrieval shows that this is not just market hype but is supported by its breakthroughs in silicon photonics technology and a partnership agreement with NVIDIA. These fundamental factors indicate that its momentum trend is sustainable. Therefore, it is recommended to increase the allocation weight to C."

3.2.4 Active Knowledge Seeking: Query as Action

Combining KG-RAG with a reinforcement learning framework can produce powerful synergies. The action space of the RL agent can be expanded to not only output trading decisions but also graph query statements. The agent learns how to actively seek information to reduce its uncertainty about the state of the world (Active Perception).

If the agent has insufficient information in a state s (e.g., a low C-Score), its policy network π(a|s) outputs an action a, which is a Cypher query. The knowledge graph returns information, updating the state to s'. This mechanism transforms the LLM from a passive "reasoner" into an active "researcher."

3.3 Frontiers: From Correlation to Causal Inference

The holy grail of quantitative finance is to understand the driving forces of market dynamics, i.e., to answer the question "why did it happen?". This requires us to move from exploring correlation to discovering causation. Causal discovery in financial time series data is an extremely challenging task.

The emergence of LLMs provides us with a completely new path: positioning them as powerful causal hypothesis generators.

3.3.1 The Ladder of Causation and the Role of LLMs

According to Judea Pearl's framework of causal theory, causality is divided into three levels: association, intervention, and counterfactuals. Advanced investment decisions need to reach the intervention level or even the counterfactual level.

In its vast training corpus, an LLM has digested decades of economic theory, financial literature, historical event analysis, and market commentary. This equips it with the ability to generate plausible causal models of how the world works (in the form of Directed Acyclic Graphs, DAGs).

3.3.2 A Human-AI Collaborative Framework for Causal Discovery

We can leverage this capability to systematize and scale the most creative "idea generation" phase of quantitative research:

1. Hypothesis Generation: Pose an open-ended question to the LLM, such as: "Please propose five causal mechanisms that could lead to a structural break in the long-term correlation between 'growth stocks' and 'value stocks'."

2. LLM Reasoning and Output: The LLM might generate a series of causal hypotheses and output them in a structured form. A possible output is: "Hypothesis 1: A sharp rise in inflation expectations. Causal path: Rising inflation expectations -> Central bank adopts more aggressive tightening policies -> Long-term interest rates and discount rates rise -> Disproportionately negative impact on the valuation of longer-duration growth stocks -> Growth stocks underperform value stocks, breaking the historical correlation."

3. Hypothesis Formalization: A quantitative researcher translates the natural language causal hypothesis generated by the LLM into a testable mathematical or statistical model. This requires introducing Structural Causal Models (SCM) and the do-operator. The LLM can also help identify potential Instrumental Variables (IVs).

4. Rigorous Testing: Use rigorous econometric tools (such as Difference-in-Differences (DiD), Regression Discontinuity Design (RDD), or Structural Vector Autoregression (VAR) models) to empirically test these formalized hypotheses.

3.3.3 Causal Analysis Applied to Momentum Strategies

We can ask the LLM to propose causal hypotheses for why a particular momentum factor fails in certain periods. For example, regarding the impact of "Factor Crowding" on momentum crashes.

LLM Hypothesis: "When a large amount of capital flows into the same momentum stocks, it creates a crowded trade. Causal path: Momentum signal is published -> Capital flows in -> Stock prices are pushed above their fundamental value -> The trade becomes crowded and unstable -> A small negative shock triggers a collective liquidation -> Stock price crashes (momentum crash)."

This hypothesis can be validated by constructing crowding indicators (e.g., based on institutional holdings data like 13F filings or short interest) and testing their predictive power for the future returns of the momentum factor. If validated, we can transform the causal insight generated by the LLM into a risk management model that dynamically adjusts the exposure of our momentum strategy.

Part Four: Practical Frameworks for Implementation and Verification

Integrating the advanced reasoning capabilities of LLMs into a real trading environment requires a rigorous and pragmatic implementation and verification framework. The biggest challenge is how to effectively control and mitigate the risk of backtest overfitting, given the immense flexibility and high-dimensional space of LLM-generated strategies.

4.1 The Quandary of Quantitative Research: Mitigating Backtest Overfitting in High-Dimensional Models

The greatest risk faced when using LLMs for strategy generation is backtest overfitting. An LLM can easily generate millions of strategy configurations. In such a massive search space, it is almost guaranteed that a strategy that performs "excellently" on historical data will be found, but its excellent performance is likely just a statistical fluke. In statistics, this is known as the multiple hypothesis testing problem.

Traditional out-of-sample testing methods are not sufficient to provide adequate protection, as there is implicit "data snooping" in large-scale searches. To meet this severe challenge, we must adopt a set of more advanced and stricter verification techniques.

4.1.1 The Overfitting Diagnostic Toolbox

The table below summarizes a standard validation process for diagnosing the overfitting risk of LLM-generated strategies.

Table 1: Overfitting Diagnostic Toolbox for LLM-Generated Strategies

Technique	Description	Primary Use	Applicability to LLM-Generated Strategies
Walk-Forward Optimization (WFO)	Optimize parameters on a rolling training time window and test on the immediately following out-of-sample window, then roll the entire window forward.	Test parameter stability and robustness to changes in market regimes.	Crucial. Must be used to validate any tunable parameters proposed in the LLM's reasoning (e.g., z-score thresholds for pairs trading, look-back windows for momentum strategies).
Deflated Sharpe Ratio (DSR)	Recalculate the statistical significance of the Sharpe ratio after considering the number of trials, backtest length, and non-normality of returns.	Correct for the selection bias (data snooping) that arises from testing a large number of strategies.	Indispensable. The generation of Ncandidate strategies by the LLM must be treated as N trials. The DSR of the "optimal" strategy must be calculated.
Combinatorially Symmetric Cross-Validation (CSCV) / PBO	A cross-validation method that calculates the Probability of Backtest Overfitting (PBO) by testing on combinations of different data partitions.	Provide a direct probabilistic measure of whether a strategy's performance is likely due to overfitting.	Highly valuable. Provides a single, interpretable metric for the finally selected LLM strategy (e.g., PBO > 0.5 is a strong red flag).
Monte Carlo / Bootstrapping	Create thousands of alternative equity curves by resampling trades (e.g., using the Stationary Block Bootstrap) or randomizing their order.	Assess whether the observed performance is statistically significant or just occurred by chance. Generate confidence intervals.	Essential. Used to ensure that what the LLM found is not just a series of lucky trades. The bootstrapped distribution of the Sharpe ratio should be significantly positive.
Regime Analysis & Stress Testing	Divide the backtest period into different market regimes (e.g., bull, bear, high/low volatility) and analyze performance in each.	Ensure the strategy is not just fitted to a single market environment.	Critical for both momentum strategies (testing their performance during crashes) and pairs trading (testing during volatility spikes and correlation breakdowns).

4.1.2 Deflated Sharpe Ratio (DSR): The Essential Tool for Multiple Testing

Among the tools in the toolbox, the Deflated Sharpe Ratio (DSR) proposed by Bailey and López de Prado deserves special emphasis. DSR corrects for selection bias by "deflating" the observed SR.

It first estimates the maximum SR value we would expect to get from N independent trials under the null hypothesis of "no real alpha," E[max(SR_N)]. Then, it calculates the probability that the observed SR exceeds this expected maximum.

The calculation of DSR considers not only the number of trials N but also the length of the backtest T and the skewness (γ_3) and kurtosis (γ_4) of the return distribution. A simplified conceptual formula can be expressed as:

DSR_hat = Z( (SR_hat - E[max(SR_N)]) sqrt(T-1) / sqrt(1 - γ_3 SR_hat + ((γ_4 - 1)/4) * SR_hat^2) )

Where Z(.) is the cumulative distribution function of the standard normal distribution. A high DSR value (e.g., > 0.95) means that even after considering the large-scale search, the strategy's performance is still statistically significant. For our LLM integration workflow, we must calculate the DSR of the optimal strategy. This step is a critical line of defense against putting overfitted "phantom alpha" into live trading.

4.1.3 Probability of Backtest Overfitting (PBO): A Direct Measure of Risk

Another powerful tool is the Probability of Backtest Overfitting (PBO). PBO provides a direct probabilistic measure of whether a strategy's superior in-sample performance is due to overfitting. The calculation of PBO is based on the Combinatorially Symmetric Cross-Validation (CSCV) framework.

CSCV evaluates the stability of a strategy's performance across different data partitions by dividing the historical data into S subsets and constructing all possible combinations of training and testing sets. PBO calculates the probability that the out-of-sample performance is below the median across all test set combinations. If PBO is close to 1, it means the strategy performs poorly in the vast majority of out-of-sample tests. For LLM-generated strategies, we should set a strict PBO threshold (e.g., < 0.1).

4.2 Architectural Blueprint for an LLM-Integrated Trading Engine

Successfully integrating LLMs into the trading workflow requires a well-thought-out system architecture. The core design philosophy of this architecture should be "quant-as-supervisor," meaning the LLM serves as a powerful auxiliary tool to enhance, not replace, human professional judgment and final decision-making authority. This helps to manage and mitigate the inherent risks of LLMs, such as hallucinations and reasoning errors.

A high-level system architecture blueprint can be envisioned as follows:

1. Data and Knowledge Layer: Includes structured market data, unstructured text data (generated by our proprietary engine), and a dynamically updated Financial Knowledge Graph (KG).

2. Reasoning Module: The core of the system, containing the LLM fine-tuned with DPO/RL. It performs tasks such as CoT/ToT analysis, self-consistency evaluation (C-Score calculation), and causal hypothesis generation.

3. Verification and Backtesting Engine: The core quantitative infrastructure. It plays a dual role: as a "verifier" during the training phase (providing feedback signals) and as a "gatekeeper" during the deployment phase (performing rigorous overfitting tests like DSR, PBO).

4. Execution & Risk Management Module: Responsible for order execution and real-time risk monitoring. This module should contain hard risk control logic (like circuit breakers) that is independent of the LLM's decisions.

5. Human-in-the-Loop Interface: A critical console that presents the output of the reasoning module to quantitative analysts and portfolio managers in a structured and interpretable way.

4.2.1 The "Daily Research Briefing": The Core Output of the LLM

In this architecture, the most valuable output of the LLM may not be direct "buy/sell" signals, but a highly condensed and insightful "Daily Research Briefing." This briefing could include:

• Anomaly Detection: Highlighting significant deviations in the behavior of a specific pairs trade spread from its historical baseline.

• Causal Narratives: Proposing causal narratives driven by news or events that might explain these anomalies (e.g., explaining why a certain momentum trend might be ending), and providing supporting evidence retrieved from the knowledge graph.

• Regime Change Alerts: Identifying early signals of a market regime shift and explaining its potential impact on existing mean reversion and momentum portfolios.

• Strategy Proposals with Confidence Scores: Generating specific trading strategy proposals with detailed reasoning chains, expected risk-return analyses, and C-Scores.

Through this interface, human experts can quickly review the LLM's analysis, verify its reasoning process, and use their own experience and intuition to make the final capital allocation decisions. Human intervention is particularly crucial when the C-Score is low.

4.3 Scalable Oversight for Potentially Superhuman Financial Models

Finally, we need to think ahead to address a long-term but plausible governance challenge. If the self-improvement loop described in this report proves successful, an investment firm could eventually develop models capable of discovering complex or non-intuitive profitable strategies that humans cannot immediately understand. This introduces a new, deeper level of model risk: how do we trust and deploy an autonomous trading agent whose logic we cannot fully comprehend?

This problem is essentially analogous to the core issue in AI safety—the alignment problem. The key to solving this problem lies in developing Scalable Oversight techniques, i.e., using less capable AI systems (or humans augmented by AI tools) to supervise and verify the behavior and output of more capable AI systems.

4.3.1 The Debate Framework and Red Teaming

In the context of financial trading, one highly promising approach is the Debate or "Red Teaming" framework:

1. Generator Agent (Agent A): An LLM tasked with generating trading strategies and the logic behind them (e.g., our trained momentum strategy agent).

2. Critic Agent (Agent B): Another independently trained LLM tasked with the "red team" role, with the sole objective of finding flaws in Agent A's reasoning, unconsidered risks, biases in the data, or potential overfitting.

3. Iterative Debate: Agent A and Agent B engage in multiple rounds of debate. Agent B raises criticisms, and Agent A must defend or revise its original strategy.

4. Human Judge: A human analyst observes the entire debate process and makes a final judgment based on the quality of the arguments from both sides. The human role shifts from directly verifying a complex strategy to assessing the quality of a structured debate, which is a more cognitively manageable task.

4.3.2 Constitutional AI and Hard Constraints

Another method for scalable oversight is "Constitutional AI." We can define a "constitution" for our trading agents—a set of inviolable principles and rules. These rules can include risk limits (such as maximum drawdown, VaR limits), compliance requirements, and robustness requirements. In its self-improvement process, the LLM agent must not only optimize for P&L but also demonstrate that its generated strategies comply with all the provisions in the constitution.

This "safety through rules and adversarial process" framework provides a viable path for verifying highly complex autonomous trading systems. It translates cutting-edge ideas from the field of AI safety into practical risk management tools for advanced quantitative firms. From a strategic perspective, investing early in research on scalable oversight techniques is not just about mitigating future risks, but about building an organizational capability to safely and confidently deploy and leverage AI trading systems that may far exceed human-level capabilities in the future. This is a key strategic R&D investment for maintaining a long-term competitive advantage in the coming era of AI-driven finance.