Mechanistic Interpretability in Algorithmic Trading - A Hybrid KAN-Based Framework

Abstract

The increasing complexity of neural networks presents a significant barrier to their adoption in high-stakes financial applications, where model transparency is paramount. This paper introduces a novel hybrid framework that pioneers a new frontier in mechanistic interpretability for time-series forecasting. We demonstrate a methodology for distilling the complex, non-linear relationships learned by an advanced neural network into a concise, human-readable symbolic equation. This equation, representing core market dynamics, provides an interpretable baseline for human analysts. The framework's predictive power is then systematically augmented by applying secondary machine learning models to the symbolic equation's residuals, capturing patterns beyond the scope of the interpretable model. This symbiotic approach bridges the gap between performance and explainability, creating a powerful tool for real-time algorithmic decision-making. Our results establish a new standard for integrating human expertise with state-of-the-art AI, unlocking previously unattainable levels of insight and control.

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GitHub Repo : https://github.com/Apoth3osis-ai/MI_KAN

Research Gate: https://www.researchgate.net/publication/392596337_Mechanistic_Interpretability_in_Algorithmic_Trading_A_Hybrid_KAN-Based_Framework

1. Introduction

The application of artificial intelligence to financial markets has unlocked unprecedented opportunities for alpha generation and risk management. However, as the sophistication of models—particularly deep neural networks—has grown, so has their opacity. This "black box" problem creates a fundamental tension between predictive power and model transparency. In high-stakes, regulated environments like algorithmic trading, the inability to understand, debug, or justify a model's decision-making process presents an unacceptable level of risk.

Traditional methods for explainable AI (XAI), such as post-hoc analyses, often provide approximations of a model's behavior rather than revealing its core underlying logic. This paper posits that a more robust solution lies in developing inherently interpretable models that do not sacrifice performance. To this end, Apoth3osis RD has developed a novel hybrid modeling framework designed to achieve true mechanistic interpretability.

Our methodology is founded on a two-phase approach. In the first phase, we utilize a Kolmogorov-Arnold Network (KAN), a new class of neural network, to learn the fundamental mathematical relationships within financial time-series data. The key innovation of KANs is their ability to be distilled into a concise, human-readable symbolic equation. This equation serves as an interpretable baseline model that can be directly validated by a human analyst or trader. In the second phase, we augment this baseline by training advanced machine learning models (e.g., LSTMs, Gradient Boosting Machines) to predict the errors, or residuals, of the symbolic equation. This allows us to capture the complex, chaotic patterns that the interpretable model misses, thereby unifying state-of-the-art accuracy with unparalleled transparency.

The primary contribution of this paper is the formalization of this hybrid framework. We demonstrate a practical pathway for creating trading systems where human intuition and AI-driven pattern recognition can operate in a symbiotic relationship. This paper will detail the theoretical underpinnings of the framework, its architectural design, and its profound implications for the future of quantitative finance.

2. Background and Related Work

Our framework builds upon several key areas of machine learning and quantitative finance research.

2.1. Explainable AI (XAI) in Finance

The need for XAI in finance is well-documented. Techniques like SHAP (SHapley Additive exPlanations) and LIME (Local Interpretable Model-agnostic Explanations) have become standard for providing post-hoc explanations of black-box model predictions. While valuable, these methods typically explain what features drove a single prediction, not how the model synthesizes those features globally. Our approach differs by aiming for intrinsic transparency, where the model's core logic is itself the explanation.

2.2. Time-Series Forecasting Models

Financial forecasting has evolved from classic statistical models like ARIMA to complex neural architectures. Long Short-Term Memory (LSTM) networks are particularly well-suited for modeling temporal dependencies, while Gradient Boosting Machines (GBMs) excel at capturing complex, non-linear feature interactions from tabular data. Our framework does not seek to replace these powerful tools but rather to orchestrate them in a more effective and transparent manner, using them as specialized "error correctors."

2.3. Kolmogorov-Arnold Networks (KANs)

The theoretical foundation of our framework is the Kolmogorov-Arnold representation theorem, which posits that any multivariate continuous function can be represented as a superposition of univariate functions. KANs operationalize this theorem in a neural network architecture. Unlike traditional Multilayer Perceptrons (MLPs) which have fixed activation functions on nodes (neurons), KANs place learnable activation functions on edges (connections). These activation functions, represented as splines, can be fitted to a library of symbolic functions (e.g., sin,exp,x2). This unique property enables the distillation of a fully trained KAN into an explicit mathematical formula, a capability not present in conventional network architectures.

3. The Hybrid Modeling Framework

Our proposed framework integrates symbolic distillation and residual modeling into a cohesive pipeline. The architecture is designed to systematically separate the interpretable signal from the complex, residual noise.

3.1. Framework Overview

The data processing and modeling pipeline proceeds through five stages:

Data Preparation: Ingesting and preprocessing high-frequency time-series data.

Phase 1 - Symbolic Distillation: Training a KAN to discover an interpretable, baseline symbolic formula.

Residual Calculation: Computing the error between the symbolic model's predictions and the actual values.

Phase 2 - Residual Augmentation: Training secondary machine learning models to predict the residuals.

Hybrid Prediction: Combining the predictions from the symbolic and residual models to generate a final, highly accurate forecast.

3.2. Data Preprocessing

The framework is designed for high-frequency time-series data. The input data is transformed into a supervised learning format using a sliding window approach, where a vector of lagged features (e.g., historical open, high, low, and close prices) is used to predict a future target value. All features and the target variable are normalized to a 0,1 range to ensure stable training for the neural network components.

3.3. Phase 1: Symbolic Distillation with KANs

The core of the framework is the creation of an interpretable model. This is achieved through a multi-step process:

Initial Training: A KAN is trained on the preprocessed dataset. The network learns the optimal spline-based activation functions that best map the input features to the target.

Pruning and Refinement: The trained network is automatically pruned to remove redundant connections, which simplifies the model's structure. The spline grids are then refined to increase precision around highly active regions.

Symbolic Fitting: The refined spline-based activation functions on each edge are fitted against a pre-defined library of symbolic functions (e.g., {x,x2,x3,sin(x),exp(x)}). The network replaces the numerical splines with their best-fit symbolic counterparts.

Final Polish: The now fully symbolic KAN is re-trained to optimize the coefficients of the final equation, ensuring machine precision.

The output of this phase is a single mathematical equation, y^​symbolic​=f(x1​,x2​,...,xn​), which serves as our transparent and human-readable baseline model.

3.4. Phase 2: Residual Augmentation

While the symbolic model captures the principal dynamics, it is an intentional simplification. The errors, or residuals, contain complex patterns that were filtered out during the distillation process. The residuals are calculated as:

Residual=yactual​−y^​symbolic​

We then train one or more secondary models to predict these residuals using the same input features. The hypothesis is that different model architectures can specialize in capturing different types of residual patterns:

LSTM: Ideal for modeling any remaining temporal or sequential patterns in the errors.

GBM: Ideal for modeling complex, non-linear, and non-temporal feature interactions within the error signal.

3.5. Final Prediction Assembly

The final hybrid prediction is the sum of the symbolic baseline prediction and the predicted residual from a secondary model:

y^​hybrid​=y^​symbolic​+y^​residual​

This approach allows the final forecast to benefit from both the stability and interpretability of the symbolic formula and the pattern-recognition power of the more complex residual model.

4. Experimental Setup and Results

To validate the framework, we conducted experiments using high-frequency minute-level foreign exchange data (EUR/USD) spanning a multi-month period. For the purpose of this paper, we present conceptual results derived from a fixed 80/20 train-validation split. Model performance was evaluated using Mean Absolute Error (MAE) and Mean Squared Error (MSE), calculated on the original, un-scaled price data for clear interpretation.

Our experiments confirmed the framework's efficacy. The performance of the standalone Symbolic KAN model served as a robust baseline. Both hybrid configurations—KAN+LSTM and KAN+GBM—demonstrably improved upon this baseline, yielding a significant reduction in both MAE and MSE. The analysis revealed that the KAN+GBM model provided the single most effective combination for this dataset, suggesting that the residuals were primarily characterized by complex feature interactions rather than long-term temporal dependencies. This result underscores the framework's utility in not only improving accuracy but also in diagnosing the nature of the model's errors.

5. Applications and Implications

The implications of this research extend beyond a single application and suggest a new direction for the development of AI in critical systems.

5.1. Potential Applications

Algorithmic Trading: The primary application. The human-readable formula provides traders and risk managers with an unprecedented level of oversight, allowing them to understand the core strategy of an algorithm and intervene with confidence.

Risk Management and Compliance: The inherent transparency of the model's core logic dramatically simplifies the process of auditing, validation, and regulatory reporting.

Portfolio Optimization: The discovered symbolic equations may reveal novel, stable factors that can be incorporated into systematic portfolio allocation models.

General Scientific Discovery: This methodology is domain-agnostic and could be applied to any scientific field where the goal is to discover underlying physical or biological laws from experimental data.

5.2. Implications of the Research

A New Paradigm for XAI: This work represents a shift from post-hoc explanation to intrinsic interpretability. Instead of asking a model to explain itself after the fact, we build it around a core that is understandable by design.

Human-AI Symbiosis: The framework fosters a true collaborative environment. The AI discovers a formula that a human can analyze, critique, and build upon, while the human relies on the AI to handle the high-dimensional complexities of the residual noise.

Increased Trust and Adoption: By demystifying the core of complex predictive models, this approach can lower the barriers to adoption for advanced AI in finance and other regulated, mission-critical industries.

6. Future Work and Limitations

This research opens several promising avenues for future work while also acknowledging certain limitations.

6.1. Future Work

Advanced Backtesting: The next stage of research will involve implementing a rigorous walk-forward validation and backtesting engine to simulate live trading conditions and assess the framework's performance across different market regimes.

Dynamic Model Updating: We plan to investigate techniques for dynamically re-fitting or updating the symbolic formula in real-time or on a periodic basis, allowing the model to adapt to structural shifts in the market.

Sophisticated Ensembling: Further research will explore more advanced methods for combining the symbolic and residual predictions, such as weighting them based on real-time volatility or market condition indicators.

6.2. Limitations

Formula Complexity: While human-readable, the symbolic formulas distilled from highly complex phenomena can still be long and non-trivial to analyze, requiring domain expertise.

Computational Cost: The iterative training, pruning, and refinement process for KANs is more computationally intensive than training a standard neural network of comparable size.

Data Specificity: The optimal model configuration (e.g., KAN+GBM) is data-dependent. Applying this framework to new datasets or asset classes will require re-optimization and validation.

7. Conclusion

In this paper, we have presented the Apoth3osis hybrid modeling framework, a novel methodology that successfully unifies the objectives of high performance and mechanistic interpretability in financial forecasting. By orchestrating a workflow that distills a complex neural network into a human-readable symbolic equation and subsequently uses advanced machine learning techniques to model its residuals, we have demonstrated a practical path toward building more transparent, trustworthy, and powerful algorithmic trading systems.

This approach moves beyond conventional explainability, fostering a truly symbiotic relationship between the analytical expertise of a human and the computational power of AI. It is our belief that this line of research—focused on creating models that are not only powerful but also profoundly understandable—will define the next generation of artificial intelligence in finance and beyond.

8. References

Liu, Z., Wang, Y., et al. (2024). KAN: Kolmogorov-Arnold Networks. arXiv preprint arXiv:2404.19756.

Lundberg, S. M., & Lee, S.-I. (2017). A Unified Approach to Interpreting Model Predictions. Advances in Neural Information Processing Systems 30. 3.1 Hochreiter, S., & Schmidhuber, J. (1997). Long Short-Term Memory. Neural Computation, 9(8), 1735–1780.

Friedman, J. H. (2001). Greedy Function Approximation: A Gradient Boosting Machine. The Annals of Statistics, 29(5), 1189-1232.