💰 quantitative finance

ARTEMIS: A Neuro Symbolic Framework for Economically Constrained Market Dynamics

The paper introduces ARTEMIS, a novel neuro-symbolic framework that integrates continuous-time Laplace Neural Operators, physics-informed neural stochastic differential equations, and differentiable symbolic bottlenecks to enforce economic plausibility and interpretability, achieving state-of-the-art directional accuracy on multiple financial datasets while bridging the gap between deep learning power and the transparency required in quantitative finance.

Original authors: Rahul D Ray

Published 2026-03-20

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Rahul D Ray

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to predict the weather. Most modern AI models are like super-smart but chaotic meteorologists. They have read every weather report in history and can spot complex patterns you can't see. However, they are "black boxes." You ask them, "Will it rain?" and they say, "Yes," but they can't explain why. Worse, sometimes they predict things that are physically impossible, like a hurricane forming in a desert because they found a weird pattern in the data that doesn't actually make sense.

This paper introduces ARTEMIS, a new kind of AI that tries to fix these problems. Think of ARTEMIS not just as a meteorologist, but as a meteorologist who is also a strict physics professor and a clear-spoken teacher.

Here is how ARTEMIS works, broken down into simple parts:

1. The Problem: The "Black Box" and the "Rule Breaker"

In finance (and other fields), deep learning models are great at guessing the future, but they have two big flaws:

They are opaque: No one knows how they make decisions. If a bank uses them to invest millions, regulators and risk managers get nervous because they can't ask, "Why did you do that?"
They break the rules: They often ignore basic economic laws. For example, they might predict a way to make infinite money with zero risk (an "arbitrage"), which is impossible in the real world. They learn "spurious" patterns—like thinking that "ice cream sales cause shark attacks" just because both happen in summer.

2. The Solution: ARTEMIS (The "Physics-Respecting" AI)

ARTEMIS is a Neuro-Symbolic Framework. That's a fancy way of saying it combines the pattern-finding power of a neural network (the "Neuro") with the logical rules of math and economics (the "Symbolic").

It has four main "superpowers":

A. The Continuous-Time Ear (Laplace Neural Operator)

Most AI models need data to be neatly lined up in a grid, like a spreadsheet. But real financial markets are messy; trades happen at random, split-second intervals.

The Analogy: Imagine trying to listen to a song where the notes are played at random speeds. A standard AI tries to force the notes into a grid, which distorts the music. ARTEMIS is like a musician with perfect pitch who can listen to the actual flow of the music, no matter how irregular the timing is. It understands the "continuous flow" of the market without forcing it into a box.

B. The Economic Bouncer (Physics-Informed Losses)

This is the most important part. ARTEMIS doesn't just guess; it is forced to obey the laws of economics.

The Analogy: Imagine a student taking a test. A normal AI is allowed to write any answer, even if it's nonsense, as long as it gets points. ARTEMIS has a strict Bouncer standing next to it.
- The "No-Arbitrage" Bouncer: If the AI tries to predict a way to make free money, the Bouncer slaps its hand and says, "No! That violates the laws of physics/economics."
- The "Sharpe Ratio" Bouncer: If the AI predicts a strategy that is too good to be true (like a 1000% return with zero risk), the Bouncer says, "That's unrealistic. Dial it back to something a real human could actually achieve."
The Result: The AI learns to predict the direction of the market (up or down) in a way that is actually possible in the real world.

C. The Translator (Differentiable Symbolic Bottleneck)

Usually, if you want to know why an AI made a decision, you have to use a "post-hoc" explanation (like asking a friend to guess what the AI was thinking). This is often inaccurate.

The Analogy: Instead of guessing, ARTEMIS has a Translator built inside it. As the AI processes data, it automatically distills its complex thoughts into simple, human-readable math formulas (like "Buy if Price > Average").
The Benefit: You don't have to guess why it bought a stock. It literally hands you a simple rule: "I bought this because the price dropped below the 50-day average." It's transparent by design, not by guesswork.

D. The Safety Net (Conformal Prediction)

In finance, knowing how sure you are is just as important as the prediction itself.

The Analogy: A normal AI says, "It will rain tomorrow." ARTEMIS says, "It will rain tomorrow, and I am 95% sure it will be between 2mm and 5mm." It gives you a confidence range, so you know when to trust the prediction and when to be careful.

3. The Results: How Did It Do?

The authors tested ARTEMIS against six other top-tier AI models (like LSTMs and Transformers) on four different datasets:

Jane Street: Real anonymized market data.
Optiver: Predicting stock volatility.
Time-IMM: Predicting air temperature (a non-financial test).
DSLOB: A synthetic "Crash" dataset. This is a fake market designed to simulate a massive, terrifying crash to see if the AI panics or stays logical.

The Winner:

Directional Accuracy: ARTEMIS was the champion at predicting direction (Up or Down). In the "Crash" test, it was correct 65% of the time, while others were barely better than flipping a coin.
Why? The ablation study (where they turned off parts of the AI) proved that the "Economic Bouncer" (the physics rules) was the secret sauce. When they removed the rules, the AI's ability to predict direction crashed to 41% (worse than random).
The Trade-off: ARTEMIS is slightly less accurate at predicting the exact price (magnitude) compared to some other models, but it is much better at predicting the direction. In trading, knowing "it will go up" is often more valuable than knowing "it will go up by $0.04."

Summary

ARTEMIS is a new AI framework that says: "We don't just want a smart guesser; we want a smart guesser who follows the rules and can explain its homework."

By forcing the AI to respect economic laws (like no free money) and translating its complex brain into simple math formulas, ARTEMIS bridges the gap between high-tech AI power and human trust. It's a step toward AI that we can actually use in high-stakes situations like managing a bank or investing your life savings, because we know why it's making its decisions and that it won't suggest impossible strategies.

1. Problem Statement

The paper addresses three critical limitations in applying deep learning to quantitative finance:

Lack of Interpretability: Deep learning models (e.g., LSTMs, Transformers) operate as "black boxes," creating regulatory and operational risks. Existing Explainable AI (XAI) techniques (like SHAP/LIME) are post-hoc approximations that do not resolve the inherent opacity of the architecture.
Violation of Economic Principles: Most models are trained purely on historical data correlations, ignoring fundamental constraints like the No-Arbitrage condition. This leads to spurious patterns and implausible predictions, especially during market regime shifts or crises.
Discrete-Time Limitations: Financial markets are continuous-time processes with irregular, high-frequency data. Standard discrete-time models require interpolation, which distorts underlying dynamics, and struggle with non-stationarity (changing market regimes).

2. Methodology: The ARTEMIS Framework

ARTEMIS (Arbitrage-free Representation Through Economic Models & Interpretable Symbolics) is a unified neuro-symbolic framework designed to overcome these challenges. It integrates four tightly coupled modules:

A. Continuous-Time Encoder (Laplace Neural Operator)

Function: Instead of resampling irregular data, ARTEMIS uses a Laplace Neural Operator (LNO) to map irregularly sampled market observations directly into a continuous latent function space.
Mechanism: It employs a learnable kernel in the Laplace domain ( $\hat{\kappa}(\omega) = \sum \frac{A_k}{\omega - \lambda_k}$ ) to process inputs without interpolation, preserving the true temporal structure of limit order book updates.

B. Economics-Informed Latent Dynamics (Neural SDE)

Function: The latent state evolves via a Neural Stochastic Differential Equation (Neural SDE): $dz = \mu_\theta(z, t)dt + \sigma_\phi(z, t)dW$ .
Physics-Informed Regularization: To ensure economic plausibility, the SDE is constrained by two novel loss terms derived from the Fundamental Theorem of Asset Pricing:
1. Feynman-Kac PDE Residual ( $L_{PDE}$ ): Enforces local no-arbitrage conditions by penalizing violations of the PDE governing derivative pricing in the latent space.
2. Market Price of Risk Penalty ( $L_{MPR}$ ): Bounds the instantaneous Sharpe ratio ( $\|\sigma^{-1}_\phi \mu_\theta\|^2$ ) to realistic values, preventing the model from learning unrealistically profitable (and likely overfitted) strategies.

C. Differentiable Symbolic Bottleneck

Function: Distills the complex latent dynamics into human-readable, closed-form trading rules.
Mechanism: A differentiable layer learns a sparse linear combination of basis functions (e.g., moving averages, ratios, differences) using a Gumbel-Softmax relaxation. This provides inherent interpretability without sacrificing end-to-end trainability.

D. Conformal Allocation Layer

Function: Quantifies uncertainty and generates risk-aware portfolio weights.
Mechanism: Uses adaptive conformal prediction to produce distribution-free prediction intervals with finite-sample coverage guarantees. These intervals feed into a differentiable Kelly criterion optimizer to determine optimal portfolio weights.

3. Key Contributions

Unified Neuro-Symbolic Architecture: First framework to combine continuous-time encoding (LNO), physics-constrained latent dynamics (Neural SDE), and differentiable symbolic regression in a single end-to-end system.
Novel Economic Regularization: Introduces the first application of Feynman-Kac PDE residuals and Market Price of Risk penalties specifically for forecasting latent dynamics, rather than just solving known pricing equations.
Inherent Interpretability: Moves beyond post-hoc explanations by forcing the model to output interpretable mathematical formulas via the symbolic bottleneck.
Robustness to Regime Shifts: Demonstrates superior performance in crash regimes compared to standard deep learning baselines.

4. Experimental Results

The model was evaluated against six strong baselines (LSTM, Transformer, NS-Transformer, Informer, Chronos-2, XGBoost) across four datasets:

Jane Street: Anonymized market data.
Optiver: Limit Order Book (LOB) volatility prediction.
Time-IMM: Environmental temperature forecasting (non-financial control).
DSLOB: A novel synthetic dataset simulating an amplified market crash regime.

Key Findings:

Directional Accuracy: ARTEMIS achieved State-of-the-Art (SOTA) directional accuracy.
- DSLOB (Crash Regime): 64.96% (outperforming all baselines; LSTM was 60.64%).
- Time-IMM: 96.0% (highest among all models).
Ablation Study (DSLOB): Confirmed the necessity of each component:
- Removing the PDE loss caused directional accuracy to drop from 64.89% to 50.32% (near random).
- Removing both physics losses collapsed accuracy to 41.77% (worse than random).
- Removing the SDE drastically improved point accuracy (RMSE) but slightly reduced directional accuracy, confirming the model's deliberate trade-off favoring sign prediction over magnitude precision.
Optiver Underperformance: ARTEMIS performed poorly on the Optiver dataset (RankIC: -0.0555). The authors attribute this to the dataset's long sequence length (600 steps), volatility-focused target (magnitude vs. direction), and limited feature set, highlighting boundary conditions for the framework.

5. Significance and Conclusion

ARTEMIS represents a paradigm shift in quantitative finance by bridging the gap between the predictive power of deep learning and the transparency/economic rigor demanded by regulators and practitioners.

Trustworthy AI: By embedding economic laws directly into the loss function, the model avoids "hallucinating" profitable but impossible strategies.
Interpretability: It provides closed-form trading rules, solving the "black box" problem without the accuracy-interpretability trade-off typical of post-hoc XAI.
Generalizability: The framework's success on the non-financial Time-IMM dataset suggests its applicability to other domains involving irregular time series and physical/economic laws (e.g., climate science, epidemiology).

The paper concludes that while ARTEMIS requires more computational resources and careful hyperparameter tuning, its ability to maintain robustness during market crashes and provide interpretable, economically grounded predictions makes it a significant advancement for high-stakes financial applications.