Beyond Black Boxes: Quantum Networks Illuminate Credit Risk

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Author: Denis Avetisyan

A new approach leverages the power of qudits to build interpretable quantum neural networks for improved credit risk assessment.

Across multiple simulation runs on the Taiwan credit dataset, the Quantum Neural Network (QNN) demonstrated a consistently higher macro-averaged $F1$-score compared to Random Forest (RF), Neural Network (NN), and Logistic Regression (LR), as evidenced by the spread indicated by standard deviations across those runs.
Across multiple simulation runs on the Taiwan credit dataset, the Quantum Neural Network (QNN) demonstrated a consistently higher macro-averaged $F1$-score compared to Random Forest (RF), Neural Network (NN), and Logistic Regression (LR), as evidenced by the spread indicated by standard deviations across those runs.

This review details a qudit-based quantum neural network with Hamiltonian encoding for competitive and interpretable credit risk prediction, focusing on feature importance analysis.

Balancing predictive power and model transparency remains a central challenge in financial modeling, particularly within high-stakes applications like credit-risk assessment. This is addressed in ‘Feature Ranking in Credit-Risk with Qudit-Based Networks’, which introduces a novel quantum neural network leveraging a single qudit and Hamiltonian encoding to simultaneously achieve competitive performance and interpretable feature importance. Benchmarked on a real-world Taiwanese credit-risk dataset, the proposed model matches the accuracy of random forests while offering a clear link between learned parameters and input feature rankings. Could this approach pave the way for more trustworthy and explainable quantum machine learning in finance?

The Erosion of Transparency in Modern Machine Learning

Many contemporary machine learning models, particularly complex neural networks, excel at identifying patterns and making predictions, often achieving state-of-the-art accuracy. However, this performance frequently comes at the cost of interpretability. These models function as ‘black boxes’ – their internal logic remains opaque, making it difficult to discern why a specific prediction was made. This lack of transparency poses significant challenges for debugging; errors are difficult to trace and correct without understanding the model’s reasoning. More critically, the inability to explain predictions erodes trust, especially in high-stakes applications where accountability and fairness are essential. Consequently, a growing body of research focuses on developing methods to open these black boxes and provide insights into their decision-making processes, aiming to balance predictive power with human understanding.

In sectors dealing with high-stakes decisions, such as credit risk assessment, the opacity of machine learning models presents significant challenges. A loan denial determined by an uninterpretable algorithm can have profound consequences for an individual, yet the reasons behind that decision may remain hidden. Regulatory pressures, like those stemming from fair lending laws, increasingly demand that financial institutions not only demonstrate the accuracy of their models but also the reasoning behind their predictions. This need for transparency extends beyond legal compliance; it fosters trust with customers, allows for effective auditing and debugging of potential biases, and ultimately promotes responsible innovation in automated decision-making systems. Consequently, the pursuit of explainable AI is not merely a technical endeavor, but a critical step towards ensuring fairness, accountability, and ethical implementation in sensitive domains.

The pursuit of highly accurate machine learning models frequently comes at the cost of interpretability, creating a significant challenge for practical application. While complex algorithms, such as deep neural networks, excel at identifying patterns and making predictions, the reasoning behind those predictions often remains opaque. This trade-off between predictive power and explainability is not merely an academic concern; it presents real-world problems, particularly when deploying these models in high-stakes scenarios. Current approaches to model interpretation, like feature importance analysis or surrogate models, often provide only a partial or approximate understanding of the decision-making process, and can sometimes be misleading. The core difficulty lies in the fact that increasing model complexity-a common path to higher accuracy-typically exacerbates the challenge of discerning the factors driving each prediction, hindering trust and making it difficult to debug or refine the system effectively. Consequently, researchers are actively exploring techniques that strive to build models that are both powerful and transparent, aiming to unlock the full potential of machine learning while maintaining accountability and fostering confidence in its outcomes.

As model size increases, both QNN and RF exhibit decreasing alignment with the interpretability of linear regression, as measured by edit distance between feature-importance vectors.
As model size increases, both QNN and RF exhibit decreasing alignment with the interpretability of linear regression, as measured by edit distance between feature-importance vectors.

Introducing the Qudit Quantum Neural Network: A Path to Transparent Computation

The Qudit Quantum Neural Network (QNN) represents a departure from traditional quantum neural network architectures by utilizing qudits – quantum digits with dimensionality greater than two – as the fundamental unit of information. This allows for a more compact representation of data and model parameters, potentially reducing the number of quantum gates required for computation compared to qubit-based systems. Furthermore, the QNN architecture is designed to enhance interpretability by facilitating a more direct correspondence between model parameters and learned features. This is achieved through specific encoding schemes and network structures that aim to make the decision-making process of the network more transparent and understandable, a significant challenge in many deep learning applications. The combination of these factors positions the QNN as a potentially advantageous approach for both computational efficiency and model explainability.

Traditional quantum circuits utilize qubits, which represent information as a superposition of 0 and 1. The Qudit Quantum Neural Network (QNN) expands upon this by employing qudits, quantum digits capable of representing states in a $d$-dimensional Hilbert space, where $d$ is an integer greater than 2. This generalization allows for a more compact representation of data; a qudit can encode log2($d$) bits of information. Consequently, the QNN requires fewer qudits to represent the same amount of data as a qubit-based system, directly reducing the number of quantum gates needed for computation. This reduction in gate count minimizes the impact of quantum decoherence and gate errors, contributing to improved computational efficiency and scalability compared to traditional quantum circuits.

Hamiltonian encoding within the Qudit Quantum Neural Network (QNN) establishes a direct correspondence between input data, model parameters, and the Hamiltonian operator, $H$. This is achieved by mapping data features to the terms within the Hamiltonian, and trainable parameters function as coefficients modulating these terms. Consequently, the network’s energy landscape directly reflects the input data, facilitating learning of complex relationships through optimization of the Hamiltonian. This approach reduces the need for extensive parameterization common in traditional neural networks and allows the QNN to efficiently represent and process high-dimensional data by leveraging the inherent structure of quantum mechanics.

This multilayer quantum neural network (QNN) employs Hamiltonian-based feature encoding and iterative gradient descent to sequentially apply unitary operations to a base qudit, ultimately producing a measurable output.
This multilayer quantum neural network (QNN) employs Hamiltonian-based feature encoding and iterative gradient descent to sequentially apply unitary operations to a base qudit, ultimately producing a measurable output.

Validating Robustness: Feature Poisoning as a Stress Test

Feature Poisoning is utilized to evaluate the robustness of the Quantum Neural Network (QNN) by introducing minor perturbations to the input features of the dataset. This technique aims to deliberately degrade model performance and assess the QNN’s susceptibility to adversarial manipulation. The process involves systematically altering feature values – introducing small, controlled noise – to determine the extent to which these changes impact the QNN’s predictive accuracy and stability. By quantifying the performance drop under these controlled attacks, we can gauge the model’s resilience and compare it to that of classical machine learning algorithms, such as Logistic Regression and Random Forest.

Quantifying interpretability loss under feature poisoning attacks involves assessing the shifts in feature importance rankings. This is achieved by training both the Quantum Neural Network (QNN) and classical machine learning models – Logistic Regression and Random Forest – and then subjecting them to manipulated input data. The degree to which the feature importance order changes for each model, when comparing pre-attack and post-attack rankings, provides a measure of how much the attack has degraded the model’s ability to consistently identify key predictive features. This comparison allows for a direct assessment of which models exhibit greater stability in their internal reasoning processes when confronted with adversarial data.

Edit Distance, specifically the Levenshtein distance, is employed as a quantitative metric to assess the similarity between Feature Importance rankings generated by the Quantum Neural Network (QNN) and classical machine learning models. This metric calculates the minimum number of single-character edits – insertions, deletions, or substitutions – required to change one ranking into another; a lower Edit Distance indicates greater similarity. By utilizing Edit Distance, a standardized and objective comparison is established, circumventing the limitations of subjective visual inspections of ranking lists and providing a robust measure for evaluating changes in interpretability under adversarial conditions like feature poisoning.

The Quantum Neural Network (QNN) achieved a macro-averaged F1-score of 0.667 when evaluated on the credit risk dataset. This performance metric indicates a balance between precision and recall across all classes in the dataset. Critically, this F1-score is comparable to the performance achieved by established classical Neural Network models when assessed using the same dataset and evaluation criteria, demonstrating the QNN’s competitive capability in a practical machine learning task. The macro-averaged F1-score is calculated as the average of the F1-scores for each class, providing an overall measure of the model’s effectiveness in multi-class classification.

Feature Importance rankings were compared between the Quantum Neural Network (QNN) and classical machine learning models using Edit Distance as a metric for assessing interpretability similarity. The QNN demonstrated an Edit Distance of 21 when compared to Logistic Regression, indicating a comparable level of alignment in feature importance as observed with Random Forest, which also yielded an Edit Distance of 21. This suggests that the QNN, despite utilizing a different computational paradigm, arrives at a similar understanding of which features drive its predictions as these established classical models.

Under conditions of data corruption, the Quantum Neural Network (QNN) achieved a macro-averaged F1-score of 0.632. This performance surpasses that of both Logistic Regression, which yielded an F1-score of 0.579, and Random Forest, which obtained a score of 0.614. These results indicate a greater degree of robustness in the QNN’s predictive capability when subjected to compromised input data, suggesting its ability to maintain accuracy despite data inconsistencies or malicious alterations.

Ridge Regression was implemented as a regularization technique during the Quantum Neural Network (QNN) training process to mitigate the impact of feature poisoning attacks. This L2 regularization adds a penalty term, $\lambda ||w||^2$, to the loss function, where $w$ represents the weight vector and $\lambda$ is the regularization parameter. By penalizing large weights, Ridge Regression promotes a more stable and generalized model, reducing the sensitivity of the QNN to subtle alterations in input features introduced by the poisoning attack. This stabilization is crucial for maintaining consistent feature importance rankings and overall model performance when faced with adversarial data.

Under the Hood: The Mathematical Foundations and Future Trajectory

The quantum neural network’s (QNN) ability to process information is deeply rooted in the mathematical structure of SU(d) algebra, a system that dictates how the network’s fundamental building blocks – the Hamiltonian generators – are constructed and interact. This algebra, representing unitary transformations, provides the framework for manipulating quantum states and implementing the computational steps within the QNN. Specifically, SU(d) defines the allowed transformations while ensuring the preservation of probability, a critical requirement for quantum computation. The choice of SU(d) isn’t arbitrary; it directly influences the expressibility and complexity of the quantum circuit, impacting the network’s capacity to learn and generalize from data. By carefully selecting the generators within this algebraic framework, researchers can tailor the QNN’s capabilities for specific tasks, effectively controlling its power and efficiency in solving complex problems.

The Baker-Campbell-Hausdorff (BCH) formula serves as a foundational tool in constructing complex quantum circuits, particularly within the realm of Variational Quantum Algorithms. This formula provides a means to approximate the composition of a sequence of quantum gates, effectively calculating the total transformation resulting from their combined application. Since directly calculating the composition of an arbitrary number of gates can be computationally expensive, the BCH formula offers a truncated series expansion – a practical approximation that balances accuracy and computational feasibility. This allows researchers to efficiently model the evolution of quantum states within the variational circuit, enabling the optimization of circuit parameters to achieve desired outcomes. The accuracy of this approximation is vital, as even small errors can accumulate and significantly impact the performance of the quantum neural network, highlighting the formula’s critical role in realizing practical quantum machine learning applications.

The training of this quantum neural network (QNN) is fundamentally driven by the principle of minimizing information loss, achieved through the implementation of Cross-Entropy Loss. This loss function quantifies the dissimilarity between the predicted probability distribution generated by the QNN and the actual, desired distribution representing the correct classification. Essentially, it measures how much “information” is lost when approximating the true distribution with the model’s output. A lower Cross-Entropy Loss indicates a closer alignment between prediction and reality, guiding the optimization process to refine the QNN’s parameters. Mathematically, it’s often expressed as $L = -\sum_{i} y_i \log(\hat{y}_i)$, where $y_i$ represents the true label and $\hat{y}_i$ the predicted probability for class $i$. By iteratively reducing this loss, the QNN learns to produce more accurate probability distributions, thereby improving its classification performance and overall reliability.

The development of quantum neural networks, as demonstrated by this research, holds significant promise for advancing the field of artificial intelligence beyond current limitations in trust and interpretability. Traditional AI, often described as a ‘black box’, struggles to provide clear reasoning for its decisions, a critical flaw in sensitive areas like financial risk assessment where transparency is paramount. By leveraging the principles of quantum mechanics, these networks offer the potential for more explainable models; the inherent structure of quantum states and operations may allow for a clearer understanding of the decision-making process. This isn’t merely about achieving higher accuracy, but about building AI systems where the basis for predictions can be audited and verified, fostering greater confidence and accountability in high-stakes applications and ultimately promoting responsible innovation in the broader AI landscape.

The pursuit of predictive accuracy, as demonstrated by this work on qudit-based networks for credit risk, inevitably introduces complexity. Systems, even those designed for stability like financial modeling, are not immune to the effects of time and increasing intricacy. As Max Planck observed, “A new scientific truth does not triumph by convincing its opponents and proclaiming that they are wrong. It triumphs by causing an older generation to die out.” This research, while offering competitive performance through Hamiltonian encoding and qudit utilization, represents a shift in approach – a new generation of methods challenging established classical models. The assessment of feature importance, a core component of this study, acknowledges the eventual decay of simpler systems and the necessity for constant re-evaluation, even in the face of apparent stability.

What Lies Ahead?

The pursuit of enhanced predictive power in credit-risk modeling, as demonstrated by this work, inevitably encounters the limitations inherent in any system attempting to forecast the future. This qudit-based network, while offering a compelling blend of performance and interpretability, is but a single version in the ongoing evolution of financial algorithms. The true test lies not in initial accuracy, but in graceful degradation as market conditions shift-a measure of resilience more telling than peak performance. Versioning, in this context, is a form of memory, retaining the lessons of past failures to inform future iterations.

Interpretability, a lauded feature, remains a relative concept. While feature importance rankings provide insight, they are snapshots, frozen moments in a dynamic system. The relationships between features and risk are rarely static; they drift, mutate, and occasionally invert. The arrow of time always points toward refactoring-toward models that not only predict, but also adapt and explain their changing internal logic.

Future work will likely focus on hybrid architectures, blending the strengths of quantum and classical approaches. However, the ultimate challenge is not computational power, but conceptual-to move beyond correlation and toward a deeper understanding of the underlying causal mechanisms driving financial risk. The model is a map, not the territory, and its fidelity will always be imperfect.

Original article: https://arxiv.org/pdf/2511.19150.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-11-25 23:16