Feature Ranking in Credit-Risk with Qudit-Based Networks

TL;DR

The paper introduces a qudit-based quantum neural network that co-encodes input features and trainable weights within a unified Hamiltonian framework over the su($d$) algebra, enabling intrinsic feature attribution via weight magnitudes. By stacking multiple Hamiltonian-encoded layers, the model achieves expressive nonlinear dynamics while maintaining interpretability through direct links between $x_j$ and $w_j$ and their associated generators. Validation on the Taiwan credit-risk dataset shows the QNN attaining macro-F1 around $0.667$, outperforming Logistic Regression and approaching a classical Neural Network in predictive power, with a smaller parameter footprint and interpretable rankings assessed via edit distance and a poisoning-based Weighted Interpretability Score (WIS). The results advocate for a practical, interpretable quantum-learning path in finance, suggesting deeper quantum architectures can further boost performance while preserving transparency; future work includes extending to multi-qudit systems and broader high-stakes applications.

Abstract

In finance, predictive models must balance accuracy and interpretability, particularly in credit risk assessment, where model decisions carry material consequences. We present a quantum neural network (QNN) based on a single qudit, in which both data features and trainable parameters are co-encoded within a unified unitary evolution generated by the full Lie algebra. This design explores the entire Hilbert space while enabling interpretability through the magnitudes of the learned coefficients. We benchmark our model on a real-world, imbalanced credit-risk dataset from Taiwan. The proposed QNN consistently outperforms LR and reaches the results of random forest models in macro-F1 score while preserving a transparent correspondence between learned parameters and input feature importance. To quantify the interpretability of the proposed model, we introduce two complementary metrics: (i) the edit distance between the model's feature ranking and that of LR, and (ii) a feature-poisoning test where selected features are replaced with noise. Results indicate that the proposed quantum model achieves competitive performance while offering a tractable path toward interpretable quantum learning.

Figures (3)

• Figure 1: Multilayer QNN architecture with Hamiltonian-based feature encoding. At each layer, classical input features are re-mapped and combined with trainable weights to form coefficients for a set of $\mathfrak{su}(d)$ generators, defining the layer Hamiltonian. This process is repeated over $L$ layers in a data re-uploading fashion. The resulting unitary operations sequentially act on a single base qudit, followed by measurement. The model parameters are optimized iteratively using gradient descent.
• Figure 2: Macro-averaged F1-score of the QNN, RF, NN, and LR on the Taiwan credit dataset. Shaded regions denote standard deviations across runs.
• Figure 3: Edit distance between feature-importance vectors of QNN and RF relative to LR as a function of model size. Lower values indicate closer alignment with LR’s interpretability.