arXiv:2511.08878v2 Announce Type: replace-cross 
Abstract: Machine learning and data processing techniques relying on covariance information are widespread as they identify meaningful patterns in unsupervised and unlabeled settings. As a prominent example, Principal Component Analysis (PCA) projects data points onto the eigenvectors of their covariance matrix, capturing the directions of maximum variance. This mapping, however, falls short in two directions: it fails to capture information in low-variance directions, relevant when, e.g., the data contains high-variance noise; and it provides unstable results in low-sample regimes, especially when covariance eigenvalues are close. CoVariance Neural Networks (VNNs), i.e., graph neural networks using the covariance matrix as a graph, show improved stability to estimation errors and learn more expressive functions in the covariance spectrum than PCA, but require training and operate in a labeled setup. To get the benefits of both worlds, we propose Covariance Scattering Transforms (CSTs), deep untrained networks that sequentially apply filters localized in the covariance spectrum to the input data and produce expressive hierarchical representations via nonlinearities. We define the filters as covariance wavelets that capture specific and detailed covariance spectral patterns. We improve CSTs' computational and memory efficiency via a pruning mechanism, and we prove that their error due to finite-sample covariance estimations is less sensitive to close covariance eigenvalues compared to PCA, improving their stability. Our experiments on age prediction from cortical thickness measurements on 4 datasets collecting patients with neurodegenerative diseases show that CSTs produce stable representations in low-data settings, as VNNs but without any training, and lead to comparable or better predictions w.r.t. more complex learning models.

تبرز الدراسة الحديثة حول تحويلات تشتت التغاير (CST) التقدم في تقنيات التعلم الآلي التي تستخدم معلومات التغاير لتحديد الأنماط في البيئات غير المراقبة. تهدف CST إلى تحسين الأساليب التقليدية مثل تحليل المكونات الرئيسية (PCA) من خلال معالجة القيود في التقاط المعلومات ذات التباين المنخفض وتوفير الاستقرار في السيناريوهات ذات العينة المنخفضة.

El reciente estudio sobre las Transformaciones de Dispersión de Covarianza (CST) destaca los avances en técnicas de aprendizaje automático que utilizan información de covarianza para identificar patrones en entornos no supervisados. Las CST buscan mejorar métodos tradicionales como el Análisis de Componentes Principales (PCA) al abordar limitaciones en la captura de información de baja varianza y proporcionar estabilidad en escenarios de bajo muestreo.

La récente étude sur les Transformées de Dispersion de Covariance (CST) met en lumière les avancées des techniques d'apprentissage automatique qui utilisent les informations de covariance pour identifier des motifs dans des contextes non supervisés. Les CST visent à améliorer les méthodes traditionnelles comme l'Analyse en Composantes Principales (ACP) en abordant les limitations dans la capture des informations à faible variance et en fournissant une stabilité dans les scénarios à faible échantillon.

The recent study on Covariance Scattering Transforms (CSTs) highlights advancements in machine learning techniques that utilize covariance information to identify patterns in unsupervised settings. CSTs aim to improve upon traditional methods like Principal Component Analysis (PCA) by addressing limitations in capturing low-variance information and providing stability in low-sample scenarios.

Covariance Scattering Transforms

arXiv:2601.08733v1 Announce Type: new 
Abstract: Artificial Intelligence (AI) systems have shown good success at classifying. However, the lack of explainability is a true and significant challenge, especially in high-stakes domains, such as health and finance, where understanding is paramount. We propose a new solution to this challenge: an explainable AI framework based on our comparative study with Quantum Boltzmann Machines (QBMs) and Classical Boltzmann Machines (CBMs). We leverage principles of quantum computing within classical machine learning to provide substantive transparency around decision-making. The design involves training both models on a binarised and dimensionally reduced MNIST dataset, where Principal Component Analysis (PCA) is applied for preprocessing. For interpretability, we employ gradient-based saliency maps in QBMs and SHAP (SHapley Additive exPlanations) in CBMs to evaluate feature attributions.QBMs deploy hybrid quantum-classical circuits with strongly entangling layers, allowing for richer latent representations, whereas CBMs serve as a classical baseline that utilises contrastive divergence. Along the way, we found that QBMs outperformed CBMs on classification accuracy (83.5% vs. 54%) and had more concentrated distributions in feature attributions as quantified by entropy (1.27 vs. 1.39). In other words, QBMs not only produced better predictive performance than CBMs, but they also provided clearer identification of "active ingredient" or the most important features behind model predictions. To conclude, our results illustrate that quantum-classical hybrid models can display improvements in both accuracy and interpretability, which leads us toward more trustworthy and explainable AI systems.

تم اقتراح نهج جديد للذكاء الاصطناعي القابل للتفسير، مستفيدًا من آلات بولتزمان الكمومية (QBMs) وآلات بولتزمان الكلاسيكية (CBMs) لتعزيز الشفافية في اتخاذ القرار. يستخدم هذا الإطار خرائط السالينسي المعتمدة على التدرجات وSHAP لتقييم نسبة الميزات، مما يعالج التحدي الحاسم المتمثل في القابلية للتفسير في المجالات عالية المخاطر مثل الصحة والمالية.

Se ha propuesto un nuevo enfoque para la inteligencia artificial (IA) explicable, aprovechando las Máquinas de Boltzmann Cuánticas (QBMs) y las Máquinas de Boltzmann Clásicas (CBMs) para mejorar la transparencia en la toma de decisiones. Este marco utiliza mapas de saliencia basados en gradientes y SHAP para la atribución de características, abordando el desafío crítico de la explicabilidad en dominios de alto riesgo como la salud y las finanzas.

Une nouvelle approche de l'intelligence artificielle (IA) explicable a été proposée, tirant parti des machines de Boltzmann quantiques (QBMs) et des machines de Boltzmann classiques (CBMs) pour améliorer la transparence des décisions. Ce cadre utilise des cartes de saillance basées sur le gradient et SHAP pour l'attribution des caractéristiques, abordant le défi critique de l'explicabilité dans des domaines à enjeux élevés comme la santé et la finance.

A novel approach to explainable artificial intelligence (AI) has been proposed, leveraging Quantum Boltzmann Machines (QBMs) and Classical Boltzmann Machines (CBMs) to enhance decision-making transparency. This framework utilizes gradient-based saliency maps and SHAP for feature attribution, addressing the critical challenge of explainability in high-stakes domains like healthcare and finance.

A Novel Approach to Explainable AI with Quantized Active Ingredients in Decision Making

One More Thing in AI – Your Shortcut to AI Mastery

Covariance Scattering Transforms

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