Structured Epistemic Representations for Trustworthy and Interpretable AI: A Positive Operator-Valued Measure-Based Quantum-Inspired Framework for Multi-Source Uncertainty
Although new AI systems have been developed based on the integration of information from multiple sources under conditions of uncertainty, classical probabilistic models are unable to provide structured, interpretable, and reliable representations in the presence of contextual and order effects. Specifically, the fundamental principles of Kolmogorov’s assumptions underlying the modeling overlook certain common violations in real-world decision-making processes, such as non-commutativity, contextual dependence among agents, and interaction effects between information sources characterized by experiential heterogeneity. A Positive Operator-Valued Measure (POVM) formalism defined on a Hilbert space of latent states forms the basis of this article’s structured epistemic representation framework to support the reliability and interpretability of the black box in AI. The resulting model generalizes the classical epistemic quadruplet: Probability, Plausibility, Credibility, and Possibility within a single geometric framework in which three essential non-classical effect mechanisms emerge—(i) the non-commutativity of information acquisition, (ii) the contextuality arising from incompatible observational frameworks, and (iii) the interference interactions between information acquisition channels. We propose the concept of a quantum-inspired fusion operator (QI-Happenability), which introduces symmetric and antisymmetric feedback interaction terms based on the estimation of ordered residuals. An analysis of the proposed framework is then performed using real data, validating the model on the Efron et al. diabetes regression dataset (N = 442; ten standardized physiological predictors; continuous disease progression target), available in scikit-learn, which showed a 17.4% reduction in mean absolute error (MAE) compared to traditional models and significant improvements over polynomial machine learning baselines, as well as ensemble machine learning methods, within a rigorous cross-validation protocol. Contextual analysis indicates that 68% of cases violate classical bounds (CHSH inequality, p < 0.001), empirically confirming the non-classical structured representation in multi-source data. The results confirm the proposed approach as a simpler, more interpretable, and more reliable alternative to black-box models: this work demonstrates how the use of structured epistemic representations in reasoning under uncertainty preserves formal interpretability while retaining useful semantic information. By linking quantum cognition and applied AI, this work could help lay the groundwork for a new generation of interpretable and reliable decision-making systems.
Although new AI systems have been developed based on the integration of information from multiple sources under conditions of uncertainty, classical probabilistic models are unable to provide structured, interpretable, and reliable representations in the presence of contextual and order effects. Specifically, the fundamental principles of Kolmogorov’s assumptions underlying the modeling overlook certain common violations in real-world decision-making processes, such as non-commutativity, contextual dependence among agents, and interaction effects between information sources characterized by experiential heterogeneity. A Positive Operator-Valued Measure (POVM) formalism defined on a Hilbert space of latent states forms the basis of this article’s structured epistemic representation framework to support the reliability and interpretability of the black box in AI. The resulting model generalizes the classical epistemic quadruplet: Probability, Plausibility, Credibility, and Possibility within a single geometric framework in which three essential non-classical effect mechanisms emerge—(i) the non-commutativity of information acquisition, (ii) the contextuality arising from incompatible observational frameworks, and (iii) the interference interactions between information acquisition channels. We propose the concept of a quantum-inspired fusion operator (QI-Happenability), which introduces symmetric and antisymmetric feedback interaction terms based on the estimation of ordered residuals. An analysis of the proposed framework is then performed using real data, validating the model on the Efron et al. diabetes regression dataset (N = 442; ten standardized physiological predictors; continuous disease progression target), available in scikit-learn, which showed a 17.4% reduction in mean absolute error (MAE) compared to traditional models and significant improvements over polynomial machine learning baselines, as well as ensemble machine learning methods, within a rigorous cross-validation protocol. Contextual analysis indicates that 68% of cases violate classical bounds (CHSH inequality, p < 0.001), empirically confirming the non-classical structured representation in multi-source data. The results confirm the proposed approach as a simpler, more interpretable, and more reliable alternative to black-box models: this work demonstrates how the use of structured epistemic representations in reasoning under uncertainty preserves formal interpretability while retaining useful semantic information. By linking quantum cognition and applied AI, this work could help lay the groundwork for a new generation of interpretable and reliable decision-making systems.
In this work, we propose a novel quantum-informed epistemic framework that extends the classical notion of probability by integrating plausibility, credibility, and possibility as distinct yet complementary measures of uncertainty. This enriched quadruple (P, Pl, Cr, Ps) enables a deeper characterization of quantum systems and decision-making processes under partial, noisy, or ambiguous information. Our formalism generalizes the Born rule within a multi-valued logic structure, linking Positive Operator-Valued Measures (POVMs) with data-driven plausibility estimators, agent-based credibility priors, and fuzzy-theoretic possibility functions. We develop a hybrid classical-quantum inference engine that computes a vectorial aggregation of the quadruples, enhancing robustness and semantic expressivity in contexts where classical probability fails to capture non-Kolmogorovian phenomena such as entanglement, contextuality, or decoherence. The approach is validated through three real-world application domains-quantum cybersecurity, quantum AI, and financial computing-where the proposed model outperforms standard probabilistic reasoning in terms of accuracy, resilience to noise, interpretability, and decision stability. Comparative analysis against QBism, Dempster-Shafer, and fuzzy quantum logic further demonstrates the uniqueness of architecture in both operational semantics and practical outcomes. This contribution lays the groundwork for a new theory of epistemic quantum computing capable of modelling and acting under uncertainty beyond traditional paradigms.
Human reasoning is traditionally modeled through rational-order frameworks that assume stability, separability, and coherence. Yet across judgment, valuation, perception, and social decision-making, empirical work consistently reveals patterned violations of these assumptions. These deviations intensify in real-world contexts shaped by institutional constraints, identity commitments, and collective narratives, where reasoning must navigate incompatible interpretive frames and interdependent evaluative pressures. Existing theories typically treat such phenomena as noise, bias, or bounded rationality, leaving no formal account of how rational-order rules interact with the variability inherent in social domains. This article proposes a structural framework that explains why these two regimes diverge and how their interaction produces systematic mismatches. Building on quantum probability theory, not as a physical metaphor but as a representational tool, it formalizes evaluative states that remain indeterminate until elicited, transform under contextual modulation, and become relationally coupled across agents and domains. Whereas, existing quantum-cognition models primarily address task-level effects such as conjunction errors or order dependence, this framework scales quantum principles to socially and institutionally embedded reasoning. The account identifies contradiction, interference, entanglement, and resolution as recurrent properties of real-world cognition and shows how quantum formalisms provide a coherent vocabulary for capturing these phenomena. To support cumulative progress, the article outlines a research agenda with empirically testable designs for distinguishing incompatible bases, assessing inseparability, modeling context-driven transformations, and integrating multi-level reasoning environments. This program positions quantum and classical approaches within a unified architecture and advances a broader science of reasoning.
Abstract Machine learning systems are increasingly deployed in environments where decision errors carry significant consequences. In such settings, predictive probabilities alone often provide an incomplete basis for decision making, as they do not reveal why uncertainty arises or whether competing hypotheses are present. This limitation can lead to overconfident decisions, particularly when models encounter ambiguous or evolving conditions.This work introduces a quantum-inspired decision framework that represents predictive uncertainty using a density matrix formulation. Without relying on quantum hardware or computational assumptions, the proposed approach models structured interactions among hypotheses through off-diagonal terms in a normalized state representation. An ambiguity-aware adaptive threshold is derived from this structure and applied as a post-hoc decision layer, thereby regulating decisions without modifying or retraining the underlying predictive model.Theoretical analysis clarifies how structured ambiguity differs from scalar uncertainty measures, and controlled synthetic experiments illustrate its impact on decision boundaries and precision–recall behavior. Results show that the proposed method enables selective suppression of decisions in ambiguous regions while maintaining interpretability and controllability. By bridging uncertainty modeling with practical decision regulation, this framework contributes a simple and extensible mechanism for more reliable AI deployment in high-stakes applications.
The rapid advancement of Artificial Intelligence (AI) has heightened concerns about the opacity of decision-making processes in complex models, particularly deep neural networks. This research explores a novel paradigm that integrates quantum computing principles into Explainable AI (XAI) to enhance interpretability without compromising predictive accuracy. The study introduces a Quantum-inspired Interpretable Model (QIIM) framework that leverages Hilbert space embeddings, unitary transformations, and operator-based learning to represent knowledge in a mathematically transparent form. The proposed model computes interpretability through the expectation values of observable operators, enabling the decomposition of decisions into quantifiable, human-understandable components. To capture hierarchical relationships, a Tensor Network Interpretable Model (TNIM) is further developed, offering scalable insights into complex dependencies among features. Experimental evaluations—performed on benchmark datasets for decision-making tasks—demonstrate that the quantum-inspired models achieve competitive accuracy while significantly improving local and global interpretability metrics compared to classical XAI techniques. The findings underscore the potential of quantum formalism as a new foundation for transparent AI systems, bridging the gap between computational efficiency and explainability. This study contributes to both theoretical understanding and practical advancement in interpretable machine learning, paving the way for ethically aligned, transparent, and human-trustworthy AI-driven decision support systems.
A long-standing goal in the field of Artificial Intelligence (AI) is to develop systems that can perceive and understand human multimodal language. This requires both the consideration of context in the form of surrounding utterances in a conversation, i.e., context modelling, as well as the impact of different modalities (e.g., linguistic, visual acoustic), i.e., multimodal fusion. In the last few years, significant strides have been made towards the interpretation of human language due to simultaneous advancement in deep learning, data gathering and computing infrastructure. AI models have been investigated to either model interactions across distinct modalities, i.e., linguistic, visual and acoustic, or model interactions across parties in a conversation, achieving unprecedented levels of performance. However, AI models are often designed with only performance as their design target, leaving aside other essential factors such as transparency, interpretability, and how humans understand and reason about cognitive states. In line with this observation, in this dissertation, we develop quantum probabilistic neural models and techniques that allow us to capture rational and irrational cognitive biases, without requiring a priori understanding and identification of them. First, we present a comprehensive empirical comparison of state-of-the-art (SOTA) modality fusion strategies for video sentiment analysis. The findings provide us helpful insights into the development of more effective modality fusion models incorporating quantum-inspired components. Second, we introduce an end-to-end complex-valued neural model for video sentiment analysis, simulating quantum procedural steps, outside of physics, into the neural network modelling paradigm. Third, we investigate non-classical correlations across different modalities. In particular, we describe a methodology to model interactions between image and text for an information retrieval scenario. The results provide us with theoretical and empirical insights to develop a transparent end-to-end probabilistic neural model for video emotion detection in conversations, capturing non-classical correlations across distinct modalities. Fourth, we introduce a theoretical framework to model user's cognitive states underlying their multimodal decision perspectives, and propose a methodology to capture interference of modalities in decision making. Overall, we show that our models advance the SOTA on various affective analysis tasks, achieve high transparency due to the mapping to quantum physics meanings, and improve post-hoc interpretability, unearthing useful and explainable knowledge about cross-modal interactions.
Contemporary discussions of the gap between natural and artificial intelligence often emphasize human capacities such as contextual reasoning, cognitive flexibility, and non-classical decision-making. This paper proposes that quantum and quantum-like models of cognition and decision processes offer a principled framework for addressing these differences. A growing body of empirical evidence shows that human reasoning systematically violates the assumptions of classical probability and logic, exhibiting contextuality, order effects, interference phenomena, and task incompatibility. Quantum probability theory and related quantum-like formalisms provide mathematically rigorous tools—based on Hilbert spaces, superposition, and entanglement—that capture these features more naturally than classical models. While quantum and quantum-like approaches share a common mathematical structure, they differ in physical implementation, motivating two complementary directions in artificial intelligence: quantum AI and quantum-like AI. Together, these approaches suggest a viable pathway toward narrowing, and potentially bridging, the divide between natural and artificial intelligence by grounding AI architectures in models aligned with the structure of human cognition.