Quantum Conflict Measurement in Decision Making for Out-of-Distribution Detection

TL;DR

This work tackles uncertainty in decision making by introducing Quantum Conflict Indicator (QCI) to quantify conflicts between quantum mass functions (QMFs) within Quantum Dempster-Shafer Theory. It defines the Quantum Correlation Coefficient (QCC) and derives QCI, proving key properties such as non-negativity, symmetry, boundedness, and extreme consistency. The authors then propose a QCI-based conflict fusion method and demonstrate its advantages over classical fusion rules on UCI benchmarks. They extend the approach to out-of-distribution detection with Class Description Domain Space (C-DDS) and its enhanced version C-DDS+, showing improved AUC and reduced FPR95 on ImageNet-scale tasks. Collectively, the methods offer a robust framework for conflict-aware information fusion and reliable OOD detection with practical impact in uncertainty-aware decision systems.

Abstract

Quantum Dempster-Shafer Theory (QDST) uses quantum interference effects to derive a quantum mass function (QMF) as a fuzzy metric type from information obtained from various data sources. In addition, QDST uses quantum parallel computing to speed up computation. Nevertheless, the effective management of conflicts between multiple QMFs in QDST is a challenging question. This work aims to address this problem by proposing a Quantum Conflict Indicator (QCI) that measures the conflict between two QMFs in decision-making. Then, the properties of the QCI are carefully investigated. The obtained results validate its compliance with desirable conflict measurement properties such as non-negativity, symmetry, boundedness, extreme consistency and insensitivity to refinement. We then apply the proposed QCI in conflict fusion methods and compare its performance with several commonly used fusion approaches. This comparison demonstrates the superiority of the QCI-based conflict fusion method. Moreover, the Class Description Domain Space (C-DDS) and its optimized version, C-DDS+ by utilizing the QCI-based fusion method, are proposed to address the Out-of-Distribution (OOD) detection task. The experimental results show that the proposed approach gives better OOD performance with respect to several state-of-the-art baseline OOD detection methods. Specifically, it achieves an average increase in Area Under the Receiver Operating Characteristic Curve (AUC) of 1.2% and a corresponding average decrease in False Positive Rate at 95% True Negative Rate (FPR95) of 5.4% compared to the optimal baseline method.

Figures (9)

• Figure 1: The Quantum Correlation Coefficient in Example 1.
• Figure 2: The Quantum Conflict Indicator in Example 2 when $y=0$.
• Figure 3: The Quantum Conflict Indicator in Example 2.
• Figure 4: The Quantum Conflict Indicator in Example 3.
• Figure 5: The Quantum Conflict Indicator in Example 4.