QEGF: A Quantum-Inspired Geometric and Energy-Based Fusion Framework for Multimodal Sentiment Analysis.

Conventional Euclidean fusion paradigms in multimodal sentiment analysis (MSA) fail to capture non-Euclidean correlations and probabilistic uncertainty across modalities, often leading to misaligned affective representations and limited robustness under real-world variability. To overcome these challenges, we introduce the novel Quantum-Inspired Geometric and Energy-Based Fusion (QEGF) framework that unifies geometric sentiment representation with probabilistic uncertainty modeling for more reliable affective perception. First, the Quantum-Inspired Geometric Fusion (QGF) operator represents each modality as a trace-normalized Symmetric Positive-Definite (SPD) density descriptor, enabling second-order correlation modeling and adaptive gating via a spectral entropy statistic from each trace-normalized SPD descriptor. This design decouples structural encoding from semantic refinement, significantly mitigating performance degradation under noisy and corrupted inputs, and achieving a 4.55% Acc-2 gain over Cross-Attention in domain shift scenarios. Second, Energy-Based Uncertainty Modeling (EBUM) introduces a contrastive energy objective with a batch-level energy-dispersion signal, stabilizing convergence and yielding a lower Brier score (0.172 to 0.135) in the output-level calibration diagnostic under domain shift. Comprehensive evaluations across major benchmarks confirm that QEGF achieves state-of-the-art performance and superior resilience, laying a pathway toward more interpretable and resilient affective human-machine interaction.