Efficient Quantification of Multimodal Interaction at Sample Level

Interactions between modalities—redundancy, uniqueness, and synergy—collectively determine the composition of multimodal information. Understanding these interactions is crucial for analyzing information dynamics in multimodal systems, yet their accurate sample-level quantification presents significant theoretical and computational challenges. To address this, we introduce the Lightweight Sample-wise Multimodal Interaction (LSMI) estimator, rigorously grounded in pointwise information theory. We first develop a redundancy estimation framework, employing an appropriate pointwise information measure to quantify this most decomposable and measurable interaction.Building upon this, we propose a general interaction estimation method that employs efficient entropy estimation, specifically tailored for sample-wise estimation in continuous distributions. Extensive experiments on synthetic and real-world datasets validate LSMI's precision and efficiency. Crucially, our sample-wise approach reveals fine-grained sample- and category-level dynamics within multimodal data, enabling practical applications such as redundancy-informed sample partitioning, targeted knowledge distillation, and interaction-aware model ensembling. The code is available at https://github.com/GeWu-Lab/LSMI_Estimator.

We quantify how information is generated through multimodal interactions, efficiently distinguishing whether it originates from shared sources across modalities, is specific to a single modality, or emerges synergistically from their combined effect. This quantification offers practical insights for real-world datasets.