TRIAD: Ternary Information Routing for Multimodal Time-Series Sensing Signals

Multimodal time series captured by heterogeneous sensors are fundamental to real-world applications, yet learning effective representations without labels remains challenging. Existing self-supervised methods adopt a binary paradigm that decomposes information into shared and private components, conflating two distinct types of shared information: redundancy, the consensus information recoverable from any single modality, and synergy, the emergent information arising only from joint observation. Most methods also rely on geometric constraints for disentanglement, which cannot guarantee semantic-level separation of information components. To address these limitations, we propose TRIAD, a framework that advances multimodal disentanglement from a binary to a ternary paradigm by separating a triad of information components: redundancy, synergy, and uniqueness. Inspired by Partial Information Decomposition theory, TRIAD employs a two-stage attention-based routing mechanism. The first stage extracts cross-modal redundancy, while the second stage disentangles synergy from modality-specific uniqueness. Predictive proxy tasks enforce the semantic definition of each component through prediction objectives. Extensive experiments on synthetic and real-world benchmarks show consistent improvements over state-of-the-art methods, with ablations, robustness tests, and interpretability analyses confirming that the learned components are functionally specialized.