Cross-Dimension and Cross-Modality Relational Tensor Representation Learning for Multimodal Health Data Modeling

Self-supervised multimodal representation learning has achieved remarkable success across diverse domains, yet capturing synergistic information remains challenging due to the complexity of cross-modal interactions. Unlike the shared information across individual modalities, synergy arises when task-relevant signals emerge only from the joint configuration of multiple modalities and cannot be recovered from any modality in isolation. This work focuses on how to preserve the information capacity for such synergistic signals in multimodal representations. The key observation is that synergistic information is reflected in higher-order statistical dependence among modalities, which provides a principled target for explicitly modeling joint interactions. Motivated by this insight, we propose Higher-order Representation and Information Learning (HRIL), which constructs an empirical cross-moment tensor over modality embeddings to represent multi-way interactions. HRIL employs Tucker decomposition to obtain a core tensor, complemented by a synergy-aware regularizer that prevents energy concentration and preserves higher-order coupling capacity for synergistic information capture. Experiments on the controlled synergy task and real-world benchmarks demonstrate consistent improvements over existing multimodal contrastive methods, with notable gains on tasks dominated by synergistic interactions. Code is released at https://github.com/brightest66/HRIL.

Accurate time-to-event (TTE) prediction from multimodal clinical data remains challenging due to modality imbalance and distribution shift. We introduce a foundation model-driven framework for cross-modal representation alignment between CT imaging and longitudinal EHR data, designed to generalize across tasks and institutions. CT and EHR modalities are encoded independently using domain-specific foundation models and aligned in a shared latent space through four principled fusion strategies: late fusion, contrastive alignment, cross-attention, and co-attention. We evaluate two clinically distinct TTE tasks: pulmonary embolism (PE) mortality and cardiovascular disease (CVD) outcomes, on large-scale multi-institutional cohorts (PE: N=3,099 train; 1,098 internal; 435 external; CVD: N=2,951 train; 837 internal; 682 external). Fusion consistently improves concordance index by 1.5-5.4% over unimodal baselines when modalities contribute comparably. Overall, contrastive multimodal fusion, particularly with CLMBR representations, provided the most consistent and statistically robust improvements, especially for PE mortality prediction. For MACE, cross-attention (one-hot) achieved the highest internal performance and image-guided co-attention achieved the best external performance. We therefore introduce a generalizable foundation model-based cross-modal alignment framework and provide the first systematic analysis of fusion behavior under modality imbalance in TTE prediction. Our results establish task-aware multimodal alignment as a necessary design principle for robust generalization and scalable clinical deployment.

Multimodal fusion learning (MFL) has shown great potential in the medical domain, where we are faced with disparate data modalities such as imaging, clinical records, and omics. However, existing MFL strategies face several major challenges. First, they struggle to capture complex cross-modal interactions effectively, which in turn limits performance improvements. Second, they incur high computational costs, restricting their applicability in resource-constrained healthcare AI applications. Finally, they are often designed and evaluated for narrow, fixed modality configurations (e.g., imaging-only, or specific pairs such as image and omics), which limits evidence of their adaptability and generalizability to broader collections of heterogeneous medical modalities. To address these challenges, we propose a novel MFL framework - Cascaded Unified Representation Learning for Efficient Fusion Network (CURE) - a lightweight and scalable framework that progressively integrates various modalities through a novel efficient Hybrid Geometry Aware Fusion layer (HyFuse), where each HyFuse layer is sequentially learned for each modality, making the framework adaptable and generalizable. Within HyFuse, an efficient residual convolution module captures rich multi-scale features to ensure cost-effective learning, while a hybrid-space aware attention mixer learns coarse-to-fine structural cues to better preserve cross-modal relationships. Complementary learnable late-fusion and shared information refinement modules are then employed to learn robust modality-order-invariant shared representations, which in turn yields consistent performance improvements. Extensive evaluations on 16 public datasets show that CURE outperforms leading multimodal fusion methods, boosting performance by up to 3.97% and lowering computational costs by up to 87.8%, ensuring more effective and reliable predictions.