Decomposed Representations Mitigate the Alignment–Specificity Trade-off in Multi-Omics

Single-cell multi-omics technologies jointly measure multiple modalities from the same cell, such as gene expression, chromatin accessibility, and surface protein abundance, providing a richer view of cellular state than any single modality alone. A central challenge is how to learn a multimodal cell representation that preserves the different types of information contained in these co-profiled measurements. Existing integration methods often emphasize either cross-modal correspondence, which benefits retrieval and imputation, or fused discriminative structure, which benefits classification, but these objectives can favor different aspects of the data. As a result, a representation optimized for one setting may fail to preserve information needed for another. We introduce scDecomp, a decomposed representation learning framework for co-profiled single-cell multi-omics data. Motivated by the concepts of redundancy, uniqueness, and synergy, scDecomp separates multimodal information into three role-specific components: a redundancy component ($R$) for information shared across modalities, a uniqueness component ($U$) for modality-specific information, and a synergy component ($S$) for interaction-dependent multi-omic signals. This design allows the learned representation to retain shared cell-state structure while also preserving modality-specific and cross-modal regulatory information. On single-cell multi-omics benchmarks, the $R$ component achieves a 5.0\% reduction in FOSCTTM compared with the strongest baseline, while $U+S$ improves cell type classification accuracy by 1.38\%. Branch-level analyses further show that the decomposed components support complementary aspects of representation quality, suggesting that structured decomposition provides a practical strategy for learning more informative multimodal cell representations.