Federated Shared–Private Basis Reallocation for Multimodal Representation Collapse

Multimodal federated learning can overuse a dominant modality, while heterogeneous client updates suppress effective directions in weaker pathways. Existing approaches regulate modality selection, optimization, or distillation, but leave weak encoder capacity unprotected during aggregation. We introduce Federated Shared and Private Basis Reallocation (FedSBR), an encoder-level framework that separates shared semantic coordinates from private residual coordinates. FedSBR preserves weak-pathway capacity through collapse-aware regularization, transfers supervision only when loss, rank, and teacher reliability indicate dominance, and coordinates class semantics through reliability-weighted federated prototypes. Identity-preserving initialization reconstructs features without changing the initial predictor. Experiments on CREMA-D, ModelNet40, CrisisMMD, and MIMIC-IV under IID and Dirichlet non-IID partitions show improvements over FedAvg and competitive fusion performance. Pathway accuracy, participation rank, modality contribution, and class-conditional analyses collectively support the proposed mechanism under federated heterogeneity.