FedCap-Priv: Geometry-Aware Privacy and Bandwidth-Efficient Routing for Federated Capsule Learning

Capsule networks explicitly encode pose and part–whole structure, making them attractive for heterogeneous visual and speech data but creating structured messages and substantial communication costs in federated learning. We present FedCap-Priv, a federated capsule framework that jointly addresses transcript privacy, predictive utility, and uplink cost through three capsule-specific procedures. Secure Routing by Agreement (SeRBA) retains dynamic routing on each client and replaces direct vote exchange with compact directional and low-rank agreement sketches. Pose-Sensitive Differential Privacy (PS-DP) clips each layer sketch and applies anisotropic Gaussian perturbation aligned with pose variability. Our client-level Rényi-DP analysis accounts for data-dependent means and covariances, visible selection indices, layer composition, client participation, and temporal composition. Sparsity-Guided Partial Aggregation (SGPA) selects salient parent blocks after perturbation and uses error feedback to reduce communication. Across MNIST, Fashion-MNIST, CIFAR-10, and Speech Commands, FedCap-Priv improves accuracy over isotropic FedDP and lowers reconstruction scores under DLG, iDLG, and cosine-TV attacks. On CIFAR-10, it reaches 73.9% accuracy versus 68.9% for isotropic FedDP while reducing the mean participating-client uplink from 220 KB to 22.1 KB per round, a 9.95-fold reduction. The sketch interface supports vector- and matrix-pose capsules and can be combined with secure aggregation.