Sheaf-Based Federated Representation Learning

Heterogeneous federated systems require agents to learn and exchange informative representations despite differences in data distributions, model architectures, and latent dimensionalities. We propose Sheaf-based Federated Representation Learning (SFRL), a framework that jointly learns and aligns heterogeneous latent representations without sharing parameters, labels, or a single latent space. SFRL relates agent-specific latent spaces through learnable orthogonal transformations and isometric embeddings, promoting consistency via a sheaf-Laplacian gluing regularizer evaluated on a shared set of pilot samples. We develop Sheaf-FRL, a decentralized alternating algorithm combining local gradient updates with closed-form Procrustes updates of the alignment maps, and establish convergence to first-order stationary points in deterministic and stochastic settings. Applied to collaborative classification in semantic communication under model and data heterogeneity, Sheaf-FRL improves private and communication accuracy over federated baselines and is more robust to latent-space compression.