Sheaf-FRL: New federated learning method aligns agents without a shared latent space

Heterogeneous federated systems pose a fundamental challenge: agents with different data distributions, sensing modalities, model architectures, and latent dimensionalities must still learn and exchange useful representations. Existing approaches typically impose a shared global latent space, which fails under extreme heterogeneity. A new paper from researchers at Sapienza University of Rome proposes Sheaf-based Federated Representation Learning (SFRL), a general framework that avoids this assumption entirely. Instead, SFRL achieves global consistency by aligning neighboring latent representations through orthogonal transformations and isometric embeddings, guided by a manifold-constrained geometric regularizer built from learnable sheaf restriction maps. Crucially, the penalty—a quadratic gluing regularizer induced by the sheaf Laplacian—adapts its geometry to observed data and is evaluated only on a small set of shared pilot samples, keeping communication costs low.

The authors introduce Sheaf-FRL, a decentralized algorithm that alternates gradient updates of local models with closed-form Procrustes updates for edge-wise restriction maps. They prove convergence to first-order stationary points in both deterministic and stochastic settings. In experiments on cooperative classification for semantic communication, Sheaf-FRL consistently outperforms baseline methods in local and post-communication accuracy across varying levels of local distribution shift. It also shows markedly greater robustness to latent-space dimensionality compression, making it practical for bandwidth-constrained deployments. This work offers a mathematically grounded path to federated learning without shared latent spaces, potentially expanding the applicability of collaborative AI to more diverse real-world systems.