Incremental Aggregation on the Grassmannian for Asynchronous Eigenspace Computation

What the math gives to ML

The paper provides a concrete template for optimizing subspace-valued parameters when workers are asynchronous and component information is stale. Its transferable asset is the combination of cached per-worker gradients, ambient-space aggregation, and a polar retraction that restores orthogonality without transporting stale tangent vectors between changing Grassmannian points. This is directly applicable to distributed or federated neural modules that learn an orthogonal low-rank projection from activation covariances, where synchronization of all data shards is otherwise a bottleneck. The most promising first test is an asynchronous online PCA or activation-compression layer inserted into a small network, comparing wall-clock convergence and communication against synchronized Oja or PCA updates.