CanonFedRec: A Canonical Geometric Framework for Personalized Federated Recommendation
With the increasing demand for privacy protection, the federated recommendation (FedRec) has become a critical research topic. Prevailing frameworks continuously decouple item representation to bypass the heterogeneity of client data, sacrificing the universality of aggregated item embeddings, losing the collaborative benefits of federated learning. This trend not only introduces prohibitive memory costs on resource-constrained edge devices, but also exacerbates the isolation of user interests, leading to a significant loss of recommendation diversity. In this paper, we attribute the failure of aggregated item embeddings to the server-side Global Geometric Misalignment and client-side Local Filtering Bubbles after empirical and theoretical analysis. Then, we propose CanonFedRec, a novel framework that resolves the above challenges through a canonical geometric perspective. First, we shift the optimization landscape from Euclidean space to a unit hypersphere to explicitly decouple local magnitude noise unrelated to popularity from semantic relationships. To rectify the global geometric inconsistency, we propose a Riemannian Projection-based Aggregation mechanism that performs global updates in a geometrically compatible tangent space. Furthermore, to mitigate the local filtering bubbles of clients, we propose a Divergence-Aware Elastic Alignment mechanism. This treats item-wise variance as a proxy for client-side cognitive divergence, and dynamically adapting optimization objectives via elastic decision boundaries. Extensive experiments on four datasets demonstrate that CanonFedRec not only significantly enhances the representational power of aggregated item embeddings, but also achieves superior performance while reducing memory costs by up to 40× compared to the best FedRec approach.