FedSEAM: Federated Continual Learning of LLMs via Subspace Expert Agreement Merging

Fatema Siddika, Abhijit Chunduru, Zilinghan Li, Ali Jannesari, Ravi Madduri

Federated continual learning trains a model on a sequence of tasks across several clients without sharing their data while retaining knowledge of earlier tasks. Sparse mixture-of-experts models support this setting by adapting selected parameters on a frozen backbone. However, clients learn different expert content as tasks evolve, making it difficult to share knowledge across clients without disrupting task-specific and client-specific specialization. Matching tile coordinates alone does not establish whether their learned content is compatible. We present FedSEAM, a federated continual learning framework that organizes task knowledge into sparse experts and selectively shares their content across tasks and clients. On each client, task-aware tile selection allocates capacity to a new task, while a subspace-based compatibility test determines which existing expert tiles to reuse and where to introduce fresh capacity. On the server, Subspace Expert Agreement Merging (SEAM) compares client updates as subspaces and moves each client towards consensus only along agreed-upon directions, leaving the rest of its update unchanged. We identify two remaining sources of forgetting, routing…