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

Federated continual learning (FCL) enables collaborative model training across distributed clients on sequentially arriving tasks without revisiting past data. However, existing approaches often suffer from catastrophic forgetting, rely on replay buffers or generative models that may violate privacy constraints, or assume knowledge of task identities during inference. We propose FedProTIP (Federated Projection-based Continual Learning with Task Identity Prediction), a replay-free FCL framework that maintains shared task-specific feature subspaces across clients. Each client extracts low-rank core bases from intermediate activations using randomized singular value decomposition, capturing dominant feature directions associated with the current task. These bases are transmitted to the server and aggregated to construct global task subspaces that capture shared feature directions across clients without requiring data sharing. During training, client updates are projected onto the orthogonal complement of previously learned subspaces to reduce cross-task interference and mitigate catastrophic forgetting. The learned subspaces are also reused during inference to estimate task identity via subspace relevance, enabling task-agnostic prediction without requiring explicit task labels. Experiments on CIFAR100, ImageNet-R, and DomainNet demonstrate that FedProTIP consistently outperforms state-of-the-art federated continual learning baselines while maintaining lower training time, memory footprint, and communication cost.

Federated continual learning (FCL) has attracted considerable interest by enabling local clients to continually acquire knowledge from new tasks. However, most FCL methods assume that the global server has prior knowledge of the arrival times and number of categories for new tasks, which is unrealistic in the real world. Furthermore, they neglect the importance of positive inter-task semantic relationships when learning new tasks and are significantly affected by irrelevant relationships from old tasks, thereby exacerbating catastrophic forgetting. To resolve the above challenges, we develop a novel Task Relevance-driven Prompt Expansion (TRPE) model. Specifically, to eliminate the reliance on prior knowledge of new tasks, we propose an out-of-distribution detector to identify the arrival of new tasks within local clients, along with a radius-adaptive DBSCAN to infer the quantity of categories in new tasks on the proxy server. Moreover, to explore positive inter-task relationships, we calculate the affinity between the original gradient for learning new task and its gradient orthogonal to the feature space of old tasks to evaluate semantic relevance between old and new tasks from a global perspective. Then, we use this global task relevance to determine the key-prompt pair for new tasks and identify highly related old tasks. After concatenating their prompts for training, we can leverage such positive inter-task relations to improve the continual learning of newly arriving tasks. To balance the learning of new tasks and the forgetting of old ones, a soft orthogonality constraint is applied to the local key and prompt gradients. Experiments spanning diverse datasets and backbones confirm the efficacy of our TRPE model.

Federated continual learning must integrate new tasks over time without losing earlier-task knowledge. Most existing methods attach an anti-forgetting mechanism to the client-trained, server-aggregated loop of federated learning, which holds back new learning to preserve earlier knowledge and burdens resource-constrained clients. We propose ReSCENE, which structurally mitigates catastrophic forgetting by having each client upload a small condensed surrogate of its local data while the server keeps the surrogates of past tasks and trains the global model on them together with the current task surrogates. For efficient server memory, we introduce temporal herding, which selects the more recent surrogates from the pool accumulated over a task into a compressed buffer. Our study provides a theoretical analysis showing that this buffer can represent the original task data more closely than full accumulation of all surrogates. Across CIFAR-10, CIFAR-100, and TinyImageNet, ReSCENE achieves the strongest accuracy over seven baselines, by up to $31.1$ points of average accuracy, while requiring as little as $0.11\times$ of the client computation and up to $179\times$ less upload than the model-update baselines. ReSCENE further demonstrates its effectiveness when scaled to larger client populations and larger models while remaining efficient, which makes it a practical method for federated continual learning.