SUM: Unified Geometric Surgery on Spatio-Temporal Adaptation Vectors for Federated Class Incremental Learning

Real-world intelligent systems often require both distributed collaboration across data-isolated clients and continual adaptation to evolving tasks. This setting naturally gives rise to Federated Class Incremental Learning (FCIL), which combines Federated Learning (FL) and Continual Learning (CL). However, their combination introduces two coupled sources of interference: spatial interference from heterogeneous clients and temporal interference from sequential tasks, jointly leading to Spatial-Temporal Catastrophic Forgetting (ST-CF). Existing approaches typically address spatial and temporal interference with separate mechanisms, often incurring additional client-side computation or communication, while leaving directional interactions among updates during aggregation unregulated. In this paper, we reinterpret FCIL as a unified multi-task learning problem, where both client and task updates are represented as adaptation vectors in a shared parameter space. Based on this view, we propose Unified Geometric Surgery on Spatio-Temporal Adaptation Vectors (SUM), a purely server-side framework that performs geometric surgery on adaptation vectors during aggregation. Spatial SUM mitigates client-level interference within each round, while causal online temporal SUM removes cross-task interference over time without additional client-side computation, communication, or memory beyond standard federated training. Empirically, SUM achieves up to 22% improvement over prior FCIL methods across diverse vision and language benchmarks while remaining robust to unreliable clients and maintaining computational efficiency.