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

Real-world intelligent systems often require both distributedcollaboration across data-isolated clients and continual adaptation toevolving tasks. This setting naturally gives rise to Federated Class In-cremental Learning (FCIL), which combines Federated Learning (FL)and Continual Learning (CL). However, their combination introducestwo coupled sources of interference: spatial interference from heteroge-neous clients and temporal interference from sequential tasks, jointlyleading to Spatialx0015Temporal Catastrophic Forgetting (ST-CF). Exist-ing approaches typically address spatial and temporal interference withseparate mechanisms, often incurring additional client-side computationor communication, while leaving directional interactions among updatesduring aggregation unregulated. In this paper, we reinterpret FCIL as aunix001Ced multi-task learning problem, where both client and task updatesare represented as adaptation vectors in a shared parameter space. Basedon this view, we proposeSurgery & Merge Sum ( ), a purely server-sideframework that performs geometric surgery on adaptation vectors duringaggregation. Spatial Sum mitigates client-level interference within eachSumround, while causal online temporal removes cross-task interferenceover time without additional client-side computation, communication, ormemory beyond standard federated training. Empirically, Sum achievesup to 22% improvement over prior FCIL methods across diverse visionand language benchmarks while remaining robust to unreliable clientsand maintaining computational ex001Eciency.