Fisher-Routed Mixture of Experts for Federated Class-Incremental Learning

Federated Learning (FL) emerged as a promising distributedmachine learning paradigm. However, extending FL to the class incre-mental learning scenarios introduces unique challenges: 1) Capacity con-flict and catastrophic forgetting from the shared model overloading, 2)Heterogeneity from Non-Independent and Identically Distributed (Non-IID) data, and 3) Synchronized class misalignment. In this paper, we pro-pose Fisher-Routed MiXture of Experts for Federated Class-IncrementalLearning (FedFMX), a novel framework to address these challenges viaadaptive expert specialization across clients. The crucial insight is toroute each sample to an expert subset that jointly optimizes knowledgeacquisition and retention. Specifically, we introduce a Fisher-Routed Ex-pert Scoring (FRES) module to estimate expert importance via Fisher-based stability cost and gradient-based plasticity gain. Then, we designan Adaptive Expert Selection (AES) module by quantifying marginalcontributions for adaptive expert subset determination. Finally, by therouting-aware regularization (RAR), we achieve load balance and effi-cient FL training. We theoretically prove the O(T −1 ) convergence rate.Extensive experiments on multiple benchmarks compared with state-of-the-art methods demonstrate the superiority of FedFMX.