Historical Gradient Reconstruction for Adaptive Federated Continual Learning

Federated continual learning (FCL) must balance the acquisition of new knowledge with the retention of earlier knowledge distributed across heterogeneous clients. Gradient-based task weighting offers a way to adapt this balance, but choosing the weights requires historical gradients from data distributed across clients. Private replay buffers provide only a local view of past data, while shared historical gradients can become inaccurate as clients update their models. We propose FedGRIT (Federated Gradient Reconstruction for Incremental Training), a replay-based framework that reconstructs historical gradients to guide adaptive local updates. By aggregating task-specific gradients and compact curvature information, FedGRIT enables clients to reconstruct historical gradients at their own changing models and adapt task weights without cross-client communication at every step. Periodic refreshes and two-stage curvature compression support repeated sharing. We derive conditional historical-loss retention and weighted stationarity bounds under partial participation, separating the effects of stochasticity, local training, and client heterogeneity. Across four class- and domain-incremental benchmarks, FedGRIT achieves the highest mean final accuracy among the evaluated methods with ablations examining shared reconstruction and adaptive weighting.