FedEcho: Echoes of the Past Guide Future Starts in Federated Learning

Federated learning typically uses the current global model both as the shared state for continual aggregation and as the common local training starting point for all participating clients, although the latter itself constitutes an independently designable degree of freedom in optimization. Prior work adjusts local initialization using historical model differences or random perturbations, but how to use the historical responses of repeatedly participating clients relative to the concurrent collaborative process to predict their relative optimization trends at the next participation, and accordingly coordinate starting-point dispatch, remains underexplored. We observe that client relative responses, measured relative to the same-round weighted-average displacement and along the concurrent global trajectory, exhibit short-term cross-participation persistence that decays as the participation gap increases. This suggests that what transfers across participations is not a stale gradient or a fixed parameter direction, but a client's response tendency relative to the collaborative process. Building on this observation, we propose FedEcho, which recasts training starting-point dispatch as a jointly coordinated, low-dimensional optimization control among clients participating in the same round. The server predicts each client's relative optimization trend from its historical relative response and jointly determines client-specific training starting points to pre-compensate for the predictable relative component of local-path divergence. The dispatch guarantees that the weighted-average starting point across participating clients equals the current global model, while leaving the original local training and server aggregation rules unchanged. Under smoothness conditions, local-path divergence upper-bounds the corresponding aggregated gradient mismatch, providing an optimization interpretation of this design. Experimental results across three datasets, three network architectures, and three data distributions show that FedEcho achieves the highest test accuracy in all 27 settings, outperforming the strongest baseline by 2.80 percentage points on average.