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Although Federated Learning (FL) enables global model training across clients without compromising their raw data, due to the unevenly distributed data among clients, existing Federated Averaging (FedAvg)-based methods suffer from the problem of low inference performance. Specifically, different data distributions among clients lead to various optimization directions of local models. Aggregating local models usually results in a low-generalized global model, which performs worse on most of the clients. To address the above issue, inspired by the observation from a geometric perspective that a well-generalized solution is located in a flat area rather than a sharp area, we propose a novel and heuristic FL paradigm named FedMR (Federated Model Recombination). The goal of FedMR is to guide the recombined models to be trained towards a flat area. Unlike conventional FedAvg-based methods, in FedMR, the cloud server recombines collected local models by shuffling each layer of them to generate multiple recombined models for local training on clients rather than an aggregated global model. Since the area of the flat area is larger than the sharp area, when local models are located in different areas, recombined models have a higher probability of locating in a flat area. When all recombined models are located in the same flat area, they are optimized towards the same direction. We theoretically analyze the convergence of model recombination. Experimental results show that, compared with state-of-the-art FL methods, FedMR can significantly improve the inference accuracy without exposing the privacy of each client. 

A comparative vacuum ultraviolet spectroscopy study conducted at ISOLDE-CERN of the radiative decay of the ${}^{229m}\mathrm{Th}$nuclear clock isomer embedded in different host materials is reported. The ratio of the number of radiative decay photons and the number of ${}^{229m}\mathrm{Th}$embedded are determined for single crystalline ${\mathrm{CaF}}_2, {\mathrm{MgF}}_2, {\mathrm{LiSrAlF}}_6$, AlN, and amorphous ${\mathrm{SiO}}_2$. For the latter two materials, no radiative decay signal was observed and an upper limit of the ratio is reported. The radiative decay wavelength was determined in ${\mathrm{LiSrAlF}}_6$and ${\mathrm{CaF}}_2$, reducing its uncertainty by a factor of 2.5 relative to our previous measurement. This value is in agreement with the recently reported improved values from laser excitation. Published by the American Physical Society2025