Statistical heterogeneity severely limits the performance of federated learning (FL), motivating several explorations e.g., FedProx, MOON and FedDyn, to alleviate this problem. Despite effectiveness, their considered scenario generally requires samples from almost all classes during the local training of each client, although some covariate shifts may exist among clients. In fact, the natural case of partially class-disjoint data (PCDD), where each client contributes a few classes (instead of all classes) of samples, is practical yet underexplored. Specifically, the unique collapse and invasion characteristics of PCDD can induce the biased optimization direction in local training, which prevents the efficiency of federated learning. To address this dilemma, we propose a manifold reshaping approach called FedMR to calibrate the feature space of local training. Our FedMR adds two interplaying losses to the vanilla federated learning: one is intra-class loss to decorrelate feature dimensions for anti-collapse; and the other one is inter-class loss to guarantee the proper margin among categories in the feature expansion. We conduct extensive experiments on a range of datasets to demonstrate that our FedMR achieves much higher accuracy and better communication efficiency. Source code is available at: https://github.com/MediaBrain-SJTU/FedMR.git.

翻译：统计异构性严重制约了联邦学习（FL）的性能，这促使了FedProx、MOON和FedDyn等方法的探索以缓解该问题。尽管这些方法有效，但它们所考虑的场景通常要求每个客户端在本地训练期间拥有几乎所有类别的样本，尽管客户端间可能存在某些协变量偏移。实际上，部分类不相交数据（PCDD）这一自然情况——即每个客户端仅提供少数类别（而非所有类别）的样本——具有现实意义却尚未被充分探索。具体而言，PCDD所特有的坍缩与侵占特性会导致本地训练中的优化方向发生偏斜，从而阻碍联邦学习的效率。为解决这一困境，我们提出了一种名为FedMR的流形重塑方法，以校准本地训练的特征空间。我们的FedMR在原始联邦学习框架上增加了两个相互作用的损失函数：其一是类内损失，用于解相关特征维度以防止坍缩；其二是类间损失，用于确保特征空间中各类别间具有适当的间隔。我们在多个数据集上进行了大量实验，结果表明我们的FedMR实现了显著更高的准确率和更好的通信效率。源代码发布于：https://github.com/MediaBrain-SJTU/FedMR.git。