  One of the challenges in federated learning is the non-independent and
identically distributed (non-iid) characteristics between heterogeneous
devices, which cause significant differences in local updates and affect the
performance of the central server. Although many studies have been proposed to
address this challenge, they only focus on local training and aggregation
processes to smooth the changes and fail to achieve high performance with deep
learning models. Inspired by the phenomenon of neural collapse, we force each
client to be optimized toward an optimal global structure for classification.
Specifically, we initialize it as a random simplex Equiangular Tight Frame
(ETF) and fix it as the unit optimization target of all clients during the
local updating. After guaranteeing all clients are learning to converge to the
global optimum, we propose to add a global memory vector for each category to
remedy the parameter fluctuation caused by the bias of the intra-class
condition distribution among clients. Our experimental results show that our
method can improve the performance with faster convergence speed on
different-size datasets.
