Understanding and Mitigating Dimensional Collapse in Federated Learning

Yujun Shi, Jian Liang, Wenqing Zhang, Chuhui Xue, Vincent Y. F. Tan, Song Bai

Abstract: Federated learning aims to train models collaboratively across different clients without sharing data for privacy considerations. However, one major challenge for this learning paradigm is the data heterogeneity problem, which refers to the discrepancies between the local data distributions among various clients. To tackle this problem, we first study how data heterogeneity affects the representations of the globally aggregated models. Interestingly, we find that heterogeneous data results in the global model suffering from severe dimensional collapse , in which representations tend to reside in a lower-dimensional space instead of the ambient space. This dimensional collapse phenomenon severely curtails the expressive power of models, leading to significant degradation in the performance. Next, via experiments, we make more observations and posit two reasons that result in this phenomenon: 1) dimensional collapse on local models; 2) the operation of global averaging on local model parameters. In addition, we theoretically analyze the gradient flow dynamics to shed light on how data heterogeneity result in dimensional collapse. To remedy this problem caused by the data heterogeneity, we propose FedDecorr , a novel method that can effectively mitigate dimensional collapse in federated learning. Specifically, FedDecorr applies a regularization term during local training that encourages different dimensions of representations to be uncorrelated. FedDecorr , which is implementation-friendly and computationally-efficient, yields consistent improvements over various baselines on five standard benchmark datasets including CIFAR10, CIFAR100, TinyImageNet, Office-Caltech10, and DomainNet.