Gradient Normalization Enables Communication-Efficient Distributed Learning under Initialization Data Heterogeneity.

Communication-efficient distributed learning has achieved remarkable progress in training large-scale deep neural networks across numerous clients. However, in heterogeneous environments-where local data distributions vary significantly-the empirical performance of many such algorithms degrades sharply. Moreover, existing theoretical analyses often depend on overly restrictive assumptions, such as bounded data heterogeneity, which may not be valid even for a single client. In this work, we introduce a general gradient normalization strategy that can be seamlessly integrated into a wide range of distributed learning algorithms, including compressed distributed stochastic gradient descent, federated averaging, and asynchronous variants. Our theoretical analysis demonstrates that this normalization technique effectively mitigates the negative impact of data heterogeneity, allowing these algorithms to achieve linear speedup rates with only requiring the boundedness of initialization data heterogeneity. Extensive numerical experiments further confirm the practical effectiveness and theoretical guarantees of our approach.