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This research aims to address slow convergence in federated learning due to non-IID data and client drift.

August 7, 2026MathematicsOpen Access

Federated Spectral Regularization for Convergence Acceleration: A Random Matrix Theory Perspective

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This research aims to address slow convergence in federated learning due to non-IID data and client drift.
Analyzed convergence issues from a spectral perspective using random matrix theory.
Proposed federated spectral regularization (Fed-SR) to constrain spectral spread via gradient norm regularization.
Implemented an optimized auto-differentiation approach to compute the regularizer gradient efficiently.
Fed-SR significantly outperformed baselines like FedAvg and FedProx in terms of accuracy and convergence speed in non-IID scenarios.
Reduced communication rounds while maintaining high accuracy and stable training performance across CIFAR-10 and CIFAR-100 datasets.
Empirical studies showed a consistent link between spectral concentration effects and performance improvements.

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Randomized trial demonstrates improved accuracy and stability in convergence for federated learning, suggesting novel spectral methods.

Cai et al. (2026) studied this question.

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