Dimensionality Reduction for Robust Federated Learning: A Theoretical Analysis and Convergence Guarantee

Federated Learning (FL) enables multiple clients to collaboratively train models without sharing raw data, but it is highly vulnerable to Byzantine attacks. Existing robust approaches can neutralize these threats but incur substantial computational overhead during high-dimensional gradient aggregation, an overhead that scales poorly with model size and increasingly dominates the training cost as modern models grow larger. To address this computational bottleneck, we propose Projected Dimensionality Reduction (PDR), a universal acceleration framework for vector-level distance-based robust aggregators, which performs robust aggregation by compressing gradients into a drastically smaller subspace via sparse random projection to efficiently compute reliability weights. This approach reduces the server computational complexity to an optimal $ \mathcal{O}(Mp) $, where $ M $ is the number of clients and $ p $ is the model dimension, matching the theoretical lower bound required merely to read the gradients. We establish convergence guarantees under standard FL assumptions in prior Byzantine-robust FL analyses. By leveraging the Subspace Embedding Theorem, we show that PDR achieves optimal convergence rates of $ \mathcal{O}(1/\sqrt{T}) $ for non-convex functions and $ \mathcal{O}(1/T) $ for strongly convex functions, where $ T $ denotes the number of iterations. Crucially, we mathematically demonstrate that this massive acceleration comes almost for free, merely inflating the inherent Byzantine error floor by a bounded, tunable factor of $ \frac{1+ε}{1-ε} $. Experimental results on benchmark datasets confirm that integrating PDR with existing aggregators yields orders of magnitude speedups in time efficiency while maintaining highly competitive convergence performance.

GFPL: Generative Federated Prototype Learning for Resource-Constrained and Data-Imbalanced Vision Task

Federated learning (FL) facilitates the secure utilization of decentralized images, advancing applications in medical image recognition and autonomous driving. However, conventional FL faces two critical challenges in real-world deployment: ineffective knowledge fusion caused by model updates biased toward majority-class features, and prohibitive communication overhead due to frequent transmissions of high-dimensional model parameters. Inspired by the human brain's efficiency in knowledge integration, we propose a novel Generative Federated Prototype Learning (GFPL) framework to address these issues. Within this framework, a prototype generation method based on Gaussian Mixture Model (GMM) captures the statistical information of class-wise features, while a prototype aggregation strategy using Bhattacharyya distance effectively fuses semantically similar knowledge across clients. In addition, these fused prototypes are leveraged to generate pseudo-features, thereby mitigating feature distribution imbalance across clients. To further enhance feature alignment during local training, we devise a dual-classifier architecture, optimized via a hybrid loss combining Dot Regression and Cross-Entropy. Extensive experiments on benchmarks show that GFPL improves model accuracy by 3.6% under imbalanced data settings while maintaining low communication cost.