Error accumulation is an essential component of the Top-$k$ sparsification method in distributed gradient descent. It implicitly scales the learning rate and prevents the slow-down of lateral movement, but it can also deteriorate convergence. This paper proposes a novel sparsification algorithm called regularized Top-$k$ (RegTop-$k$) that controls the learning rate scaling of error accumulation. The algorithm is developed by looking at the gradient sparsification as an inference problem and determining a Bayesian optimal sparsification mask via maximum-a-posteriori estimation. It utilizes past aggregated gradients to evaluate posterior statistics, based on which it prioritizes the local gradient entries. Numerical experiments with ResNet-18 on CIFAR-10 show that at $0.1\%$ sparsification, RegTop-$k$ achieves about $8\%$ higher accuracy than standard Top-$k$.

Federated Learning (FL) exhibits privacy vulnerabilities under gradient inversion attacks (GIAs), which can extract private information from individual gradients. To enhance privacy, FL incorporates Secure Aggregation (SA) to prevent the server from obtaining individual gradients, thus effectively resisting GIAs. In this paper, we propose a stealthy label inference attack to bypass SA and recover individual clients' private labels. Specifically, we conduct a theoretical analysis of label inference from the aggregated gradients that are exclusively obtained after implementing SA. The analysis results reveal that the inputs (embeddings) and outputs (logits) of the final fully connected layer (FCL) contribute to gradient disaggregation and label restoration. To preset the embeddings and logits of FCL, we craft a fishing model by solely modifying the parameters of a single batch normalization (BN) layer in the original model. Distributing client-specific fishing models, the server can derive the individual gradients regarding the bias of FCL by resolving a linear system with expected embeddings and the aggregated gradients as coefficients. Then the labels of each client can be precisely computed based on preset logits and gradients of FCL's bias. Extensive experiments show that our attack achieves large-scale label recovery with 100\% accuracy on various datasets and model architectures.

Federated edge learning is envisioned as the bedrock of enabling intelligence in next-generation wireless networks, but the limited spectral resources often constrain its scalability. In light of this challenge, a line of recent research suggested integrating analog over-the-air computations into federated edge learning systems, to exploit the superposition property of electromagnetic waves for fast aggregation of intermediate parameters and achieve (almost) unlimited scalability. Over-the-air computations also benefit the system in other aspects, such as low hardware cost, reduced access latency, and enhanced privacy protection. Despite these advantages, the interference introduced by wireless communications also influences various aspects of the model training process, while its importance is not well recognized yet. This article provides a comprehensive overview of the positive and negative effects of interference on over-the-air computation-based edge learning systems. The potential open issues and research trends are also discussed.

A wireless federated learning system is investigated by allowing a server and workers to exchange uncoded information via orthogonal wireless channels. Since the workers frequently upload local gradients to the server via bandwidth-limited channels, the uplink transmission from the workers to the server becomes a communication bottleneck. Therefore, a one-shot distributed principle component analysis (PCA) is leveraged to reduce the dimension of uploaded gradients such that the communication bottleneck is relieved. A PCA-based wireless federated learning (PCA-WFL) algorithm and its accelerated version (i.e., PCA-AWFL) are proposed based on the low-dimensional gradients and the Nesterov's momentum. For the non-convex loss functions, a finite-time analysis is performed to quantify the impacts of system hyper-parameters on the convergence of the PCA-WFL and PCA-AWFL algorithms. The PCA-AWFL algorithm is theoretically certified to converge faster than the PCA-WFL algorithm. Besides, the convergence rates of PCA-WFL and PCA-AWFL algorithms quantitatively reveal the linear speedup with respect to the number of workers over the vanilla gradient descent algorithm. Numerical results are used to demonstrate the improved convergence rates of the proposed PCA-WFL and PCA-AWFL algorithms over the benchmarks.