A.1 Proof of FAT-Clipping - PR For notional clarity, we have the following update: Local update: x The first inequality follows from the strongly-convex property, i.e., Assumption 4. (Bounded Stochastic Gradient V ariance) There exists a constant Assumption 5. (Bounded Gradient) There exists a constant We remark that for any stochastic estimator satisfies the above conditions, the above inequalities hold. The proof is the exactly same as that in original proof [18]. Theorem 6. Suppose f is We run a convolutional neural network (CNN) model on CIFAR-10 dataset using FedAvg. CNN architecture is shown in Table 2. To simulate data heterogeneity across clients, we manually The dataset and model are taken from [45]. This implies that the gradient noise is fat-tailed.

The proposed deterministic codes are proven to perfectly tolerate arbitrary Byzantine attacks.

Graph neural networks (GNN) are an effective framework that exploit interrelationships within graph-structured data for learning.

Recent works (e.g., (Li and Arora, 2020)) suggest that the use of popular normalization schemes (including Batch Normalization) in today's deep learning can

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