Title: FedPSE: Personalized Sparsification with Element-wise Aggregation for Federated Learning. Abstract: Federated learning (FL) is a popular distributed machine learning framework in which clients aggregate models' parameters instead of sharing their individual data. In FL, clients communicate with the server under limited network bandwidth frequently, which arises the communication challenge. To resolve this challenge, multiple compression methods have been proposed to reduce the transmitted parameters. However, these techniques show that the federated performance degrades significantly with Non-IID (non-identically independently distributed) datasets. To address this issue, we propose an effective method, called FedPSE, which solves the efficiency challenge of FL with heterogeneous data. FedPSE compresses the local updates on clients using Top-K sparsification and aggregates these updates on the server by element-wise average.  Then clients download the personalized sparse updates from the server to update their individual local models.  We then theoretically analyze the convergence of FedPSE under the non-convex setting.  Moreover, extensive experiments on four benchmark tasks demonstrate that our FedPSE outperforms the state-of-the-art methods on Non-IID datasets in terms of both efficiency and accuracy.