## 1 Introduction  
In general, deep learning training runs a single centralized model on a large, integrated, and well-balanced dataset. However, in real life, collecting high quality data is an expensive labor because data has become more decentralized and personalized. The rising demand for data privacy precludes certain data from collection. Those uncollectible data cherish rich knowledge. Federated learning is a methodology to access and utilize that knowledge. In a federated learning network, a client is the collector, owner, and user of its data, whereas the server has no access privilege to a client's data. Since there is only so much a single client may collect and store, an allied effort is demanded for server and clients to train a viable global model [1; 2; 3; 4; 5].  
A standard training process of federated learning begins with the server distributing copies of an initialized global model to participating clients. Clients train the copied local models with their own local data. Trained local models are transferred to the server. The server aggregates the local model parameters to update the global model parameters. This indirect approach to decentralized data destabilizes training, lowering performance compared to the traditional centralized deep learning, that is a single machine directly accessing data to train a centralized model.  
To address the inherent issues of federated learning, we focused on the concept of example forgetting event, a phenomenon inspired by catastrophic forgetting [6; 7; 8]. Catastrophic forgetting occurs in a continual learning environment when a model fails a task previously learned after learning a new task. If a model is to learn two tasksconsecutively, first task A then task B, it is known that the model's performance on task A will drop after learning task B. On the other hand, an example forgetting event happens when a model loses its previously acquired knowledge on a data point during training. While a model is training on data batches, the model will successfully predict data \(x\) on a certain point. However, after training on some more batches, the prediction on \(x\) will fail.  
We presumed that a similar information loss phenomenon will occur for federated learning. For a federated learning environment, we defined forgettable examples as those in which a forgetting event occurs immediately after the global model update. In other words, the local model will succeed in predicting these data before aggregation but global model after aggregation will not. These data are forgotten. Other data that are not forgotten are unforgettable examples. Via various experiments, we discovered that forgetting events occur more frequently in a federated learning environment than a typical centralized learning environment (single central model training).  
Based on these discoveries, we suggest a novel method for federated learning, FedWAvg: federated weighted averaging by example forgetting events. Our method reorganizes the weight of each client according to the number of forgettable examples in each round. By implementing weighted averaging as an aggregation method, global models are able to show higher performance in highly unbalanced distribution of decentralized data.