Federated Learning (FL) is a machine learning approach where a global model is trained across distributed clients without sharing raw data. This paper proposes two methods to reduce communication costs in FL: structured updates and sketched updates. Structured updates involve learning updates from a restricted space, such as low-rank matrices or random masks, which reduces the amount of data sent. Sketched updates compress full model updates using quantization, random rotations, and subsampling before sending to the server. Experiments on convolutional and recurrent networks show that these methods reduce communication costs by two orders of magnitude. FL is particularly useful for mobile devices with limited internet connections, as it allows training on local data without uploading it to the cloud. The main challenge in FL is the high uplink communication cost, which is addressed by the proposed methods. Structured updates reduce the size of updates by restricting them to a smaller space, while sketched updates compress the updates before transmission. Both methods are evaluated on real-world datasets, including CIFAR-10 and Reddit data, showing significant improvements in communication efficiency without sacrificing model accuracy. The structured update method uses low-rank matrices or random masks to represent model updates, reducing the number of parameters that need to be communicated. The sketched update method compresses updates using quantization, random rotations, and subsampling, which further reduces the communication cost. These methods are combined in experiments to achieve even greater compression rates. The results show that structured updates, especially with random masks, perform better than low-rank updates, while sketched updates with quantization and random rotations provide additional compression benefits. The experiments demonstrate that the proposed methods significantly reduce the amount of data communicated in FL, enabling efficient training on large-scale datasets with limited internet connections. The results show that the communication cost can be reduced by two orders of magnitude, allowing for high accuracy with minimal data transfer. The methods are particularly effective in scenarios where the number of clients is large, and the data is distributed across many devices. The practical utility of these methods is highlighted in the context of mobile applications, where communication efficiency is crucial.Federated Learning (FL) is a machine learning approach where a global model is trained across distributed clients without sharing raw data. This paper proposes two methods to reduce communication costs in FL: structured updates and sketched updates. Structured updates involve learning updates from a restricted space, such as low-rank matrices or random masks, which reduces the amount of data sent. Sketched updates compress full model updates using quantization, random rotations, and subsampling before sending to the server. Experiments on convolutional and recurrent networks show that these methods reduce communication costs by two orders of magnitude. FL is particularly useful for mobile devices with limited internet connections, as it allows training on local data without uploading it to the cloud. The main challenge in FL is the high uplink communication cost, which is addressed by the proposed methods. Structured updates reduce the size of updates by restricting them to a smaller space, while sketched updates compress the updates before transmission. Both methods are evaluated on real-world datasets, including CIFAR-10 and Reddit data, showing significant improvements in communication efficiency without sacrificing model accuracy. The structured update method uses low-rank matrices or random masks to represent model updates, reducing the number of parameters that need to be communicated. The sketched update method compresses updates using quantization, random rotations, and subsampling, which further reduces the communication cost. These methods are combined in experiments to achieve even greater compression rates. The results show that structured updates, especially with random masks, perform better than low-rank updates, while sketched updates with quantization and random rotations provide additional compression benefits. The experiments demonstrate that the proposed methods significantly reduce the amount of data communicated in FL, enabling efficient training on large-scale datasets with limited internet connections. The results show that the communication cost can be reduced by two orders of magnitude, allowing for high accuracy with minimal data transfer. The methods are particularly effective in scenarios where the number of clients is large, and the data is distributed across many devices. The practical utility of these methods is highlighted in the context of mobile applications, where communication efficiency is crucial.