We consider the problem where $n$ clients transmit $d$-dimensional real-valued vectors using $d(1+o(1))$ bits each, in a manner that allows the receiver to approximately reconstruct their mean. Such compression problems naturally arise in distributed and federated learning. We provide novel mathematical results and derive computationally efficient algorithms that are more accurate than previous compression techniques. We evaluate our methods on a collection of distributed and federated learning tasks, using a variety of datasets, and show a consistent improvement over the state of the art.

翻译：我们考虑了这样的问题:一美元客户用美元(1+1(1)美元)各比特传输以美元(d)+(1美元)计算的真值矢量,使接收者能够大致重建其平均值。这种压缩问题自然出现在分布式和联合化的学习中。我们提供了新的数学结果,并得出了比以往压缩技术更准确的计算效率算法。我们利用各种数据集评估了我们收集分布式和联合化学习任务的方法,并展示了相对于最新技术的一贯改进。