Title: Contractive error feedback for gradient compression. Abstract: 
On-device memory concerns in distributed deep learning are becoming more severe due to i) the growth of model size in multi-GPU training, and ii) the adoption of neural networks for federated learning on IoT devices with limited storage. In such settings, this work deals with memory issues emerging with communication efficient methods. To tackle associated challenges, key advances are that i) instead of EFSGD that inefficiently manages memory, the sweet spot of convergence and memory usage can be attained via what is here termed contractive error feedback (ConEF); and, ii) communication efficiency in ConEF should be achieved by biased and allreducable gradient compression. ConEF is validated on various learning tasks that include image classification, language modeling, and machine translation. ConEF saves 80% – 90% of the extra memory in EFSGD with almost no loss on test performance, while also achieving 1.3x – 5x speedup of SGD.