Paper:
With innovations in architecture design, deeper and wider neural network models deliver improved performance on a diverse variety of tasks. But the increased memory footprint of these models presents a challenge during training, when all intermediate layer activations need to be stored for back-propagation. Limited GPU memory forces practitioners to make sub-optimal choices: either train inefficiently with smaller batches of examples; or limit the architecture to have lower depth and width, and fewer layers at higher spatial resolutions. This work introduces an approximation strategy that significantly reduces a network's memory footprint during training, but has negligible effect on training performance and computational expense. During the forward pass, we replace activations with lower-precision approximations immediately after they have been used by subsequent layers, thus freeing up memory. The approximate activations are then used during the backward pass. This approach limits the accumulation of errors across the forward and backward pass-because the forward computation across the network still happens at full precision, and the approximation has a limited effect when computing gradients to a layer's input. Experiments, on CIFAR and ImageNet, show that using our approach with 8-and even 4-bit fixed-point approximations of 32-bit floating-point activations has only a minor effect on training and validation performance, while affording significant savings in memory usage.

Review:
The authors detail a procedure to reduce the memory footprint of deep networks by quantization of the activations only on back propagation. While this scheme does not benefit from computational speedups of activation quantization on both passes (and indeed has a slight computational overhead), the authors demonstrate that for common convolutional architectures it nicely preserves the accuracy of computation by computing the forward pass at full accuracy and limiting propagation of errors in the backward pass. This is possible because the majority of errors are introduced in gradient calculation of the weights and not the inputs each layer. The authors also wisely perform quantization after batch normalization and use the known mean and variance of the activations to scale the quantization and reduce errors. They demonstrate very slight drops in performance accuracy for ResNets on Cifar10, Cifar100, and ImageNet with memory compression factors up to 8. They also point to natural future directions such as using vector quantization to better leverage the activation statistics. The paper is also very clearly written with appropriate references to the relevant literature. 
An area of improvement I could see for the paper would be to demonstrate the utility of the reduced memory footprint. Their motivation clearly outlines that reducing memory can allow for larger batch sizes and larger networks that can improve the performance of training, but the authors do not demonstrate an example of this principle. They do mention that they are able to train with a larger batch size on ImageNet without combining batches, but more quantitative evidence of improvements in wall clock time (for different batch sizes) or improvement in performance (for larger networks) would help support the arguments of the paper. Given that the authors are focusing on single device training, they don't have to necessarily improve the state of the art, but a relative comparison would be illustrative. Also, specific measurements of the change in memory footprint for real networks would be helpful.