Paper:
A common way to speed up training of deep convolutional networks is to add computational units. Training is then performed using data-parallel synchronous Stochastic Gradient Descent (SGD) with a mini-batch divided between computational units. With an increase in the number of nodes, the batch size grows. However, training with a large batch often results in lower model accuracy. We argue that the current recipe for large batch training (linear learning rate scaling with warm-up) does not work for many networks, e.g. for Alexnet, Googlenet,... We propose a more general training algorithm based on Layer-wise Adaptive Rate Scaling (LARS). The key idea of LARS is to stabilize training by keeping the magnitude of update proportional to the norm of weights for each layer. This is done through gradient rescaling per layer. Using LARS, we successfully trained AlexNet and ResNet-50 to a batch size of 16K.

Review:
This paper proposes a training algorithm based on Layer-wise Adaptive Rate Scaling (LARS) to overcome the optimization difficulties for training with large batch size. The authors use a linear scaling and warm-up scheme to train AlexNet on ImageNet. The results show promising performance when using a relatively large batch size. The presented method is interesting. However, the experiments are poorly organized since some necessary descriptions and discussions are missing. My detailed comments are as follows.
Contributions：
1.	The authors propose a training algorithm based LARS with the adaptive learning rate for each layer, and train the AlexNet and ResNet-50 to a batch size of 16K. 
2.	The training method shows stable performance and helps to avoid gradient vanishing or exploding.
Weak points:
The training algorithm does not overcome the optimization difficulties when the batch size becomes larger (e.g. 32K), where the training becomes unstable, and the training based on LARS and warm-up can’t improve the accuracy compared to the baselines. 
Specific comments: 
1.	In Algorithm 1, how to choose $ \eta $ and $ \beta $ in the experiment?
2.	Under the line of Equation (3), $ \nabla L(x_j, w_{t+1}) \approx L(x_j, w_{t}) $ should be $ \nabla L(x_j, w_{t+1}) \approx \nabla L(x_j, w_{t}) $.
3.	How can the training algorithm based on LARS improve the generalization for the large batch? 
4.	In the experiments, what is the parameter iter_size? How to choose it?
5.	In the experiments, no descriptions and discussions are given for Table 3, Figure 4, Table 4, Figure 5, Table 5 and Table 6. The authors should give more discussions on these tables and figures. Furthermore, the captions of these tables and figures confusing.
6.	On page 4, there is a statement “The ratio is high during the initial phase, and it is rapidly decreasing after few epochs (see Figure 2).” This is quite confusing, since Figure 2 is showing the change of learning rates w.r.t. training epochs.