Paper:
Stabilizing Training of Generative Adversarial Networks through Regularization
Deep generative models based on Generative Adversarial Networks (GANs) have demonstrated impressive sample quality but in order to work they require a careful choice of architecture, parameter initialization, and selection of hyper-parameters. This fragility is in part due to a dimensional mismatch or non-overlapping support between the model distribution and the data distribution, causing their density ratio and the associated f -divergence to be undefined. We overcome this fundamental limitation and propose a new regularization approach with low computational cost that yields a stable GAN training procedure. We demonstrate the effectiveness of this regularizer accross several architectures trained on common benchmark image generation tasks. Our regularization turns GAN models into reliable building blocks for deep learning.

Review:
This paper proposed to stabilize the training of GAN using proposed gradient-norm regularizer.
This regularization is designed for conventional GAN, or more general f-GAN proposed last year.
The idea is interesting but the justification is a little bit coarse.
1. Eq. (15) is only correct for the maximizer \psi^{\star}. However, the regularizer defined in (21) is for arbitrary \psi, which contradicts this assumption.
2. It seems that increasing the weighting of the regularization term, i.e., \gamma does not affect much the training in Fig. 2.
The authors claim that 'the results clearly demonstrate the robustness of the regularizer w.r.t. the various regularization bandwidths'.
This is a little bit strange and it will be necessary to show how this regularization can affect the training. 
3. For the comparison in the experiments, it is not clear how the explicit noise approach was done. What is the power of the noise? How is the batch-size-to-noise-ratios defined? What's relation between it and the conventional SNR?
4. The results in Section 4.3 make no much sense. From the reported table, the diagonal elements are all quite close to one, which can hardly justifies the advantage of regularized GAN. 
5. It will be convincing to compare the proposed method with some other stabilizing training techniques, like Salimans et al 2016 or WGAN technique.