On the regularization of Wasserstein GANs
Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize the distance between the model and the empirical distribution in terms of a different metric, but thereby introduce a Lipschitz constraint into the optimization problem. A simple way to enforce the Lipschitz constraint on the class of functions, which can be modeled by the neural network, is weight clipping. Augmenting the loss by a regularization term that penalizes the deviation of the gradient norm of the critic (as a function of the network*s input) from one, was proposed as an alternative that improves training. We present theoretical arguments why using a weaker regularization term enforcing the Lipschitz constraint is preferable. These arguments are supported by experimental results on several data sets.
 The article deals with regularization/penalization in the fitting of GANs, when based on a L_1 Wasserstein metric. Basics on mass transportation are briefly recalled in section 2, while section 3 formulate the GANs approach in the Wasserstein context. Taking into account the Lipschitz constraint and (non-) differentiability of optimal critic functions f are discussed in section 4 and Section 5 proposes a way to penalize candidate functions f that do not satisfy the Lipschitz condition using a tuning parameter lambda, ruling a trade-off between marginal fitting and gradient control. The approach is illustrated by numerical experiments. Such results are hardly convincing, since the tuning of the parameter lambda plays a crucial role in the performance of the method. More importantly, The heuristic proposed in the paper is interesting and promising in some respects but there is a real lack of theoretical guarantees motivating the penalty form chosen, such a theoretical development could allow to understand what may rule the choice of an ideal value for lambda in particular.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
On the regularization of Wasserstein GANs
Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize the distance between the model and the empirical distribution in terms of a different metric, but thereby introduce a Lipschitz constraint into the optimization problem. A simple way to enforce the Lipschitz constraint on the class of functions, which can be modeled by the neural network, is weight clipping. Augmenting the loss by a regularization term that penalizes the deviation of the gradient norm of the critic (as a function of the network*s input) from one, was proposed as an alternative that improves training. We present theoretical arguments why using a weaker regularization term enforcing the Lipschitz constraint is preferable. These arguments are supported by experimental results on several data sets.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 The article deals with regularization/penalization in the fitting of GANs, when based on a L_1 Wasserstein metric. Basics on mass transportation are briefly recalled in section 2, while section 3 formulate the GANs approach in the Wasserstein context. Taking into account the Lipschitz constraint and (non-) differentiability of optimal critic functions f are discussed in section 4 and Section 5 proposes a way to penalize candidate functions f that do not satisfy the Lipschitz condition using a tuning parameter lambda, ruling a trade-off between marginal fitting and gradient control. The approach is illustrated by numerical experiments. Such results are hardly convincing, since the tuning of the parameter lambda plays a crucial role in the performance of the method. More importantly, The heuristic proposed in the paper is interesting and promising in some respects but there is a real lack of theoretical guarantees motivating the penalty form chosen, such a theoretical development could allow to understand what may rule the choice of an ideal value for lambda in particular.
assistant
 The article deals with regularization/penalization in the fitting of GANs, when based on a L_1 Wasserstein metric. Basics on mass transportation are briefly recalled in section 2, while section 3 formulate the GANs approach in the Wasserstein context. Taking into account the Lipschitz constraint and (non-) differentiability of optimal critic functions f are discussed in section 4 and Section 5 proposes a way to penalize candidate functions f that do not satisfy the Lipschitz condition using a tuning parameter lambda, ruling a trade-off between marginal fitting and gradient control. The approach is illustrated by numerical experiments. Such results are hardly convincing, since the tuning of the parameter lambda plays a crucial role in the performance of the method. More importantly, The heuristic proposed in the paper is interesting and promising in some respects but there is a real lack of theoretical guarantees motivating the penalty form chosen, such a theoretical development could allow to understand what may rule the choice of an ideal value for lambda in particular.