Optimal Unsupervised Domain Translation
Unsupervised Domain Translation~(UDT) consists in finding meaningful correspondences between two domains, without access to explicit pairings between them. Following the seminal work of 	extit{CycleGAN}, many variants and extensions of this model have been applied successfully to a wide range of applications. However, these methods remain poorly understood, and lack convincing theoretical guarantees. In this work, we define UDT in a rigorous, non-ambiguous manner, explore the implicit biases present in the approach and demonstrate the limits of theses approaches. Specifically, we show that mappings produced by these methods are biased towards 	extit{low energy} transformations, leading us to cast UDT into an Optimal Transport~(OT) framework by making this implicit bias explicit. This not only allows us to provide theoretical guarantees for existing methods, but also to solve UDT problems where previous methods fail. Finally, making the link between the dynamic formulation of OT and CycleGAN, we propose a simple approach to solve UDT, and illustrate its properties in two distinct settings.
Summary: The paper addresses the ill-posedness of the unsupervised domain translation (UDT) problem. It provides a more structured and rigorous problem definition than previous works (mainly CycleGAN-based), and proposes the theory of optimal transport (OT) as a better framework for solving UDT. The paper provides an interesting link between a dynamical formulation of OT and residual networks, which leads to a practical algorithm for solving OT/UDT. Experiments highlight two main points: 1) CycleGAN are biased towards learning nearly identity mappings, and 2) the OT formulation allows for modelling explicit biases in the learned solution through the design of the cost function. Strengths & Weaknesses: + The paper addresses an important problem, which as far as I know, is widely known but not properly or explicitly addressed in prior work. - While most definitions are rather intuitive, some are still vague so they cannot be constructive. For example, a UDT task is a subset of all possible mappings which are *desirable* for the given task, but it is not clear how we can exactly define *desirable* mappings. - In addition, it is not clear why the set of all mappings X_{alpha,beta} needs to be constrained to invertible mappings. I see invertibility as only a constraint added by CycleGAN to limit the set of possible learned mappings. + The paper makes an interesting observation that CycleGAN is biased towards simple, and nearly identity mappings (which I believe is the main consequence of small initialization values), which could explain its practical success. - However, the paper needs to emphasize that this is particularly tied to the choice of resnet architectures that is commonly used. + I like the proposed dynamical formulation for solving OT and the link to resnets, which provides an interesting practical algorithm. - The main problem that remains unsolved is how to choose the cost function . The paper acknowledges that, and proposes a specific cost functions for the specific tasks of the experimental section. - While experiments support the main claims of the paper, they are still quite limited and do not really have a clear practical significance. The paper would have been much stronger if the proposed approach solves a more practical problem. In conclusion, while I think that the practical significance of the proposed approach is rather limited, I think that overall it makes an interesting contribution to the domain of UDT which can be useful for future work.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Optimal Unsupervised Domain Translation
Unsupervised Domain Translation~(UDT) consists in finding meaningful correspondences between two domains, without access to explicit pairings between them. Following the seminal work of 	extit{CycleGAN}, many variants and extensions of this model have been applied successfully to a wide range of applications. However, these methods remain poorly understood, and lack convincing theoretical guarantees. In this work, we define UDT in a rigorous, non-ambiguous manner, explore the implicit biases present in the approach and demonstrate the limits of theses approaches. Specifically, we show that mappings produced by these methods are biased towards 	extit{low energy} transformations, leading us to cast UDT into an Optimal Transport~(OT) framework by making this implicit bias explicit. This not only allows us to provide theoretical guarantees for existing methods, but also to solve UDT problems where previous methods fail. Finally, making the link between the dynamic formulation of OT and CycleGAN, we propose a simple approach to solve UDT, and illustrate its properties in two distinct settings.
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>



Summary: The paper addresses the ill-posedness of the unsupervised domain translation (UDT) problem. It provides a more structured and rigorous problem definition than previous works (mainly CycleGAN-based), and proposes the theory of optimal transport (OT) as a better framework for solving UDT. The paper provides an interesting link between a dynamical formulation of OT and residual networks, which leads to a practical algorithm for solving OT/UDT. Experiments highlight two main points: 1) CycleGAN are biased towards learning nearly identity mappings, and 2) the OT formulation allows for modelling explicit biases in the learned solution through the design of the cost function. Strengths & Weaknesses: + The paper addresses an important problem, which as far as I know, is widely known but not properly or explicitly addressed in prior work. - While most definitions are rather intuitive, some are still vague so they cannot be constructive. For example, a UDT task is a subset of all possible mappings which are *desirable* for the given task, but it is not clear how we can exactly define *desirable* mappings. - In addition, it is not clear why the set of all mappings X_{alpha,beta} needs to be constrained to invertible mappings. I see invertibility as only a constraint added by CycleGAN to limit the set of possible learned mappings. + The paper makes an interesting observation that CycleGAN is biased towards simple, and nearly identity mappings (which I believe is the main consequence of small initialization values), which could explain its practical success. - However, the paper needs to emphasize that this is particularly tied to the choice of resnet architectures that is commonly used. + I like the proposed dynamical formulation for solving OT and the link to resnets, which provides an interesting practical algorithm. - The main problem that remains unsolved is how to choose the cost function . The paper acknowledges that, and proposes a specific cost functions for the specific tasks of the experimental section. - While experiments support the main claims of the paper, they are still quite limited and do not really have a clear practical significance. The paper would have been much stronger if the proposed approach solves a more practical problem. In conclusion, while I think that the practical significance of the proposed approach is rather limited, I think that overall it makes an interesting contribution to the domain of UDT which can be useful for future work.
assistant
Summary: The paper addresses the ill-posedness of the unsupervised domain translation (UDT) problem. It provides a more structured and rigorous problem definition than previous works (mainly CycleGAN-based), and proposes the theory of optimal transport (OT) as a better framework for solving UDT. The paper provides an interesting link between a dynamical formulation of OT and residual networks, which leads to a practical algorithm for solving OT/UDT. Experiments highlight two main points: 1) CycleGAN are biased towards learning nearly identity mappings, and 2) the OT formulation allows for modelling explicit biases in the learned solution through the design of the cost function. Strengths & Weaknesses: + The paper addresses an important problem, which as far as I know, is widely known but not properly or explicitly addressed in prior work. - While most definitions are rather intuitive, some are still vague so they cannot be constructive. For example, a UDT task is a subset of all possible mappings which are *desirable* for the given task, but it is not clear how we can exactly define *desirable* mappings. - In addition, it is not clear why the set of all mappings X_{alpha,beta} needs to be constrained to invertible mappings. I see invertibility as only a constraint added by CycleGAN to limit the set of possible learned mappings. + The paper makes an interesting observation that CycleGAN is biased towards simple, and nearly identity mappings (which I believe is the main consequence of small initialization values), which could explain its practical success. - However, the paper needs to emphasize that this is particularly tied to the choice of resnet architectures that is commonly used. + I like the proposed dynamical formulation for solving OT and the link to resnets, which provides an interesting practical algorithm. - The main problem that remains unsolved is how to choose the cost function . The paper acknowledges that, and proposes a specific cost functions for the specific tasks of the experimental section. - While experiments support the main claims of the paper, they are still quite limited and do not really have a clear practical significance. The paper would have been much stronger if the proposed approach solves a more practical problem. In conclusion, while I think that the practical significance of the proposed approach is rather limited, I think that overall it makes an interesting contribution to the domain of UDT which can be useful for future work.