Learning Graph Decomposition
We propose a novel end-to-end trainable framework for the graph decomposition problem. The minimum cost multicut problem is first converted to an unconstrained binary cubic formulation where cycle consistency constraints are incorporated into the objective function. The new optimization problem can be viewed as a Conditional Random Field (CRF) in which the random variables are associated with the binary edge labels of the initial graph and the hard constraints are introduced in the CRF as high-order potentials. The parameters of a standard Neural Network and the fully differentiable CRF can be optimized in an end-to-end manner. We demonstrate the proposed learning algorithm in the context of clustering of hand written digits, particularly in a setting where no direct supervision for the graph decomposition task is available, and multiple person pose estimation from images in the wild. The experiments validate the effectiveness of our approach both for the feature learning and for the final clustering task.
 The paper is very well written and the motivation of the end-to-end trainable framework for graph decomposition problem is very clear and strong. The proposed method is also fairly novel, especially the decision to convert the discrete optimization problem to an unconstrained binary cubic problem. Finally, the proposed method applied to human pose estimation achieves on par performance with the state-of-the-art performance on the MPII Human Pose dataset.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Learning Graph Decomposition
We propose a novel end-to-end trainable framework for the graph decomposition problem. The minimum cost multicut problem is first converted to an unconstrained binary cubic formulation where cycle consistency constraints are incorporated into the objective function. The new optimization problem can be viewed as a Conditional Random Field (CRF) in which the random variables are associated with the binary edge labels of the initial graph and the hard constraints are introduced in the CRF as high-order potentials. The parameters of a standard Neural Network and the fully differentiable CRF can be optimized in an end-to-end manner. We demonstrate the proposed learning algorithm in the context of clustering of hand written digits, particularly in a setting where no direct supervision for the graph decomposition task is available, and multiple person pose estimation from images in the wild. The experiments validate the effectiveness of our approach both for the feature learning and for the final clustering task.
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 paper is very well written and the motivation of the end-to-end trainable framework for graph decomposition problem is very clear and strong. The proposed method is also fairly novel, especially the decision to convert the discrete optimization problem to an unconstrained binary cubic problem. Finally, the proposed method applied to human pose estimation achieves on par performance with the state-of-the-art performance on the MPII Human Pose dataset.
assistant
 The paper is very well written and the motivation of the end-to-end trainable framework for graph decomposition problem is very clear and strong. The proposed method is also fairly novel, especially the decision to convert the discrete optimization problem to an unconstrained binary cubic problem. Finally, the proposed method applied to human pose estimation achieves on par performance with the state-of-the-art performance on the MPII Human Pose dataset.