Originality: this work tackles a traditional problem and achieves good performance improvement compared with previous states. The overall framework is quite novel. Unlike previous learning approaches which usually use a one-shot formula, the network is designed to be iterative, which is quite novel. In addition, there are also quite a few novel designs within the network. The most interesting one is the use of Gumbel-Softmax sampler within an actor-critic framework for sharp correspondence estimation. The authors have also justified the effectiveness of this through baseline comparison and ablation studies. Detecting key points for registration is also an interesting point given the main problem setup is partial scan registration. However, I feel this point is relatively weak in the whole paper with less study and justification. There's at least one work should also be mentioned and compared with, where dense correspondences between partial scans are estimated: Deep Part Induction from Articulated Object Pairs. Quality: technically, the paper is quite sound with a lot of technical details provided. However, there are still some points not clear to me. For the key point detection module, how can you guarantee the two set of top-k points are in correspondence given you are dealing with two partial scans? How does the choice of k influence the final performance? Is the key point detection module robust to the ratio of data missing? Will this l2 norm based key point detector be robust to outliers in scans? For this module design to be solid, more details should be provided. Another thing unclear is how does the discount factor influence the overall performance. Some ablation study should be provided. Clarity: the paper is clearly written and can be easily followed. Significance: point cloud registration is an important problem in computer vision and geometry processing community. The paper has done a good job in achieving state-of-the-art performance on various synthetic partial-to-partial registration tasks. The design of using Gumbel-Softmax sampler within an actor-critic framework for sharp correspondence estimation could be inspiring for other geometry processing tasks involving discrete optimization. However, all the quantitative evaluations are done with synthetic data, making the results a bit less impressive. Missing ablation studies on different design choices also weakens the overall significance a bit. Overall I like this submission but I think some points need more analysis and clarifications.

This is a very interesting paper, and its demonstration that iterative key-point methods can be learned will likely spur new research in this space. The paper provides a convincing motivation for the algorithmic approach, and strong benchmark evaluations. While the paper addresses one very specific problem in computer vision, I think the general approach to adaptive, iterative refinement of this constrained optimization problem may be of broader interest to the community. POST-REBUTTAL: Thank you for providing the ablation studies and particularly the computation speed figures. They significantly strengthen the paper.

This paper presents a novel deep network based partial-to-partial point cloud registration method named PRNet, which outperform the recently proposed DCP [2]. This paper is technically sound and the experimental results are convincing. The manuscript is well organized and well written. 3D deep learning is a hot topic in recent years, this paper goes beyond DCP and proposes a partial-to-partial registration network, which is interesting. Extensive experiments show that the proposed method achieves good performance in registration, keypoint correspondence, and transfer learning. Small issues: Can this method be used to real point cloud acquired with LIDARs mounted on mobile robots or self-driving cars? The abstract says the proposed method outperforms PointNetLK, however, the experimental results didn't include the comparison with it.