Warped Convolutions: Efficient Invariance to Spatial Transformations
Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency be attained when considering other spatial invariances? Such generalized convolutions have been considered in the past, but at a high computational cost. We present a construction that is simple and exact, yet has the same computational complexity that standard convolutions enjoy. It consists of a constant image warp followed by a simple convolution, which are standard blocks in deep learning toolboxes. With a carefully crafted warp, the resulting architecture can be made equivariant to a wide range of 2-parameters spatial transformations. We show encouraging results in realistic scenarios, including the estimation of vehicle poses in the Google Earth dataset (rotation and scale), and face poses in Annotated Facial Landmarks in the Wild (3D rotations under perspective).
This paper deals with convolution along Lie groups. Pros: - Good numerical results - Interesting applications linked to convolutions on Lie groups Cons: - Sometimes, the writing is not clear/poor. - The theorems 1 and 2 are in fact direct applications of Lie group theory, but this is not made explicit. I do not detail more my review, as I believe my questions/answers complete it fairly. However, if the authors require it, I can be more specific. I think the writing should be improved a bit.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Warped Convolutions: Efficient Invariance to Spatial Transformations
Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency be attained when considering other spatial invariances? Such generalized convolutions have been considered in the past, but at a high computational cost. We present a construction that is simple and exact, yet has the same computational complexity that standard convolutions enjoy. It consists of a constant image warp followed by a simple convolution, which are standard blocks in deep learning toolboxes. With a carefully crafted warp, the resulting architecture can be made equivariant to a wide range of 2-parameters spatial transformations. We show encouraging results in realistic scenarios, including the estimation of vehicle poses in the Google Earth dataset (rotation and scale), and face poses in Annotated Facial Landmarks in the Wild (3D rotations under perspective).
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>



This paper deals with convolution along Lie groups. Pros: - Good numerical results - Interesting applications linked to convolutions on Lie groups Cons: - Sometimes, the writing is not clear/poor. - The theorems 1 and 2 are in fact direct applications of Lie group theory, but this is not made explicit. I do not detail more my review, as I believe my questions/answers complete it fairly. However, if the authors require it, I can be more specific. I think the writing should be improved a bit.
assistant
This paper deals with convolution along Lie groups. Pros: - Good numerical results - Interesting applications linked to convolutions on Lie groups Cons: - Sometimes, the writing is not clear/poor. - The theorems 1 and 2 are in fact direct applications of Lie group theory, but this is not made explicit. I do not detail more my review, as I believe my questions/answers complete it fairly. However, if the authors require it, I can be more specific. I think the writing should be improved a bit.