Scale-Equivariant Steerable Networks
The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In this work, we pay attention to scale changes, which regularly appear in various tasks due to the changing distances between the objects and the camera. First, we introduce the general theory for building scale-equivariant convolutional networks with steerable filters. We develop scale-convolution and generalize other common blocks to be scale-equivariant. We demonstrate the computational efficiency and numerical stability of the proposed method. We compare the proposed models to the previously developed methods for scale equivariance and local scale invariance. We demonstrate state-of-the-art results on MNIST-scale dataset. Finally, we demonstrate that the proposed scale-equivariant convolutions show remarkable gains on STL-10 when used as drop-in replacements for non-equivariant convolutional layers.
The paper describes a method for integrating scale equivariance into convolutional networks using steerable filters. After developing the theory using continuous scale and translation space, a discretized implementation using a fixed set of steerable basis elements is described. Experiments are performed measuring the error from true equivariance, varying number of layers, image scale and scales in scale interactions. The method is evaluated using MNIST-scale and STL-10, with convincing results on MNIST-scale and bit less convincing but still good results on STL-10. Overall, I think this is a nice paper with generally good explanations and experiments probing the behavior. I would have liked to see more probing into the effects of number and distance between scales. Table 1 and corresponding text say that a significant advantage of the approach is that it can handle arbitrary scale values, but there was no explicit exploration of the effects of using this beyond one set of scales per experiment/dataset. What scale values can be sampled, which work best, and why? Also, while the MNIST-scale experiment seems convincing, I think the STL-10 is a bit less (but still OK): Although the method outperforms other methods and appropriate baseline models, it*s a little disappointing that pooling over scales (which I would would convert the equivariance to invariance) is best, and inter-scale interactions increase error. (Perhaps this is not too surprising in retrospect, as images may have limited scale variation from camera position in this dataset, but significant within-class viewpoint variation.) Even so, I still find the method concise and of interest, with the basics evaluated, even if some of its unique advantages may have been better explored. Additional Questions: * Inter-scale interaction could be elaborated a bit more. End of sec 4 says, *use convHH for each scale sequentially and .. sum*. I believe this is sequencing over scales in the kernel; explaining a bit better how this is implemented, including the shape of w in this case, would be helpful. * Which scales were chosen for the fixed basis? How large in spatial extent are the kernels in the basis elements, at each scale? * In the implementation, what is the value of V (sampled 2d conv kernel size)?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Scale-Equivariant Steerable Networks
The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In this work, we pay attention to scale changes, which regularly appear in various tasks due to the changing distances between the objects and the camera. First, we introduce the general theory for building scale-equivariant convolutional networks with steerable filters. We develop scale-convolution and generalize other common blocks to be scale-equivariant. We demonstrate the computational efficiency and numerical stability of the proposed method. We compare the proposed models to the previously developed methods for scale equivariance and local scale invariance. We demonstrate state-of-the-art results on MNIST-scale dataset. Finally, we demonstrate that the proposed scale-equivariant convolutions show remarkable gains on STL-10 when used as drop-in replacements for non-equivariant convolutional layers.
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 describes a method for integrating scale equivariance into convolutional networks using steerable filters. After developing the theory using continuous scale and translation space, a discretized implementation using a fixed set of steerable basis elements is described. Experiments are performed measuring the error from true equivariance, varying number of layers, image scale and scales in scale interactions. The method is evaluated using MNIST-scale and STL-10, with convincing results on MNIST-scale and bit less convincing but still good results on STL-10. Overall, I think this is a nice paper with generally good explanations and experiments probing the behavior. I would have liked to see more probing into the effects of number and distance between scales. Table 1 and corresponding text say that a significant advantage of the approach is that it can handle arbitrary scale values, but there was no explicit exploration of the effects of using this beyond one set of scales per experiment/dataset. What scale values can be sampled, which work best, and why? Also, while the MNIST-scale experiment seems convincing, I think the STL-10 is a bit less (but still OK): Although the method outperforms other methods and appropriate baseline models, it*s a little disappointing that pooling over scales (which I would would convert the equivariance to invariance) is best, and inter-scale interactions increase error. (Perhaps this is not too surprising in retrospect, as images may have limited scale variation from camera position in this dataset, but significant within-class viewpoint variation.) Even so, I still find the method concise and of interest, with the basics evaluated, even if some of its unique advantages may have been better explored. Additional Questions: * Inter-scale interaction could be elaborated a bit more. End of sec 4 says, *use convHH for each scale sequentially and .. sum*. I believe this is sequencing over scales in the kernel; explaining a bit better how this is implemented, including the shape of w in this case, would be helpful. * Which scales were chosen for the fixed basis? How large in spatial extent are the kernels in the basis elements, at each scale? * In the implementation, what is the value of V (sampled 2d conv kernel size)?
assistant
The paper describes a method for integrating scale equivariance into convolutional networks using steerable filters. After developing the theory using continuous scale and translation space, a discretized implementation using a fixed set of steerable basis elements is described. Experiments are performed measuring the error from true equivariance, varying number of layers, image scale and scales in scale interactions. The method is evaluated using MNIST-scale and STL-10, with convincing results on MNIST-scale and bit less convincing but still good results on STL-10. Overall, I think this is a nice paper with generally good explanations and experiments probing the behavior. I would have liked to see more probing into the effects of number and distance between scales. Table 1 and corresponding text say that a significant advantage of the approach is that it can handle arbitrary scale values, but there was no explicit exploration of the effects of using this beyond one set of scales per experiment/dataset. What scale values can be sampled, which work best, and why? Also, while the MNIST-scale experiment seems convincing, I think the STL-10 is a bit less (but still OK): Although the method outperforms other methods and appropriate baseline models, it*s a little disappointing that pooling over scales (which I would would convert the equivariance to invariance) is best, and inter-scale interactions increase error. (Perhaps this is not too surprising in retrospect, as images may have limited scale variation from camera position in this dataset, but significant within-class viewpoint variation.) Even so, I still find the method concise and of interest, with the basics evaluated, even if some of its unique advantages may have been better explored. Additional Questions: * Inter-scale interaction could be elaborated a bit more. End of sec 4 says, *use convHH for each scale sequentially and .. sum*. I believe this is sequencing over scales in the kernel; explaining a bit better how this is implemented, including the shape of w in this case, would be helpful. * Which scales were chosen for the fixed basis? How large in spatial extent are the kernels in the basis elements, at each scale? * In the implementation, what is the value of V (sampled 2d conv kernel size)?