This paper has resulted in a detailed discussion between the reviewers. The authors use the same techniques that have recently proved to be very popular for building neural networks that are equivariant to translations, rotations etc. to formulate a general theory of scale equivariant neural networks. I believe that the mathematical derivations are sound and that this is an interesting direction to pursue. However, at the end of the day the proposed algorithm is simple and similar to other "multi-scale" neural nets that have recently appeared in the literature. This makes one feel that the mathematical derivations are a little too meticulous, and instead the authors should have focused on conveying the intuition and providing more extensive and more convincing experimental results. The lack of the latter is particularly concerning given that comparable results published in the Vision literature are much stronger (by the authors admission they did not have the time/resources to perform similar experiments).

Preview this course - GET COUPON CODE Convolutional neural networks with mathematical derivations and practical applications is the second course in my Neural Networks and deep learning series, after the first course in the series named "College-Level Neural Networks With Mathematical Derivations". As the title implies, This course is focused on Convolutional neural networks, a special kind of neural networks mainly used for visual recognition in images and videos, yet not limited to that. In this course, I mainly focus on concepts, intuitions, mathematical derivations, and practical applications. The course is mainly divided into 4 chapters: Chapter 1 focuses on the conceptual basics and intuitions of CNNs. Why are they suitable for visual recognition? Chapter 2 takes a step deeper into the CNN mathematical derivations.