Convolutional layers have long served as the primary workhorse for image classification. Recently, an alternative to convolution was proposed using the Sharpened Cosine Similarity (SCS), which in theory may serve as a better feature detector. While multiple sources report promising results, there has not been to date a full-scale empirical analysis of neural network performance using these new layers. In our work, we explore SCS's parameter behavior and potential as a drop-in replacement for convolutions in multiple CNN architectures benchmarked on CIFAR-10. We find that while SCS may not yield significant increases in accuracy, it may learn more interpretable representations. We also find that, in some circumstances, SCS may confer a slight increase in adversarial robustness.

In this paper, we focus on recognizing 3D shapes from arbitrary views, i.e., arbitrary numbers and positions of viewpoints. It is a challenging and realistic setting for view-based 3D shape recognition. We propose a canonical view representation to tackle this challenge. We first transform the original features of arbitrary views to a fixed number of view features, dubbed canonical view representation, by aligning the arbitrary view features to a set of learnable reference view features using optimal transport. In this way, each 3D shape with arbitrary views is represented by a fixed number of canonical view features, which are further aggregated to generate a rich and robust 3D shape representation for shape recognition. We also propose a canonical view feature separation constraint to enforce that the view features in canonical view representation can be embedded into scattered points in a Euclidean space. Experiments on the ModelNet40, ScanObjectNN, and RGBD datasets show that our method achieves competitive results under the fixed viewpoint settings, and significantly outperforms the applicable methods under the arbitrary view setting.