군-등변 CNN의 성능 분석

Abstract

In this paper, we analyze the mathematical structure of group-equivariant CNNs using the vector bundle theory in homogeneous space and compare and analyze their performances with a conventional CNN through various experiments. The group-equivariant CNN uses the group-equivariant convolution, which can be implemented with an increase in weight sharing compared to the existing convolution. It is shown that the symmetric group of a CNN operating in image space is Z² , whereas those of a group-equivariant CNNs are subgroups of SE(2) or E(2). According to the experimental results of three models, such as a CNN and group-equivariant CNNs, one of the latter shows a recognition rate improvement by more than 6.5% compared to the former, especially in the rotated MNIST. Therefore, it is proposed that the symmetric group of the CNN model can be used as a useful index to evaluate its performance.