  The performance of neural networks has been significantly improved by
increasing the number of channels in convolutional layers. However, this
increase in performance comes with a higher computational cost, resulting in
numerous studies focused on reducing it. One promising approach to address this
issue is group convolution, which effectively reduces the computational cost by
grouping channels. However, to the best of our knowledge, there has been no
theoretical analysis on how well the group convolution approximates the
standard convolution. In this paper, we mathematically analyze the
approximation of the group convolution to the standard convolution with respect
to the number of groups. Furthermore, we propose a novel variant of the group
convolution called balanced group convolution, which shows a higher
approximation with a small additional computational cost. We provide
experimental results that validate our theoretical findings and demonstrate the
superior performance of the balanced group convolution over other variants of
group convolution.
