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.

翻译：神经网络性能通过增加卷积层通道数得到显著提升，但这种性能提升伴随着更高的计算成本，促使大量研究聚焦于降低计算开销。分组卷积作为解决该问题的有效方法之一，通过分组通道显著降低了计算成本。然而，据我们所知，目前尚无理论分析阐明分组卷积对标准卷积的近似程度。本文从数学角度分析了分组卷积在不同分组数量下对标准卷积的近似能力，并据此提出一种名为平衡分组卷积的新型变体，该变体在仅增加少量计算成本的前提下实现了更高近似度。我们通过实验验证了理论分析结果，并证明了平衡分组卷积相较于其他分组卷积变体的优越性能。