Compressing convolutional neural networks (CNNs) has received ever-increasing research focus. However, most existing CNN compression methods do not interpret their inherent structures to distinguish the implicit redundancy. In this paper, we investigate the problem of CNN compression from a novel interpretable perspective. The relationship between the input feature maps and 2D kernels is revealed in a theoretical framework, based on which a kernel sparsity and entropy (KSE) indicator is proposed to quantitate the feature map importance in a feature-agnostic manner to guide model compression. Kernel clustering is further conducted based on the KSE indicator to accomplish high-precision CNN compression. KSE is capable of simultaneously compressing each layer in an efficient way, which is significantly faster compared to previous data-driven feature map pruning methods. We comprehensively evaluate the compression and speedup of the proposed method on CIFAR-10, SVHN and ImageNet 2012. Our method demonstrates superior performance gains over previous ones. In particular, it achieves 4.7 \times FLOPs reduction and 2.9 \times compression on ResNet-50 with only a Top-5 accuracy drop of 0.35% on ImageNet 2012, which significantly outperforms state-of-the-art methods.
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