Filter pruning-based two-step feature map reconstruction

In deep neural network compression, channel/filter pruning is widely used for compressing the pre-trained network by judging the redundant channels/filters. In this paper, we propose a two-step filter pruning method to judge the redundant channels/filters layer by layer. The first step is to design a filter selection scheme based on ℓ2,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{2,1}$$\end{document}-norm by reconstructing the feature map of current layer. More specifically, the filter selection scheme aims to solve a joint ℓ2,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{2,1}$$\end{document}-norm minimization problem, i.e., both the regularization term and feature map reconstruction error term are constrained by ℓ2,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{2,1}$$\end{document}-norm. The ℓ2,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{2,1}$$\end{document}-norm regularization plays a role in the channel/filter selection, while the ℓ2,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{2,1}$$\end{document}-norm feature map reconstruction error term plays a role in the robust reconstruction. In this way, the proposed filter selection scheme can learn a column-sparse coefficient representation matrix that can indicate the redundancy of filters. Since pruning the redundant filters in current layer might dramatically influence the output feature map of the following layer, the second step needs to update the filters of the following layer to assure output of feature map approximates to that of baseline. Experimental results demonstrate the effectiveness of this proposed method. For example, our pruned VGG-16 on ImageNet achieves 4×\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\times $$\end{document} speedup with 0.95% top-5 accuracy drop. Our pruned ResNet-50 on ImageNet achieves 2×\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\times $$\end{document} speedup with 1.56% top-5 accuracy drop. Our pruned MobileNet on ImageNet achieves 2×\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\times $$\end{document} speedup with 1.20% top-5 accuracy drop.