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Demands to deploy deep neural network (DNN) models on mobile devices and embedded systems have drastically grown in recent years. When transplanting DNN models to such platforms, requirements pertaining to computation and memory use are bottlenecks. To overcome them, network pruning has been carefully studied as a method of network compression. The effectiveness of network pruning is significantly affected by incorrect pruning on important connections. In this paper, we propose a network pruning method based on the modified <inline-formula> <tex-math notation="LaTeX">$L_{1/2}$ </tex-math></inline-formula> penalty that reduces incorrect pruning by increasing the sparsity of the pretrained models. The modified <inline-formula> <tex-math notation="LaTeX">$L_{1/2}$ </tex-math></inline-formula> penalty yields better sparsity than the <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> penalty at a similar computational cost. Compared with the past work that numerically defines the importance of connections and re-establishes important weights when incorrect pruning occurs, our method achieves faster convergence by using a simpler pruning strategy. The results of experiments show that our method can compress LeNet300-100, LeNet-5, ResNet, AlexNet, and VGG16 by factors of <inline-formula> <tex-math notation="LaTeX">$66\times $ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$322\times $ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$26\times $ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$21\times $ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$16\times $ </tex-math></inline-formula>, respectively, with negligible loss of accuracy.