| Summary: | In this paper, a novel smooth group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>G</mi><msub><mi>L</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>) regularization method is proposed for pruning hidden nodes of the fully connected layer in convolution neural networks. Usually, the selection of nodes and weights is based on experience, and the convolution filter is symmetric in the convolution neural network. The main contribution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>G</mi><msub><mi>L</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> is to try to approximate the weights to 0 at the group level. Therefore, we will be able to prune the hidden node if the corresponding weights are all close to 0. Furthermore, the feasibility analysis of this new method is carried out under some reasonable assumptions due to the smooth function. The numerical results demonstrate the superiority of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>G</mi><msub><mi>L</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> method with respect to sparsity, without damaging the classification performance.
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