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发表时间：2015-01-01

发表刊物：中国科学 数学

所属单位：数学科学学院

卷号：45

期号：9

页面范围：1487-1504

ISSN号：1674-7216

摘要：On the premise of appropriate learning accuracy, the number of the
   neurons of a neural network should be as less as possible
   (constructional sparsification), so as to reduce the cost, and to
   improve the robustness and the generalization accuracy. We study the
   constructional sparsification of feedforward neural networks by using
   regularization methods. Apart from the traditional L1 regularization for
   sparsification, we mainly use the L_(1/2) regularization. To remove the
   oscillation in the iteration process due to the nonsmoothness of the
   L_(1/2) regularizer, we propose to smooth it in a neighborhood of the
   nonsmooth point to get a smoothing L_(1/2) regularizer. By doing so, we
   expect to improve the efficiency of the L_(1/2) regularizer so as to
   surpass the L1 regularizer. Some of our recent works in this respect are
   summarized in this paper, including the works on BP feedforward neural
   networks, higher order neural networks, double parallel neural networks
   and Takagi-Sugeno fuzzy models.

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