caa a22 4500 606160450 CHVBK 20210128100630.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00521-014-1730-x doi (NATIONALLICENCE)springer-10.1007/s00521-014-1730-x Batch gradient training method with smoothing $$\boldsymbol{\ell}_{\bf 0}$$ ℓ 0 regularization for feedforward neural networks [Elektronische Daten] [Huisheng Zhang, Yanli Tang, Xiaodong Liu] This paper considers the batch gradient method with the smoothing $$\ell _0$$ ℓ 0 regularization (BGSL0) for training and pruning feedforward neural networks. We show why BGSL0 can produce sparse weights, which are crucial for pruning networks. We prove both the weak convergence and strong convergence of BGSL0 under mild conditions. The decreasing monotonicity of the error functions during the training process is also obtained. Two examples are given to substantiate the theoretical analysis and to show the better sparsity of BGSL0 than three typical $$\ell _p$$ ℓ p regularization methods. The Natural Computing Applications Forum, 2014 Feedforward neural networks nationallicence Gradient method nationallicence $$\ell _0$$ ℓ 0 Regularization nationallicence Sparsity nationallicence Convergence nationallicence Zhang Huisheng Department of Mathematics, Dalian Maritime University, 116026, Dalian, People's Republic of China aut Tang Yanli Department of Mathematics, Dalian Maritime University, 116026, Dalian, People's Republic of China aut Liu Xiaodong Research Center of Information and Control, Dalian University of Technology, 116024, Dalian, People's Republic of China aut Neural Computing and Applications Springer London 26/2(2015-02-01), 383-390 0941-0643 26:2<383 2015 26 521 https://doi.org/10.1007/s00521-014-1730-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00521-014-1730-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhang Huisheng Department of Mathematics, Dalian Maritime University, 116026, Dalian, People's Republic of China aut NATIONALLICENCE 700 1- Tang Yanli Department of Mathematics, Dalian Maritime University, 116026, Dalian, People's Republic of China aut NATIONALLICENCE 700 1- Liu Xiaodong Research Center of Information and Control, Dalian University of Technology, 116024, Dalian, People's Republic of China aut NATIONALLICENCE 773 0- Neural Computing and Applications Springer London 26/2(2015-02-01), 383-390 0941-0643 26:2<383 2015 26 521