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ℓp regularization has been a popular pruning method for neural networks. The parameter p was usually set as 0<p≤2 in the literature, and practical training algorithms with ℓ0 regularization are lacking due to the NP-hard nature of the ℓ0 regularization problem; however, the ℓ0 regularization tends to produce the sparsest solution, corresponding to the most parsimonious network structure which is...
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...
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