标题： 深度神经网络的群稀疏正则化 显示英文标题

标题： Group Sparse Regularization for Deep Neural Networks

摘要： 本文中，我们考虑同时优化以下三个任务：(i) 深度神经网络的权重，(ii) 每个隐藏层的神经元数量，以及 (iii) 活跃输入特征的子集（即特征选择）。尽管这些问题通常被单独处理，我们提出了一种简单的正则化公式，可以使用标准优化程序同时解决这三个问题。具体而言，我们将组 Lasso 惩罚（起源于线性回归文献）扩展，以在网络连接上施加组级稀疏性，其中每个组定义为单元的所有出射权重集合。根据具体情况，权重可以与输入变量、隐藏神经元或偏置单元相关联，从而同时执行所有上述任务以获得紧凑的网络。我们通过与经典的权值衰减和 Lasso 惩罚进行比较，进行了广泛的实验评估。我们表明，组 Lasso 惩罚的稀疏版本能够实现具有竞争力的性能，同时生成更加紧凑且输入特征更少的网络。我们在手写数字识别的玩具数据集以及多个现实中的大规模分类问题上进行了评估。 显示英文摘要

摘要： In this paper, we consider the joint task of simultaneously optimizing (i) the weights of a deep neural network, (ii) the number of neurons for each hidden layer, and (iii) the subset of active input features (i.e., feature selection). While these problems are generally dealt with separately, we present a simple regularized formulation allowing to solve all three of them in parallel, using standard optimization routines. Specifically, we extend the group Lasso penalty (originated in the linear regression literature) in order to impose group-level sparsity on the network's connections, where each group is defined as the set of outgoing weights from a unit. Depending on the specific case, the weights can be related to an input variable, to a hidden neuron, or to a bias unit, thus performing simultaneously all the aforementioned tasks in order to obtain a compact network. We perform an extensive experimental evaluation, by comparing with classical weight decay and Lasso penalties. We show that a sparse version of the group Lasso penalty is able to achieve competitive performances, while at the same time resulting in extremely compact networks with a smaller number of input features. We evaluate both on a toy dataset for handwritten digit recognition, and on multiple realistic large-scale classification problems.