Using weight decay to penalize the L2 norms of weights in neural networks has been a standard training practice to regularize the complexity of networks. In this paper, we show that a family of regularizers, including weight decay, is ineffective at penalizing the intrinsic norms of weights for networks with positively homogeneous activation functions, such as linear, ReLU and max-pooling functions. As a result of homogeneity, functions specified by the networks are invariant to the shifting of weight scales between layers. The ineffective regularizers are sensitive to such shifting and thus poorly regularize the model capacity, leading to overfitting. To address this shortcoming, we propose an improved regularizer that is invariant to weight scale shifting and thus effectively constrains the intrinsic norm of a neural network. The derived regularizer is an upper bound for the input gradient of the network so minimizing the improved regularizer also benefits the adversarial robustness. Residual connections are also considered and we show that our regularizer also forms an upper bound to input gradients of such a residual network. We demonstrate the efficacy of our proposed regularizer on various datasets and neural network architectures at improving generalization and adversarial robustness.

该研究论文介绍了一种改进神经网络正则化器的方法，该正则化器不仅能对权重衰减，还能考虑权重尺度偏移对正则化的影响，有效地限制神经网络的内在范数，并优化了对抗强度以提高泛化性能。

通过权重尺度不变正则化提高神经网络的泛化性能和鲁棒性