Improve Generalization and Robustness of Neural Networks via Weight Scale Shifting Invariant Regularizations
This addresses a fundamental limitation in neural network regularization for researchers and practitioners, offering a more effective method to enhance model performance and robustness, though it is incremental in building on existing regularization concepts.
The paper tackled the ineffectiveness of standard regularizers like weight decay in penalizing intrinsic weight norms for networks with homogeneous activations, leading to overfitting, and proposed an invariant regularizer that improved generalization and adversarial robustness across datasets and architectures.
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.