Understanding Gradient Regularization in Deep Learning: Efficient Finite-Difference Computation and Implicit Bias

Gradient regularization (GR) is a method that penalizes the gradient norm of the training loss during training. Although some studies have reported that GR improves generalization performance in deep learning, little attention has been paid to it from the algorithmic perspective, that is, the algorithms of GR that efficiently improve performance. In this study, we first reveal that a specific finite-difference computation, composed of both gradient ascent and descent steps, reduces the computational cost for GR. In addition, this computation empirically achieves better generalization performance. Next, we theoretically analyze a solvable model, a diagonal linear network, and clarify that GR has a desirable implicit bias in a certain problem. In particular, learning with the finite-difference GR chooses better minima as the ascent step size becomes larger. Finally, we demonstrate that finite-difference GR is closely related to some other algorithms based on iterative ascent and descent steps for exploring flat minima: sharpness-aware minimization and the flooding method. We reveal that flooding performs finite-difference GR in an implicit way. Thus, this work broadens our understanding of GR in both practice and theory.

Self-paced Data Augmentation for Training Neural Networks

Data augmentation is widely used for machine learning; however, an effective method to apply data augmentation has not been established even though it includes several factors that should be tuned carefully. One such factor is sample suitability, which involves selecting samples that are suitable for data augmentation. A typical method that applies data augmentation to all training samples disregards sample suitability, which may reduce classifier performance. To address this problem, we propose the self-paced augmentation (SPA) to automatically and dynamically select suitable samples for data augmentation when training a neural network. The proposed method mitigates the deterioration of generalization performance caused by ineffective data augmentation. We discuss two reasons the proposed SPA works relative to curriculum learning and desirable changes to loss function instability. Experimental results demonstrate that the proposed SPA can improve the generalization performance, particularly when the number of training samples is small. In addition, the proposed SPA outperforms the state-of-the-art RandAugment method.