Study on the Large Batch Size Training of Neural Networks Based on the Second Order Gradient
This research provides theoretical and algorithmic insights into the 'generalization gap' problem for deep neural network practitioners using large batch sizes, offering geometry-based explanations and improved learning rate strategies.
This paper investigates the impact of varying batch sizes on neural network structure, specifically focusing on gradient, parameter update step length, and loss update step length. They propose a curvature-based learning rate (CBLR) algorithm and its approximation, median-curvature LR (MCLR), which achieves performance comparable to the LARS algorithm.
Large batch size training in deep neural networks (DNNs) possesses a well-known 'generalization gap' that remarkably induces generalization performance degradation. However, it remains unclear how varying batch size affects the structure of a NN. Here, we combine theory with experiments to explore the evolution of the basic structural properties, including gradient, parameter update step length, and loss update step length of NNs under varying batch sizes. We provide new guidance to improve generalization, which is further verified by two designed methods involving discarding small-loss samples and scheduling batch size. A curvature-based learning rate (CBLR) algorithm is proposed to better fit the curvature variation, a sensitive factor affecting large batch size training, across layers in a NN. As an approximation of CBLR, the median-curvature LR (MCLR) algorithm is found to gain comparable performance to Layer-wise Adaptive Rate Scaling (LARS) algorithm. Our theoretical results and algorithm offer geometry-based explanations to the existing studies. Furthermore, we demonstrate that the layer wise LR algorithms, for example LARS, can be regarded as special instances of CBLR. Finally, we deduce a theoretical geometric picture of large batch size training, and show that all the network parameters tend to center on their related minima.