Paper Info
Title
Hessian-based Analysis of Large Batch Training and Robustness to Adversaries.
Abstract
Large batch size training of Neural Networks has been shown to incur accuracy loss when trained with the current methods. The exact underlying reasons for this are still not completely understood. Here, we study large batch size training through the lens of the Hessian operator and robust optimization. In particular, we perform a Hessian based study to analyze exactly how the landscape of the loss function changes when training with large batch size. We compute the true Hessian spectrum, without approximation, by back-propagating the second derivative. Extensive experiments on multiple networks show that saddle-points are not the cause for generalization gap of large batch size training, and the results consistently show that large batch converges to points with noticeably higher Hessian spectrum. Furthermore, we show that robust training allows one to favors flat areas, as points with large Hessian spectrum show poor robustness to adversarial perturbation. We further study this relationship, and provide empirical and theoretical proof that the inner loop for robust training is a saddle-free optimization problem. We present detailed experiments with five different network architectures, including a residual network, tested on MNIST, CIFAR-10, and CIFAR-100 datasets.
Year
Venue
Keywords
2018
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 31 (NIPS 2018)
optimization problems,neural networks,loss function,inner loop,optimization problem,residual network,almost everywhere
DocType
Volume
ISSN
Conference
31
1049-5258
Citations 
PageRank 
References 
6
0.42
18
Authors
5
Name
Order
Citations
PageRank
Zhewei Yao13110.58
Amir Gholami26612.99
Qi Lei36811.12
Kurt Keutzer45040801.67
Michael W. Mahoney53297218.10