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On the Local Hessian in Back-propagation
Huishuai Zhang · Wei Chen · Tie-Yan Liu

Wed Dec 05 07:45 AM -- 09:45 AM (PST) @ Room 210 #43

Back-propagation (BP) is the foundation for successfully training deep neural networks. However, BP sometimes has difficulties in propagating a learning signal deep enough effectively, e.g., the vanishing gradient phenomenon. Meanwhile, BP often works well when combining with ``designing tricks'' like orthogonal initialization, batch normalization and skip connection. There is no clear understanding on what is essential to the efficiency of BP. In this paper, we take one step towards clarifying this problem. We view BP as a solution of back-matching propagation which minimizes a sequence of back-matching losses each corresponding to one block of the network. We study the Hessian of the local back-matching loss (local Hessian) and connect it to the efficiency of BP. It turns out that those designing tricks facilitate BP by improving the spectrum of local Hessian. In addition, we can utilize the local Hessian to balance the training pace of each block and design new training algorithms. Based on a scalar approximation of local Hessian, we propose a scale-amended SGD algorithm. We apply it to train neural networks with batch normalization, and achieve favorable results over vanilla SGD. This corroborates the importance of local Hessian from another side.

Author Information

Huishuai Zhang (Microsoft Research Asia)
Wei Chen (Microsoft Research)
Tie-Yan Liu (Microsoft Research Asia)

Tie-Yan Liu is an assistant managing director of Microsoft Research Asia, leading the machine learning research area. He is very well known for his pioneer work on learning to rank and computational advertising, and his recent research interests include deep learning, reinforcement learning, and distributed machine learning. Many of his technologies have been transferred to Microsoft’s products and online services (such as Bing, Microsoft Advertising, Windows, Xbox, and Azure), and open-sourced through Microsoft Cognitive Toolkit (CNTK), Microsoft Distributed Machine Learning Toolkit (DMTK), and Microsoft Graph Engine. He has also been actively contributing to academic communities. He is an adjunct/honorary professor at Carnegie Mellon University (CMU), University of Nottingham, and several other universities in China. He has published 200+ papers in refereed conferences and journals, with over 17000 citations. He has won quite a few awards, including the best student paper award at SIGIR (2008), the most cited paper award at Journal of Visual Communications and Image Representation (2004-2006), the research break-through award (2012) and research-team-of-the-year award (2017) at Microsoft Research, and Top-10 Springer Computer Science books by Chinese authors (2015), and the most cited Chinese researcher by Elsevier (2017). He has been invited to serve as general chair, program committee chair, local chair, or area chair for a dozen of top conferences including SIGIR, WWW, KDD, ICML, NIPS, IJCAI, AAAI, ACL, ICTIR, as well as associate editor of ACM Transactions on Information Systems, ACM Transactions on the Web, and Neurocomputing. Tie-Yan Liu is a fellow of the IEEE, and a distinguished member of the ACM.

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