Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Tao Luo, Purdue University, Department of Mathematics
Inviter:	明平兵研究员
Title:	Theory of the Frequency Principle for General Deep Neural Networks
Time & Venue:	2019.7.15 14:00-15:00 N602
Abstract:	Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function from low to high frequencies during the training. The F-Principle has been very useful in providing both qualitative and quantitative understandings of DNNs. In this talk, we rigorously investigate the F-Principle for the training dynamics of a general DNN at three stages: initial stage, intermediate stage, and final stage. For each stage, a theorem is provided in terms of proper quantities characterizing the F-Principle. Our results are general in the sense that they work for multilayer networks with general activation functions, population densities of data, and a large class of loss functions. Our work lays a theoretical foundation of the F-Principle for a better understanding of the training process of DNNs.