报告题目：Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks

报告时间：2020年5月24日（周日）上午09:35—10:20

报告人：李颖洲教授

报告地点：Zoom云会议（ID：937 6354 7091, 密码：nanxinda60）

报告摘要：Deep networks, especially convolutional neural networks (CNNs), have been successfully applied in various areas of machine learning as well as to challenging problems in other scientific and engineering fields. This paper introduces Butterfly-Net, a low-complexity CNN with structured and sparse cross-channel connections, together with a Butterfly initialization strategy. Theoretical analysis of the approximation power of Butterfly-Net to the Fourier representation of input data shows that the error decays exponentially as the depth increases. Combining Butterfly-Net with a fully connected neural network, a large class of problems are proved to be well approximated with network complexity depending on the effective dimension instead of the input dimension. Regular CNN is covered as a special case in our analysis. Experimentally, Butterfly-Net are tested on various tasks, including approximating Fourier transform operator, energy functionals, end-to-end solvers of linear and nonlinear PDEs in 1D, and denoising and deblurring of 1D signals. Moreover, all experiments support that training from Butterfly initialization outperforms training from random initialization. Also, adding the remaining cross-channel connections, although significantly increase the parameter number, does not much improve the post-training accuracy and is more sensitive to data distribution.

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数学与统计学院

2020年5月22日

附：专家简介

李颖洲，现杜克大学科研助理教授。本科毕业于复旦大学数学系，博士毕业于斯坦福大学计算数学专业。主要研究领域为快速算法设计及分析和高性能计算，包括超大规模线性特征值问题、椭圆算子预条件、波方程快速算法、机器学习等等。文章发表在ACHA，SISC，SIMAX，JCP 等等计算数学专业杂志和 JCTC，Nano Lett. 等应用领域杂志上。