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数学大讲堂

Deep Networks: Some Applications and Analysis

Abstract

The talk will be composed of two parts --

Application: Learning to Optimize Multigrid PDE Solvers -- We propose a framework for learning critical operators for solving partial differential equations with multigrid methods. Using efficient unsupervised training, our method achieves improved convergence rates for unseen 2D diffusion problems, suggesting that our method successfully learned rules for constructing these operators.  

Analysis: Frequency bias in deep learning? -- We study the relationship between the speed of learning a function and its frequency components. Building on recent results that show that the dynamics of training overparameterized, single-layer neural networks can be approximated by a linear system, we show that for uniformly distributed training data the eigenfunctions of this system are the spherical harmonics. This enables us to make specific predictions of the time it will take a network to learn functions of varying frequency.

Bio

Ronen Basri received the Ph.D. degree from the Weizmann Institute of Science in 1991. He later was a postdoctoral fellow at the Massachusetts Institute of Technology and subsequently joined the Weizmann Institute of Science, where he currently holds the position of Professor, Dean of Mathematics and Computer Science, and incumbent of the Elaine and Bram Goldsmith Chair of Applied Mathematics. His research interests include computer vision, machine learning, and human perception. His work deals with object recognition, shape modeling and reconstruction, lighting analysis, and image segmentation.