Mathematics of Deep Learning Seminar: Yi Ma

Date & Time

Title: Deep (Convolution) Networks from First Principles

Abstract: In this talk, we offer an entirely “white box’’ interpretation of deep (convolution) networks from the perspective of data compression (and group invariance). In particular, we show how modern deep layered architectures, linear (convolution) operators and nonlinear activations, and even all parameters can be derived from the principle of maximizing rate reduction (with group invariance). All layers, operators, and parameters of the network are explicitly constructed via forward propagation, instead of learned via back propagation. All components of so-obtained network, called ReduNet, have precise optimization, geometric, and statistical interpretation. There are also several nice surprises from this principled approach: it reveals a fundamental tradeoff between invariance and sparsity for class separability; it reveals a fundamental connection between deep networks and Fourier transform for group invariance – the computational advantage in the spectral domain (why spiking neurons?); this approach also clarifies the mathematical role of forward propagation (optimization) and backward propagation (variation). In particular, the so-obtained ReduNet is amenable to fine-tuning via both forward and backward (stochastic) propagation, both for optimizing the same objective.

This is joint work with students Yaodong Yu, Ryan Chan, Haozhi Qi of Berkeley, Dr. Chong You now at Google Research, and Professor John Wright of Columbia University.

About the Speaker

Yi Ma is a Professor in residence at the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley. He received his Bachelor’s degree from Tsinghua University in 1995 and MS and PhD degrees from UC Berkeley in 2000. His research interests are in computer vision, high-dimensional data analysis, and intelligent systems. He has been on the faculty of UIUC ECE from 2000 to 2011, the manager of the Visual Computing group of Microsoft Research Asia from 2009 to 2014, and the Dean of the School of Information Science and Technology of ShanghaiTech University from 2014 to 2017. He has published over 160 papers and three textbooks in computer vision, statistical learning, and data science. He received NSF Career award in 2004 and ONR Young Investigator award in 2005. He also received the David Marr prize in computer vision in 1999 and has served as Program Chair and General Chair of ICCV 2013 and 2015, respectively. He is a Fellow of IEEE, SIAM, and ACM.

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