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When Harmonic Analysis Meets Machine Learning: Lipschitz Analysis of Deep Convolution Networks

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Citation Author(s):
Radu Balan
Submitted by:
Qiang ZHU
Last updated:
19 October 2017 - 11:56am
Document Type:
Presentation Slides
Document Year:



Deep neural networks have led to dramatic improvements in performance for many machine learning tasks, yet the mathematical reasons for this success remain largely unclear. In this talk we present recent developments in the mathematical framework of convolutive neural networks (CNN). In particular we discuss the scattering network of Mallat and how it relates to another problem in harmonic analysis, namely the phase retrieval problem. Then we discuss the general convolutive neural network from a theoretician point of view. We present Lipschitz analysis results using two analytical methods: the chain rule (or backpropagation) and the storage function method inspired by Mallat's scattering network analysis. Towards the end of the talk we discuss how these theoretical results can be applied in practice, and in particular we mention various design methods that incorporate Lipschitz bounds as penalty terms into optimization problems.

Prof. Balan is a professor of applied mathematics at the University of Maryland. His research interests include topics in harmonic analysis and applications to engineering and computer science, particularly to statistical signal processing, and machine learning.

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