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

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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.

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Light dinner and refreshments will be served at 6:30pm; lecture will start at 7pm. 

If arriving by car, feel free to use parking lot 11b, which is open for general access after 4pm. If arriving by Metro, free shuttle service is available from the College Park station to campus. 

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