Inverse Problems and Invertibility in Deep Learning - Bridging the Gap with Invertible Encoder Models

Presenter: Marius Aasen, UiO, PhD student in Visual Intelligence

Abstract: In this talk, we discuss the applications and limitations of deep learning in the context of inverse problems and highlight the issues of underdetermination and stability – both in the context of stochastic and adversarial perturbations. To this end, we first introduce the mathematical theory of inverse problems in the context of imaging and statistical modelling. We then introduce the foundations of Invertible Neural Networks (INNs) and interrelated hybrid probabilistic techniques with Normalizing Flows (NFs) and classic variational methods as a promising methodology for inverse problems, and discuss our proposed methods for how we can bridge the gap between architectural components of INNs and NFs to standard feed-forward networks using manifold learning on matrix Lie groups. Lastly, we discuss some preliminary results of these modelling techniques in the framework of encoder-decoder models.

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