Mapping Properties of Neural Networks and Inverse Problems

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B1 L4 R4214

This talk will explore the injectivity and universal approximation properties of neural networks, focusing on one-to-one mappings and the approximation of probability measures using compositions of invertible flow networks and injective layers, with applications in inverse problems, imaging, and generative models.

We will consider mapping properties of neural networks. In particular, we consider the injectivity of neural networks and universal approximation results for one-to-one neural networks. In addition, we study approximation of probability measures using neural networks that are compositions of invertible flow networks and injective layers and present applications in inverse problems, imaging and generative models.

The talk is based on collaboration with Maarten de Hoop, Ivan Dokmanic, Konik Kothari, Pekka Pankka and Michael Puthawala. 

Presenters

Prof. Matti Lassas, Applied Mathematics, University of Helsinki, Finland

Brief Biography

Matti Lassas a professor of applied mathematics at University of Helsinki, Finland, and the director of the Finnish Centre of Excellence in Inverse Modelling and Imaging of Finnish Research Council. He obtained his Ph.D. in Mathematics in University of Helsinki, 1996. In 2023, he received the European Research Council (ERC) Advanced grant and he is the representative of the Finnish Mathematical Society n the board of International Council for Industrial and Applied Mathematics (ICIAM). Since 2023, he has served as the vice-president of the International Inverse Problems Association (IPIA) and since 2024, he been the chairman of the section of mathematics and computer science of the Finnish Academy of Science and Letters. In 2011-2016, he served as the President of the Finnish Mathematical Society. He has research on inverse problems for partial differential equations and in geometry and mathematics of machine learning. Applications of his research have been related medical X-ray tomography, electrical impedance tomography and inverse travel time problems.