Learning with tensor paraproducts
Abstract
Mr Oluwadamilola (Dami) Fasina will talk about; 'Learning with tensor paraproducts'
We discuss computational (Neural FIM) and analytical (tensor paraproducts) tools for learning structure of sets. In the first situation we focus on learning the metric amongst elements of a statistical manifold. To do so, we design a neural network which enables one to compute the Fisher information metric (FIM), so long the Jensen-Shannon divergences amongst probability distributions on the statistical manifold are preserved during training. In the second situation we focus on analyzing the structure of function compositions through separation of its low and high frequency components. This is accomplished by elaborating on J.M. Bony’s celebrated work on paraproducts by discretizing and allocating distinct scaling parameters along each dimension of the support of a function composition (with a prescribed regularity), permitting finer analytical control. A consequence of this extension is highlighted with a discussion of the regularity gains of kernels of integral operators.
Bio:
Oluwadamilola Fasina earned his PhD in Applied Mathematics from Yale University under the supervision of Professors Ronald Coifman and Smita Krishnaswamy. He also holds an M.S. in Medical Physics from Duke University and a B.S. in Nuclear Engineering from North Carolina State University. His research focus is in computational harmonic analysis, which he uses to analyze neural architectures and develop numerical methods for integral equations, with an application focus in the physical and biomedical sciences.
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