Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, April 20, 2020 - 12:00 to 12:50

Location:

Zoom

Guest Speaker:

Marissa Masden

Institution:

University of Oregon

Abstract:

We discuss the use of persistence barcodes both as inputs and intermediate computations in neural networks. Beginning with materials science as a motivating example, we discuss persistence barcodes and persistence landscapes as inputs to deep networks. We will then discuss various loss functions defined on persistence barcodes which may be constructed from the output of networks, as motivation for understanding A Framework for Differential Calculus on Persistence Barcodes (Leygonie, Oudot, Tillman, 2019). Then, using the barcode metric and an abstract generalization of differentiability, we discuss some conditions which ensure this form of differentiability for loss functions and similarly-constructed maps, with a few proofs and a lot of examples.