Topological Methods for Deep Learning

Gunnar Carlsson Topological Methods for Deep Learning Resumen: Deep learning is a very powerful methodology used in a number of situations. One is the study of data sets of images, where it can produce very accurate using a particular class of computation graphs called convolutional neural networks. On the other hand, topological data analysis has produced a good understanding for the statistics of natural images. In this talk, we will show how to bridge this gap, and also produce ways to understand the inner workings of convolutional neural networks. We will also show how to use topology to inform the constructions of specialized architectures that increase the generalization power as well as lessen the number of data points needed to train.