Gunnar Carlsson - Deep Learning and TDA
Explore the intersection of Topological Data Analysis (TDA) and Deep Learning in this insightful lecture. Delve into how TDA can enhance both the explainability and performance of Deep Learning models. Examine various aspects of image analysis, including the Mumford Data Set and Image Patch Analysis, focusing on primary circles, three circle models, and Klein bottle representations. Investigate the visual pathway and learn about network construction using the Mapper algorithm. Analyze weight spaces in neural networks like MNIST and VGG16 from a topological perspective. Discover how to hard code geometric structures and explore feature space modeling. Gain insights into microarray analysis for breast cancer cohorts and microbiome studies. Investigate generalized convolutional networks and their connections to Klein bottle geometry. Conclude by exploring learning on video data and considering critiques of current AI approaches.