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.

Intro
What is Deep Learning?
Problems
Convolutional Neural Networks
What Do We Want to know?
Mumford Data Set (De Silva, Ishkhanov, Zomorodian, C.)
Image Patch Analysis: Primary Circle
Image Patch Analysis: Three Circle Model
Image Patch Analysis: Klein Bottle
Primary Visual Cortex
Visual Pathway
How to Build Networks - Mapper Construction
Topological Analysis of Weight Spaces (MNIST)
Topological Analysis of Weight Spaces (VGG16)
Hard Code Primary Circle and Klein Bottle
Discovered Geometry
Feature Space Modeling
Microarray Analysis of Breast Cancer Cohort
Explaining the Different Cohorts
UCSD Microbiome
Generalized Convolutional Nets
Klein Bottle Connections
Generalization
Learning on Video
Gary Marcus
Applied Algebraic Topology Research Network