Explore topological deep learning in this comprehensive lecture by Gunnar Carlsson. Discover how topological data analysis can reduce data requirements and increase transparency in machine learning with neural networks. Delve into image and video data analysis, examining concepts such as convolutional neural networks, the Mumford Data Set, and image patch analysis. Investigate the shape of data through topology, learn about the Mapper construction for building networks, and explore topological modeling. Analyze weight spaces in various datasets, including MNIST, Cifar10, and VGG16. Examine hard-coded primary circle and Klein bottle implementations, and understand discovered geometry in convolutional situations. Study feature space modeling applications in breast cancer microarray analysis and UCSD microbiome research. Explore generalized convolutional nets, metric and graph correspondences, and Mapper architectures. Conclude with insights on Klein bottle connections, generalization, and learning on video data.
Overview
Syllabus
Intro
What is Deep Learning?
Problems
Convolutional Neural Networks
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
The Shape of Data
Topology
How to Build Networks - Mapper Construction
Topological Modeling
Topological Analysis of Weight Spaces (MNIST)
Topological Analysis of Weight Spaces (Cifar10)
Topological Analysis of Weight Spaces (VGG16)
Hard Code Primary Circle and Klein Bottle
Convolutional Situation
Discovered Geometry
Feature Space Modeling
Microarray Analysis of Breast Cancer
Explaining the Different Cohorts
UCSD Microbiome
Generalized Convolutional Nets
Metric and Graph Correspondences
The Mapper Architectures
Klein Bottle Connections
Generalization
Learning on Video
Taught by
Applied Algebraic Topology Network
