Explore topological approaches to deep learning in this 52-minute lecture by Gunnar Carlsson. Delve into TDA-inspired methods for constructing neural networks, addressing challenges like data hunger, generalization difficulties, and lack of transparency. Examine convolutional neural networks, image patch analysis, and the shape of data through topological modeling. Investigate weight space analysis for various datasets, discover geometry in convolutional situations, and explore feature space modeling. Learn about generalized convolutional nets, Klein bottle connections, and applications in microarray analysis and microbiome studies. Gain insights into learning on video and perspectives from cognitive scientist Gary Marcus.
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)
Convolutional Situation
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
Taught by
Applied Algebraic Topology Network
