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. Read more