Explore a comprehensive lecture on symmetry-preserving neural networks and their applications in breaking symmetry, presented by Tess Smidt from MIT at IPAM's Learning and Emergence in Molecular Systems Workshop. Delve into the data efficiency and generalization capabilities of equivariant neural networks across various domains, including computer vision and atomic systems. Discover how these networks can learn symmetry-breaking information to fit datasets with potential missing information, while maintaining minimal symmetry breaking due to their mathematical guarantees. Examine network architectures designed to learn symmetry-breaking parameters in two distinct settings: global asymmetries and individual example predictions. Gain insights into practical applications, including predicting structural distortions of crystalline materials, and explore topics such as molecular force fields, charge density prediction, representation theory, and structural phase transitions.