Efficient Invariant Embeddings for Universal Equivariant Learning

Explore efficient invariant embeddings for universal equivariant learning in this 47-minute lecture by Nadav Dym. Delve into the world of machine learning tasks with known group symmetries and discover how equivariant algorithms exploit these symmetries through specialized architectures. Examine examples like convolutional neural networks for image translation symmetry and neural networks for graph and set permutation symmetries. Investigate the theoretical requirement of universal equivariant architectures and the challenge of finding G-invariant mappings that separate points not related by G-symmetry. Learn about the existence of such mappings under general assumptions and the potential embedding dimension. Discuss the computational challenges in certain cases, such as graphs, and explore methodologies for efficient computation in others, like sets. Gain insights into the generalization of algebraic geometry arguments used in phase retrieval injectivity proofs.