Explore a groundbreaking lecture on tensor networks and their canonical forms presented by David Pérez-García at the Workshop on Tensors: Quantum Information, Complexity and Combinatorics. Delve into the application of geometric invariant theory in defining a canonical form for arbitrary tensor networks, known as the minimal canonical form. Discover how this construction unexpectedly yields a new canonical form for Matrix Product States. Examine potential applications of this research, with a particular focus on enhancing privacy in tensor-network based machine learning. Gain valuable insights into advanced mathematical concepts and their practical implications in quantum information and machine learning during this 58-minute presentation from the Centre de recherches mathématiques (CRM).