Explore a groundbreaking approach to machine learning in this 29-minute lecture by Hamid Krim from North Carolina State University, presented at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the reformulation of convolutional neural networks using Volterra Series and polynomial functional paradigms. Discover how this innovative method addresses sample and model complexity limitations in traditional machine learning approaches. Learn about a computational Convolutional Network solution that eliminates the need for activation functions while delivering competitive or superior inference performance with significantly reduced sample and model complexity. Gain insights into the application of Homogeneous Polynomial Functionals, originally developed by Frechet, in this cutting-edge machine learning technique.