Last Minute Lecture

The Universal Approximation Theorem and the Debate Over Deep vs. Shallow Networks | Chapter 9 of Why Machines Learn Chapter 9, “The Man Who Set Back Deep Learning,” from Why Machines Learn: The Elegant Math Behind Modern AI explores the surprising legacy of George Cybenko’s 1989 proof of the universal approximation theorem. Although now regarded as one of the foundational results in neural network theory, the theorem was ironically misinterpreted in ways that may have temporarily slowed progress toward deep learning. In this chapter, Anil Ananthaswamy connects functional analysis, the geometry of infinite-dimensional spaces, and the mysteries of modern deep networks to show how a single mathematical insight shaped decades of AI research. To follow the detailed mathematical reasoning behind Cybenko’s theorem, be sure to watch the full video summary above. Supporting Last Minute Lecture helps us continue providing accessible, academically grounded explorations of complex AI conce...

Backpropagation, Gradient Descent, and the Rise of Deep Learning | Chapter 10 of Why Machines Learn Chapter 10, “The Algorithm That Silenced the Skeptics,” from Why Machines Learn: The Elegant Math Behind Modern AI recounts the breakthrough that resurrected neural networks and paved the way for modern deep learning: the backpropagation algorithm. Through compelling historical narrative and vivid mathematical explanation, Ananthaswamy traces how Geoffrey Hinton, David Rumelhart, and Ronald Williams helped transform neural networks from a struggling curiosity into a central pillar of artificial intelligence. This post expands on the chapter’s historical insights, mathematical foundations, and conceptual breakthroughs that made multi-layer neural networks finally learnable. For a step-by-step visual explanation of backpropagation, watch the full chapter summary above. Supporting Last Minute Lecture helps us continue providing in-depth, accessible analyses of essential machine lear...