Last Minute Lecture

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...

Gradient Descent, LMS, and the Mathematics of Error Reduction | Chapter 3 of Why Machines Learn Chapter 3, “The Bottom of the Bowl,” from Why Machines Learn: The Elegant Math Behind Modern AI traces one of the most influential inventions in machine learning history: the Least Mean Squares (LMS) algorithm developed by Bernard Widrow and Ted Hoff. This chapter explores how the LMS rule allowed early artificial neurons to learn from errors through simple, iterative updates—setting the stage for modern optimization techniques like gradient descent and stochastic gradient descent. This post expands on the chapter’s narrative and explains the mathematical intuition behind how machines learn to minimize error. For a more guided walkthrough, be sure to watch the video summary above. Supporting Last Minute Lecture helps us continue creating clear, accessible study tools for students and lifelong learners. The Birth of the LMS Algorithm Widrow and Hoff developed the LMS algorithm w...

Machine Learning Algorithms — K-Means, Weighted Experts & Gradient Descent | Chapter 33 in Introduction to Algorithms Chapter 33 of Introduction to Algorithms introduces three foundational machine learning techniques: k-means clustering for unsupervised learning, multiplicative-weights algorithms for online decision-making, and gradient descent for optimization in large-scale data settings. These algorithms are essential tools across supervised, unsupervised, and online learning paradigms, and they serve as building blocks in modern data science and artificial intelligence. Watch the video for a full breakdown of how these algorithms work and where they apply. Subscribe to Last Minute Lecture for more data-driven summaries from classic textbooks. Types of Machine Learning The chapter begins by categorizing learning approaches: Supervised Learning: Learn from labeled data to predict outcomes (e.g., spam classification). Unsupervised Learning: Discover hidd...