Visual Proof: How Neural Networks Can Solve Anything | Universal Approximation Theorem скачать в хорошем качестве

Visual Proof: How Neural Networks Can Solve Anything | Universal Approximation Theorem

It feels like magic: you feed a matrix of numbers into a computer, and it recognizes a face or translates a language. But it isn't magic—it's a mathematical guarantee. In this Deep Learning deep dive (Episode 3), we visually prove the Universal Approximation Theorem, the bedrock principle that confirms a simple neural network can learn any continuous pattern in the universe, no matter how complex. We break down the math of 1989 (George Cybenko) and 1991 (Kurt Hornik) into intuitive building blocks. You will learn how to combine simple neurons to create "step functions," pair those steps to build "towers," and stack those towers to approximate any curve—just like Riemann sums in calculus. We also answer the critical engineering question: If one layer can solve anything, why do we bother with Deep Learning and 100-layer networks like GPT-4? Challenge of the Day: What is a "function" in your daily life you wish you could approximate mathematically? (e.g., Coffee input vs. Productivity output?) Drop your answer in the comments below! If this visual breakdown helped you understand the gears inside the black box, please like, subscribe to Sumantra Codes, and share this with your fellow engineers. Timestamps or Chapters: 0:00 Is AI Just Magic? (The Black Box) 0:46 The Universal Approximation Theorem Explained 2:13 Seeing the World as Functions 4:06 The "Atom": Creating a Step Function 5:50 Building "Towers" (The Lego Brick of AI) 7:54 The Visual Proof: Approximating Reality 9:38 The "Deep" Learning Paradox (Why Stack Layers?) 10:59 Compositionality: Edges, Shapes, & Objects 11:42 Challenge: What's Your Function? #DeepLearning #UniversalApproximation #NeuralNetworks #MathOfAI #ArtificialIntelligence #MachineLearning #DataScience #SumantraCodes