The Math Behind Neural Networks

A 5-minute tour of the actual mathematics running underneath every neural network: the single artificial neuron (McCulloch & Pitts, 1943), stacking neurons into layers as matrix multiplication, why nonlinearity matters (Rosenblatt's Perceptron and the 1969 XOR proof that triggered the AI winter), loss functions (MSE and cross-entropy), and how backpropagation plus gradient descent (Rumelhart, Hinton & Williams, 1986) actually trains a network. Closes by scaling the same five ideas up to GPT-3's 175 billion parameters. Some visuals in this video are AI-generated (Google Gemini). Photographs are real and credited below. Image credits "330-PSA-80-60 (USN 710739) (20897323365).jpg" (The Mark I Perceptron) — https://commons.wikimedia.org/wiki/File:33... — Public domain "Geoffrey Hinton at 2024 Nobel Prize Conference 5.jpg" — https://commons.wikimedia.org/wiki/File:Ge... — CC BY-SA 4.0 Frank Rosenblatt portrait — Cornell Chronicle (news.cornell.edu) MNIST sample digits — Wikimedia Commons (MNIST_dataset_example.png) AI-generated visuals neuron-firing-network — a single glowing artificial neuron firing signals outward across a dark network of connections — Google Gemini (gemini-3.1-flash-image-preview) matrix-layers-flow — glowing grids of numbers flowing through stacked translucent layers — Google Gemini (gemini-3.1-flash-image-preview) xor-not-separable — two classes of glowing points that no single straight line can separate — Google Gemini (gemini-3.1-flash-image-preview) loss-landscape-ball — a glowing ball rolling down a valley-shaped surface toward a minimum — Google Gemini (gemini-3.1-flash-image-preview) chain-rule-cascade — arrows and gears passing a signal backward through layered panels — Google Gemini (gemini-3.1-flash-image-preview) gpt-scale-comparison — a single node beside a vast lattice of nodes — Google Gemini (gemini-3.1-flash-image-preview)