How Artificial Neural Networks Learn from Data

Part 1: The Artificial Neuron & Forward Propagation

An artificial neuron does not think or feel; it takes several numerical inputs, multiplies each by an adjustable weight, adds a bias, and passes the sum through an activation function (like ReLU) to decide whether to fire.

Part 2: Backpropagation & The Error Gradient

1. 1. Forward Pass: Data flows forward through the layers to generate an initial prediction.
2. 2. Loss Calculation: A loss function calculates the exact mathematical gap between the prediction and ground truth.
3. 3. Backpropagation: The chain rule of calculus calculates how much each individual weight contributed to that error.
4. 4. Gradient Descent: An optimizer subtracts a small step (learning rate) in the direction of steepest error reduction.

Part 3: From Toy Perceptrons to Frontier Transformers

Modern foundation models stack hundreds of transformer attention layers with hundreds of billions of parameters, demonstrating emergent abilities across disparate cognitive tasks.