Decision boundary · XOR — four corners

Initial weights · Epoch 0 · Accuracy 0%

Amber = net says class 1, cyan = class 0. Watch the regions warp as the loss falls.

Loss

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Backpropagation

Gradient descent on a chain rule

Backpropagation is the algorithm that lets a neural network learn from its mistakes. Run an input forward through the layers, compare the output to the target, then walk the chain rule backward to find — for every weight — how much it should change to make the answer closer next time. The whole modern AI boom rests on this idea: just multivariable calculus plus a lot of GPUs. Discovered independently many times; popularised by Rumelhart, Hinton and Williams in 1986.

Network topology

Toy task

Learning rate η

0.30

Batch size

Epochs / second

What you are seeing

Random weights. The decision surface is a smooth, almost meaningless gradient — the network has no idea what the task is yet. Click play and watch backprop reshape the surface to match the data.

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