Backpropagation – why it works

Once a network has more than one layer, the perceptron update rule is no longer enough. Backpropagation is the chain-rule applied to a composition of layers: the error is computed at the output and then sent backward, so every weight learns how much it contributed to the final loss. This is the same idea as gradient descent from Part II, only now the gradient is assembled layer by layer instead of being written by hand.

• How it looks in pure PHP
• Case 1. Backpropagation by hand – one neuron in pure PHP
• Case 2. Phishing email filter – MLPClassifier in RubixML
• Case 3. Perceptron vs Neural Network – where the linear model ends
• Case 4. User risk score – MLPRegressor
• Case 5. Why the network does not learn – training diagnostics
• Case 6. Full Awareness Security pipeline – from data to prediction
• MNIST: how a neural network learns – backpropagation in practice