A4.3.8 HL · neural networks

The perceptron

A perceptron is one artificial neuron. It multiplies inputs by weights, adds a bias and applies a threshold to predict a class. With two inputs, its decision boundary is a straight line. Train it on AND, OR or NAND, then try XOR. The plot updates after each epoch (one full pass through the truth table).

Each dot is one row of the truth table, placed at its two input values. Blue dots have output 1 and orange dots have output 0. The dotted square joins the four input pairs. The solid line is the perceptron's decision boundary. A dashed ring marks a row it still gets wrong.

Gate to learn

truth table and model output

in 1	in 2	AND	model
0	0	0	0 ✓
0	1	0	0 ✓
1	0	0	0 ✓
1	1	1	0 ✗

The model column shows the output the perceptron gives for each row with its current weights. Training is finished when the model column matches the AND column on every row.

epoch

rows wrong

Each epoch checks every row and updates the weights and bias after a wrong prediction. A straight line can separate AND, OR and NAND, but cannot separate XOR. The plot updates after a full pass, so the XOR boundary can return to its previous position despite changes during training.

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