How a Perceptron Learns

Correct mistakes by nudging weights

The classic perceptron learning rule visits labeled examples, predicts a class, and adjusts weights only when the prediction is wrong. Inputs responsible for a missed positive get weights nudged upward; inputs behind a false positive get nudged downward. The learning rate controls adjustment size.

prediction = step(dot(weights, x) + bias)
error      = true_label - prediction
weights    = weights + learning_rate × error × x
bias       = bias    + learning_rate × error

This algorithm converges if a straight boundary can perfectly separate the classes. If they overlap or require a curved boundary, updates can continue without a perfect solution. Modern loss functions handle imperfect separation more gracefully by measuring degrees of error.

Scenario: A missed incident has x=[2,3], error +1, and learning rate 0.1. The weights increase by [0.2,0.3], making similar high-input cases more likely to activate next time.

Tip: The learning rule is useful intuition, not the exact training algorithm for today's deep networks. Gradient descent generalizes the nudge to differentiable losses and many layers.