Artificial Neuron and Perceptron

The Rosenblatt perceptron (1958) is an early learning unit: it scales inputs by weights, adds a bias, applies a threshold, and outputs a binary decision (0 or 1).

Weighted sum and step activation

z = Σ X_iW_i + b

ŷ = 1 if z ≥ 0, else 0 (step / threshold activation)

Perceptron learning rule

When the model misclassifies, weights update proportionally to error:

ΔW = η · (y − ŷ) · X then W_new = W_old + ΔW

η is the learning rate — how large each corrective step is.

flowchart LR X1[x1] --> S[Weighted sum z] X2[x2] --> S X3[x3] --> S S --> A[Step activation] A --> Y[Binary output]

Linear separability

A single perceptron solves only linearly separable problems — data that can be split by one straight line (or hyperplane). AND and OR gates work; XOR does not.

Minsky & Papert (1969) proved a single layer cannot learn XOR. That limitation contributed to the first AI winter and motivated multi-layer networks with non-linear hidden layers.

XOR vs AND intuition

AND / OR — one line can separate the 1s from the 0s in the input grid.
XOR — positive class sits on opposite corners; no single line separates them.