Perceptron; neural network as OR gate

A perceptron is the simplest neural network: a single neuron that forms the weighted sum of its inputs, adds a bias (or compares with a threshold θ) and outputs 1 if the sum is large enough, else 0 (step function). It acts as a linear binary classifier and can learn with the rule w ← w + η(t − y)x.

Designing an OR gate

OR is linearly separable, so one perceptron is enough.

 x1 --(w1 = 1)-->\
                  ( Σ ≥ θ ?)--> y      θ = 0.5  (or b = -0.5)
 x2 --(w2 = 1)-->/

Net input = 1·x1 + 1·x2; output y = 1 if net ≥ 0.5, else 0.

All four rows match the OR truth table.

Check using inequalities

We need 0 < θ (for 0,0), w1 ≥ θ, w2 ≥ θ and w1 + w2 ≥ θ. Choosing w1 = w2 = 1, θ = 0.5 satisfies all of them.

Decision boundary

x1 + x2 = 0.5 is a line that separates (0,0) from the other three points.

Training alternative

Start with w1 = w2 = 0, b = 0, η = 1, use the output y = 1 if net > 0 (else 0), and apply the perceptron rule to the four patterns. It converges within three epochs to w = (1, 1), b = 0, which also implements OR (any weights that separate the classes will do).

Answer: w1 = 1, w2 = 1, threshold 0.5.