Perceptron — the hard threshold unit

Background

Rosenblatt's perceptron (1958) is a binary linear classifier with a hard decision: it fires when the score is non-negative.

$$\hat{y} = \mathbb{1}[\,z \ge 0\,], \qquad z = \mathbf{w}^\top\mathbf{x} + b$$

Unlike the smooth sigmoid, this step activation jumps from 0 to 1 at $z = 0$. Same linear boundary as logistic regression, but a discontinuous output.

Problem statement

Implement perceptron(x, w, b) that returns the perceptron's hard label: 1 when $\mathbf{w}^\top\mathbf{x}+b \ge 0$, else 0.

Input

• x — array-like feature vector.
• w — array-like weight vector, same length.
• b — float, the bias.

Output

Returns an int, 0 or 1.

Examples

Example 1

Input:  x = [2, 3], w = [2, 3], b = -5
Output: 1

Explanation: $z = 8 \ge 0$, so the unit fires.

Example 2 — on the threshold fires

Input:  x = [2.5, 0], w = [2, 3], b = -5
Output: 1

Explanation: $z = 0$, and the rule is $\ge 0$, so it still outputs 1.

Constraints

• Use $\ge 0$ (inclusive) for the threshold, matching $\mathbb{1}[z \ge 0]$.
• Return a Python int (0/1).

Notes

• The step has zero gradient almost everywhere, which is exactly why modern neurons swap it for a differentiable activation so backpropagation can flow.