Neuron — one unit, three activations

Background

The lesson's one-picture summary: features → linear score z → activation f(z) → output. Change only the activation $f$ and the same neuron becomes a different model:

activation	$f(z)$	model
identity	$z$	linear regression
sigmoid	$1/(1+e^{-z})$	logistic regression
step	$\mathbb{1}[z \ge 0]$	perceptron

Problem statement

Implement neuron(x, w, b, activation) that computes $z = \mathbf{w}^\top\mathbf{x}+b$ and applies the named activation.

Input

• x, w — array-like vectors of equal length.
• b — float.
• activation — one of "identity", "sigmoid", "step".

Output

Returns a Python float: $f(z)$.

Examples

Example 1

Input:  x = [1, 1], w = [1, 2], b = -1, activation = "identity"
Output: 2.0

Explanation: $z = 2$; identity returns $z$.

Example 2

Input:  x = [1, 1], w = [1, 2], b = -1, activation = "sigmoid"
Output: 0.8807970779...

Explanation: $\sigma(2) \approx 0.8808$.

Constraints

• Compute z once, then branch on activation.
• "step" returns 1.0 when $z \ge 0$ else 0.0.
• Return a plain float.

Notes

• This is the heart of the "neuron" abstraction: one linear core, a pluggable nonlinearity. Stacking many such units with smooth activations is what makes deep networks trainable.