The Neuron

From Perceptron to Neuron

The perceptron you built in Machine Learning was a binary threshold unit. Real neural networks use a smoother model: the artificial neuron.

A neuron computes a weighted sum of its inputs plus a bias, then passes the result through an activation function:

$z = \sum_{i=1}^{n} w_i x_i + b = \mathbf{w} \cdot \mathbf{x} + b$

$a = f(z)$

• $\mathbf{x}$ — input vector (features)
• $\mathbf{w}$ — weight vector (learned parameters)
• $b$ — bias (a learnable scalar offset)
• $f$ — activation function (next lesson)
• $z$ — pre-activation (the weighted sum)
• $a$ — activation (the neuron's output)

The bias lets the neuron fire even when all inputs are zero, shifting the activation function left or right.

Why Weighted Sums?

Each weight $w_i$ controls how strongly input $x_i$ influences the output. A large positive weight means "this input strongly activates me". A large negative weight means "this input suppresses me". The bias is a free parameter that controls the threshold.

Your Task

Implement neuron(inputs, weights, bias) that returns the pre-activation value $z = \mathbf{w} \cdot \mathbf{x} + b$.

(We will apply the activation function in the next lesson.)