A neural network is built from one tiny repeated unit: the neuron. And a neuron is something you already know cold — it's logistic regression in disguise. It takes its inputs, forms the weighted sum z = \vec{w}\cdot\vec{x} + b, then squashes it through an activation function to produce its output:

The heart of it is that dot product: each input scaled by its weight, all summed. The weights decide how much each input matters; the activation adds the non-linearity that makes the whole thing more than a plain line.

Fire the neuron

Three inputs feed the neuron along weighted connections. Turn the weight dials and watch the weighted sum z form — input by input — and then the activation a = \sigma(z) light up between 0 and 1. A large positive z makes the neuron fire strongly; a negative one keeps it quiet.

One neuron, then thousands

A single neuron can only draw a straight boundary — it's just logistic regression. The magic comes from wiring many together: the output of one becomes the input of the next, and layers of neurons can carve out boundaries of any shape at all. But every neuron, everywhere in the network, is doing exactly this — a dot product, a bias, an activation. Master this unit and you've understood the atom of deep learning.