Artificial neurons

An artificial neuron is loosely inspired by biological neurons. It receives inputs $x_1,\dots ,x_d$, multiplies each by a weight, adds a bias, and passes the sum through an activation function $\varphi$:

The weights say how strongly each input matters (and in which direction); the bias shifts the threshold at which the neuron 'fires'. The activation adds non-linearity — without it, any stack of neurons collapses into one linear function.

A single neuron with a sigmoid activation *is* logistic regression; with no activation it is linear regression. Networks become powerful by connecting many neurons in layers.