Perceptron (neural network)

A perceptron is a function $p: \mathbb{R}^n \rightarrow \mathbb{R}$ defined by two steps - first a weighted linear sum, the second an activation function. To define this we need weights $w_i$ for $1 \leq i \leq n$ and an activation function $a: \mathbb{R} \rightarrow \mathbb{R}$. Where

$$p(x) = a\left (\sum_{i=1}^n w_i x_i \right ).$$