artificial neuron

An artificial neuron is the smallest computing unit of a neural network: a tiny function that takes several numbers in and produces one number out. The metaphor is borrowed from biology, where a neuron receives signals from many others through its dendrites, sums them, and fires an output along its axon if the combined signal is strong enough. The artificial version keeps that cartoon and throws away the biology: it weights each incoming number, adds them up, adds a constant, and passes the result through a simple nonlinear function to decide how strongly to fire.

Formally, given an input vector x = (x1, ..., xn), the neuron holds a weight vector w = (w1, ..., wn) and a scalar bias b. It computes the pre-activation (also called the logit or net input) z = w·x + b = (sum of wi·xi) + b, the dot product of weights and inputs plus the bias, then applies an activation function phi to get the output a = phi(z). The weights say how much each input matters (a negative weight means the input pushes the output down), while the bias shifts the threshold at which the neuron becomes active, independently of the inputs.

Geometrically, the equation w·x + b = 0 defines a hyperplane in input space, and the neuron is essentially asking which side of that plane the input lies on, and how far. Without the activation phi, a stack of neurons could only ever produce affine (linear) functions, because composing linear maps yields another linear map, so the network could not represent curved decision boundaries. The nonlinearity phi is precisely what lets layers of neurons build up genuinely complex functions, which is why phi is never the identity in a useful network.

In computer vision, a single neuron in a fully connected layer might look at every pixel of a small image, whereas a neuron in a convolutional layer looks only at a small local patch and shares its weights across the image (that constrained neuron is a filter). Modern architectures, from CNNs like ResNet to Vision Transformers and the heads of CLIP or SAM, are still, at the bottom, millions to billions of these weighted-sum-plus-nonlinearity units wired together. Understanding the single neuron is the key that unlocks all of them.