Billions of simple weighted sums produce the behavior we recognize as intelligence.
An artificial neuron multiplies its inputs by weights, adds a bias, and applies a curve. The behavior we recognize as intelligence does not live in any single unit; it emerges from the pattern of connections among them.
A neuron computes sigmoid(w1*x1 + w2*x2 + b), which draws a straight line in the input space. Weights rotate the line; bias shifts it. Everything on one side is "on," everything on the other "off."
Figure 1. A single neuron can only separate space with a straight line. The right panel plots the neuron's output over the input square $(x_1, x_2) \in [-1, 1]^2$: light cells are "off" (output near 0), dark cells are "on" (output near 1). This linear limit is why we need layers.
Stack neurons into layers and the network handles non-linear problems. Each hidden neuron draws a line; the output neuron combines them into a curved boundary that wraps the clusters.
Click the boundary map to add a training point. Shift-click to place the opposite class.
Figure 2. Training a 2-4-1 network on the XOR pattern. The boundary map on the right spans $(x_1, x_2) \in [-1, 1]^2$; orange dots are class 0, blue dots class 1. The sparkline traces mean-squared loss per epoch as error falls. Notice how the boundary warps as the weights adjust to minimize it.
Each hidden neuron learns a different linear slice. The final output is an assembly of these slices.