Perceptron

The perceptron is a binary linear classifier: it combines numerical inputs with weights and a bias, then applies a threshold to choose between two classes.

That first artificial neuron already answered «yes» or «no» against a fixed threshold; Rosenblatt added the decisive ingredient: adjustable weights that let the unit learn from examples. Primary source.

How it works: weighted sum and threshold

A perceptron assigns each input a weight that measures its importance. It multiplies every input by its weight, adds all the products together and includes a constant term called the bias. The result is a single weighted sum.

That sum then passes through a step function: if it exceeds the threshold, the output is 1; otherwise it is 0. This is why the perceptron produces a binary output. Geometrically, the weights and bias define a hyperplane that splits the input space into two regions, one for each class.

The learning rule and the XOR limit

The perceptron learns with a simple rule: for each example it compares its output with the correct answer and, when it is wrong, adjusts the weights in proportion to the error. Rosenblatt also proved the convergence theorem: if the data are linearly separable —if a line or hyperplane can separate the two classes— the rule finds that separator in a finite number of steps. Primary source.

Its limit is structural: a single perceptron cannot solve XOR because its classes are not linearly separable. Non-linear boundaries require extra layers or transformations. Primary source.

From the single perceptron to the multilayer

The way past this limit was to stack neurons: the multilayer perceptron (MLP). By inserting one or more hidden layers between input and output, with non-linear activation functions, the network can draw curved boundaries and solve XOR and far harder problems. Primary source.