The perceptron, introduced by Frank Rosenblatt in 1958, is the foundational model of artificial neural networks and connectionist approaches to cognition. It takes a weighted sum of inputs, adds a bias term, and passes the result through a step function to produce a binary classification.
Δwᵢ = η · (y − ŷ) · xᵢ
Convergence theorem: If data is linearly separable,
the perceptron learning rule converges in finite steps.
The Perceptron Convergence Theorem
Rosenblatt proved that if the training data is linearly separable, the perceptron learning rule is guaranteed to find a separating hyperplane in a finite number of steps. This was an exciting result, but Minsky and Papert's 1969 book Perceptrons demonstrated that single-layer perceptrons cannot learn XOR or any other non-linearly separable function, temporarily diminishing enthusiasm for neural network approaches.
Legacy
The limitations of single-layer perceptrons were overcome by multilayer networks trained with backpropagation. Nevertheless, the perceptron remains important as a pedagogical model, as the building block of larger networks, and as a model of individual neurons that perform linear discrimination. The perceptron learning rule is mathematically equivalent to the delta rule used in many connectionist models of learning.