perceptron

The perceptron is a simple artificial neuron and binary classifier that models a biological neuron’s basic operation. It was introduced by Frank Rosenblatt in 1957 as a foundational building block for neural networks. The perceptron computes a weighted sum of its inputs, adds a bias, and applies an activation function to produce a binary output, typically 0 or 1. The common activation is a step function, yielding 1 when the weighted input exceeds a threshold and 0 otherwise.

Architecture and operation: It consists of inputs x1, x2, ..., xn, corresponding weights w1, w2, ..., wn, and a bias term b. The net input is z = sum_i w_i x_i + b, and the output y = f(z), where f is the step function. The model thus implements a linear decision boundary in input space.

Learning rule: The perceptron learning rule adjusts weights to reduce classification error. For a training sample with target t and predicted output y, the weight update is delta w_i = eta (t - y) x_i, and the bias update is delta b = eta (t - y). Here eta is the learning rate. If the data are linearly separable, this rule converges to a solution in finite time.

Limitations and legacy: The perceptron can only represent linearly separable problems, and it cannot solve certain patterns such as the XOR problem. This limitation spurred the development of multi-layer neural networks and backpropagation, enabling non-linear decision boundaries. Despite its simplicity, the perceptron is a foundational model in neural network theory and education, illustrating learning dynamics and the need for hidden layers in more capable architectures.