01·Perceptron: input, weight, bias, activation

Introduction

The 1958 Rosenblatt perceptron is the simplest possible neural network: a single neuron computing a weighted sum of inputs plus a bias, passed through an activation function. This lesson dissects the roles of the weight vector w, the bias b, the pre-activation z = w·x + b, and the activation σ(z). You will understand why the bias is a shift of the decision boundary (not a weight), why the classical step-perceptron cannot learn XOR, and how a single neuron geometrically defines a hyperplane in the input space.