A single perceptron is one artificial neuron that can classify only linearly separable data. A multi-layer perceptron (MLP) connects neurons across an input layer, one or more hidden layers, and an output layer, allowing it to learn complex, non-linear patterns.
How Each Model Works
A perceptron receives inputs, multiplies each by a weight, adds a bias, and applies an activation function. Its output can be represented as:
Here, represents an input, its weight, the bias, and the activation function. A single perceptron creates one , so it can model functions such as AND and OR but cannot model XOR.
An MLP passes data forward through several layers. Each hidden neuron performs a weighted calculation and normally applies a non-linear activation function. During training, backpropagation calculates how much each weight contributed to the error, while an optimization method such as gradient descent adjusts the weights to reduce that error.
| Feature | Single perceptron | Multi-layer perceptron |
|---|---|---|
| Structure | One computational neuron | Multiple connected layers of neurons |
| Decision boundary | Linear | Potentially non-linear |
| Problems handled | Simple, linearly separable classification | Complex classification or regression |
| Training | Perceptron learning rule | Backpropagation with an optimizer |
| Example | AND or OR | XOR, image recognition, or pattern classification |
The common misconception is that adding more inputs makes a single perceptron capable of solving any problem. More inputs do not remove its linear limitation; hidden layers with non-linear activation functions are required to represent non-linear relationships.
IB Exam Technique
For A4.3 Machine learning approaches (HL only), explain the structural difference and connect it to capability. An effective answer states that an MLP uses hidden layers and backpropagation, then uses XOR to show why a single perceptron is limited.
