Perceptron Interactive Playground

Inside a Perceptron

Explore how inputs are multiplied by weights, summed with a bias, and passed through an activation function to produce output.

Inputs

x₁ (bit) 1

x₂ (bit) 0

Weights & Bias

w₁ 0.50

w₂ 0.50

bias -0.50

Activation

Observe

Weighted sum = w₁·x₁ + w₂·x₂ + bias
The step function outputs 1 if sum ≥ 0, else 0
Adjust weights to see how they scale each input

Weighted Sum 0.00

Activation Input 0.00

Output 0

💡 Key Insight

A perceptron computes a weighted sum and thresholds it. Changing weights controls how much each input contributes to the decision.

Decision Boundary

See how the perceptron's weights and bias define a line that separates two classes. Changing weights rotates the line; changing bias shifts it.

Weights & Bias

w₁ 1.00

w₂ 1.00

bias -0.50

Dataset

Observe

The green line is w₁·x₁ + w₂·x₂ + b = 0
Changing w₁ & w₂ rotates the line
Changing bias shifts the line
The shaded regions show predicted classes
Try XOR — no single line can separate it!

Accuracy: —

Training Animation

Watch the perceptron learn step-by-step. On each misclassification, weights are updated and the decision boundary moves.

Settings

Learning Rate 0.10

Dataset

Observe

Red highlight = misclassified point
Weights update: w += lr × error × x
The boundary shifts toward correct classification
Training converges when all points are correct

Training Log

Press Play or Step to begin training...

Ready

Convergence vs Failure

Compare a linearly separable dataset (OR) with a non-linearly separable one (XOR). The perceptron converges on OR but oscillates forever on XOR.

Settings

Learning Rate 0.10

Observe

Left: OR data is linearly separable → converges
Right: XOR data is NOT separable → oscillates
The perceptron convergence theorem guarantees convergence only for linearly separable data

OR Gate (Separable) ✓

Epoch: 0 Accuracy: —

XOR Gate (Not Separable) ✗

Epoch: 0 Accuracy: —

💡 Key Insight

A perceptron is just a moving line. It can only solve problems where a straight line can separate the classes. XOR requires at least two lines (a hidden layer).

Perceptron vs MLP

See why multi-layer networks are needed. A single perceptron can only draw linear boundaries. An MLP with a hidden layer can create nonlinear boundaries.

Settings

MLP Hidden Neurons 4

MLP Learning Rate 0.50

Observe

Left: Single perceptron — can only draw a line
Right: MLP — combines multiple lines into a curve
The MLP solves XOR by composing simple decisions
Try adjusting hidden neurons and learning rate

Single Perceptron (Linear)

Epoch: 0 Accuracy: —

MLP (Nonlinear)

Epoch: 0 Accuracy: —

💡 Key Insight

A single perceptron draws one line. An MLP stacks multiple perceptrons, creating complex decision boundaries that can solve non-linear problems like XOR.