Perceptron + ANN (Backpropagation, Gradient Descent)

Watch a single neuron learn a simple classification problem.

Decision Boundary

Network

Current input:

Target:

Weighted sum:

Output:

Error:

Learning rate:

Weight 1:

Weight 2:

Bias:

Epoch:

Gradient Descent

This is a 2-D toy loss surface used to visualize gradient descent. It has a global minimum and a higher local minimum. The ANN itself has many more dimensions, so this is a conceptual picture rather than the ANN's exact loss surface.

ANN loss across training. Each point represents one completed epoch.

Training Examples

X₁	X₂	Target

Perceptron: Important Formulas

1. Weighted sum

z = w₁x₁ + w₂x₂ + b

2. Output

y = 1 if z ≥ 0
y = 0 if z < 0

3. Error

error = target − output

4. Weight update

w₁(new) = w₁(old) + η · error · x₁
w₂(new) = w₂(old) + η · error · x₂

5. Bias update

b(new) = b(old) + η · error

6. Learning rate

η = learning rate

The weights and bias are changed only when the perceptron makes an error.