The perceptron

The perceptron is the simplest neural unit:

1. take inputs
2. compute weighted sum
3. add bias
4. apply activation

Mathematically:

z = w·x + bz = w·x + b

output = activation(z)output = activation(z)

  flowchart LR
  x1[x1] --> N[Σ (weights) + bias]
  x2[x2] --> N
  x3[x3] --> N
  N --> A[Activation]
  A --> y[Output]

What it can do

A single perceptron can learn a linear decision boundary.

That means:

• it can separate data that is linearly separable
• it cannot solve XOR alone (needs multiple layers)

Key terms

• weights: importance of each input
• bias: shift term
• activation: non-linear function

Mini-checkpoint

Why do we need activation functions?

• Without them, the network is just a linear model (even with many layers).