Perceptron

Definition

A perceptron is a simple linear classifier.

It takes an input vector, computes a weighted score, and outputs a class.

Basic flow:

input vector -> weighted sum + bias -> activation -> class

Perceptron = linear decision rule for classification.

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Components

A perceptron has:

• input features
• weights
• bias
• weighted sum
• activation rule
• output class

Example:

x = [x1, x2]
w = [w1, w2]
b = bias

Score:

score = w1*x1 + w2*x2 + b

A perceptron is built from the pieces introduced earlier.

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Weighted Score

The perceptron first computes:

score = dot(w, x) + b

Example:

w = [2, -1]
x = [3, 4]
b = 1

Score:

2*3 + (-1)*4 + 1
= 6 - 4 + 1
= 3

The score measures how the input aligns with the weights, shifted by bias.

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Activation Rule

The perceptron converts the score into a class.

Example:

if score >= 0:
  output = 1
else:
  output = -1

If:

score = 3

then:

output = 1

The activation turns a score into a prediction.

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Decision Boundary

The perceptron's decision boundary is:

dot(w, x) + b = 0

In two dimensions, this is a line.

On one side:

output = 1

On the other side:

output = -1

A perceptron separates space with one linear boundary.

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Perceptron As Computation

A perceptron is still computation.

It follows rules:

read input
compute weighted sum
add bias
apply activation
return class

There is no understanding required for the rule to run.

A perceptron is rule-based vector computation.

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What It Can Learn

The perceptron can learn weights and bias that separate linearly separable data.

Learning means adjusting:

w
b

until the classifier predicts correctly on training examples.

Perceptron learning adjusts the decision boundary.

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Final Summary

• A perceptron is a simple linear classifier.
• It takes an input vector.
• It computes dot(w, x) + b.
• It applies a threshold activation.
• It outputs a class.
• Its decision boundary is linear.
• It can learn linearly separable patterns.