LLM Primer

Decision Boundaries

A decision boundary is where the model is exactly undecided between sides.

For a binary linear classifier:

score = x . w + b

the boundary is:

x . w + b = 0

In two dimensions, this boundary is a line.

score = 0positive sidenegative side
A linear classifier separates space with a straight boundary in two dimensions.

Points on one side have positive score. Points on the other side have negative score.

Example

Let:

score = x_1 - x_2

The boundary is:

x_1 - x_2 = 0

or:

x_1 = x_2

The point (3, 1) has score:

3 - 1 = 2

The point (1, 3) has score:

1 - 3 = -2
DL-C03-T05-001Exercise: Compute boundary score

For score = x_1 - x_2, what is the score at point (4, 4)?

Compute it first, then check your number.

HintSubstitute coordinates

Compute 4 - 4.

SolutionWork it out

score = 4 - 4 = 0, so the point is on the decision boundary.

DL-C03-T05-002Exercise: Which side

For score = x_1 - x_2, what is the score at point (5, 2)?

Compute it first, then check your number.

HintSubtract second coordinate from first

Compute 5 - 2.

SolutionWork it out

score = 5 - 2 = 3, so the point is on the positive side of the boundary.