Maths for ML / Notation

\lVert \mathbf{x} \rVert_2

norm

Brackets and normsBeginner

Say it “the norm of x / the 2-norm of x”

The length or size of a vector. The subscript says which kind: ‖·‖₂ is straight-line length, ‖·‖₁ is the sum of absolute values.

Example

\lVert[3,4]\rVert_2 = \sqrt{9+16} = 5

In code

np.linalg.norm(x, ord=2)

torch.linalg.norm(x)

Where you’ll see it in ML

Weight decay, gradient clipping, normalizing embeddings.

Don’t confuse it with

$|x|$ absolute value Distance from zero, always non-negative. For a set, |S| is the number of elements.

Related

Lessons that use it

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