Maths for ML / Notation

\coloneqq

is defined as

Arithmetic and relationsBeginner

Say it “is defined as”

Introduces a new name for an expression. It's an assignment, not a claim to check.

Example

\hat{y} \coloneqq \mathbf{w}^\top\mathbf{x}

Read it like a Python assignment: yhat = w @ x.

In code

yhat = w @ x

Where you’ll see it in ML

Papers use it to introduce shorthand like z := Wx + b before using z later.

Don’t confuse it with

$=$ equals Both sides have exactly the same value.
$\equiv$ identical to Equal for every possible input, or true by definition. Some authors use it to mean 'defined as'.

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