Maths for ML / Notation

f: \mathbb{R}^{n} \to \mathbb{R}

function arrow (type)

FunctionsBeginner

Say it “f maps R n to R”

Says what kind of input a function takes and what kind of output it gives — its type signature.

Example

f: \mathbb{R}^{784} \to \mathbb{R}^{10}

A digit classifier: 784 pixels in, 10 scores out.

In code

def f(x: np.ndarray) -> np.ndarray: ...

Where you’ll see it in ML

Describing a model or layer's input/output shapes.

Don’t confuse it with

$x \mapsto x^2$ maps to Describes what a function does to a single input, like a lambda.
$\lim_{x\to a} f(x)$ limit The value f gets closer and closer to as x approaches a.
$\Rightarrow,\ \iff$ implies / if and only if ⇒: if the left is true, the right is true. ⇔ (iff): both directions hold.

Lessons that use it

Functions and arrows: f: ℝⁿ → ℝ, ↦ and f ∘ g

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