Maths for ML / Notation

f \circ g

composition

FunctionsIntermediate

Say it “f after g”

Apply g first, then f to the result: (f∘g)(x) = f(g(x)).

Example

f_3 \circ f_2 \circ f_1

A 3-layer network: data flows through f₁ first.

In code

f(g(x))

nn.Sequential(g, f)

Where you’ll see it in ML

A deep network is a composition of layers — this is why the chain rule matters.

Don’t confuse it with

$\mathbf{a}\cdot\mathbf{b}$ dot product Multiply matching entries and add them up. Gives one number that's large when the vectors point the same way.
$\mathbf{a}\odot\mathbf{b}$ Hadamard (element-wise) product Multiply matching entries and keep them as a vector/matrix — no summing.

Lessons that use it

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