Maths for ML / Notation

\frac{\partial f}{\partial x}

partial derivative

CalculusBeginner

Say it “partial f partial x / del f del x”

Slope with respect to one input while holding all the others fixed.

Example

\frac{\partial}{\partial w}(wx+b) = x

In code

w.grad  # after loss.backward()

Where you’ll see it in ML

∂L/∂w is 'how much the loss changes if I nudge this one weight'.

Don’t confuse it with

$\frac{df}{dx},\ f'(x)$ derivative How fast f changes when x changes a tiny bit — the slope.
$\Delta x$ Delta (change) A (finite) change in a quantity. Lowercase δ often means a small change or an error term.
$\nabla_{\theta} L$ nabla / gradient The vector of all partial derivatives. It points in the direction the function increases fastest.

Lessons that use it

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