Maths for ML / Notation

\Delta x

Delta (change)

CalculusBeginner

Say it “delta x / change in x”

A (finite) change in a quantity. Lowercase δ often means a small change or an error term.

Example

\Delta w = -\eta\,\nabla_w L

The weight update in one step.

In code

dw = w_new - w_old

Where you’ll see it in ML

Weight updates, finite differences, δ in backprop.

Don’t confuse it with

$\frac{\partial f}{\partial x}$ partial derivative Slope with respect to one input while holding all the others fixed.
$\nabla_{\theta} L$ nabla / gradient The vector of all partial derivatives. It points in the direction the function increases fastest.

Lessons that use it

The derivative: slope, and sensitivity

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