Maths for ML / Notation

\log x,\ \ln x

logarithm

FunctionsBeginner

Say it “log of x”

The inverse of exp: what power of the base gives x. In ML papers log almost always means natural log (base e).

Example

\log(ab) = \log a + \log b

Turns products into sums.

In code

np.log(x)

torch.log(x)

Where you’ll see it in ML

Log-likelihood, cross-entropy, log-softmax for numerical stability.

Don’t confuse it with

$e^{x},\ \exp(x)$ exponential Raises e (≈ 2.718) to the power x. Always positive; grows very fast.
$\prod_{i=1}^{n} x_i$ product Multiply the expression together for every value of the index.
$D_{\mathrm{KL}}(P \,\Vert\, Q)$ KL divergence Measures how different distribution Q is from P. Not symmetric: swapping P and Q changes the answer.

Lessons that use it

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