Maths for ML / Notation

\mathcal{N}(\mu, \sigma^2)

normal (Gaussian) distribution

Probability and statisticsBeginner

Say it “normal with mean mu and variance sigma squared”

The bell curve, set by a mean μ and a variance σ².

Example

\mathcal{N}(0, 1)

Standard normal: centered at 0, spread 1.

In code

rng.normal(mu, sigma)

torch.normal(mu, sigma)

Where you’ll see it in ML

Weight init, VAEs, diffusion noise, Gaussian likelihood ⇒ MSE.

Don’t confuse it with

$\mu$ mu (mean) Conventionally the mean of a distribution.
$\sigma,\ \sigma^2,\ \sigma(z)$ sigma Lowercase σ is the standard deviation (σ² the variance) — or, as a function σ(z), the sigmoid. Capital Σ is a sum or a covariance matrix.
$x \sim p(x)$ is distributed as / sampled from x is a random value drawn from the distribution p.

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