Notation

Notation on this site follows the book's conventions. This page is the single source of truth; any page that deviates from it is a bug.

Symbol	Meaning
$x, y, a, γ$	Scalars — plain italic lowercase.
$x, w$	Vectors — bold lowercase. Components are scalars with subscripts: $x = (x_{1}, \dots, x_{d})$ .
$X, K$	Matrices — bold uppercase.
$w^{⊤} x$ , $⟨ w, x ⟩$	The dot product — both forms appear; they mean the same thing. The book prefers $w^{⊤} x$ ; proofs here sometimes use $⟨ \cdot, \cdot ⟩$ when it reads better.
$∥ x ∥$	Euclidean norm, $x^{⊤} x$ .
$y \in {- 1, + 1}$	Class labels in the perceptron/SVM chapters (1–5).
$y \in {0, 1}$	Class labels in the probabilistic chapters (6 onward), matching the Bernoulli convention.
$y$	A model's prediction; more generally, a hat marks an estimate.
$w, b$	Weights and bias of a linear model; $\tilde{w} = (w, b)$ when the bias is absorbed.
$N$ , $d$	Number of training examples; input dimension.
$D$	The data-generating distribution.
$E [\cdot]$ , $P (\cdot)$	Expectation; probability.
$ℓ$ , $R (h)$ , $R (h)$	Loss function; true risk; empirical risk.
$σ (z)$	The sigmoid $1/ (1 + e^{- z})$ .
$η$	Learning rate (step size).
$φ$ , $k (x, x^{'})$	Feature map; kernel function.
$\nabla f$	Gradient of $f$ .
∎	End of proof.

One deliberate difference from the book's Introduction. The book's front matter writes vectors as bold uppercase ( $X$ ); the chapters themselves, and this site, use bold lowercase ( $x$ ) for vectors and reserve bold uppercase for matrices — the standard convention in the machine-learning literature.

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The Mathematics of Rust for Machine Learning

Notation