Under construction, coming soon!

Lorem ipsum dolor sit amet, consectetur adipiscing elit. This note exists to test the math pipeline. Inline expressions such as $f_\theta(x)$, $x \in \mathbb{R}^d$, and $O(n \log n)$ should render at build time without any client-side JavaScript.

A regularised least-squares objective is a useful display test:

$$\mathcal{L}(\theta) = \frac{1}{N} \sum_{i=1}^{N} \left( y_i - f_\theta(x_i) \right)^2 + \lambda \lVert \theta \rVert_2^2$$

The gradient and update rule can be aligned:

$$\begin{aligned} \nabla_\theta \mathcal{L} &= \frac{2}{N} \sum_{i=1}^{N} \left( f_\theta(x_i) - y_i \right) \nabla_\theta f_\theta(x_i) + 2\lambda\theta, \\ \theta_{t+1} &= \theta_t - \eta \nabla_\theta \mathcal{L}. \end{aligned}$$

Matrices work too:

$$A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}, \qquad \mathbb{E}[X] = \sum_{x} x \, p(x).$$

Sed ut perspiciatis unde omnis iste natus error sit voluptatem accusantium doloremque laudantium. The rest of the note is ordinary prose so you can judge the distance between a paragraph and a display equation.