Heading 1

This is a paragraph under heading 1 to test the margin and line height. The quick brown fox jumps over the lazy dog. Here is some bold text and some italic text. You can also have ~~strikethrough text~~.

Heading 2

Testing the secondary heading and ensuring that it has distinct visual weight without the explicit # characters.

Heading 3

A tertiary heading for good measure. Let's see how nested this gets.

Lists

Here is an unordered list:

Item 1
Item 2
- Subitem A
- Subitem B
Item 3

Here is an ordered list:

First step
Second step
Third step

Blockquotes

This is a blockquote. It should have a nice left border and italicized text to make it stand out from regular paragraphs. It might contain multiple lines of text.

You can even have multiple paragraphs inside a blockquote.

Code and Preformatted Text

Inline code has a subtle background color.

Here is a preformatted code block:

function greet(name) {
  console.log(`Hello, ${name}!`);
  return true;
}
 
greet("World");

Tables

Using GFM (GitHub Flavored Markdown), we can render tables.

Syntax	Description	Example
Header	Title	Here's this
Paragraph	Text	And more
Code	Snippet	`let x = 1`

Links and Images

This is an inline link.

Here is an image:

Placeholder Image

The End

That covers the basics of Markdown syntax testing!

Math (LaTeX)

Here is some inline math: $E = mc^2$ .

And here is a block math equation:

\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Machine Learning Formulas

Gradient Descent Update Rule:

\theta_{j} := \theta_{j} - \alpha \frac{\partial}{\partial \theta_{j}} J(\theta)

Softmax Function:

\sigma(\mathbf{z})_i = \frac{e^{z_i}}{\sum_{j=1}^K e^{z_j}} \ \text{for } i=1, \dots, K

Matrix Multiplication:

\begin{bmatrix} y_1 \\ y_2 \\ y_3 \end{bmatrix} = \begin{bmatrix} w_{11} & w_{12} \\ w_{21} & w_{22} \\ w_{31} & w_{32} \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix}

Cross-Entropy Loss:

L = - \sum_{c=1}^M y_{o,c} \log(p_{o,c})