notes

robotics & embodied AI learning log

Hello world (syntax demo — delete me)

· #meta

This is a throwaway post that exercises everything the build pipeline supports. Delete this file once you've written your first real note. Notes live in notes/, one .md file per post — a YYYY-MM-DD- filename prefix (or a date: in frontmatter) sets the date, and draft: true hides a post.

Math

Inline math works: the policy \(\pi_\theta(a_t \mid s_t)\) and a norm \(\lVert x \rVert_2\). Display math too:

\[ q(x_t \mid x_{t-1}) = \mathcal{N}\!\left(x_t;\ \sqrt{1-\beta_t}\,x_{t-1},\ \beta_t \mathbf{I}\right) \]

Code

import torch

def q_sample(x0, t, alphas_bar):
    """Sample x_t ~ q(x_t | x_0) in closed form."""
    noise = torch.randn_like(x0)
    a = alphas_bar[t].sqrt().view(-1, 1)
    s = (1 - alphas_bar[t]).sqrt().view(-1, 1)
    return a * x0 + s * noise, noise

Inline code like torch.einsum gets highlighted too.

Everything else

Blockquotes look like this.

syntax where
tags: [a,b] frontmatter
$$...$$ display math
```python highlighted code

  1. A footnote, rendered at the bottom of the post.