Qiwen Xiao

2026

What Lives Here

A short note about what this blog is for: paper notes, talk takeaways, experiments, and thoughts that become clearer after writing them down.

Meta Notes Thoughts
What Lives Here teaser

This section is where I keep the kind of writing that does not neatly fit into a project page or a research summary.

Sometimes it will be a reading note on a paper. Sometimes it will be notes from a talk, a half-formed idea, or a small technical observation that is useful to remember later.

I want this space to stay lightweight. The goal is not to make every post polished. The goal is to keep useful thoughts from disappearing.

Over time, this section will collect:

  • paper notes
  • talk notes
  • experiment logs
  • short essays
  • loose technical thoughts

If you are reading this early, this is the seed of the section rather than the finished archive.

LaTeX test:

L(θ)=∑i=1Nlog⁡pθ(xi)=∑i=1Nlog⁡∫pθ(xi,z)dz≥∑i=1N∫q(z)log⁡pθ(xi,z)q(z)dz=∑i=1N(∫q(z)log⁡pθ(xi,z)dz−∫q(z)log⁡q(z)dz)=∑i=1N(∫q(z)log⁡pθ(xi∣z)dz+∫q(z)log⁡pθ(z)dz−∫q(z)log⁡q(z)dz)=∑i=1N(∫q(z)log⁡pθ(xi∣z)dz−DKL(q(z)∣∣pθ(z)))\begin{aligned} \mathcal{L}(\theta) &= \sum_{i=1}^N \log p_\theta(x_i) \\ &= \sum_{i=1}^N \log \int p_\theta(x_i, z) dz \\ &\geq \sum_{i=1}^N \int q(z) \log \frac{p_\theta(x_i, z)}{q(z)} dz \\ &= \sum_{i=1}^N \left( \int q(z) \log p_\theta(x_i, z) dz - \int q(z) \log q(z) dz \right) \\ &= \sum_{i=1}^N\left( \int q(z) \log p_\theta(x_i | z) dz + \int q(z) \log p_\theta(z) dz - \int q(z) \log q(z) dz \right) \\ &= \sum_{i=1}^N\left( \int q(z) \log p_\theta(x_i | z) dz - D_{KL}(q(z) || p_\theta(z)) \right) \end{aligned}