Blogs

Introduction Some commands and tips, often used when working on a server, I feel tired of asking gpt again and again. 1. Kill Jupyter Notebook Kernel When you use Jupyter Notebook on a server,especially when in VSCode, sometimes the kernel may get stuck or become unresponsive. Unfortunately, VSCode does not provide a direct way to kill or shutdown the kernel from its interface.This make a lot of jupyter processes running on the server, consuming resources and causing confusion. ...

The Mathematical Properties of Varentropy Now we discuss some mathematical properties of varentropy at a discrete distribution with a fixed entropy. Let $X$ be a discrete random variable with support $\{x_1, x_2, \ldots, x_k\}$ and corresponding probabilities $P(X = x_i) = p_i$, and let $H(X) = H_0$ be the entropy of $X$. The varentropy $V(X)$ can be expressed as: $$ V(X) = \sum_{i=1}^{V} p_i \left( -\log(p_i) \right)^2 - H_0^2 $$Lagrange Multiplier Method To find the lower bound of varentropy for a fixed entropy $H_0$, we can use the method of Lagrange multipliers. We want to maximize $V(X)$ subject to the constraints that the probabilities sum to 1 and the entropy is fixed. We can consider it as the following optimization problem: ...

This blog post discusses the role of information theory in LLM reasoning.

This blog post introduces RLHF-PPO algorithm with code implementation.

This blog note how to use Zotero with iCloud as the storage.

This blog post notes my understanding of Direct Preference Optimization and the math derivation behind it.