Hello World - Xiuhong Li

Welcome

This is a test blog post with various markdown features.

def hello():
    print("Hello, World!")

Inline math: $E = mc^2$

Display math:

\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}

S_t \in \mathbb{R}^{d_k \times d_v}

S_r^{[t]} = \underbrace{\left(\prod_{i=1}^r (I - \beta_i^{[t]} k_i^{[t]} k_i^{[t]\top}) Diag(\alpha_i^{[t]})\right)}_{:= P_r^{[t]}} S_0^{[t]} + \underbrace{\sum_{i=1}^r \left(\prod_{j=i+1}^r (I - \beta_j^{[t]} k_j^{[t]} k_j^{[t]\top}) Diag(\alpha_j^{[t]})\right) \beta_i^{[t]} k_i^{[t]} v_i^{[t]\top}}_{:= H_r^{[t]}}

This is a blockquote to test styling.