In this post, I will introduce the score function of a random vector.
Let x \in \mathbb{R}^d be a random vector with a probability density function (pdf) p(x)
Definition of score function
The score function of the random vector x is defined as the gradient of log of its pdf:
\nabla_{x} \log p(x) \tag{score function of $x$ (or $p(x)$)}