Score matching helps to train a neural network model without evaluating the partition function , $Z$ or its derivative. The strategy used is to minimize the expected squared difference between the derivatives of the model's log density with respect to the input and the derivatives of the data's log density with respect to the input.

$L(x,\theta) = \frac{1}{2} \| \nabla_x \log p_{model}(x;\theta),- \nabla_x \log p_{data}(x) \|_{2}^{2}$

$J(\theta) = \frac{1}{2} E_{p_{data}}(x)L(x,\theta)$

$\theta^* = \min\limits_{\theta} J(\theta)$