The wavefunction should be a probability amplitude depending on \( \boldsymbol{x} \). The RBM model is given by the joint distribution of \( \boldsymbol{x} \) and \( \boldsymbol{h} \)
$$ P_{\mathrm{rbm}}(\boldsymbol{x},\boldsymbol{h}) = \frac{1}{Z} \exp{-E(\boldsymbol{x},\boldsymbol{h})}. $$To find the marginal distribution of \( \boldsymbol{x} \) we set:
$$ P_{\mathrm{rbm}}(\boldsymbol{x}) =\frac{1}{Z}\sum_{\boldsymbol{h}} \exp{-E(\boldsymbol{x}, \boldsymbol{h})}. $$Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS)
$$ \vert\Psi (\boldsymbol{X})\vert^2 = P_{\mathrm{rbm}}(\boldsymbol{x}). $$