The formula $\pi_{\theta_{\text{ref}}}(\mathbf{y}|\mathbf{x}) \exp(\frac{1}{\beta}r(\mathbf{x}, \mathbf{y}))$ represents a method for adjusting a probability distribution from a reference model, denoted by $\pi_{\theta_{\text{ref}}}$. The term $\pi_{\theta_{\text{ref}}}(\mathbf{y}|\mathbf{x})$ is the base probability of generating output $\mathbf{y}$ from input $\mathbf{x}$ according to the reference model parameterized by $\theta_{\text{ref}}$. This probability is then scaled by the exponential of a reward function $r(\mathbf{x}, \mathbf{y})$, which is itself scaled by an inverse temperature parameter, $\frac{1}{\beta}$. The temperature $\beta$ controls the extent to which the reward influences the final probability, with smaller values of $\beta$ amplifying the effect of the reward.