Consider the formula for finding an optimal soft prompt, $\hat{\sigma}$, by minimizing the difference between two probability distributions: $\hat{\sigma} = \underset{\sigma}{\arg\min}\, \text{KL}(\text{Pr}(\cdot|\mathbf{c}, \mathbf{z}) \|\| \text{Pr}(\cdot|\sigma, \mathbf{z}))$ In this formula, $\text{Pr}(\cdot|\mathbf{c}, \mathbf{z})$ is the probability distribution over possible outputs given a full context $\mathbf{c}$ and an input $\mathbf{z}$, while $\text{Pr}(\cdot|\sigma, \mathbf{z})$ is the distribution given a soft prompt $\sigma$ and the same input $\mathbf{z}$.

Explain why $\text{Pr}(\cdot|\mathbf{c}, \mathbf{z})$ is treated as the first argument (the 'true' distribution) and $\text{Pr}(\cdot|\sigma, \mathbf{z})$ as the second argument within the KL divergence function, and not the other way around. What would be the conceptual implication of swapping their positions?