A machine learning engineer is training a soft prompt to summarize complex technical articles. The goal is to create a short, efficient prompt that produces summaries of the same quality as those generated from a much longer, more detailed prompt. The engineer uses the optimization formula:

$\hat{\sigma} = \arg \min_{\sigma} s(\hat{\mathbf{y}}, \hat{\mathbf{y}}_{\sigma})$

Where:

• $\hat{\mathbf{y}}$ is the high-quality summary from the long prompt.
• $\hat{\mathbf{y}}_{\sigma}$ is the summary from the soft prompt being trained.
• $s$ is a function measuring the dissimilarity between the two summaries.

After extensive training, the dissimilarity score $s$ remains high, and the summaries generated using the soft prompt are of poor quality. Analyze two distinct potential reasons for this failure. For each reason, explain how it relates to the components of the provided optimization formula.