A research team is developing a system to answer questions based on a large document. Instead of feeding the entire document into a language model for every question, they want to learn a compressed, continuous representation of the document (a 'soft prompt', σ). Their process is as follows:

1. First, for a given question (z), they run the model with the full document to get a high-quality, 'gold standard' answer (ŷ).
2. Next, they try to find the optimal soft prompt (σ) that, when paired with

Interpreting the Soft Prompt Optimization Formula

A team is training a soft prompt (σ) to help a language model generate a specific, high-quality target sentence (ŷ) when given an input (z). They are considering two different optimization objectives:

• Objective 1: Adjust the soft prompt σ to maximize the probability of the model generating the exact target sentence ŷ.
• Objective 2: Adjust the soft prompt σ so that the model's entire probability distribution over the next possible word matches the distribution it would have had if it