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In prompt optimization, expansion is a key operation used to explore different states in the search space. It can be defined as a function $$C' = \mathrm{Expand}(C, f)$$, where a set of new candidate prompts $$C'$$ is generated from the existing pool $$C$$ using a model $$f$$. When $$f$$ is a Large Language Model, it is instructed to generate new, relevant prompts based on the ones currently in $$C$$, after which $$C$$ is replaced with $$C'$$. This process can be repeated iteratively alongside evaluation and pruning.

Expansion in Prompt Search

To instruct a Large Language Model to perform a prompt expansion operation, one can provide a template such as: `Below is a prompt for an LLM. Please provide some new prompts to perform the same task. Input: *prompt*`. This instructs the model to generate new variations of an existing prompt to be added to the candidate pool.

Example of a Prompt for LLM-based Prompt Expansion

A prominent approach to prompt optimization utilizes Large Language Models (LLMs) to iteratively discover the best prompts. The process begins with a few initial seed prompts and repeats three main steps: first, evaluating the current prompts on a validation set; second, retaining only the most promising prompts in a candidate pool; and third, using LLMs to generate new, similar candidate prompts based on that pool. This cycle continues until a predefined stopping criterion is satisfied.

Iterative LLM-Based Prompt Search

In an automated process for finding effective prompts, an 'expansion' step is used to generate new candidate prompts from an existing set. Consider a scenario where the initial set of prompts are all very similar to each other (e.g., 'Summarize this text,' 'Provide a summary,' 'Give me a summary'). What is the primary risk of starting with such a low-diversity set, and how does the expansion operation specifically address this risk?

The Role of Expansion in Prompt Diversity

The expansion operation within a search algorithm is formally expressed as the function $$C' = \text{Expand}(C, f)$$. Generally, $$C'$$ is the new set of states derived from the current set, $$C$$, using an expansion rule, $$f$$. In the context of prompt optimization, this formula is applied where $$C$$ is an existing set of prompts, $$f$$ is a model (typically a Large Language Model), and $$C'$$ is the newly generated set of prompts. The expansion is performed by instructing the LLM to create new, relevant prompts based on the initial set.

Expansion Function in Search Algorithms

Analyze the team's methodology. Identify the key operation they are neglecting in their search for a better prompt and explain how systematically incorporating this operation would help them break out of their current cycle of poor results.

Troubleshooting a Prompt Optimization Process

An alternative approach during the prompt expansion step is to define specific edit operations, such as insertions and modifications, at the token level. A new candidate prompt is generated by applying these defined operations to an existing prompt.

Prompt Expansion via Edit Operations

The quality of generated prompts during the expansion phase can be enhanced by incorporating a feedback mechanism. A Large Language Model evaluates an input prompt and generates feedback, which is then used to revise the prompt. This feedback-and-revision cycle repeats until the prompt converges or reaches a desired quality level.

Prompt Expansion via Feedback

Treating prompt generation as a paraphrasing task is a method used during the expansion step of prompt optimization. It involves applying off-the-shelf paraphrasing systems, which can be based on Large Language Models or other architectures, to transform an input prompt into new, semantically equivalent candidate prompts to explore the search space.

Prompt Paraphrasing

A team is using an automated process to discover a high-performing prompt for a text summarization task. They begin with an initial set of prompts: `C = {'Summarize the following text for me.', 'Give me the main points of this article.'}`. They then apply a single 'expansion' operation, which uses a large language model to generate a new set of candidate prompts based on the ones in `C`. Which of the following best represents a plausible output set from this single expansion operation?

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