  Prompt engineering is an essential technique for enhancing the abilities of
large language models (LLMs) by providing explicit and specific instructions.
It enables LLMs to excel in various tasks, such as arithmetic reasoning,
question answering, summarization, relation extraction, machine translation,
and sentiment analysis. Researchers have been actively exploring different
prompt engineering strategies, such as Chain of Thought (CoT), Zero-CoT, and
In-context learning. However, an unresolved problem arises from the fact that
current approaches lack a solid mathematical solution for determining optimal
prompts. To address this issue in prompt engineering, we propose a new and
effective approach called Prompt Space. Our methodology utilizes text
embeddings to obtain basis vectors by matrix decomposition, and then constructs
a space for representing all prompts. Prompt Space significantly outperforms
state-of-the-art prompt paradigms on ten public reasoning benchmarks. Notably,
without the help of the CoT method and the prompt "Let's think step by step",
Prompt Space shows superior performance over the few-shot method. Overall, our
approach provides a robust and effective mathematical framework for selecting
simple and effective prompts. This advancement marks a significant step towards
improving prompt engineering for a wide variety of applications in LLMs. Our
code is publicly available at
\textcolor{blue}{\url{https://github.com/YouBLEI/Prompt-Space}}
