Prompt Space Optimizing Few-shot Reasoning Success with Large Language Models

TL;DR

This paper introduces Prompt Space, a mathematical framework utilizing text embeddings and matrix decomposition to optimize prompt selection, significantly improving few-shot reasoning performance in large language models across multiple benchmarks.

Contribution

The paper proposes Prompt Space, a novel prompt engineering method that mathematically constructs a prompt representation space, outperforming existing techniques without relying on Chain of Thought prompts.

Findings

Prompt Space outperforms state-of-the-art prompt methods on ten reasoning benchmarks.

It achieves superior performance even without Chain of Thought prompts.

The approach provides a robust mathematical framework for prompt selection.

Abstract

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}}