Why Prompt Design Matters and Works: A Complexity Analysis of Prompt Search Space in LLMs

• URL: http://arxiv.org/abs/2503.10084v2
• Date: Sun, 01 Jun 2025 05:23:51 GMT
• Title: Why Prompt Design Matters and Works: A Complexity Analysis of Prompt Search Space in LLMs
• Authors: Xiang Zhang, Juntai Cao, Jiaqi Wei, Chenyu You, Dujian Ding,
• Abstract summary: We provide a theoretical framework that explains why some prompts succeed while others fail.<n>We analyze the complexity of finding optimal prompts and characterize the size of the prompt space for a given task.<n>Our theory reveals principles behind effective prompt design and shows that naive CoT-using self-guided prompts like "think step by step"-can severely hinder performance.
• Score: 15.941209553757274
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Despite the remarkable successes of large language models (LLMs), the underlying Transformer architecture has inherent limitations in handling complex reasoning tasks. Chain-of-thought (CoT) prompting has emerged as a practical workaround, but most CoT-based methods rely on a single, generic prompt such as "think step by step", with no task-specific adaptation. These approaches expect the model to discover an effective reasoning path on its own, forcing it to search through a vast prompt space. In contrast, several studies have explored task-specific prompt designs to boost performance. However, these designs are typically developed through trial and error, lacking theoretical grounding. As a result, prompt engineering remains largely ad hoc and unguided. In this paper, we provide a theoretical framework that explains why some prompts succeed while others fail. We show that prompts function as selectors, extracting task-relevant information from the model's full hidden state during CoT reasoning. Each prompt defines a unique trajectory through the answer space, and the choice of trajectory is crucial for task performance and future navigation within the space. We analyze the complexity of finding optimal prompts and characterize the size of the prompt space for a given task. Our theory reveals principles behind effective prompt design and shows that naive CoT-using self-guided prompts like "think step by step"-can severely hinder performance. Through experiments, we show that optimal prompt search can lead to more than a 50% improvement on reasoning tasks, providing a theoretical foundation for prompt engineering.

Related papers

• Grammar-Guided Evolutionary Search for Discrete Prompt Optimisation [63.97051732013936]
  We propose an evolutionary search approach to automated discrete prompt optimisation consisting of two phases.<n>In the first phase, grammar-guided genetic programming is invoked to synthesise prompt-creating programmes.<n>In the second phase, local search is applied to explore the neighbourhoods of best-performing programmes.
  arXiv  Detail & Related papers  (2025-07-14T14:34:15Z)
• Evolving Prompts In-Context: An Open-ended, Self-replicating Perspective [65.12150411762273]
  We show that pruning random demonstrations into seemingly incoherent "gibberish" can remarkably improve performance across diverse tasks.<n>We propose a self-discover prompt optimization framework, PromptQuine, that automatically searches for the pruning strategy by itself using only low-data regimes.
  arXiv  Detail & Related papers  (2025-06-22T07:53:07Z)
• Why Reasoning Matters? A Survey of Advancements in Multimodal Reasoning (v1) [66.51642638034822]
  Reasoning is central to human intelligence, enabling structured problem-solving across diverse tasks. Recent advances in large language models (LLMs) have greatly enhanced their reasoning abilities in arithmetic, commonsense, and symbolic domains. This paper offers a concise yet insightful overview of reasoning techniques in both textual and multimodal LLMs.
  arXiv  Detail & Related papers  (2025-04-04T04:04:56Z)
• When More is Less: Understanding Chain-of-Thought Length in LLMs [53.77747102201451]
  Chain-of-thought (CoT) reasoning enhances the multi-step reasoning capabilities of large language models (LLMs)<n>However, for most models and tasks, does an increase in CoT length consistently lead to improved reasoning accuracy?<n>In this paper, we observe a nuanced relationship: as the number of reasoning steps increases, performance initially improves but eventually decreases.
  arXiv  Detail & Related papers  (2025-02-11T05:28:59Z)
• Supervised Chain of Thought [5.389461633686935]
  Chain of Thought (CoT) prompting offers a promising approach to solving complex reasoning tasks. One-prompt-for-all approach poses significant challenges for models to generate the correct reasoning steps. We show how task-specific supervision is essential for navigating the prompt space accurately and achieving optimal performance.
  arXiv  Detail & Related papers  (2024-10-18T06:25:27Z)
• Make LLMs better zero-shot reasoners: Structure-orientated autonomous reasoning [52.83539473110143]
  We introduce a novel structure-oriented analysis method to help Large Language Models (LLMs) better understand a question. To further improve the reliability in complex question-answering tasks, we propose a multi-agent reasoning system, Structure-oriented Autonomous Reasoning Agents (SARA) Extensive experiments verify the effectiveness of the proposed reasoning system. Surprisingly, in some cases, the system even surpasses few-shot methods.
  arXiv  Detail & Related papers  (2024-10-18T05:30:33Z)
• Instance-adaptive Zero-shot Chain-of-Thought Prompting [32.700073951068575]
  Zero-shot Chain-of-Thought (CoT) prompting emerges as a simple and effective strategy for enhancing the performance of large language models (LLMs) in real-world reasoning tasks. This work introduces an instance-adaptive prompting algorithm as an alternative zero-shot CoT reasoning scheme by adaptively differentiating good and bad prompts.
  arXiv  Detail & Related papers  (2024-09-30T16:00:34Z)
• PECTP: Parameter-Efficient Cross-Task Prompts for Incremental Vision Transformer [76.39111896665585]
  Incremental Learning (IL) aims to learn deep models on sequential tasks continually. Recent vast pre-trained models (PTMs) have achieved outstanding performance by prompt technique in practical IL without the old samples.
  arXiv  Detail & Related papers  (2024-07-04T10:37:58Z)
• On the Empirical Complexity of Reasoning and Planning in LLMs [29.588100727466976]
  Chain-of-thought (CoT), tree-of-thought (ToT), and related techniques work surprisingly well in practice for some complex reasoning tasks with Large Language Models (LLMs) This work seeks the underlying reasons by conducting experimental case studies and linking the performance benefits to well-established sample and computational complexity principles in machine learning.
  arXiv  Detail & Related papers  (2024-04-17T03:34:27Z)
• Exploring Prompt Engineering Practices in the Enterprise [3.7882262667445734]
  A prompt is a natural language instruction designed to elicit certain behaviour or output from a model. For complex tasks and tasks with specific requirements, prompt design is not trivial. We analyze sessions of prompt editing behavior, categorizing the parts of prompts users iterated on and the types of changes they made.
  arXiv  Detail & Related papers  (2024-03-13T20:32:32Z)
• Towards Generalist Prompting for Large Language Models by Mental Models [105.03747314550591]
  Large language models (LLMs) have demonstrated impressive performance on many tasks. To achieve optimal performance, specially designed prompting methods are still needed. We introduce the concept of generalist prompting, which operates on the design principle of achieving optimal or near-optimal performance.
  arXiv  Detail & Related papers  (2024-02-28T11:29:09Z)
• Large Language Models as an Indirect Reasoner: Contrapositive and Contradiction for Automated Reasoning [74.90592233107712]
  We propose a Direct-Indirect Reasoning (DIR) method, which considers Direct Reasoning (DR) and Indirect Reasoning (IR) as multiple parallel reasoning paths that are merged to derive the final answer.<n>Our DIR method is simple yet effective and can be straightforwardly integrated with existing variants of CoT methods.
  arXiv  Detail & Related papers  (2024-02-06T03:41:12Z)
• Parrot Mind: Towards Explaining the Complex Task Reasoning of Pretrained Large Language Models with Template-Content Structure [66.33623392497599]
  We show that a structure called template-content structure (T-C structure) can reduce the possible space from exponential level to linear level. We demonstrate that models can achieve task composition, further reducing the space needed to learn from linear to logarithmic.
  arXiv  Detail & Related papers  (2023-10-09T06:57:45Z)
• Tree-of-Mixed-Thought: Combining Fast and Slow Thinking for Multi-hop Visual Reasoning [16.495754104540605]
  Large language models (LLMs) can generate code-like plans for complex inference tasks such as visual reasoning. We propose a hierarchical plan-searching algorithm that integrates the one-stop reasoning (fast) and the Tree-of-thought (slow)
  arXiv  Detail & Related papers  (2023-08-18T16:21:40Z)
• Prompt Space Optimizing Few-shot Reasoning Success with Large Language Models [7.453926835095568]
  Prompt engineering enables large language models (LLMs) to excel in various tasks, such as arithmetic reasoning, question answering, summarization, relation extraction, machine translation, and sentiment analysis. Current approaches lack a solid mathematical solution for determining optimal prompts. Our methodology utilizes text embeddings to obtain basis vectors by matrix decomposition, and then constructs a space for representing all prompts.
  arXiv  Detail & Related papers  (2023-06-06T15:43:16Z)
• On the Role of Attention in Prompt-tuning [90.97555030446563]
  We study prompt-tuning for one-layer attention architectures and study contextual mixture-models. We show that softmax-prompt-attention is provably more expressive than softmax-self-attention and linear-prompt-attention. We also provide experiments that verify our theoretical insights on real datasets and demonstrate how prompt-tuning enables the model to attend to context-relevant information.
  arXiv  Detail & Related papers  (2023-06-06T06:23:38Z)
• Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective [39.47116013338394]
  Chain-of-Thought prompting (CoT) can dramatically improve the performance of Large Language Models (LLMs) We show that CoT can handle a general class of decision-making problems known as Dynamic Programming.
  arXiv  Detail & Related papers  (2023-05-24T17:59:21Z)
• Active Prompting with Chain-of-Thought for Large Language Models [26.5029080638055]
  This paper proposes a new method, Active-Prompt, to adapt large language models to different tasks. By borrowing ideas from the related problem of uncertainty-based active learning, we introduce several metrics to characterize the uncertainty. Experimental results demonstrate the superiority of our proposed method, achieving state-of-the-art on eight complex reasoning tasks.
  arXiv  Detail & Related papers  (2023-02-23T18:58:59Z)
• Towards Understanding Chain-of-Thought Prompting: An Empirical Study of What Matters [82.84696222087396]
  Chain-of-Thought (CoT) prompting can dramatically improve the multi-step reasoning abilities of large language models (LLMs) We show that CoT reasoning is possible even with invalid demonstrations.
  arXiv  Detail & Related papers  (2022-12-20T05:20:54Z)
• Decomposed Prompting: A Modular Approach for Solving Complex Tasks [55.42850359286304]
  We propose Decomposed Prompting to solve complex tasks by decomposing them (via prompting) into simpler sub-tasks. This modular structure allows each prompt to be optimized for its specific sub-task. We show that the flexibility and modularity of Decomposed Prompting allows it to outperform prior work on few-shot prompting.
  arXiv  Detail & Related papers  (2022-10-05T17:28:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.