2310.04959v1

## Towards Better Chain-of-Thought Prompting Strategies: A Survey Zihan Yu Liang He Zhen Wu ∗ Xinyu Dai Jiajun Chen National Key Laboratory for Novel Software Technology, Nanjing University, China Collaborative Innovation Center of Novel Software Technology and Industrialization, China {zihan.y, heliang}@smail.nju.edu.cn {wuz, daixinyu, chenjj}@nju.edu.cn ## Abstract Chain-of-Thought (CoT), a step-wise and coherent reasoning chain, shows its impressive strength when used as a prompting strategy for large language models (LLM). Recent years, the prominent effect of CoT prompting has attracted emerging research. However, there still lacks of a systematic summary about key factors of CoT prompting and comprehensive guide for prompts utilizing. For a deeper understanding about CoT prompting, we survey on a wide range of current research, presenting a systematic and comprehensive analysis on several factors that may influence the effect of CoT prompting, and introduce how to better apply it in different applications under these discussions. We further analyze the challenges and propose some future directions about CoT prompting. This survey could provide an overall reference on related research. ## 1 Introduction Recent years, large language models (LLM) with prompting strategies have achieved prominent performance on many traditional NLP benchmarks (Brown et al., 2020; Cui et al., 2021; Chowdhery et al., 2022; Chung et al., 2022; Li et al., 2022a). But some work finds vanilla prompting strategies still struggle to improve LLM performance on multi-step tasks (Wei et al., 2022b; Kojima et al., 2022; Lyu et al., 2023; Shao et al., 2023). Based on natural step-by-step thinking ability of humans, Chain-of-Thought (CoT) prompting is proposed for LLM to solve multi-step reasoning problems (Wei et al., 2022b). This prompting strategy tries to incorporate intermediate steps to guide a progressive reasoning, achieving surprising improvement on many reasoning benchmarks (Wei et al., 2022b; Wang et al., 2022e) even in some special scenarios including cross-domain (Huang et al., 2022), length-generalization (Anil ∗ *Corresponding author et al., 2022; Zhou et al., 2022a) and cross-lingual reasoning (Shi et al., 2022a). Additionally, CoT prompting ensures a logical and traceable reasoning process, which is more interpretable for humans (Jung et al., 2022; Weng et al., 2022). The impressive result of CoT prompting provokes an upsurge of explorations on CoT prompting strategies design across different tasks on different models (Shao et al., 2023; Wang et al., 2022e; Khot et al., 2022; Zhou et al., 2022a). But before designing a specific strategy, it's necessary to systematically understand what factors may influence the performance of CoT prompting. Besides, although CoT prompting shows its advantages in reasoning tasks, it still has some limitations on generality and concerning on its opaque mechanism as well as unfaithful generation (Lyu et al., 2023; Shi et al., 2022a; Suzgun et al., 2022; Zhang et al., 2023b). To better guide further work, it is essential to make a discussion on current challenges of CoT. Existing surveys lack of a specialized formulation as well as a deep analysis on CoT prompting. We discuss existing surveys and compare them to our work in Appendix A. This survey presents a comprehensive and systematic analysis of the CoT prompting effect, making several noteworthy contributions to this field. First, we formalize the CoT prompting and summarize the pipeline when using it (as shown in Figure 1), which forms the basis of our analysis and discussions. Then, we identify four key factors that significantly affect the performance of CoT prompting: task types, prompts design, extension strategies, and models. We conduct a detailed exploration on how these factors impact the prompting effect and introduce innovative methods inspired by them. Moreover, we provide a comprehensive vision of current challenges of CoT prompting and outline numerous opportunities for future research. Figure 1: Illustration of the general pipeline to utilize Chain-of-Thought prompting strategy. Given a specific task, CoT prompts are designed on it. With the assistance of optional extension strategies, models predict the answers (typically with CoT rationales) based on the input prompts. <details> <summary>Image 1 Details</summary>  ### Visual Description ## Diagram: LLM Task Processing ### Overview The image is a diagram illustrating how a Large Language Model (LLM) processes different types of tasks using Chain-of-Thought (CoT) prompts and various extension strategies. The diagram shows tasks being fed into the LLM, which then outputs the final answer. ### Components/Axes * **Tasks:** This is the input to the system, categorized into: * Mathematical Reasoning * Date Reasoning * Commonsense Reasoning * (Indicated by ellipsis) * **CoT Prompts:** These are prompts designed to encourage the LLM to think step-by-step. * **Models:** This refers to the LLM itself, which is the core processing unit. * **Extension Strategies:** These are methods used to enhance the LLM's capabilities, including: * Sub-problem Division * Prediction Ensemble * External Search Engine * **LLM:** A blue rectangle in the center of the diagram. ### Detailed Analysis or ### Content Details **1. Tasks and CoT Prompts:** * **Mathematical Reasoning:** * Question 1: "Q: Leah had 32 chocolates and her sister had 42. If they ate 35, how many pieces do they have left in total? A: Originally, Leah had 32 chocolates and her sister had 42. So in total they had 32 + 42 = 74. After eating 35, they had 74 - 35 = 39 pieces left in total. The answer is 39." * Question 2: "Q: If there are 3 cars in the parking lot and 2 more cars arrive, how many cars are in the parking lot?" * **Date Reasoning:** * Question 1: "Q: It is 4/19/1969 today. What is the date 24 hours later in MM/DD/YYYY? Let's think step by step. A: Today is 04/19/1969. 24 hours later is one day after today, which would be 04/20/1969. The answer is 04/20/1969." * Question 2: "Q: Today is May 25 2013. What is the tomorrow of today in MM/DD/YYYY? Let's think step by step." * **Commonsense Reasoning:** * Question: "Q: Who lived longer, Theodor Haecker or Harry Vaughan Watkins? Let's think step by step." **2. Extension Strategies:** * **Sub-problem Division:** Connected to the Mathematical Reasoning task. * **Prediction Ensemble:** Connected to the Date Reasoning task. * **External Search Engine:** Connected to the Commonsense Reasoning task. **3. LLM Processing:** * The LLM (represented by a blue rectangle) receives input from the tasks and extension strategies. * The LLM processes the information and generates an output. **4. Outputs:** * Mathematical Reasoning output: "5" * Date Reasoning output: "05/26/2013" * Commonsense Reasoning output: "Theodor Haecker" ### Key Observations * The diagram illustrates a pipeline where different types of reasoning tasks are processed by an LLM. * CoT prompts are used to guide the LLM's reasoning process. * Different extension strategies are employed based on the type of task. * The outputs are the final answers to the questions posed in the tasks. ### Interpretation The diagram demonstrates how an LLM can be used to solve various types of problems by leveraging CoT prompting and different extension strategies. The choice of extension strategy appears to be tailored to the specific type of task. For example, sub-problem division is used for mathematical reasoning, while an external search engine is used for commonsense reasoning. This suggests a modular approach where the LLM's capabilities are augmented based on the demands of the task at hand. The diagram highlights the importance of both the LLM's core reasoning abilities and the external tools and techniques that can be used to enhance its performance. </details> Overview of this survey: We first present some background knowledge in § 2 then make an introduction of CoT prompting in § 3. Subsequently, we discuss several key factors about CoT prompting including tasks (§ 4), prompts (§ 5), extension strategies (§ 6) and models (§ 7). We further discuss the challenges and future directions in § 8. ## 2 Background Knowledge In this part, we will make a brief introduction about background knowledge before talking about CoT. ## 2.1 Large Language Models Large Language Models (LLM) refer to huge transformer architecture models (typically above ten billions of parameters) pre-trained with massive corpus (Zhao et al., 2023). With the increment of model size and training corpus, it starts to emerge some new abilities (Wei et al., 2022a). Recent years, LLM have achieved remarkable progress in many NLP fields (Brown et al., 2020; Chowdhery et al., 2022; Chung et al., 2022). ## 2.2 Prompting and In-context-learning Prompting is a strategy to better elicit the knowledge and ability acquired during training stage of language models by modifying the input samples in a specific manner (Liu et al., 2023; Brown et al., 2020; Schick and Schütze, 2021). In-contextlearning is a special designed prompting strategy, which prefixed the query sample with a few example demonstrations including both queries and answers (Wei et al., 2022a), enabling the model to analogously make predictions (Dong et al., 2023). In-context-learning is a training-free paradigm and can significantly boost LLM performance and dataefficiency across many NLP benchmarks on fewshot scenarios (Sun et al., 2022). ## 2.3 Reasoning on LLM Reasoning is a complex process which involves using evidence, logically thinking and making arguments (Huang and Chang, 2022). It has been a long journey to explore the way to make neural network a reasoning machine (Peng et al., 2015; Barrett et al., 2018; Qu and Tang, 2019; Angelov and Soares, 2020). Recently, combined with incontext-learning strategy, LLM showed the prominent progress in reasoning tasks (Brown et al., 2020; Chowdhery et al., 2022; Chung et al., 2022). Especially, with assistance of Chain-of-Thought prompt (Wei et al., 2022b), neural networks made an unprecedented breakthrough on many reasoning benchmarks (Wang et al., 2022e; Lyu et al., 2023; Fu et al., 2022). Some work showed that the reasoning ability may emerge when language models are at a certain scale (Cobbe et al., 2021; Wei et al., 2022a,b; Huang and Chang, 2022). ## 3 What is Chain-of-Thought Prompting? Before formally introducing Chain-of-Thought prompting, we first give a definition of CoT prompts. CoT prompts are special designed input sequences to instruct the model to generate co- Figure 2: Taxonomy of Chain-of-Thought Prompting Strategies <details> <summary>Image 2 Details</summary>  ### Visual Description ## Diagram: Chain-of-Thought Prompting Taxonomy ### Overview The image presents a hierarchical diagram outlining a taxonomy of Chain-of-Thought (CoT) prompting techniques. It categorizes these techniques based on task types, prompt design, and extension strategies, providing specific examples and associated publications for each category. ### Components/Axes * **Main Category:** "Chain-of-Thought Prompting" (located on the left side of the diagram) * **Level 1 Categories:** * "Task Types § 4" * "Prompts Design § 5" * "Extension Strategies § 6" * **Level 2 Categories (under Task Types):** * "Close Domain Reasoning and QA § 4.1" * "Open Domain Reasoning and QA § 4.2" * "Code Generation § 4.3" * **Level 2 Categories (under Prompts Design):** * "Demonstrations § 5.1" * "Textual Instructions § 5.2" * **Level 2 Categories (under Extension Strategies):** * "Ensemble § 6.1" * "Sub-problems Division § 6.2" * "External Assistance § 6.3" * "Rationalization § 6.4" * **Examples/Techniques:** Each Level 2 category is further detailed with specific techniques and associated publications (e.g., "Vanilla CoT(Wei et al., 2022b)"). ### Detailed Analysis or ### Content Details **1. Task Types § 4** * **Close Domain Reasoning and QA § 4.1:** * Vanilla CoT(Wei et al., 2022b) * Zeroshot-CoT(Kojima et al., 2022) * Synthetic(Shao et al., 2023) * Auto-CoT(Zhang et al., 2022b) * ART(Paranjape et al., 2023) * Active-Prompt(Diao et al., 2023) * APE(Zhou et al., 2022d) * Faithfull-CoT(Lyu et al., 2023) * Explanation Selection(Ye and Durrett, 2023) * Complexity-based prompting (Fu et al., 2022) * SC(Wang et al., 2022e) * DIVERSE (Li et al., 2022b) * Rationale-augmented (Wang et al., 2022d) * Table-CoT(Chen, 2023) * Dater(Ye et al., 2023) * SOLIS(Zhou et al., 2022b) * LtM(Zhou et al., 2022a) * Decomposed(Khot et al., 2022) * PAL(Gao et al., 2022) * PoT(Chen et al., 2022) * Selectioninference(Creswell et al., 2022) * Algorithmic prompt (Zhou et al., 2022c) * LP(Guo et al., 2023) * MoT(Li and Qiu, 2023) * SV(Weng et al., 2022) * MathPrompter(Imani et al., 2023) * Automate-CoT(Shum et al., 2023) * PHP(Zheng et al., 2023) * **Open Domain Reasoning and QA § 4.2:** * Vanilla CoT(Wei et al., 2022b) * Zeroshot-CoT(Kojima et al., 2022) * Auto-CoT(Zhang et al., 2022b) * ART(Paranjape et al., 2023) * Active-Prompt(Diao et al., 2023) * APE(Zhou et al., 2022d) * Explanation Selection(Ye and Durrett, 2023) * iCAP(Wang et al., 2022a) * Multimodal-CoT(Zhang et al., 2023b) * Complexity-based prompting (Fu et al., 2022) * Self-ask(Press et al., 2022) * SC(Wang et al., 2022e) * DIVERSE (Li et al., 2022b) * SV(Weng et al., 2022) * Rationale-augmented (Wang et al., 2022d) * IRCoT(Trivedi et al., 2022) * LtM(Zhou et al., 2022a) * MCR(Yoran et al., 2023) * Decomposed(Khot et al., 2022) * Maieutic(Jung et al., 2022) * PINTO(Wang et al., 2022c) * MoT(Li and Qiu, 2023) * Chameleon(Lu et al., 2023) * Automate-CoT(Shum et al., 2023) * RR(He et al., 2023) * **Code Generation § 4.3:** * Self-planning (Jiang et al., 2023) * XRICL(Shi et al., 2022b) * DIN-SQL(Pourreza and Rafiei, 2023) * Imitation Attack CoT(Li et al., 2023c) **2. Prompts Design § 5** * **Demonstrations § 5.1:** * Self-ask(Press et al., 2022) * Auto-CoT(Zhang et al., 2022b) * Synthetic(Shao et al., 2023) * MMRSelect(Fu et al., 2022) * Complexity-based prompting (Fu et al., 2022) * Active-Prompt(Diao et al., 2023) * Explanation Selection(Ye and Durrett, 2023) * Algorithmic prompt (Zhou et al., 2022c) * Concise-CoT(Madaan and Yazdanbakhsh, 2022) * MoT(Li and Qiu, 2023) * Automate-CoT(Shum et al., 2023) * **Textual Instructions § 5.2:** * Zeroshot-CoT(Kojima et al., 2022) * APE(Zhou et al., 2022d) * Auto-CoT(Zhang et al., 2022b) **3. Extension Strategies § 6** * **Ensemble § 6.1:** * SC(Wang et al., 2022e) * SV(Weng et al., 2022) * Complexity-based prompting (Fu et al., 2022) * MCR(Yoran et al., 2023) * DIVERSE (Li et al., 2022b) * Rationale-augmented (Wang et al., 2022d) * **Sub-problems Division § 6.2:** * LtM(Zhou et al., 2022a) * Self-ask(Press et al., 2022) * Selectioninference(Creswell et al., 2022) * Decomposed(Khot et al., 2022) * HuggingGPT(Shen et al., 2023) * Toolformer(Schick et al., 2023) * Dater(Ye et al., 2023) * Dynamix-LtM(Drozdov et al., 2022) * RR(He et al., 2023) * **External Assistance § 6.3:** * iCAP(Wang et al., 2022a) * PoT(Chen et al., 2022) * PAL(Gao et al., 2022) * Decomposed (Khot et al., 2022) * HuggingGPT(Shen et al., 2023) * Toolformer(Schick et al., 2023) * Faithfull-CoT(Lyu et al., 2023) * IRCoT(Trivedi et al., 2022) * ART(Paranjape et al., 2023) * Synthetic(Shao et al., 2023) * Chameleon(Lu et al., 2023) * **Rationalization § 6.4:** * STaR(Zelikman et al., 2022) * LP(Guo et al., 2023) * PINTO(Wang et al., 2022c) * PHP(Zheng et al., 2023) ### Key Observations * The diagram provides a structured overview of CoT prompting techniques, categorizing them based on different aspects of their application and design. * Each category includes a list of specific techniques, along with citations to relevant publications. * The diagram highlights the breadth and depth of research in CoT prompting, showcasing a variety of approaches and strategies. * Many techniques appear in multiple categories, suggesting that they can be applied in different contexts or combined with other strategies. For example, Auto-CoT appears in Close Domain Reasoning, Open Domain Reasoning, Demonstrations, and Textual Instructions. ### Interpretation The diagram serves as a valuable resource for researchers and practitioners interested in CoT prompting. It provides a clear and organized overview of the field, making it easier to understand the different approaches and their relationships. The inclusion of citations allows users to delve deeper into specific techniques and explore the underlying research. The diagram suggests that CoT prompting is a rapidly evolving field, with new techniques and strategies being developed continuously. The categorization helps to identify areas where further research is needed and to explore potential synergies between different approaches. The overlap of techniques across categories indicates that CoT prompting is a flexible and adaptable approach that can be tailored to different tasks and contexts. </details> herent series of intermediate reasoning steps (Wei et al., 2022b). Specially, what refers to the ' intermediate reasoning steps " shows discrepancy in different work. The scope of our survey is a more general covering of present work on prompts for multi-step tasks, which ranges from common stepwise reasoning to multi-step tasks deployment, so we encompass various non-programmatic problems division process including sub-problems decomposition (Zhou et al., 2022a; Press et al., 2022) and multi-step deployment (Khot et al., 2022; Shen et al., 2023; Schick et al., 2023) into our definition. CoT prompting is a strategy to utilize CoT prompts, which works as following pipeline. As shown in Figure 1, given a specific task , CoT prompts are designed on it. With the assistance of optional extension strategies , models predict the answers (typically as well as CoT rationales) based on the input prompts. Above four elements in bold are key factors of CoT prompting pipeline which make significant impact on the final performance. We will separately discuss how these factors influence the prompting effect and introduce the work motivated by these factors in remaining survey. We present the taxonomy of various CoT prompting strategies in Figure 2. ## 4 Task Types Task is the target when utilizing CoT prompting, which makes a foundational difference. Before designing CoT prompting strategies, it is necessary to clarify what types of tasks are prone to being boosted by CoT prompts. ## 4.1 Close Domain Reasoning and QA These kinds of tasks include all necessary conditions and background knowledge in the problems. Models need to select informative materials and conduct reasoning on these materials. CoT prompts could provide a reasoning pattern to instruct how to select key materials and reason on them, showing superiority on these tasks like mathematical reasoning (Zhang et al., 2022b; Shao et al., 2023; Wang et al., 2022e), symbolic reasoning (Wei et al., 2022b; Anil et al., 2022; Suzgun et al., 2022) and table QA (Ye et al., 2023; Chen, 2023). ## 4.2 Open Domain Reasoning and QA These kinds of tasks aim to answer questions based on a large-scale unstructured knowledge base, and don't include all of necessary knowledge in the problem. In this case, LLM are forced to use their own knowledge to solve the problems and the performance of CoT prompting highly depends on Figure 3: Some example CoT prompts. For rationales in § 5.1.2, bridging objects are marked in red and language templates are marked in blue. <details> <summary>Image 3 Details</summary>  ### Visual Description ## Chain-of-Thought (CoT) Prompt Examples ### Overview The image presents examples of Chain-of-Thought (CoT) prompts used for different reasoning tasks: Mathematical Reasoning, Date Reasoning, and Commonsense Reasoning. It illustrates few-shot and zero-shot approaches, with and without textual instructions. ### Components/Axes * **Titles:** * "A CoT prompt for Mathematical Reasoning" (top-left) * "A CoT prompt for Date Reasoning" (top-center) * "A CoT prompt for Commonsense Reasoning" (top-right) * **Sections:** * "Question" (blue vertical line pointing to the question) * "Demonstrations" (blue vertical line pointing to the rationale and answer) * "Rationale" (blue vertical line pointing to the rationale) * "Answer" (blue vertical line pointing to the answer) * "Query" (purple vertical line pointing to the query) * **Textual Instructions:** Green dashed line pointing to the "Let's think step by step." prompt. * **Prompt Types:** * "Few-shot CoT prompt w/o textual instructions" (bottom-left) * "Few-shot CoT prompt w/ textual instructions" (bottom-center) * "Zero-shot CoT prompt" (bottom-right) ### Detailed Analysis or ### Content Details **1. A CoT prompt for Mathematical Reasoning (top-left)** * **Question:** "Q: Leah had 32 chocolates and her sister had 42. If they ate 35, how many pieces do they have left in total?" * **Rationale:** "A: Originally, Leah had 32 chocolates and her sister had 42. So in total they had 32 + 42 = 74. After eating 35, they had 74 - 35 = 39 pieces left in total." * **Answer:** "The answer is 39." * **Query:** "Q: If there are 3 cars in the parking lot and 2 more cars arrive, how many cars are in the parking lot?" **2. A CoT prompt for Date Reasoning (top-center)** * **Question:** "Q: It is 4/19/1969 today. What is the date 24 hours later in MM/DD/YYYY?" * **Textual Instructions:** "Let's think step by step." * **Rationale:** "A: Today is 04/19/1969. 24 hours later is one day after today, which would be 04/20/1969." * **Answer:** "The answer is 04/20/1969." * **Query:** "Q: Today is May 25 2013. What is the tomorrow of today in MM/DD/YYYY?" * **Textual Instructions:** "Let's think step by step." **3. A CoT prompt for Commonsense Reasoning (top-right)** * **Question:** "Q: Who lived longer, Theodor Haecker or Harry Vaughan Watkins?" * **Textual Instructions:** "Let's think step by step." ### Key Observations * The examples demonstrate how CoT prompts can be structured to guide the model's reasoning process. * Few-shot prompts provide examples of question-answer pairs, while zero-shot prompts rely on the model's pre-existing knowledge. * Textual instructions, such as "Let's think step by step," can further enhance the model's reasoning abilities. * The mathematical reasoning example includes a detailed step-by-step calculation. * The date reasoning example involves calculating a date based on a given date and time interval. * The commonsense reasoning example requires the model to apply its knowledge of historical figures. ### Interpretation The image illustrates the application of Chain-of-Thought (CoT) prompting to various reasoning tasks. CoT prompting is a technique used to improve the performance of large language models (LLMs) by encouraging them to generate intermediate reasoning steps before providing a final answer. The examples show how CoT prompts can be tailored to different types of reasoning, such as mathematical, date-based, and commonsense reasoning. The inclusion of demonstrations (few-shot learning) and textual instructions further guides the model's reasoning process, leading to more accurate and coherent responses. The image highlights the flexibility and effectiveness of CoT prompting as a method for enhancing the reasoning capabilities of LLMs. </details> the LLM knowledge quality (Suzgun et al., 2022). Some tasks even require a deeper understanding on the semantic meaning of natural language (Shi et al., 2022a; Suzgun et al., 2022; Zhang et al., 2023b). Improperly involving CoT prompting into these knowledge or semantic oriented tasks may even hurt the performance (Shi et al., 2022a). To address these problems, some work uses external tools to inject required knowledge (We will introduce in § 6.3). ## 4.3 Code Generation Code generation aims to generate codes according to an input instruction. Due to the internal logical form of codes, the step-by-step reasoning chain of CoT is coherent with abilities needed for code generation (Shi et al., 2022b; Chen et al., 2022; Gao et al., 2022; Jiang et al., 2023; Pourreza and Rafiei, 2023). ## 5 Prompts Design When the task is determined, it's necessary to design an effective CoT prompt. Besides the query, there are two special elements in CoT prompts: CoT demonstrations and textual instructions . CoT demonstrations are several step-wise reasoning exemplars and textual instructions are textual sequences to actively guide a progressive solving process. A CoT prompt should contain at least one of these elements. Typically, a CoT prompt with (or without) demonstrations is called few-shot CoT (or zero-shot CoT). We present several example CoT prompts in Figure 3. In this section, we will discuss how to design an effective CoT prompt from each element. ## 5.1 Demonstrations In few-shot CoT, demonstrations are the indispensable part. As shown in Figure 3, a CoT demonstra- tion is a (problem, rationale, answer) triple, where the rationale contains the intermediate reasoning steps that lead from the problem to the answer . In this part, we will discuss what factors of demonstrations may affect the final prompting performance from problem, rationale and holistic perspectives 1 . ## 5.1.1 Problem Perspective Complexity: Complexity measures the difficulty of a problem, which can be reflected as the number, the length and the logical difficulty of reasoning steps to solve this problem. Empirically, more complex demonstration problems usually guarantee longer reasoning steps, which can provide more reasoning context and induce the model to generate a longer rationale, avoiding a short-cut prediction (Shao et al., 2023; Anil et al., 2022; Saparov and He, 2022). To get more complex demonstration problems, a direct way is to select the samples with most reasoning steps (Shao et al., 2023; Fu et al., 2022). Diao et al. (2023) select the demonstrations with higher uncertainty, which represents the extent a problem is able to confuse the model. Relevance and Diversity: Relevance measures how similar the demonstration problems are to the query problem. Relevant demonstration problems could provide similar knowledge and reasoning pattern for the query, which make LLM easier to imitate (Ye et al., 2022). Diversity measures how different a demonstration problem is from other demonstration problems within a single prompt. Diverse demonstrations could fuse different reasoning process and make model less sensitive to a specific reasoning process, 1 We don't specially analyze factors of the answer since the answer is directly associated with the problem. increasing the prompt robustness (Shao et al., 2023; Zhang et al., 2022b). Both relevance and diversity can be ensured by representative features of problems (Ye et al., 2022; Zhang et al., 2022b) or manual topic informing (Shao et al., 2023). Specially, we need to point out that diversity and relevance are a trade-off process (Ye et al., 2022). Too monotonous demonstrations may lead to a less robust model performance while involving too many irrelevant demonstrations may inject more noise. ## 5.1.2 Rationale Perspective Structural Completeness: A CoT rationale can be divided into two fine-grained components 2 : bridging objects and language templates (Wang et al., 2022b; Ye et al., 2022). A structural complete rationale should contain both of two components. Bridging objects refer to the critical elements that convey the logical process when solving problems, which are meant to be traversed in a single prediction. Language templates refer to complementary textual parts that connect the bridging objects, which involve complementary knowledge for the problems and construct logical connections with bridging objects (Wang et al., 2022b). Figure 3 presents some examples about each component of CoT rationales on different tasks. For a sound reasoning, bridging objects provide the reasoning materials and lead to logical language templates, while language templates provide the essential knowledge and help to better organize bridging objects in back (Madaan and Yazdanbakhsh, 2022). In a word, bridging objects and language templates are two codependent and indispensable components for an effective CoT rationale. More detailed two components can also jointly reduce the ambiguity of demonstration rationales (Zhou et al., 2022c). Validity: Validity measures the correctness and coherence of a reasoning chain. The validity of a CoT rationale can be measured from different metrics like accuracy of answers (Ye and Durrett, 2022; Saparov and He, 2022), perplexity (Press et al., 2022) and more detailed measurement on each reasoning step (Saparov and He, 2022). It's also possible to train a verifier model to evaluate 2 Besides, Madaan and Yazdanbakhsh (2022) decomposed a CoT prompt into a finer granularity: symbols (the tokens which are meant to be reasoned), patterns (the essential or structural tokens which connect symbols) and text (other textual components). This division scheme can be easily inducted into the scheme we introduced. the validity of CoT rationales (Li et al., 2022b). Some work is conducted to explore how the validity plays a role in CoT prompt. In a nutshell, a valid CoT rationale does promote a better prompting performance while an effective CoT prompt does not necessarily demand a totally valid rationale (Wang et al., 2022b; Madaan and Yazdanbakhsh, 2022; Ye et al., 2022; Chen et al., 2023). Wang et al. (2022b) found that a completely wrong rationale may bring a similar reasoning boost as vanilla CoT as long as it is coherent, i.e. , latter steps should not contain any condition or text information which doesn't present in previous steps. It seems that a coherent CoT rationale demonstrates a relative logical manner of reasoning, which help to elicit the LLM ability of progressive reasoning. Thus, the coherence should be primarily ensured if we have to compromise to incorrect CoT rationales. ## 5.1.3 Holistic Perspective Number and Order: When prompted with multiple CoT demonstrations, the model accesses the intersection information of each demonstration (Ye et al., 2022). The number and order of demonstrations leave a impact on the final performance (Wei et al., 2022b; Lu et al., 2022a; Chen et al., 2023) Some work finds model performance would gain prominently when the CoT demonstrations number is gradually increasing from zero to two while the improvement remains slowly and negligibly if demonstrations number continually increases (Shi et al., 2022a; Lu et al., 2022a; Chen, 2023; Chen et al., 2023). Too many demonstrations can lead to a mass of computation cost while insufficient demonstrations may make LLM more sensitive to a single demonstration and increase the variance (Chen et al., 2022). Changing the order of demonstrations may result in a non-trivial effect, but we still can't draw a conclusion for a universal order strategy since the impact of order may vary according to the models, tasks and dataset (Lu et al., 2022b; Liu et al., 2022). An compromised method is to use some prompting searching strategies (Lu et al., 2022b; Ye and Durrett, 2023) or some heuristic measurements like complexity and relevance order Liu et al. (2022). ## 5.2 Textual Instructions LLM show ability to follow explicit instructions even in zero-shot scenarios (Ouyang et al., 2022; Sanh et al., 2022). Inspired by this, some work finds explicitly prompting LLM with an active tex- tual instruction like ' Let's think step by step " can guide a progressive reasoning (Kojima et al., 2022; Zhou et al., 2022d). Without any demonstrations, this simple zero-shot strategy shows impressive result comparing to non-CoT methods, implying these textual instructions can similarly elicit the reasoning ability of LLM. Some work also finds combining these textual instruction with few-shot CoT can achieve a further performance increment (Kojima et al., 2022). ## 6 Extension Strategies Given a CoT prompt, there are many possible extension strategies to enhance the prompt performance. In this section, we will highlight four CoT-related strategies and analyze when and how to use them. ## 6.1 Ensemble Ensemble learning is an effective strategy which combines diverse learners, enhancing the model performance comparing to a single learner (Zhou, 2012). Recent work achieved superior performance when using ensemble strategy on CoT prompting (Wang et al., 2022d; Li et al., 2022b; Wang et al., 2022e), which can help to correct errors made by individual reasoning process and integrate diverse prompts and demonstrations into a single prediction. Wang et al. (2022e) point out ensemble methods can even bring performance increment on tasks where vanilla CoT fails. However, unnecessary ensembles on problems which vanilla CoT can already effectively solve may inject noise to a confident prediction and instead do harm to model performance (Wang et al., 2022d). To go a step further, what elements should be embraced into ensemble also matters a lot. According to different ensemble materials, we categorize these methods into prompts ensemble method and predictions ensemble method. Prompts ensemble focuses on the ensemble of results generated with various prompts. This method construct diverse CoT prompts by repeating sampling different demonstrations from exemplars set (Li et al., 2022b). Predictions ensemble focuses on integrating output space materials including rationales and answers. This method generates various predictions given a fixed input query by LLM sampling algorithms (Wang et al., 2022e; Fu et al., 2022; Yoran et al., 2023). It is found predictions ensemble may lead to more performance gain comparing to prompts ensemble (Wang et al., 2022d), but mul- tiple decoding for predictions ensemble may lead to higher computation cost. How to choose the ensemble strategy depends on the access of demonstrations number and computing resource. It's also possible to jointly combine two ensemble methods (Wang et al., 2022d). ## 6.2 Sub-problems Division When confronting a problem needs to be recursively inferred or harder than demonstrations, dividing a problem into several sub-problems could be a better option (Zhou et al., 2022a; Press et al., 2022; Khot et al., 2022; Schick et al., 2023). Comparing to vanilla CoT, sub-problems division strategy decomposes a complex problem into a series of simple sub-problems, which are much easier to solve, enabling models to accomplish query problems harder than demonstrations (Zhou et al., 2022a; Press et al., 2022). Also, when dealing with each sub-problem, model is free from information which is irrelevant to current sub-problem and more informative information is prone to guiding a valid reasoning (Creswell et al., 2022; Zhou et al., 2022a). Additionally, the required abilities for separate subproblems are different. This strategy makes it more convenient to deploy each sub-problem with different modules and inject external assistance (Khot et al., 2022; Schick et al., 2023; Shen et al., 2023), which we will introduce in § 6.3. ## 6.3 External Assistance In order to expand the ability of LLM and assist LLMto perform on broader applications, it's useful to introduce external sources including knowledge, tools or codes interpreters into reasoning process. Knowledge injection is especially helpful in tasks which need external knowledge like commonsense QA (Wang et al., 2022a). Tools and codes assisted strategies show preponderance in problems which need abilities beyond LLM capacities such as accurate numerical calculation or search engine (Chen et al., 2022; Khot et al., 2022; Schick et al., 2023; Paranjape et al., 2023). With proper prompts, LLM can generate task deployment chains to instruct when and where to call external tools (Khot et al., 2022; Schick et al., 2023), codes interpreter (Gao et al., 2022; Chen et al., 2022; Lyu et al., 2023) or even other models (Shen et al., 2023), to solve more complex problems. Codes interpreters can also serve as external verifiers to check the validity of generated rationales by checking whether they can be interpreted and lead to a correct answer (Shao et al., 2023; Gao et al., 2022; Chen et al., 2022). Additionally, Lyu et al. (2023) point out executing reasoning chains with programmatic modules can enhance the faithfulness of CoT (We will discuss in § 8). ## 6.4 Rationalization Usually, the rationales predicted by LLM would make some mistakes and lead to wrong answers. If these mistakes can be corrected, it is possible to rationalize the reasoning process and boost the performance. Manual rationalization would be effective but sometimes too costly (Wang et al., 2022c; Kim et al., 2023). A simple way is to use some hints to guide the model to rethink (Zelikman et al., 2022; Guo et al., 2023). When the model produces a wrong answer, we can tell model the correct answer and ask it to self-revise illogical reasoning and regenerate a rationale based on the golden answer. This process can be regarded as a self-learning process, where the model can progressively improve its reasoning ability just with answers supervised. However, it's still hard to rationalize imperfect rationales which lead to correct answers. ## 7 Models LLM, as the primary role of solving problems, makes a significant difference to the final prediction. In this section, we will discuss from model size and training corpus to introduce what kinds of models are more effective with CoT prompting. ## 7.1 Model Size Many researches have found as the model size is relatively small (typically below ten billions parameters), CoT doesn't remain a positive impact. But as the model size increases to a certain size (above ten billions parameters), it will exhibit a sudden performance breakout (Wei et al., 2022b; Suzgun et al., 2022; Magister et al., 2022; Fu et al., 2023). This implies CoT is an emergent ability (Wei et al., 2022a) of LLM. Prompting small models with CoT will commonly lead to hallucination (Ji et al., 2023), which often presents as fluent but illogical generation (Wei et al., 2022b). But it's still possible to enhance small models reasoning ability by CoT. Some work fine-tuned a small-scaled model with self-constructed CoT dataset(Zelikman et al., 2022) or knowledge distillation (Magister et al., 2022; Ho et al., 2022; Wang et al., 2022c; Fu et al., 2023), making small models compatible to perform step-by-step reasoning even on few-shot scenarios. However, small models will forget general abilities on other tasks except stepby-step reasoning after CoT tuning (Fu et al., 2023) and still lag behind large models on tasks which demands substantial knowledge to conduct reasoning (Magister et al., 2022). ## 7.2 Training Corpus It is believed that the abilities LLM exhibit originate from training corpus. Some work finds models pre-trained with codes could acquire more performance gain when prompted with CoT (Diao et al., 2023). Instruction tuning also shows relevance to the CoT prompting and zero-shot learning performance(Chung et al., 2022; Fu et al., 2023), which may be illustrated by the presence of CoT-like samples in the training corpus of instruction tuning. Recent work even tries to explicitly involve CoT samples into training corpus to enhance the stepby-step reasoning ability and avoid over-fitting to monotonous sample templates (Chung et al., 2022; Ho et al., 2022; Yu et al., 2022). In a word, embracing aforementioned contents into training corpus could introduce more reasoning materials and necessary knowledge for LLM, leading to a profound influence on CoT reasoning ability. ## 8 Discussion and Future Work Faithfulness: Though CoT prompting increases the reasoning interpretability, it still remains a problem whether present methods for generating CoT rationales are faithful. A faithful reasoning process implies the answer generated by model is accurately reasoned from corresponding generated rationale, which can ensure the controllability and credibility of reasoning process. The rationale which looks like plausible but unfaithful may make humans over-trust the model, resulting in implicit bias risk on realistic applications (Pruthi et al., 2020; Slack et al., 2020). Most of current work generates CoT rationales together with the final answer, which can't guarantee the answer is directly acquired from rationales. Although there exists some work that tries to construct a faithful process by directly reasoning answers on generated rationales (Lyu et al., 2023; Wang et al., 2022c), it still can't ensure the faithfulness about how rationales generated from the query problem (Lyu et al., 2023). How to perform a truly faithful step-by-step reasoning on LLM can be critical for controllable and reliable CoT reasoning. Generality: Currently, it has still a challenge for CoT-assisted LLM to handle the problems which need a great amount of external knowledge or deeper understanding of language (Shi et al., 2022a; Suzgun et al., 2022; Zhang et al., 2023b). Much relevant work focus on an external retriever to supplement necessary knowledge for conduct reasoning. However, a pre-trained LLM has already obtained a tremendous amount of knowledge. The key conundrum is how to instruct LLM to recognize and make use of learned knowledge. Besides, although LLM with CoT assistance have already showed impressive advantages on some reasoning tasks, these tasks are a little bit naïve and still far from complicated realistic applications, which demand a high level of perception on external environments, deduction of potential results and planning on the final goal even with cost restriction. Valmeekam et al. (2022) proposed a more complicated planning benchmark which evaluates the model reasoning ability about actions execution and environment change, finding that LLM have dismal performance on this benchmark. How to combine the CoT prompting with LLM on more challenging and realistic benchmarks can be a promising future direction. Self-rationalization: Recent work has proposed effective self-rationalization methods by informing the model correct answers and ask models to self-revise the mistakes(Zelikman et al., 2022; Guo et al., 2023). But sometimes models may learn some short-cut and generate correct answers while incorrect rationales (Saparov and He, 2022). In this scenario, answer accuracy is not enough to measure the validity of reasoning process. How to spot these short-cut and help models to self-rationalize incorrect reasoning should be carefully discussed. Rationale Analysis: Existing work has made a step towards a clear understanding of CoT rationale, but most existing conclusions are confined to limited models and tasks (Wang et al., 2022b; Ye et al., 2022; Madaan and Yazdanbakhsh, 2022). The specific form of CoT rationale varies according to the specific task setting. How a certain component is represented and how each component behaves on the given setting may leave a great distinction. Therefore, for a more practical application, it's vital to thoroughly analyze the function of each rationale component among different settings. As we discussed in § 5.1, in order to achieve a promising prompt performance, a relatively complex and detailed reasoning chain is needed. With this purpose, the input tokens are usually long, increasing the inference cost and noise interference. Madaan and Yazdanbakhsh (2022) proposed Concise-CoT to prune a few trivial tokens but there is still a long journey to go. If we could fully understand how each component work for each task, we could directly prompt partial demanded reasoning materials instead of a complete reasoning chain to improve the efficiency of CoT prompting. Theoretical Analysis: We have already showed CoT prompting can benefit the reasoning performance from different dimensions. But it naturally leaves a question about the theoretical explanation about CoT prompt effect. There are some hypotheses to explain the mechanism of in-context-learning (Chan et al., 2022; Xie et al., 2022; Olsson et al., 2022; Garg et al., 2022; Li et al., 2023a; Dai et al., 2023). But CoT prompts are typically more complicated due to the step-bystep reasoning chains, thus there may exist more to explore for CoT prompting. Unfortunately, there isn't enough theoretical analysis on CoT prompting and more work draws empirical conclusions. Some work finds prompting with wrong and irrelevant rationales can somewhat boost the reasoning performance of LLM (Wang et al., 2022b; Madaan and Yazdanbakhsh, 2022). This may imply CoT prompts don't 'teach" LLM how to reason, but instead provide necessary reasoning materials to help LLM to recall what they have learned at training stage. Prystawski and Goodman (2023) give a hypothesis from training data locality structure and Li et al. (2023b) provide an explanation from learning perspective. But how these hypotheses can explain aforementioned demonstration factors we emphasized is still a mystery. Also, we still don't know how a simple ' Let's think step by step " help to boost the performance. Clarifying the working mechanism of CoT prompting is a fundamental milestone to ensure a truly interpretable and transparent prompting strategy. ## 9 Conclusion In this survey, we reviewed the research status of Chain-of-Thought prompting. We highlighted four factors that may affect the CoT prompting performance and introduced methods based on these fac- tors. We gave a general direction to properly utilize CoT prompting when confronting different setting. Furthermore, we discussed current challenges about CoT prompting and proposed some potential directions. We hope this survey could provide an overall reference on future research. ## Limitations Due to the page limitation, we couldn't concretely introduce the methods designed on various tasks and applications setting, but only provide an systematic analysis and instructive perspective on prompting applications. We don't specifically introduce the work which tries to use CoT prompting for more realistic applications such as examinations problems answering (Zhang et al., 2022a), domain specialization (Singhal et al., 2022; Prystawski et al., 2022; Zhang et al., 2023a), since these work doesn't exceed the scope we discussed in § 4. There are also other applications for CoT on imitation learning and reinforced learning (Yang et al., 2022; Jia et al., 2023; Bai et al., 2022). We don't discuss in out paper because we only focus on prompting applications of CoT. Besides, since the scope of our survey focuses on the factors analysis and strategies designing of CoT prompting, we don't encompass application resources in main text (refer to Appendix B). ## References Plamen P. Angelov and Eduardo A. Soares. 2020. Towards deep machine reasoning: a prototype-based deep neural network with decision tree inference. In 2020 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2020, Toronto, ON, Canada, October 11-14, 2020 , pages 2092-2099. IEEE. Cem Anil, Yuhuai Wu, Anders Andreassen, Aitor Lewkowycz, Vedant Misra, Vinay Ramasesh, Ambrose Slone, Guy Gur-Ari, Ethan Dyer, and Behnam Neyshabur. 2022. Exploring length generalization in large language models. 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(2023) introduced Chain-of-Thought prompting on few-shot and zero-shot scenarios but did not make a deep analysis on CoT prompting strategies designing. Huang and Chang (2022) and Dong et al. (2023) introduced common methods of CoT prompting, but they did not give a detailed formalization on CoT prompt and a systematic taxonomy of these methods. These work also didn't cover comprehensive work of CoT prompting. Closer to our work, Qiao et al. (2022) presented a survey on prompts for reasoning tasks and introduced some work on CoT prompting. Comparing to their work, we focus more on the deep analysis when utilizing CoT prompting. For example, when it comes to task applications, Qiao et al. (2022) just introduce the form of different tasks while we discussed the characteristic of these tasks and explained why and how to use CoT prompting on these tasks. We are also the only survey which contains a fine-grained formulation of CoT prompt. In short, unlike methods collection surveys, our survey aims to provide a deeper and more comprehensive analysis on CoT prompting. We want to give a general guide for communities to better utilize the CoT prompting and provide a clear vision on prompting strategies designing. ## B Relevant Resources Since CoT shows prominent strength in many tasks involving multi-steps, the acquisition of step-wise data is a key aspect for CoT application. Considering the great manual efforts demand for CoT data annotation, a comprehensive dataset and efficient annotation tool is of great importance. We will introduce some CoT resources in this section. Saparov and He (2022) presented a ontology structure based CoT logical reasoning dataset, PRONTOQA. Ott et al. (2023) proposed a CoT reasoning meta-dataset, ThoughtSource, which integrates six scientific/medical , three general-domain and five math word question answering datasets with manual or AI-generated CoT annotated. The dataset embraces various types of question answering including number, multiple choice, text, bool, etc . This dataset can be effectively used in both fewshot in-context-learning and fine-tuning paradigm. For more efficient CoT data annotation, Kim et al. (2023) proposed a CoT annotation toolkit, CoTEVer, enabling a more applicable manner to reduce manual efforts. CoTEVer can retrieve evidence for generate CoT explanations and provide a more efficient way to verify and correct the wrong explanations.