Beyond Chain-of-Thought: A Survey of Chain-of-X Paradigms for LLMs
Yu Xia Rui Wang Xu Liu Mingyan Li Tong Yu Xiang Chen Julian McAuley Shuai Li


First detection of the [CII] 158 μm line in the intermediate-velocity cloud Draco
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    draft of April 29, 2024
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Chain-of-Thought (CoT) has been a widely adopted prompting method, eliciting impressive reasoning abilities of Large Language Models (LLMs). 
Inspired by the sequential thought structure of CoT, a 

number of Chain-of-X (CoX) methods have been developed to address various challenges across diverse domains and tasks involving LLMs. 

In this paper, we provide a comprehensive survey of Chain-of-X methods for LLMs in different contexts.
Specifically, we categorize them by taxonomies of nodes, i.e., the X in CoX, and application tasks. 
We also discuss the findings and implications of existing CoX methods, as well as potential future directions. 
Our survey aims to serve as a detailed and up-to-date resource for researchers seeking to apply the idea of CoT to broader scenarios.
    
    




§ INTRODUCTION


Large Language Models (LLMs) have shown strong reasoning capabilities when prompted with the Chain-of-Thought (CoT) method <cit.>. 
The essence of CoT is to decompose complex problems into sequences of intermediate subtasks <cit.>.
By handling these subtasks step by step, LLMs are able to focus on important details and assumptions, which substantially improves their performance across a wide range of reasoning tasks <cit.>. 
Additionally, CoT's intermediate steps offer a more transparent reasoning process, facilitating easier interpretation and evaluation of LLMs <cit.>.

With the success of CoT, a number of Chain-of-X (CoX) methods have subsequently been developed <cit.>. 
Extending beyond reasoning thoughts, recent CoX methods have constructed the chain with various components, such as Chain-of-Feedback <cit.>, Chain-of-Instructions <cit.>, Chain-of-Histories <cit.>, etc. 
These methods have been applied to tackle challenges in diverse tasks involving LLMs beyond reasoning, including multi-modal interaction <cit.>, hallucination reduction <cit.>, planning with LLM-based agents <cit.>, etc.



  
Motivation
Despite their growing prevalence, these CoX methods have not yet been collectively examined or categorized, leaving a gap in our understanding of their potential and nuances. To this end, this survey aims to offer a structured overview that captures the essence and diversity of CoX methods for further exploration and innovation.




  
Distinguishing Focus
While several surveys have explored CoT <cit.>, they focus primarily on the reasoning thoughts of different structures, e.g., Chain-of-Thought as illustrated in Figure <ref>(a).

In contrast, this paper focuses on the multifaceted component designs of Chain-of-X beyond reasoning thoughts as shown in Figure <ref>, offering insights of the CoT concept in broader domains.
We present a comprehensive review by taxonomies of the X in CoX and tasks to which these methods are applied.



  
Overview of the Survey 
We first provide background information on Chain-of-Thought and define Chain-of-X as its generalization (<ref>).
Next, we categorize CoX methods by the types of components used to construct the chains (<ref>).
Furthermore, based on the application areas of these CoX methods, we categorize them by tasks (<ref>).
Then, we discuss insights from existing CoX methods and explore potential future directions (<ref>).
A detailed structure of the survey is presented in Figure <ref>.































§ WHAT IS CHAIN-OF-X?


In this section, we introduce some background information about Chain-of-Thought prompting and then define a generalized concept of Chain-of-X.



  
Chain-of-Thought




    
  * formulation: RL
    
  * node taxonomy
    
    
  * thought
    
  * tooling prompting
    
  * feedback/refinement: feedback from different environment (human in the loop, automatic (natural language, programmatic, from compiler)), hallucination, for accuracy


  * tasks
    
  * reasoning
    
  * decision making
    
  * hallucination
    
  * retrieval augmentation
    
  * modal interaction
    
  * evaluation and benchmark


  * analysis/Understanding: Theory, Empirical

    
  * 



CoT prompting is a methodology that substantially enhances the reasoning capabilities of LLMs. 
Introduced by <cit.>, CoT involves prompting LLMs with a structured format of , where `thoughts' encompass coherent and intermediate natural language reasoning steps leading to the final answer. 
CoT's effectiveness is most pronounced in tasks that require complex reasoning. 
Traditional few-shot learning methods often falter in such scenarios, as they tend to provide direct answers without the necessary intermediate steps. 
<cit.> highlighted this limitation, noting the inadequacy of these methods with increased model size. 
In contrast, CoT prompting excels by incorporating intermediate reasoning steps.
These steps guide the model through a logical progression, enhancing its capability to tackle complex problems, such as those involving arithmetic, commonsense, and symbolic reasoning <cit.>.
The essence of CoT lies in its strategy to tackle complex problems by breaking them down into manageable intermediate steps <cit.>.
<cit.> have also demonstrated strong performance of zero-shot CoT by prompting “Let's think step by step.”.
The explicit reasoning steps also provide a transparent pathway for the model's thought process, allowing for further evaluations and corrections <cit.>.



  
Chain-of-X
Inspired by the nature of the sequential breakdown of CoT, a substantial number of CoX methods have been developed recently <cit.>. 
Here, we define CoX as a generalization of the CoT method for diverse tasks beyond LLM reasoning. 
We refer to the X in CoX as the `node' of the chain structure. 
Beyond the thoughts in CoT prompts, the X in CoX can take various forms tailored to specific tasks, including intermediates (<ref>), augmentation (<ref>), feedback (<ref>), and even models (<ref>), as illustrated in Figure <ref>.
We summarize the types of nodes in existing CoX methods in Figure <ref>.
The idea of CoX is to construct a sequence of problem-related components that either compositionally contribute to the solution or iteratively refine the outputs for a complex task.
Similarly, we define a structured format for CoX as  where n is the length of the chain.
Note that this format extends beyond prompting strategies like CoT and can be adapted to a variety of algorithmic frameworks or structures for diverse tasks involving LLMs.
For instance, Chain-of-Verification <cit.> is a hallucination reduction framework that employs an LLM to generate initial responses, composes a sequence of verification questions, and revises its previous responses based on these questions.
In addition to hallucination reduction, CoX methods have been applied to a variety of tasks, as shown in Figure <ref>, including multi-modal interaction (<ref>), factuality & safety (<ref>), multi-step reasoning (<ref>), instruction following (<ref>), LLMs as Agents (<ref>), and evaluation tools (<ref>).














§ CHAIN-OF-X NODES

In this section, we survey existing CoX methods by taxonomy of nodes, categorizing them as shown in Figure <ref> based on the distinct nature of the nodes.



 §.§ Chain-of-Intermediates

Building on the concept of utilizing explicit intermediate steps, a natural evolution of CoT involves replacing reasoning thoughts with other types of intermediate components, i.e., Chain-of-Intermediates. 
Based on the primary focuses, we further divide them into the following subtypes.





  
Problem Decomposition
In problem decomposition, the intermediate steps consist of manageable subtasks derived from an original complex problem.
This approach is exemplified by the classic Chain-of-Thought prompting <cit.>.
Extending this further, <cit.> introduce Chain-of-Code, which segments a task into programmatic subtasks, enhancing the reasoning process through simulated code outputs.
Similarly, <cit.> have developed the Chain-of-Table framework. 
This framework restructures complex tables into question-specific formats via a sequence of strategic operations, making the data more accessible and tailored to the inquiry.
Moreover, the Chain-of-Logic, introduced by <cit.>, applies a logical decomposition to rule-based reasoning tasks, transforming them into a series of logical expressions. 
The methodological breakdown facilitates clearer reasoning pathways. 

These decomposition methods are also echoed in Chain-of-Event <cit.>, which simplify multi-document summarization into discrete and manageable event extraction tasks, significantly enhancing quality and reducing potential errors.



  
Knowledge Composition
In knowledge composition, the primary goal of the intermediate steps is not on simplification but on the accumulation of relevant information and evidence. 
This approach aims to enrich the solution with a depth of understanding and details.
For instance, <cit.> propose Chain-of-Symbol method that meticulously collects spatial relations during spatial planning tasks, enhancing the model's precision and effectiveness.
Likewise, <cit.> adopt Chain-of-Simulation prompting to ensures that each step in code execution is informed by program traces, thereby avoiding memorization pitfalls.
<cit.> take a similar approach with Chain-of-Knowledge, extracting crucial pieces of evidence at each step to support more grounded and reliable question-answering sessions.
This technique is particularly effective in fostering a deeper understanding of the queried material.
In visual tasks, methods like Chain-of-Spot <cit.> and Chain-of-Reasoning <cit.> assist vision-language models in focusing on specific image details, which is crucial for tasks requiring detailed visual evidences.
Through these evidence-rich methods, LLMs achieve a comprehensive and nuanced understanding of complex scenarios, leading to higher quality outputs.



 §.§ Chain-of-Augmentation

A popular variant of CoX methods is Chain-of-Augmentation, where the chain is augmented with additional knowledge.
Based on the types of augmented data, we categorize them as follows.



  
Instructions
Instructions serve as an important augmentation, guiding LLMs through complex reasoning or task execution processes where determining the next step can be nontrivial <cit.>.
For instance, the Chain-of-InstructEditing framework <cit.> harnesses this concept by generating sequential instructions to guide image editing tasks, illustrating how specific editions can refine the output by focusing on relevant areas.
Moreover, <cit.> introduce the Chain-of-Command to tackle ambiguities in user instructions for table manipulations.
Inferring from user instructions, it enables LLMs to employ a series of precise pre-defined commands for more accurate table execution. 
In the realm of e-commerce, <cit.> implement a similar structured approach with their Chain-of-Task, which breaks down customer interactions into manageable atomic tasks, significantly simplifying complex operations.

Similarly, the Chain-of-Instructions framework proposed by <cit.> iteratively solves decomposed subtasks using outputs of previous steps as instructions for the next step. 
The results show that stepwise guidance can substantially improve both the process and the outcomes of complex problem-solving tasks.



  
Histories
Utilizing historical data for informed predictive modeling is another facet of Chain-of-Augmentation, drawing contextual insights from past interactions or events. 
This approach is exemplified by <cit.>'s Chain-of-Opinion, which analyzes historical user opinions to predict future reactions, offering valuable foresight into user sentiment.
In user-interface exploration, <cit.> apply a Chain-of-Action^a framework, leveraging past actions to guide future interactions, thereby optimizing user experience through learned behaviors. 
<cit.> take a similar approach in gaming environments like StarCraft II, where a Chain-of-Summarization provides strategic recommendations based on a synthesis of past gameplay observations.
The development of taxonomy structures also benefits from historical data, as seen in the Chain-of-Layer by <cit.>, which builds upon previously identified categories to enhance classification tasks. 
Temporal knowledge graphs receive a forward-looking treatment as well with methods like Chain-of-History from <cit.> and <cit.>, where historical graph structures inform predictions about future linkages and interactions.



  
Retrieval
Chain-of-Retrievals methods are designed to intersperse the generation process with sequences of explicit retrievals, enhancing the quality of the generated content <cit.>.
For instance, <cit.> introduce the Chain-of-Query framework, which improves the search capabilities of LLMs through a systematic arrangement of query-answer pairs, each aimed at enhancing information retrieval.
Similarly, Chain-of-Question proposed by <cit.> focuses on refining query mechanisms, where each sub-question decomposed from the original question helps in retrieving more accurate knowledge from external knowledge base.

Further refining this concept, <cit.> have crafted Chain-of-Knowledge, which dynamically pulls relevant information from a knowledge base to correct and align inconsistent rationales within CoT frameworks.

These methods illustrate how strategic retrieval integration  improve LLMs' problem-solving accuracy, leading to enhanced output fidelity.




  
Others
Beyond the conventional types of augmentation, various domain-specific augmentations have also been applied to CoX methods for LLMs.
In the realm of emotional intelligence, <cit.> introduce the Chain-of-Empathy, infusing psychotherapy insights to cultivate empathetic responses from LLMs. 
Meanwhile, <cit.> propose Chain-of-Reference method that integrates legal frameworks to meticulously deconstruct and address complex legal inquiries, showcasing the versatility of CoX in specialized fields.
On a similar note, <cit.> develop a Chain-of-Abstraction framework that uses domain-specific tools to fill in abstract placeholders intentionally left in LLMs' reasoning chains.
The enhancement of linguistic tools is also evident in Chain-of-Dictionary <cit.>, which enhances machine translation with a multilingual dictionary tailored to each sentence.

These diverse augmentations not only broaden the operational scope of LLMs but also underscore the potential of tailored, domain-specific enhancements.




 §.§ Chain-of-Feedback

Chain-of-Feedback represents another variant of CoX. 
Unlike augmentation which typically precedes generation, feedback is interlaced throughout the generation process to enhance and fine-tune responses. 
Based on the feedback source, we categorize them as external and self-refinement feedback.



  
External Feedback
Feedback from external sources provides valuable external perspectives that can guide the refinement process in LLMs. 
For instance, <cit.> introduce Chain-of-3DThought using external critiques help iteratively hone an LLM’s understanding of 3D spaces. 

Similarly, <cit.> employ a teacher-student framework in their Chain-of-Repair, where feedback from the compiler is first interpreted by a teacher LLM and then used to guide a student LLM in code generation. 
This approach not only corrects errors but also facilitates a learning process whereby the student model gains proficiency over time. 
Additionally, <cit.> have developed Chain-of-Hindsight, transforming direct human preference into natural language feedback that better aligns with how LLMs process information. 
These feedback allows for more precise refinement to model's outputs, ensuring that responses are both accurate and contextually appropriate.



  
Self-Refine
The potential costs and unavailability of external feedback have led to a growing interest in self-refinement abilities within LLMs <cit.>. 
Highlighted by <cit.>, Chain-of-NLI guides an LLM to evaluate and refine its outputs through a series of natural language inference tasks constructed based on its initial responses. 
Echoing this approach, <cit.> introduce Chain-of-Verification empowers LLMs to self-assess through a sequence of self-generated verification questions, leading to progressively refined answers.
Both methods identify and correct ungrounded outputs autonomously, enhancing the reliability of responses.
<cit.> further this concept with Chain-of-Density, which allows LLMs to iteratively incorporate self-detected missing information into their previous outputs.
Together with Chain-of-SelfRevisions <cit.> and Chain-of-Feedback <cit.>, these frameworks exemplify how LLMs can utilize their own outputs for continuous self-improvement. 



 §.§ Chain-of-Models

Previous CoX methods have mostly been designed for a single LLM. 
Recognizing that different LLMs may have distinct specialties <cit.>, another line of work proposes constructing a chain of models to leverage distinct strengths of each model.
The Chain-of-Experts <cit.> exemplifies this collaborative strategy. 
It involves a consortium of expert LLMs that work in sequence, each contributing its specialized knowledge to build upon the reasoning developed by its predecessors. 
This method is particularly effective in addressing intricate problems in operation research, where the complexity often exceeds the processing capabilities of a single LLM.
Similarly, <cit.> deploy a chain of specialized LoRA (Low Rank Adaptation <cit.>) networks, each fine-tuned to effectively handle different domains of a broader problem. 
This tailored approach ensures that specific tasks benefit from the most relevant and effective expertise, enhancing overall efficiency and outcome accuracy.
In parallel, <cit.> have developed the Chain-of-Discussion, where multiple LLMs engage in a structured dialogue, critiquing and refining each other’s contributions before reaching a consensus in the final response. 
This process ensures that the synthesized output is not only comprehensive but also critically evaluated from multiple perspectives.



§ CHAIN-OF-X TASKS

As presented in the previous section, the nodes of CoX can be of various forms, enabling their applications to extend beyond LLM reasoning. 
This section surveys existing CoX methods categorized by tasks, as shown in Figure <ref>.




 §.§ Multi-Modal Interaction

Although CoT was originally proposed for text generation, various CoX methods have been developed to tackle challenges in multi-modality.



  
Text-Image
In the realm of vision-language models, the synergy between textual and visual data is critical <cit.>.
CoX methods have been instrumental in enhancing this interplay. 
For instance, Chain-of-InstructEditing <cit.> utilizes text-based instructions to guide the nuanced task of image editing, specifically for facial manipulations. 
This method ensures that image alterations adhere closely to textual descriptions, enhancing the accuracy and relevance of the edits.
Similarly, Chain-of-Look <cit.> introduces a structured approach to visual entity recognition by constructing a visual semantic reasoning chain that mirrors the logical progression of CoT. 
This method facilitates deeper understanding and identification of visual elements through descriptive textual cues. 
Furthermore, Chain-of-QA <cit.> expands this approach into a dynamic dialogue between an LLM and a visual question-answering model, tackling complex queries with a combination of textual and visual analyses.
Additionally, Chain-of-Reasoning <cit.> and Chain-of-Manipulation <cit.> focus on refining the process of identifying and interpreting critical details within images. 
These methods systematically guide the model to focus on specific regions of an image, thereby improving the model’s visual reasoning ability for more precise responses.





  
Text-Table
The challenges of complex tabular data manipulation have also been studied using CoX methods.
Chain-of-Command <cit.>, for example, provides LLMs with a sequence of pre-defined commands, guiding them through the accurate manipulation of tables. 
This structured guidance helps prevent errors that might arise from ambiguous or incorrect interpretations of the task requirements.
On a related note, Chain-of-Table <cit.> leverages tabular data as a part of the reasoning chain. 
Here, tables are not just data sources but act as evolving entities within the reasoning process, dynamically updating and refining themselves in response to the LLM’s queries and tasks. 
This iterative process allows the model to engage with the table more naturally and effectively, leading to a more nuanced understanding and manipulation of the contained information.





  
Text-Code
Code generation is another task that has benefited from the introduction of CoX methods <cit.>.

Chain-of-Code <cit.>, for example, tackles code generation by breaking down problems into a sequence of programs and then simulates code execution to solve the task to address the overarching task effectively.
Expanding on this idea, Chain-of-Simulation <cit.> takes a granular approach by executing code line by line. 
In contrast, Chain-of-Repair <cit.> draws inspiration from traditional debugging processes, where feedback from compilers is used not just to identify but also to explain bugs, facilitating a deeper learning process for the LLM as it generates fixes.
Meanwhile, Chain-of-SelfRevisions <cit.> explores a creative reuse strategy, where snippets of code from previous tasks are recycled into new projects, enhancing efficiency and promoting a modular approach to code generation. 
Together, these methods underscore the versatility of CoX techniques in refining code generation tasks, highlighting their ability to adapt and respond to the intricacies of programming.



  
Text-Speech
Similarly, the field of speech generation has seen innovative applications of CoX methods.
Chain-of-Information <cit.>, for instance, enhances speech synthesis by methodically separating and then reassembling semantic and perceptual components, which allows for more nuanced and accurate speech output.
Another approach is the Chain-of-Modality <cit.>, which merges textual and vocal instructions to guide the speech generation process. 
This method not only enhances the quality of speech generation but also equips LLMs with the ability to handle conversational nuances, effectively bridging the gap between textual and speech data. 





 §.§ Factuality & Safety

Ensuring factual consistency and safety in LLM outputs has been critical <cit.>.
To make LLMs generate more factual and safer outputs, recent studies have explored the use of CoX methods in both hallucination reduction and alignment. 



  
Hallucination Reduction
LLMs have shown a propensity for generating hallucinations <cit.>.
Studies have explored the use of CoX methods to reduce hallucinations.
For example, Chain-of-NLI <cit.> utilizes a sequence of natural language inference problems derived from initial model outputs to guide systematic revisions, enhancing the factual accuracy of subsequent responses.
Similarly, Chain-of-Verification <cit.> prompts an LLM to generate and answer its own verification questions, enabling it to critically assess and refine its responses. 
Furthermore, recognizing the effectiveness of retrieval-augmented approaches in grounding responses with accurate information <cit.>, several CoX methods, e.g., Chain-of-Note <cit.>, Chain-of-Knowledge^a <cit.>, Chain-of-Action^b <cit.>, have been implemented to retrieve and integrate domain-specific knowledge at each step, effectively reducing the occurrence of incorrect or misleading information.




  
Alignment
Aligning LLMs with human preferences is another critical area where CoX methods have shown promising results <cit.>.
To enhance LLMs' understanding of human preferences, Chain-of-Hindsight <cit.> transforms them into a sequence of natural language feedback for fine-tuning.
Leveraging the language comprehension capabilities of LLMs, Chain-of-Hindsight achieves superior alignment performance compared to previous methods like RLHF <cit.>.
Meanwhile, Chain-of-Utterance prompting <cit.> has been proposed for LLM red-teaming, establishing a jailbreaking conversation between a harmful LLM and a helpful but unsafe LLM.
The harmful questions gathered through Chain-of-Utterances are utilized to create the HarmfulQA dataset, which serves as a basis for further safety alignment efforts <cit.>.
By integrating these methods, CoX frameworks not only enhance the immediate utility of LLMs but also contribute to broader efforts in developing AI systems that are both effective and ethically responsible.



 §.§ Multi-Step Reasoning

Reasoning has been a widely studied topic, particularly multi-step reasoning tasks that demand a robust understanding of context and logic <cit.>.
The sequential nature of CoX methods makes them ideally suited for this task.
For instance, Chain-of-Knowledge^b <cit.> elicits explicit knowledge evidence at each step, thereby improving LLMs' performance in various reasoning tasks.

Meanwhile, Chain-of-Feedback <cit.> revises initial incorrect reasoning steps by breaking them down into smaller, individual tasks for more grounded reasoning.
Other specialized reasoning tasks include rule-based reasoning <cit.>, database reasoning <cit.>, legal reasoning <cit.>, user behavioral reasoning <cit.>, structure and graph reasoning <cit.>, as well as reasoning for text summarization <cit.> and machine translation <cit.>.
Through these varied applications, CoX methods demonstrate their ability to decompose complex tasks into manageable steps, enhancing LLMs' ability to process and analyze information effectively.



 §.§ Instruction Following

Instruction following, as a celebrated abilities of LLMs, enables humans to provide explicit guidance for various tasks <cit.>.
The evolution of CoX methods has also led to various approaches for enhancing this feature.
Chain-of-Task <cit.>, for instance, offers a structured method where each instruction consists of intermediate atomic tasks, specifically curated to fine-tune an e-commerce LLM's responses to better meet customer needs. 
Extending this concept, Chain-of-Instructions <cit.> introduces a compositional approach where each output feeds directly into the next, creating a continuous loop of task-specific tuning that refines the LLM's task handling progressively.
For applications in speech generation, Chain-of-Modality <cit.> constructs fine-tuning sequences with concatenated textual and speech instructions. 
Furthermore, Chain-of-LoRA <cit.> uses LoRA networks to specialize instruction handling, optimizing performances across varied tasks by tailoring instruction tuning processes to each LoRA. 
These developments underscore how CoX methods can improve the instruction-following capabilities of LLMs, enabling them to understand and execute tasks with more clarity.



 §.§ LLMs as Agents

With the strong planning abilities, LLMs have been utilized as agents across a wide range of tasks <cit.>.
CoX methods have been explored to further boost the planning abilities of LLM-based agents.
In this vein, Chain-of-Action^a <cit.> and Chain-of-ActionThought <cit.> utilize a series of planned actions to guide agent decision-making, ensuring each step is informed by the previous one. 
While in games like StarCraft II, Chain-of-Summarization <cit.> employs LLMs to summarize past observations to suggest future strategies.
Chain-of-3DThought <cit.> further utilizes LLM agents to compose objects in images through trial and error within a 3D simulation environment.
LLMs also serve as planners in human-scene interaction tasks with Chain-of-Contacts <cit.>, and in tool using tasks with Chain-of-Abstraction <cit.>.
CoX methods have also been applied to multi-agent settings, such as Chain-of-Experts <cit.> and Chain-of-Discussion <cit.>. 
These methods highlights the integration of CoX methods in enhancing the multi-dimensional abilities of LLMs as autonomous and collaborative agents.



 §.§ Evaluation Tools

Evaluating LLMs has become increasingly challenging as they grow more sophisticated <cit.>, making CoX methods a valuable asset for evaluation purposes.
Chain-of-Utterances prompting <cit.> is a prime example of how CoX methods can illuminate specific areas of concern, such as safety issues in scenarios where LLMs interact with potentially harmful models. 
This method uncovers vulnerable conversations that could lead to LLM jailbreaking, providing essential insights into the robustness of LLM safety.
Besides, Chain-of-Feedback <cit.> method has demonstrated the impact of prompts on LLM performance. 
By repeatedly providing LLMs with non-informative prompts like “make another attempt”, researchers have observed a gradual decrease in the quality of responses. 
In visual reasoning, the Chain-of-Images <cit.> introduces a benchmark involving a sequence of images designed to progressively assess the LLM’s reasoning ability. 
It provides a robust tool for measuring the model's capabilities in interpreting visual data.


These CoX methods underscore the importance of nuanced evaluation for more thorough assessments of LLMs.


§ FUTURE DIRECTIONS


While LLMs have demonstrated remarkable abilities in step-by-step problem-solving for various tasks, several challenges remain to be addressed.





  
Causal Analysis on Intermediates
Existing works generally focus on improving task-specific generative results. However, understanding and explaining the underlying mechanisms of LLM reasoning is also essential in realistic scenarios.
For example, <cit.> show that LLMs may skip rational steps when generating final results. <cit.> observe a performance gain from CoT even with invalid rationales. These observations indicate the value of a causal analysis on how intermediate steps truly affect the final results.




  
Reducing Inference Cost
A chain leading to the final node of generation often requires multiple sequential inference steps, which are computationally heavy and time-consuming, especially with LLMs.
It would be interesting if future research could reduce the length of CoX chains while maintaining the quality of generation.
For example, it would be worth studying whether the intermediate nodes of CoX could be executed in parallel or jointly within a single inference step.





  
Knowledge Distillation
The knowledge elicited by the intermediate nodes of CoX contains fine-grained task instructions, which can benefit the training of smaller student models when using a teacher LLM for knowledge distillation.

<cit.> and <cit.> have shown that the student model can effectively learn from the rationales of CoT generated by an LLM.

Nonetheless, it remains an open question whether the intermediate nodes from broader CoX methods are equally informative in inspiring student learning.





  
End-to-End Fine-tuning
One drawback of CoX is that it does not follow an end-to-end paradigm; i.e., generation errors may accumulate along the chain when self-correction <cit.> is not enforced. 
Future research can explore fine-tuning LLMs with CoX prompting and penalizing errors from the final output. By reducing the generation errors end-to-end, we expect this will improve the quality of both the intermediate and final nodes in CoX.













§ CONCLUSION

This survey explored Chain-of-X methods, building upon the concept of Chain-of-Thought. 
By categorizing them based on nodes and tasks, we provide a comprehensive overview that highlights the potential of CoX in enhancing LLM capabilities and opens new avenues for future research. 
Through this survey, we aim to inspire further exploration in a deeper understanding and more creative use of CoX paradigms for LLMs.






















§ TAXONOMIES OF NODES AND TASKS

We present in Figure <ref> the complete version of Figure <ref> on Chain-of-X taxonomies categorized by nodes and tasks.



