Chain of Methodologies: Scaling Test Time Computation without Training (2025)

Abstract: Large Language Models (LLMs) often struggle with complex reasoning tasks due to insufficient in-depth insights in their training data, which are frequently absent in publicly available documents. This paper introduces the Chain of Methodologies (CoM), a simple and innovative iterative prompting framework designed to build structured reasoning processes by injecting human methodological insights, thereby enabling LLMs to perform long and effective reasoning for complex tasks. Assuming that LLMs possess certain metacognitive abilities, CoM leverages user-defined methodologies to stimulate the cognitive insights that LLMs have learned implicitly from training data. Experimental results indicate that CoM outperforms competitive baselines, highlighting the potential of training-free prompting methods as general solutions for complex reasoning tasks and the possibility of incorporating human-like methodological insights to bridge the gap to human-level reasoning.

## introduction recently, openai's o1 @xcite showcases the possibility of using a long chain of thoughts to improve the reasoning ability of large language models (llms). during these long thoughts, openai's o1 displays high-level cognitive abilities, such as problem decomposition, error recognition, and correction, which constantly steer the thoughts in the right direction. openai confers o1 with such abilities through reinforcement learning. this paper explores whether llms can achieve similar self-guiding abilities for long, structured reasoning across domains using only prompts, without instruction fine-tuning. this is a challenging problem: while fine-tuning with large datasets can broadly improve instruction-following, conventional prompts are typically limited to specific tasks with few-shot examples due to constraints like context length and information extraction accuracy. as a result, pure prompting methods are rarely used for cross-domain tasks, despite their advantages-low cost, rapid deployment, high sample efficiency, and avoidance of catastrophic forgetting or data bias. our work is inspired by prior research on metacognitive knowledge in llms, which refers to the ability to reason about one's own reasoning processes. pedagogical studies show that enhancing metacognitive knowledge improves reasoning in humans, and similar benefits have been observed in llms through prompts encouraging introspection and self-reflection @xcite . besides, microsoft's @xcite uses system prompts like "do not hallucinate" to reduce hallucination, while @xcite shows im-proved mathematical reasoning when llms identify required skills to retrieve relevant examples. these findings provide both intuitive and empirical support for our approach. we propose the chain of methodologies (com), an intuitive task-agnostic prompting technique designed to enable cross-domain self-guided reasoning without instruction fine-tuning. com uses methodology as catalysts to stimulate llms to generate the next reasoning step based on the reasoning history. while llms often struggle with complex reasoning tasks due to insufficient in-depth insights between problems and their respective solutions in the training data, com bridges this gap and enables smooth transitions from a problem to its solution by inserting a methodological analysis before each solution step. this leverages the metacognitive knowledge of llms to select or generate methodologies that justify or explain the next steps. com features two key components: (1) a list of methodologies formatted in our "when-what" format, which facilitates selection based on the reasoning history and connects it to the next reasoning step, and (2) a methodology-reasoning loop that iteratively selects the next methodology to guide reasoning along an extended and well-structured reasoning path. an example of com's interleaving methodology-selecting and reasoning path is illustrated in figure 1 . two examples of user-defined methodologies are listed in figure 3 . our contributions include the simple com framework and extensive experiments. com produces structured, explainable, and faithful reasoning paths. it is also highly extensible in that users can enhance the framework by modifying the list of methodologies in plain text. we evaluated our task-agnostic com framework on two types of representative and challenging tasks: mathematical reasoning and retrieval-augmented generation. experiments show that com outperforms competitive baselines on these tasks across diverse llms. ## related work prompting a significant body of work has explored various prompt designs to enhance the reasoning capabilities of llms. notable approaches include chain-of-thought @xcite , leastto-most @xcite , self-consistency @xcite , and tree-of-thoughts @xcite . methods to enhance problem-specific performance, include question rephrasing, dividing subtasks, verification, symbolic grounding @xcite @xcite @xcite , factuality and faithfulness verification for reasoning chains @xcite , as well as explicit separation of knowledge retrieval and reasoning steps to organize decision-making @xcite . iterative prompting prior research has also investigated iterative prompting methods to struc-ture reasoning processes. examples include self-refine @xcite , ircot @xcite , icap @xcite , metagpt @xcite , and chain of ideas @xcite . these approaches typically rely on predefined, hardcoded actions to guide reasoning. in contrast, our work introduces a task-agnostic framework that leverages the metacognitive abilities of llms to dynamically select methodologies based on reasoning history. furthermore, while prior work focuses on generating the next reasoning step, our approach adopts a justification-before-action style, where the model introspectively justifies why a specific methodology is needed before executing it. this mirrors human metacognitive processes and distinguishes our work from implicit contextaware token generation. metacognition-based several contemporary works are closely related to our approach. buffer of thoughts @xcite derives high-level guidelines from previously completed tasks and stores them in a buffer for future reuse, enabling learning from experience and improving efficiency by distilling level-2 slow thinking into level-1 fast thinking. however, unlike our work, its high-level guidelines contain problem-specific reasoning chains or code templates tailored to particular tasks, such as complex multi-query tasks. skill-based @xcite explores the metacognitive capabilities of llms in mathematical problem-solving by labeling questions with corresponding skills, clustering them to reduce redundancy, and retrieving skill-relevant examples for in-context learning during inference. induction-augmented generation @xcite identifies key concepts in questions and uses inductive prompting templates to extract their close concepts and common attributes, facilitating more accurate reasoning processes. search-based rstar @xcite introduces a self-play mutual reasoning approach that significantly improves the reasoning capabilities of small language models without fine-tuning. this method employs a costly monte carlo tree search (mcts) with a set of five reasoning-inducing prompts. training-based finally, training-based methods have been developed to enable llms to handle long chains of thought. for example, star @xcite demonstrates that iterative training on reasoning histories leading to correct answers enables models to solve increasingly complex problems. similarly, @xcite rest-mcts @xcite integrates process reward guidance with tree search mcts to collect higher-quality reasoning traces, while aflow (anonymous, 2024a) iteratively refines taskspecific workflows. these methods highlight the potential of training-based approaches but often require significant computational resources. ## conclusion and future work this paper enhances llms' reasoning capabilities for complex tasks by simulating metacognitive processes and leveraging user-defined methodologies, enabling effective navigation of complex reasoning tasks without extensive retraining. takeaways include: (1) llms exhibit latent metacognitive abilities that can be activated through structured, justification-driven prompting-eliminating the need for fine-tuning; and (2) generating explicit methodology justifications improves traceability and task comprehension, boosting zero-shot accuracy and cross-domain adaptation, which is often constrained by limited in-context examples.