# Chain of Methodologies: Scaling Test Time Computation without Training

arXiv: https://arxiv.org/abs/2506.06982 · HTML: https://mlsanity.com/paper/2506.06982/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 8 Jun 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 23 of 23)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Interleaving Retrieval with Chain-of-Thought Reasoning for Knowledge-Intensive Multi-Step Questions](https://mlsanity.com/paper/2212.10509/) (2022)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [Marco-o1: Towards Open Reasoning Models for Open-Ended Solutions](https://mlsanity.com/paper/2411.14405/) (2024)
- [Mutual Reasoning Makes Smaller LLMs Stronger Problem-Solvers](https://mlsanity.com/paper/2408.06195/) (2024)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)
- [Boosting Language Models Reasoning with Chain-of-Knowledge Prompting](https://mlsanity.com/paper/2306.06427/) (2023)
- [Iteratively Prompt Pre-trained Language Models for Chain of Thought](https://mlsanity.com/paper/2203.08383/) (2022)
- [Metacognitive Prompting Improves Understanding in Large Language Models](https://mlsanity.com/paper/2308.05342/) (2023)
- [Disentangling Memory and Reasoning Ability in Large Language Models](https://mlsanity.com/paper/2411.13504/) (2024)
- [Probabilistic Tree-of-thought Reasoning for Answering Knowledge-intensive Complex Questions](https://mlsanity.com/paper/2311.13982/) (2023)
- [IAG: Induction-Augmented Generation Framework for Answering Reasoning Questions](https://mlsanity.com/paper/2311.18397/) (2023)
- [Action Inference by Maximising Evidence: Zero-Shot Imitation from Observation with World Models](https://mlsanity.com/paper/2312.02019/) (2023)

## Abstract (arXiv)

Large Language Models (LLMs) often struggle with complex reasoning tasks due to insufficient in-depth insights in their training data, which are typically absent in publicly available documents. This paper introduces the Chain of Methodologies (CoM), an innovative and intuitive prompting framework that enhances structured thinking by integrating human methodological insights, enabling LLMs to tackle complex tasks with extended reasoning. CoM leverages the metacognitive abilities of advanced LLMs, activating systematic reasoning throught user-defined methodologies without explicit fine-tuning. Experiments show that CoM surpasses competitive baselines, demonstrating the potential of training-free prompting methods as robust solutions for complex reasoning tasks and bridging the gap toward human-level reasoning through human-like methodological insights.