Chain of Methodologies: Scaling Test Time Computation without Training

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 trainingfree prompting methods as robust solutions for complex reasoning tasks and bridging the gap toward human-level reasoning through humanlike methodological insights.