We focus on the problem of fusing two or more heterogeneous large language models (LLMs) to leverage their complementary strengths. One of the challenges of model fusion is high computational load, specifically in fine-tuning or aligning vocabularies. To address this, we propose Cool-Fusion, a simple yet effective approach that fuses the knowledge of source LLMs, which does not require training. Unlike ensemble methods, Cool-Fusion is applicable to any set of source LLMs that have different vocabularies. To overcome the vocabulary discrepancies among LLMs, we ensemble LLMs on text level, allowing them to rerank the generated texts by each other with different granularities. Extensive experiments have been conducted across a variety of benchmark datasets. On GSM8K, Cool-Fusion increases accuracy from three strong source LLMs by a significant margin of 17.4%.

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.