Large Language Model Cascades with Mixture of Thought Representations for Cost-Efficient Reasoning

Large language models (LLMs) such as GPT-4 have exhibited remarkable performance in a variety of tasks, but this strong performance often comes with the high expense of using paid API services. In this paper, we are motivated to study building an LLM cascade to save the cost of using LLMs, particularly for performing reasoning (e.g., mathematical, causal) tasks. Our cascade pipeline follows the intuition that simpler questions can be addressed by a weaker but more affordable LLM, whereas only the challenging questions necessitate the stronger and more expensive LLM. To realize this decision-making, we consider "answer consistency" of the weaker LLM as a signal of the question difficulty and propose several methods for the answer sampling and consistency checking, including one leveraging a mixture of two thought representations (i.e., Chain-of-Thought (Wei et al., 2022) and Program-of-Thought (Chen et al., 2022; Gao et al., 2023) ). Through experiments on six reasoning benchmark datasets, with GPT-3.5-turbo and GPT-4 being the weaker and stronger LLMs, respectively, we demonstrate that our proposed LLM cascades can achieve performance comparable to using solely the stronger LLM but require only 40% of its cost. Our codes are available at https://github.com/MurongYue/LLM_MoT_cascade .