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 (e.g., mathematical, causal) reasoning tasks. Our cascade pipeline follows the intuition that simpler questions can be addressed by a weaker but more affordable LLM, whereas only the most challenging questions necessitate the stronger and more expensive LLM. To realize this decision-making, we consider the "answer consistency" of the weaker LLM as a signal of the question difficulty and propose several methods for answering sampling and consistency checking, including one leveraging a mixture of two thought representations (i.e., Chain-of-Thought and Program-of-Thought). Through experiments on six reasoning benchmark datasets, with GPT-3.5-turbo and GPT-4 being the weaker and stronger LLMs, respectively, our cascade pipeline demonstrates comparable performance but reduces about 60% of the cost compared with fully using the stronger LLM.