Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving
This work addresses the problem of enhancing LLM reasoning capabilities for researchers and practitioners by demonstrating that metacognitive-like skill labeling can boost performance in mathematical problem-solving, though it is incremental as it builds on existing prompting techniques.
The paper investigates whether large language models (LLMs) possess metacognitive knowledge by developing a prompt-guided method to assign and cluster skill labels to math problems, which when used to provide exemplars during problem-solving, improves accuracy on GSM8K and MATH datasets for several LLMs.
Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly possess some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.