Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving

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.