My team at Pareto.ai has been trying to understand LLM's potential for metacognition. As it turns out, they don't tend to have it beyond what they appear to have memorized awareness of from pre-training.
Check out the details here: pareto.ai/blog/llm-met...
pareto.ai
LLM Metacognition: Shared and Shallow?
Across 19 frontier models, metacognitive confidence on question and answer tasks tracks a shared difficulty heuristic with only a weak relationship to actual performance.