Decoding Intelligence: A Framework for Certifying Knowledge Comprehension in LLMs

Knowledge comprehension capability is an important aspect of human intelligence. As Large Language Models (LLMs) are being envisioned as superhuman agents, it is crucial for them to be proficient at knowledge comprehension. However, existing benchmarking studies do not provide consistent, generalizable, and formal guarantees on the knowledge comprehension capabilities of LLMs. In this work, we propose the first framework to certify knowledge comprehension in LLMs with formal probabilistic guarantees. Our certificates are quantitative -- they consist of high-confidence, tight bounds on the probability that a target LLM gives the correct answer on any knowledge comprehension prompt sampled from a distribution. We design and certify novel specifications that precisely represent distributions of knowledge comprehension prompts leveraging knowledge graphs. We certify SOTA LLMs for specifications over the Wikidata5m knowledge graph. We find that the knowledge comprehension capability improves significantly with scaling the size of the models.