Does GPT Really Get It? A Hierarchical Scale to Quantify Human vs AI's Understanding of Algorithms

As Large Language Models (LLMs) perform (and sometimes excel at) more and more complex cognitive tasks, a natural question is whether AI really understands. The study of understanding in LLMs is in its infancy, and the community has yet to incorporate well-trodden research in philosophy, psychology, and education. We initiate this, specifically focusing on understanding algorithms, and propose a hierarchy of levels of understanding. We use the hierarchy to design and conduct a study with human subjects (undergraduate and graduate students) as well as large language models (generations of GPT), revealing interesting similarities and differences. We expect that our rigorous criteria will be useful to keep track of AI's progress in such cognitive domains.