Siyuan Guo

Aniket Didolkar, Anirudh Goyal, Nan Rosemary Ke et al. · mila

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.

Siyuan Guo, Aniket Didolkar, Nan Rosemary Ke et al. · mila

We are beginning to see progress in language model assisted scientific discovery. Motivated by the use of LLMs as a general scientific assistant, this paper assesses the domain knowledge of LLMs through its understanding of different mathematical skills required to solve problems. In particular, we look at not just what the pre-trained model already knows, but how it learned to learn from information during in-context learning or instruction-tuning through exploiting the complex knowledge structure within mathematics. Motivated by the Neural Tangent Kernel (NTK), we propose \textit{NTKEval} to assess changes in LLM's probability distribution via training on different kinds of math data. Our systematic analysis finds evidence of domain understanding during in-context learning. By contrast, certain instruction-tuning leads to similar performance changes irrespective of training on different data, suggesting a lack of domain understanding across different skills.