Learning Beyond Pattern Matching? Assaying Mathematical Understanding in LLMs

• URL: http://arxiv.org/abs/2405.15485v1
• Date: Fri, 24 May 2024 12:04:54 GMT
• Title: Learning Beyond Pattern Matching? Assaying Mathematical Understanding in LLMs
• Authors: Siyuan Guo, Aniket Didolkar, Nan Rosemary Ke, Anirudh Goyal, Ferenc Huszár, Bernhard Schölkopf,
• Abstract summary: This paper assesses the domain knowledge of LLMs through its understanding of different mathematical skills required to solve problems. Motivated by the use of LLMs as a general scientific assistant, we propose textitNTKEval to assess changes in LLM's probability distribution. Our systematic analysis finds evidence of domain understanding during in-context learning. Certain instruction-tuning leads to similar performance changes irrespective of training on different data, suggesting a lack of domain understanding across different skills.
• Score: 58.09253149867228
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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