Language Models, Grade-School Math, and the Hidden Reasoning Process
Keywords: linear probing, language model, grade math problems, logic following, reasoning
TL;DR: Probing reveals that LLMs develop some "level-2" reasoning skill beyond Humans on solving grade-school level math problems
Abstract: Recent advances in language models have demonstrated their capability to solve mathematical reasoning problems, achieving near-perfect accuracy on grade-school level math benchmarks like GSM8K. In this paper, we formally study how language models solve these problems. We design a series of controlled experiments to address several fundamental questions: (1) Can language models truly develop reasoning skills, or do they simply memorize templates? (2) What is the model's hidden (mental) reasoning process? (3) Do models solve math questions using skills similar to or different from humans? (4) Do models trained on GSM8K-like datasets develop reasoning skills beyond those necessary for solving GSM8K problems? (5) What mental process causes models to make reasoning mistakes? (6) How large or deep must a model be to effectively solve GSM8K-level math questions?
Our study uncovers many hidden mechanisms by which language models solve mathematical questions, providing insights that extend beyond current understandings of LLMs.
Primary Area: interpretability and explainable AI
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Submission Number: 13188
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