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arXiv · 2407.00900

From Next-Token to Mathematics: The Learning Dynamics of Mathematical Reasoning in Language Models

Shubhra Mishra·Gabriel Poesia·Noah D. Goodman
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Abstract

Large Language Models (LLMs) solely trained on next-token prediction learn to solve a wide range of problems involving mathematical reasoning. But how does this ability evolve during training? We show the first analysis of how mathematical reasoning abilities of several open-weight LLMs develop during pre-training and post-training. To this end, we construct MathCAMPS, a synthetic dataset of novel mathematical reasoning problems grounded in 44 fine-grained skills taken from the Common Core curriculum from K to 8th grades. In one experiment, we show that mathematical skills are learned during pre-training in an order that measurably correlates with the human-designed curriculum, even though training data are randomly ordered. We also show a detailed analysis of which mathematical abilities benefit from instruction tuning, a widely used post-training method and, in contrast, which skills suffer. Our work paves the way for an empirical understanding of LLM training dynamics in relation to reasoning.

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Shubhra Mishra, Gabriel Poesia, Noah D. Goodman. 2024-07-01. From Next-Token to Mathematics: The Learning Dynamics of Mathematical Reasoning in Language Models. https://arxiv.org/abs/2407.00900

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