NUMCoT: Numerals and Units of Measurement in Chain-of-Thought Reasoning using Large Language Models

TL;DR

This paper investigates how large language models handle numerals and measurement units in reasoning tasks, revealing their difficulties with conversions and the impact of minor perturbations on problem complexity.

Contribution

It introduces datasets with perturbations for numerals and units, analyzes LLM reasoning processes, and highlights challenges in numeral and measurement conversions.

Findings

LLMs struggle with numeral and measurement conversions.

Minor perturbations significantly affect LLM reasoning performance.

Annotated ancient Chinese math problems reveal additional challenges.

Abstract

Numeral systems and units of measurement are two conjoined topics in activities of human beings and have mutual effects with the languages expressing them. Currently, the evaluation of Large Language Models (LLMs) often involves mathematical reasoning, yet little attention is given to how minor changes in numbers or units can drastically alter the complexity of problems and the performance of LLMs. In this paper, we scrutinize existing LLMs on processing of numerals and units of measurement by constructing datasets with perturbations. We first anatomize the reasoning of math word problems to different sub-procedures like numeral conversions from language to numbers and measurement conversions based on units. Then we further annotate math word problems from ancient Chinese arithmetic works which are challenging in numerals and units of measurement. Experiments on perturbed datasets demonstrate that LLMs still encounter difficulties in handling numeral and measurement conversions.