  Quantities are distinct and critical components of texts that characterize
the magnitude properties of entities, providing a precise perspective for the
understanding of natural language, especially for reasoning tasks. In recent
years, there has been a flurry of research on reasoning tasks based on large
language models (LLMs), most of which solely focus on numerical values,
neglecting the dimensional concept of quantities with units despite its
importance. We argue that the concept of dimension is essential for precisely
understanding quantities and of great significance for LLMs to perform
quantitative reasoning. However, the lack of dimension knowledge and
quantity-related benchmarks has resulted in low performance of LLMs. Hence, we
present a framework to enhance the quantitative reasoning ability of language
models based on dimension perception. We first construct a dimensional unit
knowledge base (DimUnitKB) to address the knowledge gap in this area. We
propose a benchmark DimEval consisting of seven tasks of three categories to
probe and enhance the dimension perception skills of LLMs. To evaluate the
effectiveness of our methods, we propose a quantitative reasoning task and
conduct experiments. The experimental results show that our dimension
perception method dramatically improves accuracy (43.55%->50.67%) on
quantitative reasoning tasks compared to GPT-4.
