  Large Language Models (LLMs), combined with program-based solving techniques,
are increasingly demonstrating proficiency in mathematical reasoning. For
example, closed-source models such as OpenAI GPT-4 and Claude show excellent
results in solving math word problems. However, progress in math word
problem-solving for open-source LLMs is limited, and the challenges these
models face are not well-studied. In this paper, we study the performance of
strong open-source LLMs, including Llama 2 (7B), Code Llama (7B), and Mistral
(7B) on math word problems using program-based solving techniques.
Specifically, we analyze the outputs of these models when applied to math word
problems and identify a category of problems that pose a significant challenge,
particularly those involving quantities spanning multiple units. To address
this issue, we propose a systematic approach by defining the units for each
quantity and ensuring the consistency of these units during mathematical
operations. We developed Unit Consistency Programs (UCPs), an annotated dataset
of math word problems, each paired with programs containing unit specifications
and unit verification routines. We fine-tuned Llama 2 (7B), Code Llama (7B),
and Mistral (7B) models with UCPs to produce theirVerityMath variants. Our
findings indicate that our approach, which incorporates unit consistency,
currently slightly underperforms compared to an approach that does not. To
understand the reasons behind this, we conduct an in-depth error analysis and
suggest options for future improvements. Our code and dataset are available at
https://github.com/vernontoh/VerityMath.
