Exploring Equation as a Better Intermediate Meaning Representation for
  Numerical Reasoning
Dingzirui Wang Longxu Dou Wenbin Zhang Junyu Zeng Wanxiang Che
Numerical reasoning is vital for natural language processing models to
understand and process numerical information in real-world scenarios. Most
current methods first generate the Intermediate Meaning Representations (IMRs)
of questions and then generate answers. Current SOTA methods generate programs
as IMRs with large language models (LLMs). Intuitively, equations have fewer
restrictions and closer semantics to the question than programs, leading to
higher generation accuracy. However, current LLMs generate equations worse than
programs, where we assume that the equation data is rare in pre-training data
compared to programs. So in this paper, we try to use equations as IMRs to
solve the numerical reasoning task by addressing two problems: (1)
Theoretically, how to prove that the equation is an IMR with higher generation
accuracy than programs; (2) Empirically, how to improve the generation accuracy
of equations with LLMs. For the first problem, we propose and prove a
proposition to theoretically compare the generation accuracy of different IMRs.
For the second problem, we present a method called Boosting Numerical
Reason\textbfing by Decomposing the Generation of Equations (Bridge), which can
improve the accuracy of LLMs in generating equations as IMRs by reducing the
tendency of generating constant expressions and programs. Our method improves
the performance by 2.2%, 0.9%, and 1.7% on GSM8K, SVAMP, and Algebra datasets
compared to the previous state-of-the-art methods under the single reasoning
path setting. Our codes and prompts are released in
https://github.com/zirui-HIT/Bridge_for_Numerical_Reasoning.