# Exploring Equation as a Better Intermediate Meaning Representation for Numerical Reasoning

arXiv: https://arxiv.org/abs/2308.10585 · HTML: https://mlsanity.com/paper/2308.10585/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 41 references that are in the map.
- First posted on arXiv 21 Aug 2023.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 30 of 32)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [FinQA: A Dataset of Numerical Reasoning over Financial Data](https://mlsanity.com/paper/2109.00122/) (2021)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [Progressive-Hint Prompting Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2304.09797/) (2023)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [Multi-hop Reading Comprehension through Question Decomposition and Rescoring](https://mlsanity.com/paper/1906.02916/) (2019)
- [Goat: Fine-tuned LLaMA Outperforms GPT-4 on Arithmetic Tasks](https://mlsanity.com/paper/2305.14201/) (2023)
- [Representing Numbers in NLP: a Survey and a Vision](https://mlsanity.com/paper/2103.13136/) (2021)
- [Natural SQL: Making SQL Easier to Infer from Natural Language Specifications](https://mlsanity.com/paper/2109.05153/) (2021)
- [A Survey on Semantic Parsing](https://mlsanity.com/paper/1812.00978/) (2018)
- [Tab-CoT: Zero-shot Tabular Chain of Thought](https://mlsanity.com/paper/2305.17812/) (2023)
- [N-LTP: An Open-source Neural Language Technology Platform for Chinese](https://mlsanity.com/paper/2009.11616/) (2020)
- [Reasoning in Large Language Models Through Symbolic Math Word Problems](https://mlsanity.com/paper/2308.01906/) (2023)
- [GraphQ IR: Unifying the Semantic Parsing of Graph Query Languages with One Intermediate Representation](https://mlsanity.com/paper/2205.12078/) (2022)
- [Leveraging Training Data in Few-Shot Prompting for Numerical Reasoning](https://mlsanity.com/paper/2305.18170/) (2023)
- [Meta-Reasoning: Semantics-Symbol Deconstruction for Large Language Models](https://mlsanity.com/paper/2306.17820/) (2023)

## Built on by (most cited first, 7 of 7)

- [CoMAT: Chain of Mathematically Annotated Thought Improves Mathematical Reasoning](https://mlsanity.com/paper/2410.10336/) (2024)
- [Could Thinking Multilingually Empower LLM Reasoning?](https://mlsanity.com/paper/2504.11833/) (2025)
- [A Theory for Length Generalization in Learning to Reason](https://mlsanity.com/paper/2404.00560/) (2024)
- [Python is Not Always the Best Choice: Embracing Multilingual Program of Thoughts](https://mlsanity.com/paper/2402.10691/) (2024)
- [Conditions for Length Generalization in Learning Reasoning Skills](https://mlsanity.com/paper/2311.16173/) (2023)
- [DAC: Decomposed Automation Correction for Text-to-SQL](https://mlsanity.com/paper/2408.08779/) (2024)
- [Solving Math Word Problems Using Estimation Verification and Equation Generation](https://mlsanity.com/paper/2509.18565/) (2025)

## Abstract (arXiv)

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 Reasontextbfing 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/BridgeforNumericalReasoning.