# Reasoning in Large Language Models Through Symbolic Math Word Problems

arXiv: https://arxiv.org/abs/2308.01906 · HTML: https://mlsanity.com/paper/2308.01906/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 11 of its 22 references that are in the map.
- First posted on arXiv 3 Aug 2023.

## Placed in

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

## Builds on (most cited first, 11 of 11)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Using DeepSpeed and Megatron to Train Megatron-Turing NLG 530B, A Large-Scale Generative Language Model](https://mlsanity.com/paper/2201.11990/) (2022)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)

## Built on by (most cited first, 16 of 16)

- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)
- [Cognitive Mirage: A Review of Hallucinations in Large Language Models](https://mlsanity.com/paper/2309.06794/) (2023)
- [Efficient Inference for Large Reasoning Models: A Survey](https://mlsanity.com/paper/2503.23077/) (2025)
- [Evaluating Mathematical Reasoning of Large Language Models: A Focus on Error Identification and Correction](https://mlsanity.com/paper/2406.00755/) (2024)
- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Teaching LLMs to Plan: Logical Chain-of-Thought Instruction Tuning for Symbolic Planning](https://mlsanity.com/paper/2509.13351/) (2025)
- [Cutting Through the Noise: Boosting LLM Performance on Math Word Problems](https://mlsanity.com/paper/2406.15444/) (2024)
- [MARS: Benchmarking the Metaphysical Reasoning Abilities of Language Models with a Multi-task Evaluation Dataset](https://mlsanity.com/paper/2406.02106/) (2024)
- [Neuro-Symbolic AI: Explainability, Challenges, and Future Trends](https://mlsanity.com/paper/2411.04383/) (2024)
- [Exploring Equation as a Better Intermediate Meaning Representation for Numerical Reasoning](https://mlsanity.com/paper/2308.10585/) (2023)
- [Fine-Grained and Thematic Evaluation of LLMs in Social Deduction Game](https://mlsanity.com/paper/2408.09946/) (2024)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)
- [Bridging the Gap: Representation Spaces in Neuro-Symbolic AI](https://mlsanity.com/paper/2411.04393/) (2024)
- [Transformers Can Learn Connectivity in Some Graphs but Not Others](https://mlsanity.com/paper/2509.22343/) (2025)
- [Understanding Large Language Models](https://mlsanity.com/paper/2607.01006/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have revolutionized NLP by solving downstream tasks with little to no labeled data. Despite their versatile abilities, the larger question of their ability to reason remains ill-understood. This paper addresses reasoning in math word problems (MWPs) by studying symbolic versions of the numeric problems, since a symbolic expression is a "concise explanation" of the numeric answer. We create and use a symbolic version of the SVAMP dataset and find that GPT-3's davinci-002 model also has good zero-shot accuracy on symbolic MWPs. To evaluate the faithfulness of the model's reasoning, we go beyond accuracy and additionally evaluate the alignment between the final answer and the outputted reasoning, which correspond to numeric and symbolic answers respectively for MWPs. We explore a self-prompting approach to encourage the symbolic reasoning to align with the numeric answer, thus equipping the LLM with the ability to provide a concise and verifiable reasoning and making it more interpretable. Surprisingly, self-prompting also improves the symbolic accuracy to be higher than both the numeric and symbolic accuracies, thus providing an ensembling effect. The SVAMP_Sym dataset will be released for future research on symbolic math problems.