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Reasoning in Large Language Models Through Symbolic Math Word Problems

Paper · 2023 · Vedant Gaur and Nikunj Saunshi

Summary

The paper asks how to judge whether large language models actually reason when they solve math word problems, rather than only checking whether the final answer is correct. The authors argue that a symbolic expression is a compact explanation of a numeric answer that can be checked automatically. They convert SVAMP into SVAMP-Sym by replacing every number with a variable, which needs no manual annotation. They then test GPT-3 davinci-002 zero-shot, with and without CoT prompting, using a pipeline of answer extraction, rule-based filtering, and equivalence checking.

Besides accuracy, they measure alignment: whether the model's symbolic expression evaluates to its own numeric answer. Solving the symbolic version independently gives decent accuracy but weak alignment. They therefore propose self-prompting, which places the model's numeric solution in context before the symbolic question and adds an extra alignment prompt when the answers disagree. This raises alignment substantially. It also gives higher accuracy than either the numeric or symbolic runs alone, which suggests an ensembling effect. The approach points toward explanations that are interpretable and verifiable at scale.

Key points

  • SVAMP-Sym is released on GitHub (vedantgaur/Symbolic-MWP-Reasoning). Experiments use 150 of SVAMP's 1000 problems, each run 5 times, with temperature 0 and a 256-token limit.
  • Zero-shot accuracy with GPT-3 davinci-002:
    • Numeric: 65.6% vanilla and 68.9% with CoT.
    • Symbolic, using variables (w,x,y,z): 59.7% vanilla and 64.2% with CoT.
    • Variables (i,j,k,l) score somewhat lower than the other variable sets.
  • Answer equivalence is decided by comparing two expressions on 20 random variable assignments. Removing the filtering step lowers symbolic accuracy by 12–14 points, versus 4–5 points for numeric accuracy.
  • Raw symbolic outputs agree with the numeric answers only about 51–53% of the time.
  • Self-prompting with the alignment prompt (SP+AP, CoT) lifts alignment to 74% and symbolic accuracy to 71.7%. It also makes the complete numeric and symbolic outputs more alike, as measured by BLEU and Levenshtein scores.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🏢GoogleMountain View · United States533 works · 443,884 citations🎓Princeton UniversityPrinceton · United States137 works · 53,849 citations

 Fields, topics and concepts

📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 19,503 worksArtificial Intelligence · 18,805 worksArts and Humanities · 17,959 worksLanguage and Linguistics · 17,789 worksComputer Vision and Pattern Recognition · 3,621 works

🧭 Topics 2Research subjects and languages the work is about.Language models & pretraining · 4,145 worksReasoning · 1,948 works

Cite

Cite as Vedant Gaur and Nikunj Saunshi. 2023. Reasoning in Large Language Models Through Symbolic Math Word Problems. Findings of the Association for Computational Linguistics: ACL 2023.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2023.findings-acl.364 · arXiv 2308.01906

@inproceedings{gaur2023reasoning,
  title = {{Reasoning in Large Language Models Through Symbolic Math Word Problems}},
  author = {Vedant Gaur and Nikunj Saunshi},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2023},
  year = {2023},
  doi = {10.18653/v1/2023.findings-acl.364},
  eprint = {2308.01906},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.18653/v1/2023.findings-acl.364}
}

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