Reasoning in Large Language Models Through Symbolic Math Word Problems

TL;DR

This paper investigates the reasoning capabilities of large language models on math word problems by using symbolic representations, proposing self-prompting to improve interpretability and accuracy, and releasing a new symbolic dataset.

Contribution

It introduces a symbolic version of the SVAMP dataset and demonstrates that self-prompting enhances reasoning accuracy and interpretability in LLMs.

Findings

Self-prompting improves symbolic reasoning accuracy beyond numeric accuracy.

GPT-3 davinci-002 performs well on symbolic math problems in zero-shot settings.

The SVAMP_Sym dataset is released for future research.

Abstract

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.