Don't Trust: Verify - Grounding LLM Quantitative Reasoning with Autoformalization

Core Concepts

Leveraging autoformalization to improve LLM quantitative reasoning.

Abstract

This paper discusses the use of autoformalization to enhance large language models' (LLMs) ability to solve mathematical quantitative reasoning problems. By translating informal mathematical statements into formal languages, LLMs can be verified automatically for internal consistency, leading to improved accuracy in identifying correct answers. The method, known as Don't Trust: Verify (DTV), outperforms traditional methods like majority voting, showcasing consistent improvements across different datasets and model sizes. Directory: Introduction LLMs' advancements in quantitative reasoning tasks. Need for improved heuristics to identify correct answers. Autoformalization Translating informal mathematical statements into formal languages. Leveraging LLMs' capabilities for autoformalization. Verification Process Using automated theorem provers to verify formal solutions. Importance of internal consistency in formal reasoning. Experiments Evaluation on GSM8K, MATH, and MultiArith datasets. Comparison with baselines and performance improvements. Ablation Study Impact of solution formalization and statement filters on performance. Qualitative Analysis Case studies showcasing successful formalization and verification. Limitations and Future Work Scope limitations of current formal theorem proving environments. Potential improvements through reinforcement learning and effective filters.

Stats

Large language models (LLMs) are becoming increasingly capable of solving mathematical quantitative reasoning problems. Autoformalization can automatically reject solutions inconsistent with formalized versions. DTV outperforms vanilla majority voting by more than 12% on GSM8K.

Quotes

"The product of the two numbers is the product of their LCM and their GCD: 3720 * 8 = 29760." - Informal Solution "Since one of the numbers is 120, we can divide this product by 120 to obtain the other number: 29760 / 120 = 248." - Informal Solution

Key Insights Distilled From

Don't Trust

by Jin Peng Zho... at arxiv.org 03-28-2024

https://arxiv.org/pdf/2403.18120.pdf

Deeper Inquiries

How can autoformalization be further improved to handle more complex mathematical statements?

Autoformalization can be enhanced to handle more complex mathematical statements by incorporating more sophisticated language models that have been specifically trained on formal mathematics. These models can have a deeper understanding of mathematical concepts and structures, enabling them to generate more accurate and detailed formalizations. Additionally, fine-tuning the language models on a larger and more diverse set of formal mathematical data can improve their ability to handle complex statements. Implementing specialized architectures or techniques that focus on capturing the intricacies of mathematical reasoning can also enhance the performance of autoformalization for complex statements.

What are the implications of DTV's success for the future development of large language models?

The success of DTV has significant implications for the future development of large language models. It showcases the potential of leveraging autoformalization to enhance the reasoning capabilities of these models, particularly in the domain of quantitative reasoning. By integrating formal theorem proving environments into the workflow of language models, DTV demonstrates a novel approach to improving the accuracy and reliability of their outputs. This success highlights the importance of incorporating structured and formalized knowledge into the training and inference processes of large language models, paving the way for more robust and trustworthy AI systems in various applications.

How can the concept of autoformalization be applied to other domains beyond quantitative reasoning?

The concept of autoformalization can be applied to other domains beyond quantitative reasoning by adapting the methodology to suit the specific requirements of different fields. For example, in natural language processing tasks, autoformalization can be used to convert informal text into formal representations, enabling more precise and structured analysis of language data. In scientific research, autoformalization can assist in translating research findings and hypotheses into formal proofs or models, facilitating the validation and verification of scientific claims. Moreover, in legal and regulatory compliance, autoformalization can aid in converting legal documents and regulations into formal logic, ensuring consistency and accuracy in legal interpretations. By customizing the autoformalization process to the unique characteristics of each domain, the concept can be effectively applied to a wide range of applications beyond quantitative reasoning.