When Not to Answer: Evaluating Prompts on GPT Models for Effective Abstention in Unanswerable Math Word Problems

TL;DR

This paper evaluates GPT models' ability to abstain from answering unanswerable math problems, revealing significant hallucination issues and emphasizing the need for improved uncertainty management in complex reasoning tasks.

Contribution

It introduces evaluation metrics for GPT abstention on unanswerable math problems and highlights the gaps in current models' handling of uncertainty and complex reasoning.

Findings

GPT models often hallucinate on unanswerable problems

Current prompts are insufficient for effective abstention

Need for improved models to manage uncertainty in math reasoning

Abstract

Large language models (LLMs) are increasingly relied upon to solve complex mathematical word problems. However, being susceptible to hallucination, they may generate inaccurate results when presented with unanswerable questions, raising concerns about their potential harm. While GPT models are now widely used and trusted, the exploration of how they can effectively abstain from answering unanswerable math problems and the enhancement of their abstention capabilities has not been rigorously investigated. In this paper, we investigate whether GPTs can appropriately respond to unanswerable math word problems by applying prompts typically used in solvable mathematical scenarios. Our experiments utilize the Unanswerable Word Math Problem (UWMP) dataset, directly leveraging GPT model APIs. Evaluation metrics are introduced, which integrate three key factors: abstention, correctness and confidence. Our findings reveal critical gaps in GPT models and the hallucination it suffers from for unsolvable problems, highlighting the need for improved models capable of better managing uncertainty and complex reasoning in math word problem-solving contexts.