Solving for X and Beyond: Can Large Language Models Solve Complex Math Problems with More-Than-Two Unknowns?

TL;DR

This paper introduces BeyondX, a new benchmark with multi-unknown math problems, revealing current LLMs struggle with complexity, and proposes a Formulate-and-Solve prompting strategy to improve their performance.

Contribution

The paper presents BeyondX, a novel multi-unknown math problem benchmark, and introduces the Formulate-and-Solve strategy to enhance LLM reasoning on complex problems.

Findings

LLMs' performance drops up to 70% with more unknowns

Formulate-and-Solve improves LLM accuracy on BeyondX

BeyondX reveals limitations of current LLM reasoning capabilities

Abstract

Large Language Models (LLMs) have demonstrated remarkable performance in solving math problems, a hallmark of human intelligence. Despite high success rates on current benchmarks; however, these often feature simple problems with only one or two unknowns, which do not sufficiently challenge their reasoning capacities. This paper introduces a novel benchmark, BeyondX, designed to address these limitations by incorporating problems with multiple unknowns. Recognizing the challenges in proposing multi-unknown problems from scratch, we developed BeyondX using an innovative automated pipeline that progressively increases complexity by expanding the number of unknowns in simpler problems. Empirical study on BeyondX reveals that the performance of existing LLMs, even those fine-tuned specifically on math tasks, significantly decreases as the number of unknowns increases - with a performance drop of up to 70\% observed in GPT-4. To tackle these challenges, we propose the Formulate-and-Solve strategy, a generalized prompting approach that effectively handles problems with an arbitrary number of unknowns. Our findings reveal that this strategy not only enhances LLM performance on the BeyondX benchmark but also provides deeper insights into the computational limits of LLMs when faced with more complex mathematical challenges.