More Capable, Less Faithful: A Multilingual Analysis of Mathematical (Un)Solvability Detection in LLMs

2026-08-31

AI Summary

研究通过构建多语言数学问题基准，分析大型语言模型的解题能力及信念表达，发现解题信念普遍跨语言存在，但资源丰富语言如英语的解题忠实度较低。

Abstract

Solvability detection is one of the most challenging aspects of mathematical reasoning for Large Language Models (LLMs). While prior work has studied this capability extensively, these analyses have been limited to English. Consequently, it remains unclear whether multilingual failures arise from differences in internal Solvability Belief or from language-dependent failures to express it. To address this gap, we introduce the first multilingual benchmark of paired solvable and unsolvable mathematical problems, extending ReliableMath to French and Greek. Using this, we train multilingual probes predicting Solvability Belief and analyze the solvability detection capabilities of state-of-the-art LLMs behaviorally, representationally, and in terms of faithfulness. We find that Solvability Belief is encoded as a largely universal, language-agnostic feature, and that higher-resource languages such as English, despite achieving stronger mathematical reasoning performance, exhibit lower solvability-detection faithfulness.

Problem

• Solvability Detection
• Multilingual Analysis
• Large Language Models
• Mathematical Reasoning
• Solvability Belief

Innovation

• multilingual benchmark
• Solvability Belief
• faithfulness