大模型算术能力差，主要因对齐和进位错误。
AI-rithmetic
- 分析主流模型在加法任务中的错误模式。
- 数字位数越多，准确率越低，进位与对齐错误占87%以上。
- 适合关注AI基础能力缺陷的研究者与开发者。
现代AI系统已在国际数学竞赛中获奖、辅助科研并证明新定理，但在基础算术上仍表现不佳，频繁在加两个数的任务中出错。本文系统研究该现象，实证发现所有前沿模型在整数加法任务中，随着数字位数增加，准确率显著下降。此外，大多数错误可归因于操作数对齐错误或未能正确进位；这两类错误分别解释了Claude Opus 4.1、GPT-5和Gemini 2.5 Pro错误的87.9%、62.9%和92.4%。进一步分析表明，对齐错误常与分词机制相关，而进位错误则多为独立随机失败。
原文摘要 · Abstract (English)
Modern AI systems have been successfully deployed to win medals at international math competitions, assist with research workflows, and prove novel technical lemmas. However, despite their progress at advanced levels of mathematics, they remain stubbornly bad at basic arithmetic, consistently failing on the simple task of adding two numbers. We present a systematic investigation of this phenomenon. We demonstrate empirically that all frontier models suffer significantly degraded accuracy for integer addition as the number of digits increases. Furthermore, we show that most errors made by these models are highly interpretable and can be attributed to either operand misalignment or a failure to correctly carry; these two error classes explain 87.9%, 62.9%, and 92.4% of Claude Opus 4.1, GPT-5, and Gemini 2.5 Pro errors, respectively. Finally, we show that misalignment errors are frequently related to tokenization, and that carrying errors appear largely as independent random failures.
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