Large Language Models (LLMs) excel at various tasks, including solving math
word problems (MWPs), but struggle with real-world problems containing
irrelevant information. To address this, we propose a prompting framework that
generates adversarial variants of MWPs by adding irrelevant variables. We
introduce a dataset, ProbleMATHIC, containing both adversarial and
non-adversarial MWPs. Our experiments reveal that LLMs are susceptible to
distraction by numerical noise, resulting in an average relative performance
drop of ~26% on adversarial MWPs. To mitigate this, we fine-tune LLMs (Llama-2,
Mistral) on the adversarial samples from our dataset. Fine-tuning on
adversarial training instances improves performance on adversarial MWPs by ~8%,
indicating increased robustness to noise and better ability to identify
relevant data for reasoning. Finally, to assess the generalizability of our
prompting framework, we introduce GSM-8K-Adv, an adversarial variant of the
GSM-8K benchmark. LLMs continue to struggle when faced with adversarial
information, reducing performance by up to ~6%.

提出了一种提示框架，通过添加无关的变量生成数学应用问题的对抗性变体，用于改进大型语言模型在数学应用问题中的性能下降问题。实验证明，对抗性训练实例的微调提高了对抗性数学应用问题的性能，并提高了识别相关数据进行推理的能力。然而，大型语言模型在面对对抗性信息时仍然存在困难，导致性能下降。