There is much excitement about the opportunity to harness the power of large language models (LLMs) when building problem-solving assistants. However, the standard methodology of evaluating LLMs relies on static pairs of inputs and outputs, and is insufficient for making an informed decision about which LLMs and under which assistive settings can they be sensibly used. Static assessment fails to account for the essential interactive element in LLM deployment, and therefore limits how we understand language model capabilities. We introduce CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We conduct a study with CheckMate to evaluate three language models (InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analysing MathConverse, we derive a taxonomy of human behaviours and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness in LLM generations, amongst other findings. Further, we garner a more granular understanding of GPT-4 mathematical problem-solving through a series of case studies, contributed by expert mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models that communicate uncertainty respond well to user corrections, and are more interpretable and concise may constitute better assistants. Interactive evaluation is a promising way to navigate the capability of these models; humans should be aware of language models' algebraic fallibility and discern where they are appropriate to use.

翻译：在构建问题解决助手时，利用大型语言模型（LLM）的能力令人振奋。然而，评估LLM的标准方法依赖于静态的输入-输出配对，这不足以帮助我们明智地决定哪些LLM以及在何种辅助设置下可以合理使用。静态评估未能考虑LLM部署中关键的交互要素，因此限制了我们理解语言模型的能力。我们引入了CheckMate，一个可适配的原型平台，供人类与LLM交互并对其进行评估。我们使用CheckMate进行了一项研究，评估了三种语言模型（InstructGPT、ChatGPT和GPT-4）作为本科数学证明助手的表现，参与者包括从本科生到数学教授的混合群体。我们发布了由此产生的交互和评分数据集MathConverse。通过分析MathConverse，我们推导出了一套人类行为分类学，并发现尽管总体呈正相关，但在LLM生成内容中，正确性与感知有用性之间存在显著偏差，以及其他发现。此外，通过一系列由数学专家贡献的案例研究，我们对GPT-4在数学问题解决方面的能力有了更细致的理解。最后，我们为机器学习从业者和数学家提供了可操作的要点：能够表达不确定性的模型能更好地响应用户纠正，且更具可解释性和简洁性的模型可能成为更好的助手。交互式评估是探索这些模型能力的一种有前景的方法；人类应意识到语言模型在代数方面的易错性，并辨别其适用的场景。