The standard methodology of evaluating large language models (LLMs) based on
static pairs of inputs and outputs is insufficient for developing assistants:
this kind of assessments fails to take into account the essential interactive
element in their 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 preliminary 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 identify useful scenarios and existing
issues of GPT-4 in mathematical reasoning through a series of case studies
contributed by expert mathematicians. We conclude with actionable takeaways for
ML practitioners and mathematicians: models which communicate uncertainty,
respond well to user corrections, are more interpretable and concise may
constitute better assistants; interactive evaluation is a promising way to
continually navigate the capability of these models; humans should be aware of
language models' algebraic fallibility, and for that reason discern where they
should be used.

使用交互式评估方法评估大型语言模型在大学级数学推理方面的能力，为人工智能从业者和数学教授提供可行的建议，重点在于模型应该如何处理不确定性和人类纠错。