title: Evaluating Language Models for Mathematics through Interactions
summary: 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.
paper_authors._id: 647d3eda1f878439e202a465
paper_authors.name: Katherine M. Collins
paper_authors.status: claimed_verified
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paper_authors.fullname: Katie Collins
paper_authors.type: user
paper_authors.user: kmcollins
paper_authors._id: 647d3eda1f878439e202a466
paper_authors.name: Albert Q. Jiang
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2023-06-05T15:20:05.892Z
paper_authors._id: 6137dff56ecbbda5c86755e9
paper_authors.avatarUrl: /avatars/1aadefd3acb7ad24df15463dadceb7d4.svg
paper_authors.fullname: Albert Q Jiang
paper_authors.type: user
paper_authors.user: aqj213
paper_authors._id: 647d3eda1f878439e202a467
paper_authors.name: Simon Frieder
paper_authors.status: claimed_verified
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paper_authors.fullname: Simon Frieder
paper_authors.type: user
paper_authors.user: friederrr
paper_authors._id: 647d3eda1f878439e202a468
paper_authors.name: Lionel Wong
paper_authors._id: 647d3eda1f878439e202a469
paper_authors.name: Miri Zilka
paper_authors._id: 647d3eda1f878439e202a46a
paper_authors.name: Umang Bhatt
paper_authors._id: 647d3eda1f878439e202a46b
paper_authors.name: Thomas Lukasiewicz
paper_authors._id: 647d3eda1f878439e202a46c
paper_authors.name: Yuhuai Wu
paper_authors._id: 647d3eda1f878439e202a46d
paper_authors.name: Joshua B. Tenenbaum
paper_authors._id: 647d3eda1f878439e202a46e
paper_authors.name: William Hart
paper_authors._id: 647d3eda1f878439e202a46f
paper_authors.name: Timothy Gowers
paper_authors._id: 647d3eda1f878439e202a470
paper_authors.name: Wenda Li
paper_authors._id: 647d3eda1f878439e202a471
paper_authors.name: Adrian Weller
paper_authors._id: 647d3eda1f878439e202a472
paper_authors.name: Mateja Jamnik
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2023-06-05T15:20:17.142Z
paper_authors._id: 647dd136770c299e56f7e7b8
paper_authors.avatarUrl: /avatars/063a5793669932674a78b07029f9dfde.svg
paper_authors.fullname: Mateja Jamnik
paper_authors.type: user
paper_authors.user: matejajamnik
paper_title: Evaluating Language Models for Mathematics through Interactions
paper_summary: 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.
paper_ai_summary: CheckMate evaluates large language models as assistants in mathematics through human interaction, revealing the need for models that communicate uncertainty and respond to corrections.
paper_ai_keywords: large language models LLMs CheckMate MathConverse InstructGPT ChatGPT GPT-4 mathematical reasoning human behaviour correctness perceived helpfulness uncertainty interpretability conciseness