Evaluating Language Models for Mathematics through Interactions
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.
647d3eda1f878439e202a465
Katherine M. Collins
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2023-06-05T15:20:11.799Z
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Katie Collins
user
kmcollins
647d3eda1f878439e202a466
Albert Q. Jiang
claimed_verified
2023-06-05T15:20:05.892Z
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Albert Q Jiang
user
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647d3eda1f878439e202a467
Simon Frieder
claimed_verified
2023-06-05T15:20:21.056Z
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Simon Frieder
user
friederrr
647d3eda1f878439e202a468
Lionel Wong
647d3eda1f878439e202a469
Miri Zilka
647d3eda1f878439e202a46a
Umang Bhatt
647d3eda1f878439e202a46b
Thomas Lukasiewicz
647d3eda1f878439e202a46c
Yuhuai Wu
647d3eda1f878439e202a46d
Joshua B. Tenenbaum
647d3eda1f878439e202a46e
William Hart
647d3eda1f878439e202a46f
Timothy Gowers
647d3eda1f878439e202a470
Wenda Li
647d3eda1f878439e202a471
Adrian Weller
647d3eda1f878439e202a472
Mateja Jamnik
claimed_verified
2023-06-05T15:20:17.142Z
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/avatars/063a5793669932674a78b07029f9dfde.svg
Mateja Jamnik
user
matejajamnik
Evaluating Language Models for Mathematics through Interactions
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.
CheckMate evaluates large language models as assistants in mathematics through human interaction, revealing the need for models that communicate uncertainty and respond to corrections.
large language models LLMs CheckMate MathConverse InstructGPT ChatGPT GPT-4 mathematical reasoning human behaviour correctness perceived helpfulness uncertainty interpretability conciseness