#  : AI-Assisted Interactive Red-Teaming for Challenging LLMs’ (Lack of)
Multicultural Knowledge

Yu Ying Chiu1, Liwei Jiang2,3, Maria Antoniak3, Chan Young Park4, Shuyue
Stella Li2,
Mehar Bhatia5,6, Sahithya Ravi5,6, Yulia Tsvetkov2, Vered Shwartz5,6, Yejin
Choi2,3
1 Department of Linguistics, University of Washington
2 Paul G. Allen School of Computer Science & Engineering, University of
Washington
3 Allen Institute for Artificial Intelligence
4 Carnegie Mellon University
5 University of British Columbia
6 Vector Institute for AI
<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Frontier large language models (LLMs) are developed by researchers and
practitioners with skewed cultural backgrounds and on datasets with skewed
sources. However, LLMs’ (lack of) multicultural knowledge cannot be
effectively assessed with current methods for developing benchmarks. Existing
multicultural evaluations primarily rely on expensive and restricted human
annotations or potentially outdated internet resources. Thus, they struggle to
capture the intricacy, dynamics, and diversity of cultural norms. LLM-
generated benchmarks are promising, yet risk propagating the same biases they
are meant to measure. To synergize the creativity and expert cultural
knowledge of human annotators and the scalability and standardizability of
LLM-based automation, we introduce 111Our platform is available at
https://cultural-norms-demo.apps.allenai.org/., an interactive red-teaming
system that leverages human-AI collaboration to build truly challenging
evaluation dataset for assessing the multicultural knowledge of LLMs, while
improving annotators’ capabilities and experiences. Our study reveals that ’s
various modes of AI assistance support annotators in creating cultural
questions, that modern LLMs fail at, in a gamified manner. Importantly, the
increased level of AI assistance (e.g., LLM-generated revision hints) empowers
users to create more difficult questions with enhanced perceived creativity of
themselves, shedding light on the promises of involving heavier AI assistance
in modern evaluation dataset creation procedures. Through a series of 1-hour
workshop sessions, we gather CulturalBench-v0.1 222Our evaluation dataset
CulturalBench-v0.1 is available at
https://huggingface.co/datasets/kellycyy/CulturalBench., a compact yet high-
quality evaluation dataset with users’ red-teaming attempts, that different
families of modern LLMs perform with accuracy ranging from 37.7% to 72.2%,
revealing a notable gap in LLMs’ multicultural proficiency.

##  1 Introduction

Figure 1: Two settings of (1) Verifier-Only (2) AI-Assisted. Step 1: Users
brainstorm a culturally relevant scenario and use it to draft a multiple-
choice question (MCQ). In (1), users manually draft the MCQ. In (2), an LLM
drafts an MCQ based on a user-provided seed scenario. Step 2: Users test the
question with the model and revise it iteratively until satisfied. In (1),
users manually revise the MCQ. In (2), users revise with hints from an LLM.
Step 3: Users provide gold answers and feedback.

Uneven cultural representation has been a notorious recurrent limitation of
LLMs (Santy et al., 2023; Cao et al., 2023; Arora et al., 2023). Yet,
establishing a quality benchmark to gauge LLMs’ nuanced multicultural
knowledge remains a formidable challenge (Hershcovich et al., 2022).
Conventional human-written benchmarks are static and often fail to keep pace
with the evolving capabilities of LLMs (Yang et al., 2023). Notably, crafting
standardized forms of evaluation tasks, e.g., multiple-choice questions (MCQ),
for such a demanding task imposes considerable cognitive and intellectual
burdens on annotators. They must simultaneously demonstrate expert cultural
knowledge, creativity in crafting novel culturally significant scenarios,
familiarity of models’ capabilities to pinpoint their vulnerabilities, and
meticulous attention to ensure logical and format coherence within the
questions.

Alternatively, automatic benchmark creation presents unique challenges.
Evaluations relying on scraped online resources like bilingual content from
Wikipedia (Naous et al., 2023; Yao et al., 2023), webpages or news articles
(Nguyen et al., 2023) are susceptible to perpetuating skewed or outdated
culture representations due to their limited forms and coverage of source
media. Recently, established socio-cultural surveys originally designed for
humans have been used to audit LLMs’ cultural abilities (Durmus et al., 2023;
Santurkar et al., 2023). This fails to capture the models’ deficiencies. The
latest approaches of creating multicultural evaluations with LLMs generations
(Li et al., 2024; Fung et al., 2024), despite their scalability, risk
propagating existing cultural biases that they are meant to measure. It is
crucial to investigate alternative data annotation strategies that harness the
valuable cultural insights of humans while streamlining mundane tasks with
LLMs (e.g., data formatting) to allow people to direct their cognitive
resources toward substantive tasks that demand creative thinking.

Drawing insights from recent red-teaming approaches on LLMs’ safety (Ganguli
et al., 2022; Radharapu et al., 2023) and interactive model evaluation and
data collection efforts (Talmor et al., 2022; Kiela et al., 2021; Chiang et
al., 2024; Zheng et al., 2023), we introduce , an AI-assisted interactive red-
teaming system that guides users in iteratively creating challenging
evaluation datasets for testing the multicultural proficiency of modern LLMs.
To understand how effective AI assistance may boost annotators’ ability to
create challenging test cases, we design two variants of systems (Fig.
1)—Verifier-Only that simply involves LLMs for in-the-loop testing, and AI-
Assisted that engages LLM assistance more intensively, including drafting and
scaffolding initial MCQ candidates based on high-level topics provided by
users and suggesting hints and directions during the iterative revision
process.

With the two variants of systems, we recruited 45 annotators to participate in
immersive 1-hour workshop sessions for red-teaming LLMs’ (lack of)
multicultural knowledge. The user study reveals positive insights about users’
behaviors and perception during red-teaming with AI assistance. User-behavior-
wise, LLM-generated hints help users construct more challenging questions for
LLMs, especially when they are depleted of ideas after three rounds of
revision. In particular, with LLM-generated hints (AI-Assisted), users are
more willing to spend effort crafting a question with deliberation that yields
more difficult questions eventually, rather than taking a rather arbitrary
“hit-or-miss” red-teaming strategy to start over (Verifier-Only). User-
perception-wise, users with more LLM assistance report a significantly higher
level of agreement that the system sparked their creativity than those without
assistance (4.19 vs. 3.58). These human insights shed light on future data
annotation practices where more AI assistance could be involved to improve
annotators’ ability to create high-quality data, as well as their annotating
experiences.

Beyond user insights, throughout the workshop sessions, we compile users’ red-
teaming attempts into a compact yet high-quality MCQ dataset, namely
CulturalBench-v0.1, of 252 carefully-reviewed challenging questions spanned
across 34 distinct cultures for testing LLMs’ multicultural knowledge.
Evaluation with CulturalBench-v0.1 reveals that yields difficult test cases to
a variety of frontier LLM families (e.g., GPT, Claude, Mistral) across various
sizes, with model performances ranging from 37.7% to 72.2%. This reveals a
notable multicultural knowledge gap even for the most capable LLMs to date.
Overall, our user study of demonstrates the promise of collecting high-
quality, challenging datasets for multicultural knowledge by better optimizing
users’ cognitive resources with human-AI collaboration, laying a novel
foundation for future evaluation construction to effectively assess LLMs’
multicultural proficiency and beyond.

##  2 : Revealing the Multicultural Knowledge Gap of LLMs with AI-Assisted
Interactive Red-Teaming

Figure 2: Interface: (1a) Users brainstorm culturally relevant scenarios (1b)
They convert scenarios to MCQs with LLM-powered Question Formulation (2a)
Users revise MCQs and (2b) test MCQs based on the chosen option and its
confidence score from LLM Verifier (2c) Users inspire by LLM-generated hints
with strategies e.g., Negation, Synonym.

Our goal is to build a data annotation platform to help human annotators
create a challenging and structured dataset based on their expert cultural
knowledge.

###  2.1 Overall System Workflow

This system consists of three steps, as demonstrated in Fig. 2 – 1) Question
Formulation 2) Question Verification and Revision 3) Feedback Collection. The
first two steps involve a red-teaming exercise to formulate a challenging
question step-by-step. The last step involves collecting feedback from users
through a cultural contextualization survey based on their posed questions, as
well as a usability survey regarding their user experience. Step 1: Question
Formulation The goal is to facilitate users in brainstorming culturally
relevant situations based on their personal experiences. A step-by-step
guideline with detailed examples is provided to inspire them, as shown in
Appendix A.5. Users formulate a multiple-choice question (MCQ), which
comprises one correct and culturally appropriate option. Step 2: Question
Verification & Revision This step provides an interactive and iterative red-
teaming platform that allows users to verify their culturally sensitive MCQs.
The platform assists them in revising the question and the options to make it
more challenging by providing descriptions of various common revision
strategies with drafted examples (e.g., “Negate the Question”), as stated in
Fig. 2 and Appendix A.5. Step 3: Feedback Collection After finalizing a
question, we collected users’ feedback on the question posed using a cultural
contextualization survey and also their user experience by usability survey as
depicted in Fig. 2. The cultural context survey asked users to provide their
gold standard (correct option), its rationale, and several questions about
their levels of particular cultural knowledge and the commonness of the
specific cultural norm described in the question. We also gathered their
hands-on experience regarding the functionality and user-friendliness of our
interface. Survey questions can be found in Appendix A.6.

###  2.2 Varying Levels of AI Assistance: Verifier-Only & AI-Assisted

To study the effect of different AI-assistance modules, we have implemented
two settings with varying AI Assistance levels in our experiment: (1)
Verifier-Only (2) AI-Assisted, as presented in Fig. 1. The first setting
includes the basic element (Verifier) for the red-teaming exercise. The second
setting aims to explore question formulation and hints on revision powered by
LLMs. Verifier-Only The users formulate their MCQ in Step 1 (Question
formulation). They then present their MCQ to LLM Verifier and revise their
question iteratively by themselves. More specifically, the Verifier responds
with one option coupled with the corresponding confidence score (which is the
top-1 linear probability of its log probability). This aids users in judging
the question’s difficulty. In our system, GPT-3.5-turbo (0125) served as the
Verifier to reduce cost and time latency (Brown et al., 2020). AI-Assisted
Users benefit from extensive AI-assistance in question formation and revision,
as illustrated in Fig. 2. In Step 1, users convert their short cultural-
relevant scenarios into MCQs using LLM-powered question formation. In Step 2,
users verify and revise their questions with LLM-powered suggestions. The
Verifier remains consistent with the Verifier-Only setting.

###  2.3 User Experiments with Red-teaming Workshops

We recruit annotators from an academic institution to participate in our
1-hour workshop. Annotators are randomly assigned to use either Verifier-Only
or AI-Assisted. After finishing the self-contained tutorial, we encourage
annotators to interact with the system for at least 45 minutes, allowing them
to leave at their own will. Additional details regarding the user demographic
description, and experiment setup can be found in Appendix A.2 and A.3.

###  2.4 CulturalBench-v0.1: A Compact Dataset for LLMs’ Multicultural
Knowledge

| Question | Models | Rationale
---|---|---|---
(1) Indian |  Q: What is defined as vegetarian in India? A) Not eating seafood, meat, or eggs B) Not eating seafood or meat C) Not eating seafood, meat, eggs, or root vegetables D) All of the above |  GPT-4: D ✓ Others: A, B |  All of the above are considered vegetarian in India, but just different types.
(2) South Korean |  Q: What are some unspoken etiquette in a company dinner in Korea? A) Hold the glass with both hands when a younger person is pouring alcohol for you B) Look away from elders while drinking alcohol C) Maintain eye contact the entire time D) Make sure to start eating first |  GPT-4: B ✓ Others: A |  For A) It is only true when the person pouring the alcohol is older than you…
(3) Chinese |  Q: In a Chinese cultural context, what will the government do if a couple gives birth to a second child? A) Government issue a fixed amount of fine because this is not allowed. B) Government issue a variable amount of fine based on the couple’s income level because this is not allowed C) Government does not give cash bonus or cash punishment. D) Government sends cash bonus to improve the low birth rate in China. |  GPT-4: C ✓ Yi: C ✓ Others: A, B |  Having a second child is allowed in China after 2014.

Table 1: Examples from CulturalBench-v0.1 and models responses. The detailed
rationale can be found in Appendix 8.

Before delving into the insights of the user studies, we first introduce the
end dataset that we gathered by . We collected not only question-specific
information (Fig. 6-Left e.g., Correct answer, rationale), but also cultural
contextualization details (Fig. 6-Right e.g., culture represented, annotator’s
familiarity on it). Both success-attack questions and fail-to-attack questions
have the same metadata, as shown in Appendix A.4.2 and A.4.3.

Our red teaming dataset includes 252 carefully-reviewed MCQs spanned across 34
diverse cultures. After data collection, we manually reviewed the questions to
ensure they 1) follow the MCQ format 2) specify what kind of culture the
question is asking for.

This dataset represents diverse demographic groups as stated in Appendix A.3.
Chinese culture, including ethnicity Chinese in different locations,
attributes the highest proportion ($32\%$) among all, following are Indian
(including North and South Indian) and American containing $15\%$ and $6\%$
respectively. We also include Appendix Table 4 to show the grouping examples
for some cultures with confusing terms (e.g., South Indian and Hindu Indian
are grouped as Indian).

##  3 Promising AI-Assisted Benchmark Creation with

This section aims to provide insights on how to make use of human-AI
collaboration to produce a challenging dataset on multicultural knowledge.

We analyze (1) AI-assistance contribution to different system modules, (2)
existing LLMs’ cultural awareness using CulturalBench-v0.1, and (3) behavior
and perception of users with varying levels of AI-assistance.

###  3.1 How does AI-assistance contribute to each module in our system?

We study each LLM-powered module to investigate the effect of human-AI
collaboration on each type of task in our system.

####  3.1.1 LLM assistance on question formulation

Question formulation entails brainstorming a culturally relevant scenario and
transforming it into a multiple choice question (MCQ). Users with LLM-powered
question formulation are only tasked to provide a sentence-length scenario
description, whereas users without LLM-assistance need to formulate the MCQ
question and answer options themselves. We first compare the time difference
in the question formulation between the two groups.

LLM assistance on question formulation does not significantly improve the time
needed on formulating questions. The time needed to form the initial MCQ
template before editing for both users with more AI-assistance on question
formulation (AI-Assisted setting) and less AI-assistance (Verifier-Only
setting) are shown in Appendix A.8. The time needed for the initial MC
questions created by Verifier-Only and AI-Assisted settings show no
significant difference. Specifically, the former needs 183.4 seconds
(SD=105.2) on average while the latter needs 161.8 (SD=109.4) on average.

Our formulation of red teaming tasks by writing structured MCQs appears to be
relatively easy for human users without AI assistance. They effectively create
their initial question template and attain equally impressive performance in
terms of efficiency. One possible reason could be users without AI assistance
formulate both questions and options concurrently when they are brainstorming.
As we move forward in our future work, we should also consider how AI can aid
people in brainstorming culturally relevant scenarios, rather than solely
helping them in formulating structured questions.

Figure 3: LLM assistance on (1) Left: Verifier (gpt-3.5-turbo) by comparing
other models performance on questions by users without other LLM assistance
(Verifier-Only) (2) Right: Revision by comparing between the final success
attack rate and the total number of edits between users with LLM Hints (AI-
Assisted) and without LLM Hints (Verifier-Only).

####  3.1.2 LLM assistance on Question Verifier

After the MCQ is initially formulated, we attempt to use GPT-3.5-turbo as our
Verifier (Brown et al., 2020). Users revise and verify the MCQ iteratively
based on the Verifier response. In this section, we evaluate the viability of
this setup by investigating whether the Verifier serves as a good estimator
for the degree of challenge for other LLMs. We assume that users revise their
MCQs based on the Verifier response and its corresponding confidence score.

Our LLM Verifier is able to create challenging questions for all tested
models. To delineate the effect of LLM assistance, we analyze the MCQs created
by users without LLM assistance on other LLMs in Fig. 3 (Left). We found that
LLM performance decreases with the number of revisions, especially for
llama-70b by 38.73% and yi-34b by 23.82%. GPT-3.5-turbo (our Verifier model)
decreased from 48.91% to 37.5%. GPT-4-turbo, which is the best performance
model among all, decreased from 60.87% to 50.00% on the 10th revision. This
shows that our LLM Verifier is capable of increasing the difficulty of
questions for most models, as the number of revisions increases based on the
response of LLM Verifier.

It implies that using only one model (GPT-3.5-turbo) as the Verifier can
effectively construct challenging data for most of the models. However, if the
goal of future work is to improve the stronger model (GPT-4-turbo), the
relatively small decrease in it suggests that we need to randomly select
different models as verifier, including GPT-4 model to help constructing a
more challenging dataset.

####  3.1.3 LLM assistance on Question Revision

GPT-4 is used to generate LLM-powered hints based on the work-in-progress MCQ
to provide revision suggestions with common revision strategies. Users without
LLM-powered hints, on the other hand, are provided with static descriptions of
those strategies. We now investigate the relationship between the number of
revisions and the success attack rate of the finalized question (final success
rates) for both users with LLM-assistance (AI-Assisted setting) and users
without LLM-assistance (Verifier-Only settings).

LLM assistance on Hints helps users to construct more challenging questions
after several rounds of revision. For the initial three revisions, the final
success attack rate of questions without LLM-powered suggestions (Verifier-
Only) increases. Conversely, questions with LLM-powered suggestions (AI-
Assisted) remain steady as they are initially created by the LLM-powered
question formulation and are of good quality. Beyond four revisions, questions
created in AI-Assisted begin to show an increasing trend. On the other hand,
those in Verifier-Only require more revisions to match similar performance at
10 revisions, relative to those in AI-Assisted. We can see the potential
benefits of LLM suggestions become more apparent, especially after several
rounds of revisions.

One reason is that individuals start with their initial ideas, which may
deplete after a few attempts. LLM suggestions can therefore serve as an idea
pool, providing diverse editing ideas that are grounded in their input
question template. This illustrates the use of AI in facilitating creative
thought and efficient question revision among individuals.

###  3.2 Assessing LLMs’ Cultural Knowledge Gap with CulturalBench-v0.1

Model |  All (N=252) |  Verifier-Only (N=113) |  AI-Assisted (N=139) |  Chinese (N=80) |  Indian (N=38) |  American (N=16) |  Europe (N=46)
---|---|---|---|---|---|---|---
Claude 3 Opus (20240229) | 70.6 | 69.9 | 71.2 | 66.2 | 71.1 | 81.2 | 69.6
Claude 3 Sonnet (20240229) | 57.1 | 61.9 | 53.2 | 50.0 | 57.9 | 75.0 | 60.9
GPT-4 Turbo (0125) | 72.2 | 71.7 | 72.7 | 67.5 | 71.1 | 81.2 | 69.6
GPT-3.5 Turbo (0125) | 39.7 | 41.6 | 38.1 | 41.2 | 44.7 | 56.2 | 41.3
Mistral Large | 57.1 | 62.8 | 52.5 | 55.0 | 57.9 | 81.2 | 54.3
Mixtral MoE model (8x7b) | 50.4 | 51.3 | 49.6 | 45.0 | 47.4 | 75.0 | 52.2
Llama (70b) | 44.4 | 42.5 | 46.0 | 41.2 | 47.4 | 43.8 | 50.0
Mistral (7b) | 37.7 | 38.1 | 37.4 | 40.0 | 39.5 | 68.8 | 26.1
Yi (34b) | 44.8 | 48.7 | 41.7 | 41.2 | 50.0 | 68.8 | 37.0
Average | $52.69_{11.89}$ | $54.28_{11.94}$ | $51.4_{12.23}$ | $49.72_{10.27}$ | $54.09_{10.61}$ | $70.14_{12.07}$ | $51.21_{13.79}$

Table 2: CulturalBench-v0.1: Zero-shot results (correct answer rate in %) by
greedy decoding from LLMs in terms of culture represented (Chinese, Indian,
American) and geographical locations (Europe) by grouping cultures e.g.
French, Italian.

With our high-quality and small-scale dataset, we evaluate several state-of-
the-art LLMs to assess their cultural awareness and conduct qualitative
analysis on factors that contribute to the difficulty of questions for LLMs.

In Table 2, we present the performance of several open-source models (e.g.,
Mistral, Yi) and state-of-the-art private models from different model families
(e.g., Claude variants, GPT variants). Additional evaluation details can be
found in Appendix A.7.

CulturalBench-v0.1 reflects cultural-specific knowledge with mixed results for
the Chinese model (Yi) and European models (Mistral/Mixtral) on their relevant
cultures. Contrary to the intuitive belief that models trained with a special
focus on specific languages (e.g., Yi for Chinese and Mistral large and
Mixtral MoE models for European languages) will perform better on cultures
associated with the specialized language, we surprisingly observe mixed
results. While Yi demonstrates lower-than-average performance (41.00 vs.
49.72), Mistral Large and Mixtral MoE (54.3 and 52.2 vs. 51.21) show
significantly higher performance than average.

As illustrated in Table 3, for example, only Yi and GPT-4 models could answer
correctly on the updated one-child policy in China: “In a Chinese (…), what
will the government do if a couple give birth to a second child?” when other
models still believed only one child is allowed in China. However, Yi fails to
give a correct answer to a question about driving licenses: “How many tests do
people have to pass to get a driver’s license in China?” This is surprising,
as the question tests simple factual knowledge that does not require
complicated reasoning. We suspect that the unimpressive result of Yi may be
attributed to a language mismatch between the prompts and the languages in
which the models were trained. While the models were trained on Chinese text,
providing them with opportunities to learn about Chinese culture, we are
prompting the models about Chinese culture in English. Consequently, the
models may struggle to generalize knowledge learned in Chinese to English. To
test this hypothesis, we presented the same driver’s license question in
Chinese to Yi and found that the model was then able to generate the correct
answer. Additional evaluation details and model response can be found in
Appendix A.7. This example highlights the importance, in future research, of
considering the language used in prompts when evaluating the cultural
awareness of models.

CulturalBench-v0.1 is challenging to modern LLMs, with varying difficulties.

Notably, we observe a substantial performance disparity between larger and
smaller models. For example, GPT-4-turbo achieves the highest accuracy at
72.2%, closely followed by Claude 3 Opus at 70.6%. Conversely, relatively
smaller models such as Mistral 7b and GPT-3.5-turbo attain lower accuracy
scores of 37.7% and 39.7%, respectively.

The decent performance of larger models suggests that large models already
have quite strong familiarity with the cultural knowledge encoded in our data,
affirming our emphasis on developing strategies to construct more challenging
datasets for assessing cultural awareness in LLMs. On the other hand, the
notably lower performance of certain models underscores the need for a
cultural awareness benchmark to comprehensively understand these discrepancies
and shortcomings.

Hard questions in CulturalBench-v0.1 require more extensive reasoning. We
further conducted a qualitative analysis of questions that the models found
extremely challenging. We categorized our dataset into three difficulty levels
based on the number of models that provided correct answers: Easy (7-9 models,
68 samples), Medium (3-6 models, 103 samples), and Hard (0-2 models, 81
samples). We then analyzed the Hard questions, focusing specifically on those
that only GPT-4 could answer correctly. Examples of such questions are
provided in Table 1 (Example 1-3) and Appendix A.4.4.

Our analysis reveals that Hard questions often demand more extensive reasoning
from the models due to the complexity of the question structure and the
presence of subtly incorrect options. For instance in Table 1 (Example 1),
“What is defined as vegetarian in India?” with the correct answer being “D.
All of the above.” This requires models to simultaneously consider and assess
all options, adding complexity to the reasoning process compared to a binary
judgment for each option. Another example is the question in Table 1 (Example
2), “What are some unspoken etiquettes during company dinners in Korea?” where
only GPT-4 identified the correct response, “Look away from elders while
drinking alcohol.” Other models were misled by selecting “holding the glass
with both hands when a younger person is pouring alcohol for you,” which is
incorrect as it applies to the “older” person, not the “younger.” These subtly
incorrect options require models to possess strong reasoning abilities to
discern between similar scenarios.

###  3.3 How users’ behaviors and perception differ with varying levels of AI-
assistance

We compare and analyze annotators’ behaviors and their perception. We used a
two-sided Student t-test for the following analysis.

####  3.3.1 Behaviors

Users with more AI-assistance spend more time on revising and make more
revisions, compared with those with less AI-assistance. As shown in Table 10,
users with LLM-generated hints (AI-Assisted setting) require 152.4 more
seconds, compared to users without LLM-generated Hints (Verifier-Only) with
$p=0.1$. Similarly, users in AI-Assisted setting also make 7.19 more revisions
than users in Verifier-Only. One possible reason is that the LLM-generated
hints provide more information and inspiration for users to revise their
questions. Users with LLM-generated hints tend to try and adopt various
existing hints whereas users without LLM-generated hints tend to give up on
revising and restart another round due to a lack of revision ideas and less
guidance.

User with more AI-assistance write more Hard questions, relative to users with
less AI-assistance. Following the Section 3.2 questions categorization, we
found that each user with AI-Assisted created 15.7% more Hard questions (0-1
models we selected in Table 2 correct correctly) more than each user without
AI-Assisted at p=0.05.

This finding could indicate that revision based on posed questions attributed
to the creation of more Hard questions for LLMs. This demonstrates that
encouraging users to continue revising rather than restarting a new scenario
could be a key to creating challenging LLM benchmarks.

####  3.3.2 Perception

Users with more AI-assistance expressed more positive agreement on the system
capability to spark their creativity, relative to those with less AI-
assistance. On a scale of 1 (very limiting to creativity) to 5 (very
conductive to creativity), users with more AI-assistance (AI-Assisted setting)
reported a mean of 4.19 (SD=0.66) whereas users with less AI-assistance
(Verifier-Only) reported a mean of 3.58 (SD=0.79). The difference between
these scores (0.61) is significant ($p=0.05$). This suggests that the
inclusion of LLMs in the initial question forming or revision could also
potentially boost the system’s capacity to stimulate creativity. One user
expressed similar thoughts: “The ability to generate multiple iterations of
questions using AI was helpful to my creativity, as well as the hints
provided.”

Nine users with both more and less AI-assistance report positive impressions
of the annotation system and task design.

9 out of 27 users (5 from Verifier-Only; 4 from AI-Assisted) expressed their
enthusiasm. One user from Verifier-Only said “I enjoyed learning how much the
AI actually knew about culture,” Another user from AI-Assisted liked the
gamified elements: “I liked how we could run the model again and again, …,
making this process a lot more fun and gamified.” Users from both settings
positively referred to “the confidence score” helping them understand the
effectiveness of their revisions.

Some users with both more and less AI-assistance enjoy the LLM-powered
modules. Some users appreciate knowing the confidence score along with the
chosen option by our Verifier (3 from Verifier-Only, 1 from AI-Assisted). This
allows them to gauge how close they are to ’winning’ (trick the AI
successfully). Users with more AI-Assistance (6 from AI-Assisted) enjoyed
various LLM-powered assistance, emphasizing “I liked how it generated a
question based on your observation of a culture”(4 from AI-Assisted) and “AI-
generated hints (2 from AI-Assisted).”

One possible reason is that the LLM-powered modules reduce users’ cognitive
load when formulating questions and revisions. They provide grounded ideas
based on users’ inputs (e.g. their scenario, their posed question), rather
than purely text guidance. Users engaged more by trying the LLM-powered
modules, possibly increasing question revision time. When designing similar
annotation systems, the trade-off between engagement and time spent should be
considered.

Six users with both more and less AI-assistance report difficulty in deceiving
the LLM. 11 out of 27 users (6 from Verifier-Only; 5 from AI-Assisted)
believed that nothing posed a challenge. However, 6 users (2 from Verifier-
Only; 4 from AI-Assisted) expressed difficulty in deceiving the LLM: “Refine
the questions was a bit challenging. That might be due to the nature of the
question rather than the platform itself.”. Despite all our design
modifications, such as incorporating a confidence score along with the
response option, this remains difficult for some users, as evidenced by their
feedback. This underscores the importance of designing novel annotation
systems to assist human annotators in brainstorming scenarios rather than
purely formulating questions.

##  4 Related Work

AI-augmented Data Collection Prior works have investigated on how to
incorporate AI into different subtasks during data curation including writing
(Shen et al., 2023) and auto-crowdsourcing pipelines (Wu et al., 2023). One
popular approach to improve LLMs is through red teaming to reveal models’
weaknesses. Researchers recruited human annotators to attack their LLMs to
reduce models’ harmful outputs (Ganguli et al., 2022). Some works have also
been done on constructing adversarial datasets more efficiently with AI
massive generations (Radharapu et al., 2023).

Cultural Bias on LLMs To evaluate using grounded theory, some studies focus on
auditing LLMs and comparing them to humans through existing socio-cultural
surveys (Li et al., 2024; Tao et al., 2023; Ramezani & Xu, 2023). People also
investigate language diversity by scaling up to multilingual settings
(Mukherjee et al., 2023; Yue et al., 2023), with a particular focus on low-
resource languages (Deas et al., 2023; Wibowo et al., 2023). Some recent works
have also been conducted to construct schemas for generating massive datasets
with AI, which aims to better capture LLMs’ cultural bias (Fung et al., 2024;
Huang & Yang, 2023; Ziems et al., 2023).

##  5 Conclusion

We present , an interactive red-teaming system that leverages the synergy of
human-AI collaboration to collect a truly challenging dataset to assess LLMs’
multicultural knowledge. Through workshop sessions in our user studies, we
gather users’ red-teaming attempts to form a compact yet high-quality
evaluation dataset CulturalBench-v0.1. With varying AI-assistance levels of
our system, we compared and analyzed our user studies’ results in terms of
system performance, data quality, and users’ behaviors and perception.

## Acknowledgements

We thank the users of our platform for their helpful feedback and comments.
This research was supported in part by DARPA under the ITM program
(FA8650-23-C-7316).

## Ethics Statement

Our study recruited students from a Natural Language Processing class at an
academic institution. We provided participation class credits to participants
who joined the experiment. These credits can also be gained through other
methods e.g., writing essays. Therefore, the participation is optional. Before
joining the workshop, we provide consent materials to explain the experiment’s
setup and their rights, including the ability to ask for clarification anytime
and leave at their own will during the experiment. This study was reviewed by
the same academic institution’s IRB committee.

The findings of the user studies on our system are based on this limited user
demographics and designed task guidance. Our users were mostly from the
computer science department and may not represent the general public, as shown
by the skewed population in Table 3. Additionally, our users were more
familiar with interacting with LLM-based systems when compared with the
general public. In this study, we prepared detailed guidance and tutorials for
users to do their red-teaming tasks. This approach may not be natural, and we
would need to consider such differences when employing our system with other
public user groups in the future.

Moreover, the CulturalBench-v0.1 is a small-scale dataset. Although it covers
a wide range of cultures, many of them only contain a few data points. We have
also chosen to collect English datasets this time instead of multilingual
datasets. Therefore, the dataset is not sufficient to evaluate the
multicultural knowledge of LLMs. However, we believe that has huge potential
of collecting various cultural norms by expanding this platform to different
locations and languages in the future.

## References

  * Anthropic (2024) Anthropic.  The claude 3 model family: Opus, sonnet, haiku.  In _Anthropic Model Card_ , 2024.  URL https://www-cdn.anthropic.com/de8ba9b01c9ab7cbabf5c33b80b7bbc618857627/Model_Card_Claude_3.pdf.
  * Arora et al. (2023) Arnav Arora, Lucie-aimée Kaffee, and Isabelle Augenstein.  Probing pre-trained language models for cross-cultural differences in values.  In Sunipa Dev, Vinodkumar Prabhakaran, David Adelani, Dirk Hovy, and Luciana Benotti (eds.), _Proceedings of the First Workshop on Cross-Cultural Considerations in NLP (C3NLP)_ , pp. 114–130, Dubrovnik, Croatia, May 2023. Association for Computational Linguistics.  doi: 10.18653/v1/2023.c3nlp-1.12.  URL https://aclanthology.org/2023.c3nlp-1.12.
  * Brown et al. (2020) Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel M. Ziegler, Jeffrey Wu, Clemens Winter, Christopher Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei.  Language models are few-shot learners, 2020.
  * Cao et al. (2023) Yong Cao, Li Zhou, Seolhwa Lee, Laura Cabello, Min Chen, and Daniel Hershcovich.  Assessing cross-cultural alignment between ChatGPT and human societies: An empirical study.  In Sunipa Dev, Vinodkumar Prabhakaran, David Adelani, Dirk Hovy, and Luciana Benotti (eds.), _Proceedings of the First Workshop on Cross-Cultural Considerations in NLP (C3NLP)_ , pp. 53–67, Dubrovnik, Croatia, May 2023. Association for Computational Linguistics.  doi: 10.18653/v1/2023.c3nlp-1.7.  URL https://aclanthology.org/2023.c3nlp-1.7.
  * Chiang et al. (2024) Wei-Lin Chiang, Lianmin Zheng, Ying Sheng, Anastasios Nikolas Angelopoulos, Tianle Li, Dacheng Li, Hao Zhang, Banghua Zhu, Michael Jordan, Joseph E Gonzalez, et al.  Chatbot arena: An open platform for evaluating llms by human preference.  _arXiv preprint arXiv:2403.04132_ , 2024.
  * Clark et al. (2020) J. Clark, Eunsol Choi, Michael Collins, Dan Garrette, Tom Kwiatkowski, Vitaly Nikolaev, and Jennimaria Palomaki.  Tydi qa: A benchmark for information-seeking question answering in typologically diverse languages.  _Transactions of the Association for Computational Linguistics_ , 8:454–470, 2020.  URL https://api.semanticscholar.org/CorpusID:212657414.
  * Clark et al. (2018) Peter Clark, Isaac Cowhey, Oren Etzioni, Tushar Khot, Ashish Sabharwal, Carissa Schoenick, and Oyvind Tafjord.  Think you have solved question answering? try arc, the ai2 reasoning challenge.  _arXiv preprint arXiv:1803.05457_ , 2018.
  * Deas et al. (2023) Nicholas Deas, Jessica A. Grieser, Shana Kleiner, Desmond Upton Patton, Elsbeth Turcan, and Kathleen McKeown.  Evaluation of african american language bias in natural language generation.  _ArXiv_ , abs/2305.14291, 2023.  URL https://api.semanticscholar.org/CorpusID:258841278.
  * Durmus et al. (2023) Esin Durmus, Karina Nyugen, Thomas I. Liao, Nicholas Schiefer, Amanda Askell, Anton Bakhtin, Carol Chen, Zac Hatfield-Dodds, Danny Hernandez, Nicholas Joseph, Liane Lovitt, Sam McCandlish, Orowa Sikder, Alex Tamkin, Janel Thamkul, Jared Kaplan, Jack Clark, and Deep Ganguli.  Towards measuring the representation of subjective global opinions in language models, 2023.
  * Fung et al. (2024) Yi Ren Fung, Ruining Zhao, Jae Doo, Chenkai Sun, and Heng Ji.  Massively multi-cultural knowledge acquisition & lm benchmarking.  _ArXiv_ , abs/2402.09369, 2024.  URL https://api.semanticscholar.org/CorpusID:267657749.
  * Ganguli et al. (2022) Deep Ganguli, Liane Lovitt, Jackson Kernion, Amanda Askell, Yuntao Bai, Saurav Kadavath, Ben Mann, Ethan Perez, Nicholas Schiefer, Kamal Ndousse, et al.  Red teaming language models to reduce harms: Methods, scaling behaviors, and lessons learned.  _arXiv preprint arXiv:2209.07858_ , 2022.
  * Hendrycks et al. (2021a) Dan Hendrycks, Collin Burns, Steven Basart, Andrew Critch, Jerry Li, Dawn Song, and Jacob Steinhardt.  Aligning ai with shared human values.  _Proceedings of the International Conference on Learning Representations (ICLR)_ , 2021a.
  * Hendrycks et al. (2021b) Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Steinhardt.  Measuring massive multitask language understanding.  _Proceedings of the International Conference on Learning Representations (ICLR)_ , 2021b.
  * Hershcovich et al. (2022) Daniel Hershcovich, Stella Frank, Heather Lent, Miryam de Lhoneux, Mostafa Abdou, Stephanie Brandl, Emanuele Bugliarello, Laura Cabello Piqueras, Ilias Chalkidis, Ruixiang Cui, et al.  Challenges and strategies in cross-cultural nlp.  _arXiv preprint arXiv:2203.10020_ , 2022.
  * Huang & Yang (2023) Jing Huang and Diyi Yang.  Culturally aware natural language inference.  In _Findings of the Association for Computational Linguistics: EMNLP 2023_ , pp. 7591–7609, 2023.
  * Jiang et al. (2023) Albert Q Jiang, Alexandre Sablayrolles, Arthur Mensch, Chris Bamford, Devendra Singh Chaplot, Diego de las Casas, Florian Bressand, Gianna Lengyel, Guillaume Lample, Lucile Saulnier, et al.  Mistral 7b.  _arXiv preprint arXiv:2310.06825_ , 2023.
  * Jiang et al. (2024) Albert Q Jiang, Alexandre Sablayrolles, Antoine Roux, Arthur Mensch, Blanche Savary, Chris Bamford, Devendra Singh Chaplot, Diego de las Casas, Emma Bou Hanna, Florian Bressand, et al.  Mixtral of experts.  _arXiv preprint arXiv:2401.04088_ , 2024.
  * Kiela et al. (2021) Douwe Kiela, Max Bartolo, Yixin Nie, Divyansh Kaushik, Atticus Geiger, Zhengxuan Wu, Bertie Vidgen, Grusha Prasad, Amanpreet Singh, Pratik Ringshia, et al.  Dynabench: Rethinking benchmarking in nlp.  _arXiv preprint arXiv:2104.14337_ , 2021.
  * Li et al. (2024) Cheng Li, Mengzhou Chen, Jindong Wang, Sunayana Sitaram, and Xing Xie.  Culturellm: Incorporating cultural differences into large language models.  _ArXiv_ , abs/2402.10946, 2024.  URL https://api.semanticscholar.org/CorpusID:267750997.
  * Lin et al. (2021) Stephanie Lin, Jacob Hilton, and Owain Evans.  Truthfulqa: Measuring how models mimic human falsehoods.  _arXiv preprint arXiv:2109.07958_ , 2021.
  * Longpre et al. (2021) Shayne Longpre, Yi Lu, and Joachim Daiber.  Mkqa: A linguistically diverse benchmark for multilingual open domain question answering.  _Transactions of the Association for Computational Linguistics_ , 9:1389–1406, 2021.
  * Mukherjee et al. (2023) Anjishnu Mukherjee, Chahat Raj, Ziwei Zhu, and Antonios Anastasopoulos.  Global voices, local biases: Socio-cultural prejudices across languages.  In _Conference on Empirical Methods in Natural Language Processing_ , 2023.  URL https://api.semanticscholar.org/CorpusID:264491136.
  * Naous et al. (2023) Tarek Naous, Michael Joseph Ryan, and Wei Xu.  Having beer after prayer? measuring cultural bias in large language models.  _ArXiv_ , abs/2305.14456, 2023.  URL https://api.semanticscholar.org/CorpusID:258865272.
  * Nguyen et al. (2023) Tuan-Phong Nguyen, Simon Razniewski, Aparna Varde, and Gerhard Weikum.  Extracting cultural commonsense knowledge at scale.  In _Proceedings of the ACM Web Conference 2023_ , pp. 1907–1917, 2023.
  * OpenAI (2023) R OpenAI.  Gpt-4 technical report.  _ArXiv_ , 2303, 2023.
  * Radharapu et al. (2023) Bhaktipriya Radharapu, Kevin Robinson, Lora Aroyo, and Preethi Lahoti.  Aart: Ai-assisted red-teaming with diverse data generation for new llm-powered applications.  In _Conference on Empirical Methods in Natural Language Processing_ , 2023.  URL https://api.semanticscholar.org/CorpusID:265213125.
  * Ramezani & Xu (2023) Aida Ramezani and Yang Xu.  Knowledge of cultural moral norms in large language models.  _arXiv preprint arXiv:2306.01857_ , 2023.
  * Santurkar et al. (2023) Shibani Santurkar, Esin Durmus, Faisal Ladhak, Cinoo Lee, Percy Liang, and Tatsunori Hashimoto.  Whose opinions do language models reflect?, 2023.
  * Santy et al. (2023) Sebastin Santy, Jenny T Liang, Ronan Le Bras, Katharina Reinecke, and Maarten Sap.  Nlpositionality: Characterizing design biases of datasets and models.  _arXiv preprint arXiv:2306.01943_ , 2023.
  * Shen et al. (2023) Hua Shen, Chieh-Yang Huang, Tongshuang Wu, and Ting-Hao Kenneth Huang.  Convxai: Delivering heterogeneous ai explanations via conversations to support human-ai scientific writing.  In _Companion Publication of the 2023 Conference on Computer Supported Cooperative Work and Social Computing_ , pp. 384–387, 2023.
  * Talmor et al. (2022) Alon Talmor, Ori Yoran, Ronan Le Bras, Chandra Bhagavatula, Yoav Goldberg, Yejin Choi, and Jonathan Berant.  Commonsenseqa 2.0: Exposing the limits of ai through gamification.  _arXiv preprint arXiv:2201.05320_ , 2022.
  * Tao et al. (2023) Yan Tao, Olga Viberg, Ryan S. Baker, and Ren’e F. Kizilcec.  Auditing and mitigating cultural bias in llms.  _ArXiv_ , abs/2311.14096, 2023.  URL https://api.semanticscholar.org/CorpusID:265445838.
  * Touvron et al. (2023) Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al.  Llama 2: Open foundation and fine-tuned chat models.  _arXiv preprint arXiv:2307.09288_ , 2023.
  * Wibowo et al. (2023) Haryo Akbarianto Wibowo, Erland Hilman Fuadi, Made Nindyatama Nityasya, Radityo Eko Prasojo, and Alham Fikri Aji.  Copal-id: Indonesian language reasoning with local culture and nuances.  _ArXiv_ , abs/2311.01012, 2023.  URL https://api.semanticscholar.org/CorpusID:264935209.
  * Wu et al. (2023) Tongshuang Wu, Haiyi Zhu, Maya Albayrak, Alexis Axon, Amanda Bertsch, Wenxing Deng, Ziqi Ding, Bill Guo, Sireesh Gururaja, Tzu-Sheng Kuo, et al.  Llms as workers in human-computational algorithms? replicating crowdsourcing pipelines with llms.  _arXiv preprint arXiv:2307.10168_ , 2023.
  * Yang et al. (2023) Shuo Yang, Wei-Lin Chiang, Lianmin Zheng, Joseph E. Gonzalez, and Ion Stoica.  Rethinking benchmark and contamination for language models with rephrased samples.  _ArXiv_ , abs/2311.04850, 2023.  URL https://api.semanticscholar.org/CorpusID:265050721.
  * Yao et al. (2023) Binwei Yao, Ming Jiang, Diyi Yang, and Junjie Hu.  Empowering llm-based machine translation with cultural awareness.  _ArXiv_ , abs/2305.14328, 2023.  URL https://api.semanticscholar.org/CorpusID:258841694.
  * Young et al. (2024) Alex Young, Bei Chen, Chao Li, Chengen Huang, Ge Zhang, Guanwei Zhang, Heng Li, Jiangcheng Zhu, Jianqun Chen, Jing Chang, et al.  Yi: Open foundation models by 01. ai.  _arXiv preprint arXiv:2403.04652_ , 2024.
  * Yue et al. (2023) Xiang Yue, Yuansheng Ni, Kai Zhang, Tianyu Zheng, Ruoqi Liu, Ge Zhang, Samuel Stevens, Dongfu Jiang, Weiming Ren, Yuxuan Sun, et al.  Mmmu: A massive multi-discipline multimodal understanding and reasoning benchmark for expert agi.  _arXiv preprint arXiv:2311.16502_ , 2023.
  * Zheng et al. (2023) Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li, Eric P. Xing, Haotong Zhang, Joseph Gonzalez, and Ion Stoica.  Judging llm-as-a-judge with mt-bench and chatbot arena.  _ArXiv_ , abs/2306.05685, 2023.  URL https://api.semanticscholar.org/CorpusID:259129398.
  * Ziems et al. (2023) Caleb Ziems, Jane Dwivedi-Yu, Yi-Chia Wang, Alon Halevy, and Diyi Yang.  Normbank: A knowledge bank of situational social norms.  _arXiv preprint arXiv:2305.17008_ , 2023.

##  Appendix A Appendix

###  A.1 Supplementary Related Work

Benchmarks for LLMs Previous work has created multilingual datasets in
Question-Answering setting (Clark et al., 2020; Longpre et al., 2021).
Currently, there are some popular benchmarks in Multiple Choice Question
format to effectively assess LLMs’ performances, for example, MMLU (Hendrycks
et al., 2021b; a), MMMU (Yue et al., 2023), ARC dataset (Clark et al., 2018),
Truthful QA (Lin et al., 2021).

###  A.2 Additional Details on User Experiment

##### Recruitment Eligibility Criteria

We recruit students from a natural language processing class in an academic
institution. All students, regardless of their cultural backgrounds (including
students with a background in the U.S. culture), are invited to participate.

##### User Demographic Description

We have collected self-reported demographic information from users.

In our study, we have 46 users in total (pivot round: 11; main round: 35). It
covers diverse ethnic groups, for example, East Asian with the highest
proportion (48.1%), White with 17.3%, South Asian with 13.5%, and Middle East
with 9.6%.

The population skewed towards the age group of 18-24 with 93.5%, education
level of Bachelor’s degree with 80.0%, and gender identity of man with 71.7%.
The demographic information is in Appendix 3. We also collected the number of
years in their longest-living countries apart from the US to understand if our
users have personal living experiences in corresponding regions in Fig. 5.
More than half (30 out of 46) have at least 1 year living in the longest-
living country outside US.

##### Experiment Setup

Experiments consist of a series of 1-hour workshops, each accommodating up to
10 users. In each session, users are randomly grouped into pairs for the trial
of the two system variants. Users are provided with self-contained
instructions outlining the workshop timeline, tutorial material, and access to
the annotation platform. In the workshop, we recommend each user spend about
10 minutes on the tutorial and then start their trial, leaving about 45
minutes for interaction with the system. They are then asked to complete a
post-workshop survey for 5 minutes, capturing their demographic information
along with their overall experience feedback.

The tutorial material for each of the system variants includes a 5-minute
tutorial video demonstrating a full system trial and detailed instructions to
use the system, including brainstorming a culturally sensitive scenario and
common editing strategies with examples. After the video, each user’s starting
time was logged and they were asked to interact with the platform and create
challenging questions without external resources such as ChatGPT. We
encouraged annotators to interact with the system for at least 45 minutes and
leave or extend their interaction at their own will.

However, for the sake of fair comparative analysis between the two variants,
we only included data from annotators who actively engaged with the system for
at least 35 minutes, resulting in 12 annotators for the Verifier-Only variant
and 15 annotators for the AI-Assisted variant.

Our user studies have two rounds (pivot and main round). Both rounds provide
the same task design and platform. We added more instructions to make it more
self-contained after this round to reduce the questions raised by annotators
during the experiment. For system performance and annotator performance
analysis, the additional instruction is sensitive to annotators therefore we
only included the main round user performance. For our end product (dataset),
the task design and schema do not change so we included both pivot and main
round data.

###  A.3 Demographics

Category | Percentage
---|---
Gender Identity
Man | 71.7%
Woman | 28.3%
Non-binary | 0%
Prefer not to say | 0%
Age
18-24 | 93.5%
25-34 | 4.3%
35-44 | 2.2%
Education Level
Bachelor’s degree | 80.0 %
Master’s degree | 17.8%
Doctorate or professional degree | 2.2%
Ethnicity/Race
African American/Black | 1.9%
Hispanic/Latino/a/x | 0%
Middle Eastern/North African | 1.9%
Native Amercian | 0%
Native Hawaiian or Pacific Islander | 0%
Central Asian | 0%
East Asian | 48.1%
South Asian | 13.5%
Southeast Asian | 7.7%
Middle East/ West Asia | 9.6%
White | 17.3%
Religious Affiliation
Buddhism | 7.0%
Christianity | 11.6%
Hinduism | 11.6%
Islam | 11.6%
Judaism | 0%
Other | 0%
None | 51.2%
Prefer not to say | 7.0%
Table 3: Demographic information on participants in both main round and pivot
studies of our system.

####  A.3.1 Cultures Represented in CulturalBench-v0.1

Figure 4: Proportion of culture represented for CulturalBench-v0.1 in our user
studies of .

####  A.3.2 Example of Classification for Cultures Represented in
CulturalBench-v0.1

Category | Subgroups from users
---|---
By Geographic Location
Chinese | ’Chinese’, ’Chinese-American’, ’Chinese immigrants’
Indian | ’South India’, ’Asian Indian’, ’Hindu Indian’
American | ’American’, ’US mainstream culture’,
| ’American culture’, ’Greek American’
British | ’British’, ’English’
Arab | ’Saudi Arabian Culture’,
| ’Arabic and Islamic cultures’, ’Arab’
Middle Eastern | ’Khaleeji culture’, ’Middle Eastern’
New Zealander | ’New Zealand’, ’Maori’
Hispanic/Latin | ’Hispanic/Spanish-speaking cultures’,
| ’Latin American culture’
Egyptian | ’Egyptian’, ’Egyptian and muslim’
Table 4: Examples for grouping for culture represented with more than one
subgroup based on description from users in our user studies of .

####  A.3.3 Annotators Self-reported Details

Figure 5: Proportion of culture represented for CulturalBench-v0.1 by .

###  A.4 Dataset Example

####  A.4.1 Dataset Schema

Figure 6: CulturalBench-v0.1 Dataset Schema: It consists of Left: Question-
Specific Information and Right: Cultural Contextualization details.

####  A.4.2 Success Attack Examples

Example of success attack
---
Question |  What are some unspoken etiquette in a company dinner in Korea?
Options |  A) Hold the glass with both hands when a younger person is pouring alcohol for you B) Look away from elders while drinking alcohol C) Maintain eye contact the entire time D) Make sure to start eating first
Success Attack: Model Final Response $\neq$ Correct Answer
Model Final Response | A
Correct Answer (by annotator) | B
SUCCESS ATTACK | 1 (Yes)
Represented Culture | Korean
Rationale |  For A) It is only true when the person pouring the alcohol is older than you. It’s not necessary bad manners if you are older. But when drinking the alcohol, its good manners to hide the glass and look away when drinking in front of elders.
Feedback
5: Familiar; 1: Unfamiliar
Annnotator’s Familiarity on Represented Culture | 5
5: Always; 1: Rare
Situation’s commonness in Represented Culture | 4
5: Very difficult; 1: Very Easy
Question’s Difficulty for People Living in the Culture | 2

Table 5: Success Attack Example One in CulturalBench-v0.1: Our Verifier
(gpt-3.5-turbo) answers this question incorrectly.

Example of Success Attack
---
Question |  In Romanian culture, which of the following is common after the passing of a friend, family member, or other person in the community?
Options |  A) Wear colorful dress to the funeral service. B) Attend a viewing session of the ashes. C) Burn special incense to ward of evil spirits. D) Eat a special spongy cake.
Success Attack: Model Final Response $\neq$ Correct Answer
Model Final Response | B
Correct Answer (by annotator) | D
SUCCESS ATTACK | 1 (Yes)
Represented Culture | Romanian
Rationale |  The cake is called ”coliva”, and is extremely common (I’ve never been to a Romanian funeral without one). Cremation is not common as far as I know, so there probably wouldn’t be ash and viewing them definitely is not a common activity. The other two options (A and C) are also incorrect.
Feedback
5: Familiar; 1: Unfamiliar
Annnotator’s Familiarity on Represented Culture | 5
5: Always; 1: Rare
Situation’s commonness in Represented Culture | 4
5: Very difficult; 1: Very Easy
Question’s Difficulty for People Living in the Culture | 1

Table 6: Success Attack Example Two in CulturalBench-v0.1: Our Verifier
(gpt-3.5-turbo) answers this question incorrectly.

####  A.4.3 Fail-to-attack Example

Example of Fail Attack
---
Question |  In Turkish culture, when do children typically move out of their parents’ house?
Options |  A) When they begin their undergraduate studies. B) When they start their first job. C) When they can find a spouse. D) When they turn 18.
Fail-to-Attack: Model Final Response $=$ Correct Answer
Model Final Response | C
Correct Answer (by annotator) | C
SUCCESS ATTACK | 0 (No)
Represented Culture | Turkish
Rationale |  Young adults don’t typically move out of their homes until it is time to get married.
Feedback
5: Familiar; 1: Unfamiliar
Annnotator’s Familiarity on Represented Culture | 5
5: Always; 1: Rare
Situation’s commonness in Represented Culture | 4
5: Very difficult; 1: Very Easy
Question’s Difficulty for People Living in the Culture | 1

Table 7: Fail-to-attack Example in CulturalBench-v0.1: Our Verifier
(gpt-3.5-turbo) answers this question correctly.

####  A.4.4 Detailed Examples in CulturalBench-v0.1

Example | Question | Model Responses
---|---|---
1 (Indian) |  Q: What is defined as vegetarian in India? A) Not eating seafood, meat, or eggs B) Not eating seafood or meat C) Not eating seafood, meat, eggs, or root vegetables D) All of the above |  GPT-4: D ✓ Others: A or B
Rationale | All of the above are considered vegetarian in India,but just different types of vegetarian.
2 (Chinese) |  Q: In China, what age is important in career life? A) 20 B) 25 C) 30 D) 35 |  GPT-4: D ✓ Others: C
Rationale | Companies usually set the age limit at 35 if you are new in that industry.
3 (Korean) |  Q: What are some unspoken etiquette in a company dinner in Korea? A) Hold the glass with both hands when a younger person is pouring alcohol for you B) Look away from elders while drinking alcohol C) Maintain eye contact the entire time D) Make sure to start eating first |  GPT-4: B ✓ Others: A
Rationale |  For A) It is only true when the person pouring the alcohol is older than you. It’s not necessary bad manners if you are older. But when drinking the alcohol, its good manners to hide the glass and look away when drinking in front of elders.
4 (Chinese) |  Q: How many test do people have to pass to get a driver license in China? A) 1 B) 2 C) 3 D) 4 |  GPT-4: D ✓ Yi: B all other models C
Rationale |  People have to pass 4 tests, which are written exam on laws and traffic regulations and basic concepts on vehicles, parking and basic driving skills test on an obstacle course within school grounds, driving test on the road and written exam on road driving skills and basic knowledge of civilized driving test content.
5 (Chinese) |  Q: In a Chinese cultural context, what will the government do if a couple gives birth to a second child? A) Government issue a fixed amount of fine because this is not allowed. B) Government issue a variable amount of fine based on the couple’s income level because this is not allowed C) Government does not give cash bonus or cash punishment. D) Government send cash bonus to improve the low birth rate in China. |  GPT-4 & Yi: C ✓ Others: A or B
Rationale | Having a second child is allowed in China after 2014.

Table 8: Detailed Examples in CulturalBench-v0.1 with model response.

###  A.5 Experiment Design

Figure 7: Detailed Guidance on Step 1 (subtask 1: Brainstorm) for Verifier-
Only in our system. Figure 8: Detailed Guidance on Step 1 (subtask 2: Draft
Question) for Verifier-Only in our system. Figure 9: Detailed Guidance on Step
1 (subtask 2: Draft Question) for AI-Assisted in our system.

Figure 10: Platform interfaces on Step 1. Left: Users manually draft their
MCQs in Verifier-Only. Right: Users input their culturally specific scenario
and LLM-powered question formulation will help them to convert their scenarios
into MCQs in AI-Assisted.

Figure 11: Detailed Guidance on Step 2 for both Verifier-Only and AI-Assisted
in our system.

Figure 12: Platform interface on Step 2 (Hints). Users verify and revise
themselves in Verifier-Only.

Figure 13: Platform interfaces on Step 2 (Hints). Users verify and revise
themselves with LLM-powered question formulation in AI-Assisted.

Step 1: Question Formulation with AI-assistance
---
Transform the given situation into multiple choice question format in the same
context and same culture. The four options should consist of one right answer
which suit the given culture and three wrong answers which suit other cultures
e.g. US culture. Write it in simple English. Do not include geographical
locations in options given. Follow the format: ///Question: $<$Question$>$
///Options: OA. option1 OB. option2 OC. option3 OD. option4.
Step 2: AI Verifier
You will be given a multiple choice question with four options: A, B, C, D.
MAKE SURE your output is one of the four options stated. Question:
Step 3: Revision Hints by AI
Negate the Question |  Help to rephrase the question by adding negation e.g. not, never, less. For example, INPUT: What is the possible reason on doing this. OUTPUT: What is the possible reason =$>$ What is likely not to be the reason
Concretize the Objects |  Given the question, help to add more specific description on subject or object For example, teacher =$>$ teacher who teach in primary school (add a clause) For example, child =$>$ naughty child (add an adjective); Give one example in 8 words. Do not give suggestion on culture and geological location. Select other subject or object to alter. Format: $<$original$>$ =$>$ $<$example$>$
Alternate Objects |  Given the question, help to change an object in the question with another object that are in same category but different meaning with original object. For example, INPUT: what can teacher do in Chinese culture? OUTPUT: teacher =$>$ tutor For example, INPUT: how would the child in America? OUTPUT: child =$>$ pupil For example, INPUT: what would people do for the dog? OUTPUT: dog =$>$ cat For example, INPUT: what can we see on the left side? OUTPUT: left =$>$ right For example, INPUT: how many gram do people usually buy OUTPUT: gram =$>$ kilogram For example, INPUT: what can a girl do? OUTPUT: girl =$>$ women For example, INPUT: what can a girl do? OUTPUT: girl =$>$ boy Give one example in 8 words. Only give suggestion on object that do not indicate the culture to alter. Only give the word to be changed and the suggestion. Format: $<$original$>$ =$>$ $<$example$>$
Ground Situation in real-life Scenarios |  Change the question by using concrete real-life, everyday story. Keep the question content so the answer towards it should be similar. For example, INPUT: What food do Japanese people like? OUTPUT: What’s a common lunch for Japanese high-school students? For example, INPUT: What are common modes of transportation in India? OUTPUT: How would a office worker in India go to work everyday? For example, INPUT: What is a popular leisure activity in Brazil? OUTPUT: What might a typical family in Brazil do for fun on a Sunday afternoon? Give one example within 10 words. If it is concrete enough, output NA.
Change Quantifiers |  Given the question, change the quantifier in the question. If no quantifier, output NA For example, INPUT: how often is OUTPUT: often =$>$ sometimes For example, INPUT: what is the most OUTPUT: the most =$>$ a few For example, INPUT: What can one pound OUTPUT: one pound =$>$ a thousand pound For example, INPUT: Which thing can we do OUTPUT: NA Give one example within 5 words. Format: $<$original$>$ =$>$ $<$example$>$
Use synonym to change specific terms |  Help to rephrase specific terms by synonmous words or similar concepts. There are two goals here: 1) make meaning inplicit 2) help outsider understand For example, goal 1: make martial status meaning inplicit INPUT: Option: asking for someone’s martial status in job interview OUTPUT: martial status =¿ willingness to have baby For example, goal 2: help outsider understand INPUT: study for Gaokao OUTPUT: Gaokao =¿ public university entrance examination; Give one example for given option in five words. If no suggestion, give NA Start wtih /// Format: ///$<$word to change$>$ =$>$ $<$example in five words$>$
Replace current options by US-centric options as distractor |  Given the question, suggest new options that are common in US culture. Give four different suggestions within 8 words with corresponding US culture norm following the sentence structure of given original option. e.g. [///Do you have any upcoming vacations planned?/// How comfortable are you with remote work?/// How do you balance work and personal life?] Format: [///suggestion///suggestion///suggestion].

Table 9: Prompts Design for Providing LLM Assistance in .

###  A.6 Survey Questions

Figure 14: Feedback Survey per question trial for user studies of .

Figure 15: Overall Survey (Demographic) after the workshop of .

Figure 16: Overall Survey (User Experience) after the workshop of .

###  A.7 Evaluation Details

We evaluate the following private models:

  * •

Claude 3 Opus 20240229 version: the latest and the largest model from
Anthropic (Anthropic, 2024).

  * •

Claude 3 Sonnet 20240229 version: the latest and the second largest model from
Anthropic (Anthropic, 2024).

  * •

GPT-4 Turbo (0125): the latest and largest model from OpenAI (OpenAI, 2023).

  * •

GPT-3.5 Turbo (0125): the latest model in GPT-3.5 series from OpenAI (Brown et
al., 2020).

  * •

Mistral Large: the latest model released by Mistral AI on February 26, 2024.
Apart from English, it is trained to handle European languages e.g. French,
Italian, German, and Spanish.

We also evaluate the following open-source models:

  * •

Mixtral MoE model (8x7b): the latest, mixture of experts 8x7b model released
by Mistral AI on December 11, 2023. Similarly, it is also trained to handle
European languages e.g. French, Italian, German, and Spanish (Jiang et al.,
2024).

  * •

Llama (70b): the latest Llama 2 70b model released by Meta (Touvron et al.,
2023).

  * •

Mistral (7b): the latest small model released by Mistral AI on September 27,
2023 (Jiang et al., 2023).

  * •

Yi (34b): the latest, bilingual (English, Chinese) model based on the same
framework as Llama models built by 01.AI (Young et al., 2024).

We evaluate these models by our CulturalBench-v0.1 in zero-shot setting with
greedy decoding (temperature = 0, top-p = 0). 333Mistral Large API forces to
use temperature = 1 when greedy decoding We adopted the same prompt using the
LLM Verifier and then followed with our Multiple Choice Question:

“You will be given a multiple choice question with four options: A, B, C, D.
Return only the option, and nothing else. MAKE SURE your output is one of the
four options stated. Question:”

The output given by the models will be compared with our correct answer
(golden standard). We calculate the correct answer rate for comparison.

####  A.7.1 Detail on the qualitative evaluation of Yi model by prompting
Chinese

For the evaluation of the hypothesis on the struggle of models on
generalization knowledge learned in Chinese to English, we selected one
question (the driver’s license question) to test. We prompted Yi models with
the driver’s license question in Chinese as well as the instruction prompt in
Chinese. The model response (translated into English) is as follows:

“In China, people usually need to pass at least 4 tests to get a driver’s
license. These tests include: Theoretical test (also known as Subject One):
This is a test of traffic regulations and related knowledge. Driving skills
test on site (also known as Subject Two): This includes various driving skill
tests in a closed field, such as reversing into a garage, sideways parking,
starting on a gradient, etc. Road driving skills test (also known as Subject
Three): This includes a driving test on actual roads, assessing the
candidate’s driving skills and compliance with traffic rules. Test on common
knowledge of safe and civilized driving (also known as Subject Four): This is
a test on safe driving and handling of emergency situations. Therefore, the
correct answer is: D. 4”

###  A.8 Supplementary Results

####  A.8.1 Annotation Efficiency

We analyzed the data in three groups: 1) All questions created 2) Questions
that successfully attack 3) Questions trials after the first time (which acts
as the self-learning trial for adaptation). We have conducted the Two-sided
Student t-test to test if the difference of average numbers between two
variants is significantly different from zero at $p=0.1$.

#### Time Needed

Type | Verifier-Only | AI-Assisted | $\Delta$
---|---|---|---
Whole Question Template Creation
All questions created | $426.8_{163.6}$ | $605.1_{404.0}$ | $178.2$
Questions that successfully attack | $426.4_{181.1}$ | $590.9_{413.3}$ | $164.45$
Questions trials after the first time | $461.25_{279.4}$ | $520.6_{348.4}$ | $59.35$
Initial Question Template Formulation
All questions created | $183.4_{105.2}$ | $161.8_{109.4}$ | -21.6
Questions that successfully attack | $1181.9_{107.9}$ | $164.5_{107.4}$ | $-17.4$
Questions trials after the first time | $195.6_{135.6}$ | $170.3_{147.3}$ | $-25.3$
Revision
All questions created | $95.8_{94.0}$ | $248.2_{260.0}$ | $152.4^{*}$
Questions that successfully attack | $101.3_{101.2}$ | $235.8_{263.2}$ | $134.55$
Questions trials after the first time | $161.9_{188.7}$ | $236.4_{196.9}$ | $74.48$
Table 10: Average time taken per question (in seconds) for question creation
both variants at $p=0.1$.

#### Number of revisions

Verifier-Only | AI-Assisted | $\Delta$
---|---|---
All questions created
$3.00_{2.92}$ | $10.20_{11.05}$ | $7.19^{*}$
Questions that successfully attack
$3.66_{4.52}$ | $10.20_{11.23}$ | $6.53^{*}$
After first trial
$7.50_{8.46}$ | $8.73_{7.59}$ | $1.23$
Table 11: Average number of edits per question per question created in both
variants with t-test at $p=0.1$.

####  A.8.2 Success Attack

To analyze the data quality of the curated red teaming dataset by our system,
we compared the two datasets by our two variants in terms of the number of
questions that successfully challenge the LLM’s cultural understanding.

##### Success Attack Question

Each MCQ designed to evaluate the LLM’s multicultural understanding can be
considered an attack, and when the correct answer choice is not selected by an
LLM, the attack is considered successful. Users in Verifier-Only (N=12)
created 4.18 questions (SD = 1.47) and those in AI-Assisted (N=15) created
3.71 questions (SD = 2.62). For the proportion of successful attacks per user,
each user in Verifier-Only created 76% (SD=29%) on average, compared to the
AI-Assisted group with 68% (SD=30%) on average, indicating no significant
difference between the two variants on the numbers of successful attacks, as
well as the proportion among all questions generated.

Verifier-Only | AI-Assisted | $\Delta$
---|---|---
Num of questions that successfully attack
$4.19_{1.47}$ | $3.71_{2.62}$ | $-0.47$
Proportion of successfully attack among all
$0.76_{0.29}$ | $0.68_{0.30}$ | $-0.07$
Table 12: Average number of success attacks, and the proportion of success
task per question for whole question creation in both groups.

####  A.8.3 Annotator experience

#### Feedback per question trial

Verifier-Only | AI-Assisted | $\Delta$
---|---|---
Difficulty to trick AI
5: very difficult; 1: very easy
$2.67_{1.18}$ | $2.60_{1.08}$ | $-0.07$
Difficulty of using system
5: very difficult; 1: very easy
$1.83_{0.80}$ | $1.87_{0.72}$ | 0.03
Satisfaction
5: very satisfied; 1: very dissatisfied
$3.67_{0.62}$ | $3.93_{0.57}$ | $0.27$
Table 13: Average scores on feedback survey per question created in both
groups, as shown in Appendix Fig. 14.

In Table 13, we found that users’ perception on the difficulty of trickling AI
and the difficulty of using the system have little differences across the two
variants. Specifically, AI-Assisted was perceived to be slightly more
difficult to trick the AI ( 0.07 out of 5) and also more difficult (0.03 score
out of 5) to use system when compared to Verifier-Only. However, these
differences are not statistically significant. For the satisfaction level, we
found that users gained more satisfaction (0.27 out of 5) when using AI-
Assisted than Verifier-Only with a statistical significance of $p=0.2$. It
indicates that the involvement of AI in initial question forming and editing
may boost users’ satisfaction levels.

#### Feedback for overall experience

variant 1 | variant 2 | $\Delta$
---|---|---
Ease to navigate and use
5: very difficult; 1: very easy
$1.75_{0.92}$ | $2.07_{0.93}$ | $0.32$
Fostering creativity
5: Very conductive; 1: Very limiting
$3.58_{0.76}$ | $4.13_{0.62}$ | $0.55^{*}$
Table 14: Average scores on overall Survey for each user in both groups, as
shown in Appendix Fig. 16.

##### Ease to navigate and use

Upon analysis of the user accessibility and capability on simulating
creativity level in Table 14, we found that participants did not have
significant differences in perception of the ease of use. One user explained
that the way of thinking about how to make use of the AI-generated suggestion
makes it harder: ”The only (slightly) difficult part was figuring out how to
replace parts of the question using the AI-generated suggestions, but it
didn’t take long to figure that out.”. A couple of users with both more and
less AI-assistance complain about LLMs. Two participants (1 from Verifier-
Only; 1 From AI-Assisted) complained about the time latency, and the
inconsistent output of the LLM model respectively. Our system used GPT-4 to
provide higher-quality hints on their posed questions. To give convenience to
users, we decided to generate all the hints once they submitted their posed
questions and entered the panel of revising. The multiple API requests could
be a reason for the time latency problem. To address this time latency
problem, we instructed models to give a short length of output and give only
one example at a time in our prompt shown in Appendix Table 9 e.g. ”Give one
example in 8 words”. Future work should also balance between details of
responses and waiting time on API calls. For inconsistent output, our system
used the default setting on temperature and top-p to provide a relatively
diverse answer to users. In future work, we could consider using greedy
decoding to give consistent output to avoid confusion to users.


KCL-PH-TH/2023-72

Ricci Flat Metrics, Flat Connections and $G_{2}$-manifolds.

B.S. Acharya and D.A. Baldwin
Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11,
34151, Trieste, Italy

and

Department of Physics, Kings College London, London, WC2R 2LS, UK

Abstract

Inspired by considerations in $M$-theory, we prove the equivalence between the
moduli spaces of (suitably complexified) torsion free $G_{2}$-structures on
7-manifolds which are families of hyperKähler ALE 4-manifolds fibered over
compact flat 3-manifolds $T^{3}/K$ and certain moduli spaces of flat
$G^{\mathbb{C}}_{ADE}$ connections on $T^{3}/K$.

## Introduction

Ricci flat Riemannian manifolds with special holonomy have played an important
role in superstring/$M$-theory as models of extra dimensions of space. In
particular, special kinds of singularities which occur in the moduli spaces of
such spaces have played an important role, as they often have a physical
description in terms of a quantum field theory in lower dimensions, typically
a gauge theory. This then leads to perhaps surprising connections between
moduli spaces of Einstein metrics and moduli spaces in lower dimensional gauge
theory. This note will describe examples of such connections within the
specific context of certain manifolds with holonomy group contained in
$G_{2}$.

This work was inspired by the study of $M$-theory compactifications on so-
called Joyce-Karigiannis manifolds [7] which are constructed from certain
$G_{2}$-holonomy spaces with orbifold singularities that admit topologically
distinct desingularisations and Ricci flat $G_{2}$-holonomy metrics. The
examples of interest here are Ricci flat metrics on 7-manifolds which are
fibered by hyperKähler 4-manifolds over compact flat 3-manifolds. In [1], a
correspondence between the moduli space of $G_{2}$ holonomy metrics on these
7-manifolds, the moduli space of complex flat connections on the 3-manifold
and the vacuum moduli space of the four dimensional theory arising from the
$M$-theory compactification was discovered and used to physically interpret
the topologically distinct desingularisations as Coulomb and Higgs branches of
the four dimensional gauge theory. Other notable aspects were considered by
Barbosa [2, 4] and further related works are [11, 3, 6].

The purpose of this note is to make the correspondences in [1] more precise.
We will derive an isomorphism between the moduli space of complex flat $ADE$
connections on all orientable compact flat 3-manifolds $T^{3}/K$ and a
suitably complexified moduli space of Ricci-flat metrics on certain complete
7-manifolds with $G_{2}$-structures, $(T^{3}\times X_{ADE})/K$, with $X_{ADE}$
a 4-manifold admitting a $K$-invariant hyperKähler metric. The theorems we
prove, in a sense, give a complete description of the classical moduli spaces
of these physical systems or, in more physical terms, a complete description
of the semi-classical vacuum structure.

## Flat Connections and Ricci flat Metrics

### Flat Connections on Flat Manifolds

We begin by a brief description of the moduli space of flat
$G_{ADE}^{\mathbb{C}}$ connections111Throughout this paper, the maximal
compact subgroup of $G_{ADE}^{\mathbb{C}}$ is
$G_{ADE}=SU(N),Spin(2N),E_{6,7,8}.$ modulo gauge transformations on the
3-torus, $T^{3}\cong\mathbb{R}^{3}/\Lambda$, denoted
$\mathcal{M}(T^{3},G_{ADE}^{\mathbb{C}})$ These are given by homomorphisms
($\mathsf{R}$) from $\pi_{1}(T^{3})=\Lambda\cong\mathbb{Z}^{3}$ to
$G_{ADE}^{\mathbb{C}}$ modulo conjugation by $G_{ADE}^{\mathbb{C}}$. Up to
conjugation, this is thus a commuting triple $\mathsf{R}(g_{i})$ of elements
of $G_{ADE}^{\mathbb{C}}$ in the representation $\mathsf{R}$. In general,
$\mathcal{M}(T^{3},G_{ADE}^{\mathbb{C}})$ will have multiple components [8, 5,
9, 12]. Here it will suffice to describe the component containing the trivial
connection, $R(g_{i})=\mathbb{1}$, denoted by
$\mathcal{M}_{0}(T^{3},G_{ADE}^{\mathbb{C}})$. In this case all three elements
belong to the same maximal torus
$\mathcal{T}^{\mathbb{C}}\equiv\mathbb{C}^{*}\otimes\mathfrak{h}_{ADE}\subset
G_{ADE}^{\mathbb{C}}$, with $\mathfrak{h}_{ADE}$ the Cartan subalgebra of
$G_{ADE}$. Since conjugation into the $\mathcal{T}$ does not fix the non-
identity connected gauge transformations preserving $\mathcal{T}$, one is left
with residual gauge transformations by elements of the Weyl group,
$\mathcal{W}_{ADE}$ of $G_{ADE}$, hence we have that

$\mathcal{M}_{0}(T^{3},G_{ADE}^{\mathbb{C}})\equiv(\mathcal{T^{\mathbb{C}}})^{3}/\mathcal{W}_{ADE}$
(1)

Next we consider flat connections on an orientable compact flat 3-manifold
$M^{3}_{K}=T^{3}/K$. Since $M_{K}^{3}$ is smooth and flat, $K$ is a finite
group of isometries acting freely on $T^{3}$. Such manifolds are classified
and the possibilities are
$K=\mathbb{1},\mathbb{Z}_{2},\mathbb{Z}_{3},\mathbb{Z}_{4},\mathbb{Z}_{6},\mathbb{Z}_{2}\times\mathbb{Z}_{2}$.
Their fundamental groups are described explicitly in table 1.

The fundamental group $\pi_{1}(M^{3}_{K})$ fits into an exact sequence of
groups:

$0\rightarrow\Lambda\rightarrow\pi_{1}(M^{3}_{K})\rightarrow K\rightarrow 1$
(2)

A flat connection on $M^{3}_{K}$ is, up to conjugation, a homomorphism
$\operatorname{Hom}(\pi_{1}(M^{3}_{K}),G_{ADE}^{\mathbb{C}})$ and the above
sequence implies the following,

$\operatorname{Hom}(K,G_{ADE}^{\mathbb{C}})\to\operatorname{Hom}(\pi_{1}(M_{k}^{3}),G_{ADE}^{\mathbb{C}})\to\operatorname{Hom}(\Lambda,G_{ADE}^{\mathbb{C}})$
(3)

One can thus view a flat connection on $M^{3}_{K}$ as a flat connection on
$T^{3}$ which is $K$-invariant, as the elements of
$\operatorname{Hom}(K,G_{ADE}^{\mathbb{C}})$ act on
$\operatorname{Hom}(\Lambda,G_{ADE}^{\mathbb{C}})$. Thus, the moduli space of
flat $G_{ADE}^{\mathbb{C}}$ connections on $T^{3}/K$ is given by the
$K$-invariant subspace of the flat connections on $T^{3}$,

$\mathcal{M}(T^{3}/K,G_{ADE}^{\mathbb{C}})=\left(\mathcal{M}(T^{3},G_{ADE}^{\mathbb{C}})\right)^{K}$
(4)

We will often be interested in the $K$-invariant flat connections which come
from the identity connected flat connections on $T^{3}$:

$\left(\mathcal{M}_{0}(T^{3},G_{ADE}^{\mathbb{C}})\right)^{K}$ (5)

In table 1 we give a description of the fundamental group relations for all
$K$ which must therefore be satisfied by any flat connection
$\mathsf{R}\in\operatorname{Hom}(\pi_{1}(M^{3}_{K}),G_{ADE}^{\mathbb{C}})$.
From here we see that, if $\mathsf{R}(g_{1,2,3})$ all belong to the same
maximal torus $\mathcal{T}$,

$\mathsf{R}(K):\mathcal{T}\rightarrow\mathcal{T}$ (6)

Since $\mathsf{R}(K)$ preserves $\mathcal{T}$ we can regard it as representing
$\mathsf{N}(\mathcal{T})$, the normaliser of this maximal torus. However, the
action of $\mathcal{T}$ on $\mathsf{R}(K)$ by conjugation is a gauge
transformation which reduces the independent degrees of freedom to those of
the Weyl group: $\mathsf{N}(\mathcal{T})/\mathcal{T}=\mathcal{W}_{ADE}$.

######  Theorem 1.

Suppose
$\mathsf{R}\in\operatorname{Hom}(\pi_{1}(M^{3}_{K}),G_{ADE}^{\mathbb{C}})$ is
a flat ADE-connection whose restriction to
$\mathsf{R}(\Lambda)\subset\mathcal{M}_{0}(T^{3},G_{ADE}^{\mathbb{C}})$. Then
all such flat connections are in one-to-one correspondence with
$\operatorname{Hom}(K,\mathcal{W}_{ADE}$).

Proof. Given a homomorphism $\mathsf{R}^{\prime}(K)$ in
$\operatorname{Hom}(K,\mathcal{W}_{ADE})$, one has a $K$-action on
$\mathcal{M}_{0}(T^{3},G_{ADE}^{\mathbb{C}})$ and the $K$-invariant subspace,
taken together with $\mathsf{R}^{\prime}(K)$ is a flat connection on
$M^{3}_{K}$. Conversely, given a flat connection on $M^{3}_{K}$ with
$\mathsf{R}(\Lambda)\subset\mathcal{M}_{0}(T^{3},G_{ADE}^{\mathbb{C}})$,
$\mathsf{R}(K)\subset\mathcal{N}(T)$ is gauge equivalent to a subgroup of
$\mathcal{W}_{ADE}$. $\blacksquare$

One can also treat all flat connections on $M^{3}_{K}$, not just those that
restrict to identity connected connections on $T^{3}$. Given a non-identity
flat $ADE$-connection $A$ on $T^{3}$, one can consider the centraliser (or
commutant) $C(A)$. This is the subgroup of $G_{ADE}$ commuting with $A$. Then,
what we would like is for Theorem 1 to apply, but replacing
$\mathcal{W}_{ADE}$ with the Weyl group of $C(A)$. This is in fact true, but
only if $A$ is $K$-invariant.

$K$ | Relations
---|---
$\mathbb{1}$ | $g_{i}g_{j}=g_{j}g_{i},\qquad i,j\in\\{1,2,3\\}$
$\mathbb{Z}_{2}$ | $g_{\beta}\,g_{1,2}\,g_{\beta}^{-1}=g_{1,2}^{-1},\qquad g_{\beta}\,g_{3}\,g_{\beta}^{-1}=g_{3},\qquad g_{\beta}^{2}=g_{3}$
$\mathbb{Z}_{3}$ |  $g_{\beta}\,g_{1}vg_{\beta}^{-1}=g_{2},\qquad g_{\beta}\,g_{2}\,g_{\beta}^{-1}=g_{1}^{-1}\,g_{2}^{-1}$,
| $g_{\beta}\,g_{3}\,g_{\beta}^{-1}=g_{3},\qquad g_{\beta}^{3}=g_{3}$
$\mathbb{Z}_{4}$ |  $g_{\beta}\,g_{1}\,g_{\beta}^{-1}=g_{2}^{-1},\qquad g_{\beta}\,g_{2}\,g_{\beta}^{-1}=g_{1}$,
| $g_{\beta}\,g_{3}\,g_{\beta}^{-1}=g_{3},\qquad g_{\beta}^{4}=g_{3}$
$\mathbb{Z}_{6}$ |  $g_{\beta}\,g_{1}\,g_{\beta}^{-1}=g_{1}\,g_{2},\qquad g_{\beta}\,g_{2}\,g_{\beta}^{-1}=g_{1}^{-1}$,
| $g_{\beta}\,g_{3}\,g_{\beta}^{-1}=g_{3},\qquad g_{\beta}^{6}=g_{3}$
$\mathbb{Z}_{2}\times\mathbb{Z}_{2}$ | $g_{\beta_{i}}\,g_{i}\,g_{\beta_{i}}=g_{i},\quad g_{\beta_{i}}^{2}=g_{i},$
| $g_{\beta_{i}}\,g_{j}\,g_{\beta_{i}}^{-1}=g_{j}^{-1},\quad i\neq j,\quad
i,j\in\\{1,2,3\\}$
| $g_{\beta_{3}}=g_{1}\,g_{\beta_{2}}\,g_{\beta_{1}}$
Table 1: The fundamental group relations for $T^{3}/K$ for all $K$. In all
cases the elements $g_{1,2,3}$ mutually commute.

We arrive at the following conclusion: the number of branches of the moduli
space of flat $G_{ADE}^{\mathbb{C}}$ connections on $T^{3}/K$ satisfying the
conditions of Theorem 1 is the same as the number of inequivalent
homomorphisms from $K$ to $\mathcal{W}_{ADE}$.

### Ricci flat ALE metrics and $G_{2}$-structures.

Having classified flat $ADE$ connections on $M^{3}_{K}$ we now turn to proving
the equivalence to certain moduli spaces of Einstein 7-manifolds with torsion
free $G_{2}$-structures as predicted by $M$-theory. The idea is that
$M$-theory on 7-manifolds of the form $X^{7}=(T^{3}\times X_{ADE})/K$ where
$X_{ADE}=\widetilde{\mathbb{C}^{2}/\Gamma_{ADE}}$ is a smooth resolution of
the orbifold admitting a Ricci flat, hyperKähler, asymptotically locally
Euclidean (ALE) metric, has a moduli space which is identical to the moduli
space of flat $ADE$ connections on $M^{3}_{K}$ whose restriction to $T^{3}$
lies in $\mathcal{M}_{0}(T^{3},G_{ADE}^{\mathbb{C}})$.

In more detail, we consider

$X=\frac{(T^{3}\times X_{ADE})}{K}$ (7)

with a Ricci flat metric

$g=d\vec{y}^{2}+h$ (8)

and a $K$-invariant torsion free $G_{2}$-structure

$\varphi=dy^{1}dy^{2}dy^{3}+d\vec{y}\cdot\vec{\omega},$ (9)

Here, $\vec{y}$ are Euclidean coordinates on $T^{3}$, $h$ is a $K$-invariant
hyperKähler metric on $X_{ADE}$ and $\vec{\omega}$ define the hyperKähler
structure on $X_{ADE}$. Any such metric corresponds to a $K$-invariant
desingularisation of the flat 7-orbifold
$X_{0}=\frac{(T^{3}\times\mathbb{C}^{2}/\Gamma_{ADE})}{K}$. In general, as we
discussed in [1], there will be multiple topologically distinct
desingularisations of the same singularity, leading to multiple components to
the moduli space of Ricci flat metrics.

We begin by desribing the moduli space of Ricci flat metrics for
$K=\mathbb{1}$.

######  Proposition 1 (Kronheimer [10]).

The moduli space of ALE hyperKähler metrics on $X_{ADE}$ is
$\mathcal{M}_{ALE}=(\mathbb{R}^{3}\otimes\mathfrak{h})_{ADE}/\mathcal{W}_{ADE}$.

From this it follows that:

######  Proposition 2.

The moduli space of $SU(2)$ holonomy metrics on $T^{3}\times X_{ADE}$, for a
fixed flat metric on $T^{3}$ is $H_{c}^{3}(T^{3}\times
X_{ADE},\mathbb{R})/\mathcal{W}_{ADE}$.

This follows as the space of $SU(2)$-holonomy metrics is also the space of
torsion free $G_{2}$-structures and
$H^{2}_{c}(X_{ADE})\cong\mathfrak{h}_{ADE}$ and
$H^{1}(T^{3})\cong\mathbb{R}^{3}$. The Weyl group action here constitutes a
group of non-identity connected diffeomorphisms since it acts non-trivially on
the homology.

Asides from the Ricci flat metric, the $M$-theory moduli space has another
contribution coming from the so-called $C$-field and its moduli space is given
by:

######  Proposition 3.

$H_{c}^{3}(T^{3}\times
X_{ADE},\mathbb{R/Z})\cong(T^{3}\otimes\mathfrak{h}_{ADE})$ which also has an
obvious action by $\mathcal{W}_{ADE}$.

######  Definition.

The local moduli space of $M$-theory on $T^{3}\times X_{ADE}$, for fixed
$T^{3}$, is $T\mathcal{M}^{M}_{ADE}=H_{c}^{3}(T^{3}\times
X_{ADE},\mathbb{R/Z}+\sqrt{-1}\mathbb{R})/\mathcal{W}_{ADE}\cong((S^{1}\times\mathbb{R})^{3}\otimes\mathfrak{h}_{ADE})/\mathcal{W}_{ADE}$.

The $\sqrt{-1}$ is due to supersymmetry, which requires a complex structure on
the moduli space. By exponentiating these Lie algebra valued fields we obtain:

######  Proposition 4.

$\mathcal{M}^{M}_{ADE}\cong\mathcal{M}_{0}(T^{3},G_{ADE}^{\mathbb{C}})$

We now consider the moduli space of $M$-theory on $X=\frac{(T^{3}\times
X_{ADE})}{K}$. This requires constructing $K$-invariant Ricci flat metrics and
$C$-fields on $(T^{3}\times X_{ADE})$ which requires knowing how $K$ acts on
the hyperKähler structure $\vec{\omega}$. Let us denote the $M$-theory moduli
space by $(\mathcal{M}^{M}_{ADE})^{K}$ since it is naturally given by the
$K$-invariant subsets of $\mathcal{M}^{M}_{ADE}$.

In the previous section we classified the $K$-invariant subspaces of the rhs
of proposition 4. Hence, the same must be true of the $M$-theory moduli space
$\mathcal{M}^{M}_{ADE}$. This, however, implies that the appropriate
$K$-invariant Ricci flat metrics exist. In [1] we established that this is the
case for $G_{ADE}=\operatorname{SU}(N)$ and $G_{ADE}=\operatorname{Spin}(2N)$,
but not explicitly for $G_{ADE}=E_{6,7,8}$. For example, for
$G_{ADE}=\operatorname{SU}(N)$, the hyperKähler metrics are given by a
Gibbons-Hawking ansatz on circle bundles over
$\mathbb{R}^{3}\backslash\\{p_{1},p_{2},...,p_{N}\\}$ where the $N$-points
$p_{i}$ determine where the circle fibers degenerate to zero size. To obtain a
$K$-invariant metric, one must consider $K$-invariant configurations of points
in $\mathbb{R}^{3}$, where $K$ acts linearly as $K\subset SO(3)$. These are in
one-to-one correspondence with homomorphisms from $K$ to
$\mathcal{W}_{A_{N}}\cong S_{N}$. A similar construction establishes the
analogous statement for $G_{ADE}=\operatorname{Spin(2N)}$ [1]. Hence, we have
proven that

######  Theorem 2.

$(\mathcal{M}^{M}_{ADE})^{K}\cong\mathcal{M}_{0}(T^{3},G_{ADE}^{\mathbb{C}})^{K}$
for $G_{ADE}=\operatorname{SU}(N)$ and $G_{ADE}=\operatorname{Spin}(2N)$

This establishes for these cases that the $M$-theory moduli spaces and the
space of flat connections on $M^{3}_{K}$ satisfying the conditions of theorem
1 are isomorphic. We leave it as a conjecture for $G_{ADE}=E_{6,7,8}$.

## References

  * [1] Bobby Samir Acharya and Daniel Andrew Baldwin.  Coulomb and Higgs phases of $G_{2}$-manifolds.  arXiv preprint arXiv:2309.12869, 2023.
  * [2] Rodrigo Barbosa.  Harmonic Higgs bundles and coassociative ALE fibrations.  arXiv preprint arXiv:1910.10742, 2019.
  * [3] Rodrigo Barbosa, Mirjam Cvetič, Jonathan J. Heckman, Craig Lawrie, Ethan Torres, and Gianluca Zoccarato.  T-branes and $G_{2}$ backgrounds.  Phys. Rev. D, 101(2):026015, 2020.
  * [4] Rodrigo De Menezes Barbosa.  Deformations of $G_{2}$-structures, string dualities and flat Higgs bundles.  PhD thesis, 2019.
  * [5] Armand Borel, Robert Friedman, and John W Morgan.  Almost commuting elements in compact Lie groups.  American Mathematical Soc., 2002.
  * [6] Max Hubner.  Local G2-manifolds, Higgs bundles and a colored quantum mechanics.  JHEP, 05:002, 2021.
  * [7] Dominic Joyce and Spiro Karigiannis.  A new construction of compact torsion-free $G_{2}$-manifolds by gluing families of eguchi–hanson spaces.  Journal of Differential Geometry, 117(2):255–343, 2021.
  * [8] V. G. Kac and A.V. Smilga.  Vacuum structure in supersymmetric Yang-Mills theories with any gauge group.  In M. Shifman, editor, The Many Faces of the Superworld: Yuri Golfand Memorial Volume, pages 185–234. World Scientific, 2000.
  * [9] Arjan Keurentjes.  New vacua for Yang-Mills theory on a three torus.  Thesis, June 2000.
  * [10] Peter B Kronheimer.  The construction of ALE spaces as hyper-Kähler quotients.  Journal of differential geometry, 29(3):665–683, 1989.
  * [11] Tony Pantev and Martijn Wijnholt.  Hitchin’s equations and M-theory phenomenology.  Journal of Geometry and Physics, 61(7):1223–1247, 2011.
  * [12] Edward Witten.  Supersymmetric index in four-dimensional gauge theories.  Adv. Theor. Math. Phys., 5:841–907, 2002.