# Multi-Cultural Commonsense Knowledge Distillation

Tuan-Phong Nguyen♠ Simon Razniewski♢ Gerhard Weikum♠
$\spadesuit$ Max Planck Institute for Informatics, Saarbrücken, Germany
$\diamondsuit$ Bosch Center for Artificial Intelligence, Renningen, Germany
<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Despite recent progress, large language models (LLMs) still face the challenge
of appropriately reacting to the intricacies of social and cultural
conventions. This paper presents Mango, a methodology for distilling high-
accuracy, high-recall assertions of cultural knowledge. We judiciously and
iteratively prompt LLMs for this purpose from two entry points, concepts and
cultures. Outputs are consolidated via clustering and generative
summarization. Running the Mango method with GPT-3.5 as underlying LLM yields
167K high-accuracy assertions for 30K concepts and 11K cultures, surpassing
prior resources by a large margin. For extrinsic evaluation, we explore
augmenting dialogue systems with cultural knowledge assertions. We find that
adding knowledge from Mango improves the overall quality, specificity, and
cultural sensitivity of dialogue responses, as judged by human annotators.
Data and code are available for download111https://bit.ly/cultural-csk.

Multi-Cultural Commonsense Knowledge Distillation

Tuan-Phong Nguyen♠ Simon Razniewski♢ Gerhard Weikum♠ $\spadesuit$ Max Planck
Institute for Informatics, Saarbrücken, Germany $\diamondsuit$ Bosch Center
for Artificial Intelligence, Renningen, Germany {tuanphong,weikum}@mpi-
inf.mpg.de<EMAIL_ADDRESS>

##  1 Introduction

#### Motivation:

The theme of enhancing computers with commonsense knowledge (CSK) has been
revived in recent years, to improve the robustness and versatility of AI-
powered NLP methods (e.g., Bosselut et al. (2019); Hwang et al. (2021); West
et al. (2022); Choi (2022)). CSK collections, such as ConceptNet Speer et al.
(2017) and ATOMIC Sap et al. (2019), capture assertions about mundane objects
and human activities in a broad sense, so as to provide universal background
knowledge. However, norms for human behavior are often diverse, with
substantial diversity across different parts of the world and different socio-
cultural groups. For example, when two people meet, they shake hands in the
Western world, but this would be uncommon in Southeast Asia (where people wai
each other), and teenagers have yet another way of greeting. Therefore, to
adapt AI applications to specific user contexts, the goal of this research is
to capture culturally aware commonsense knowledge, CCSK for short.

An NLP task where cultural knowledge can play a game-changing role is human-
computer dialogue, where the system should consider the human’s cultural
background. An even more challenging case is conversations between two
partners from different cultures; we call this case intercultural dialogue.
Computers can take one, both or none of the roles in this setting; in the
latter case, it could still be important to have cultural knowledge to analyze
and post-process the dialogue (e.g., generate a de-briefing summary).

#### State of the Art and its Limitations:

On this nascent direction, resources for cultural knowledge have limited scope
and scale (e.g., Acharya et al. (2020), StereoKG Deshpande et al. (2022),
Candle Nguyen et al. (2023b)). The by far largest of these is the Candle
knowledge base, which comprises ca. 60K assertions automatically distilled
from nearly 1M sentences mined from a large web crawl. This is still
insufficient in coverage of concepts and cultural groups. Note that cultures
are not just geo-regions, but should ideally consider also demographic and
social traits of the respective groups (e.g., female teenagers in Korea,
French people of North-African descent, etc.).

An obvious idea is to abandon explicit assertions, and instead rely on the
latent knowledge provided by large language models (LLMs). Indeed, LLMs
perform well on tasks that require understanding the personal background of
users in conversational settings. However, there are severe disadvantages: (i)
strong dependence on the quality of the training corpus (which may exhibit
certain biases and risks of hallucination); (ii) lack of transparency of what
piece of knowledge is utilized in which context; (iii) as a result, lack of
controllability for programmed applications; and (iv) lack of interpretability
by end-users. For these reasons, our approach is to construct transparent and
tangible collections of explicit assertions, which can later be judiciously
injected into LLMs for specific tasks.

#### Challenges and Research Questions:

The twofold challenge is to expand the coverage of cultural groups and
culture-specific assertions, while maintaining or even improving the quality
of the assertions. This poses three research questions:

  * •

RQ1: How can we systematically capture more and diverse cultural groups?

  * •

RQ2: How can we substantially enlarge the amount of captured assertions, going
beyond single-sentence retrieval from the web?

  * •

RQ3: How can we ensure the specificity of assertions, while avoiding undue
stereotypes and limiting redundancy due to frequency bias?

#### Approach and Contribution:

The methodology devised in this work, called Mango (multi-cultural commonsense
knowledge distillation), comprises two stages: a coverage-oriented stage for
assertion generation, and a quality-oriented stage for assertion
consolidation. The first stage addresses RQ1 and RQ2, and the second addresses
RQ3.

To enlarge the pool of candidates, we leverage a large language model (LLM),
specifically GPT-3.5, to generate assertions. Unlike prior works that tapped
into web crawls, this is an implicit way of tapping the LLM’s pre-training
collection. Compared to web retrieval, the scales are similar but the
advantage is that LLM training data involves efforts to remove spam and
offensive content. Asking an LLM to generate assertions requires judicious
prompting. For high coverage of diverse cultures, an important novelty in our
method is to construct prompts for both concepts (incl. human activities) from
an existing (culturally agnostic) commonsense knowledge base and groups from a
large pool of cultures.

To ensure the informativeness of assertions and to tame the redundancy of
generated candidates (RQ3), the second stage consists of steps for assertion
consolidation. This is carried out by clustering the pool of assertions into
topically and culturally coherent groups, considering both the key concept in
an assertion and the culture to which it refers. The LLM is leveraged again to
generate a concise summary statement for each cluster. This exploits the LLM’s
language skills, but does not rely on actual knowledge by the LLM.

The main contributions of this work are:

  * 1\.

The Mango methodology for efficiently distilling CCSK from LLMs, at high
precision and recall.

  * 2\.

Running the Mango method with GPT-3.5, to obtain 167K assertions for 30K
concepts and 11K cultures, substantially surpassing prior CCSK resources in
size and quality.

  * 3\.

An extrinsic evaluation for intercultural dialogues, where the injection of
Mango assertions significantly improves the specificity and cultural
sensitivity of responses.

##  2 Related Work

#### Commonsense Knowledge Acquisition:

Commonsense knowledge (CSK) has a long tradition in AI Lenat (1995); Liu and
Singh (2004); Gordon et al. (2010). Early projects such as Cyc Lenat (1995)
and ConceptNet Liu and Singh (2004); Speer and Havasi (2012); Speer et al.
(2017) rely on human contributors and focus on collecting CSK about everyday
concepts. This approach has been revived in the ATOMIC project Sap et al.
(2019), which collects CSK about social interactions and events.

Another line of CSK acquisition methods is based on text extraction, for
example, WebChild Tandon et al. (2014), Quasimodo Romero et al. (2019),
TransOMCS Zhang et al. (2020), and Ascent Nguyen et al. (2021, 2023a). These
are more scalable, but contain noise and have lower assertion quality.

With the advent of LLMs, methods have been devised for generating CSK
assertions from language models (e.g., Bosselut et al. (2019); Petroni et al.
(2019); Hwang et al. (2021); West et al. (2022); Cohen et al. (2023); West et
al. (2023)). None of these captures culture-aware knowledge, though.

#### Cultural Knowledge Acquisition:

There are only few works on culture-aware knowledge: Anacleto et al. (2006),
Acharya et al. (2020), Shwartz (2022), StereoKG Deshpande et al. (2022),
Candle Nguyen et al. (2023b), and GD-COMET Bhatia and Shwartz (2023). These
methods are based on extraction from text Deshpande et al. (2022); Shwartz
(2022); Nguyen et al. (2023b), or fine-tuning LLMs Bhatia and Shwartz (2023).
The resulting assertions either suffer from high noise or limited coverage,
with the largest resource, Candle, providing 60K assertions. Most recently,
CH-Wang et al. (2023) aligned social situations from an English knowledge base
Forbes et al. (2020) and Chinese QA forums to mine 3,069 social norms for
these two cultures. All of these prior works are very limited in scope and
scale.

#### Culture-aware NLP:

Several benchmarks exist for tasks that involve cultural knowledge beyond the
Western world, e.g., MaRVL Liu et al. (2021), GD-VCR Yin et al. (2021),
GeoMLAMA Yin et al. (2022), CALI Huang and Yang (2023), and FORK Palta and
Rudinger (2023). Some methods (e.g., Li and Zhang (2023), Zhou et al. (2023))
have used LLMs to solve tasks of this kind. Most recently, contemporaneous
work Fung et al. (2024) extracts 148K cultural norms and norm violations from
Wikipedia texts, and uses these to benchmark cultural knowledge and reasoning
skills of LLMs.

Harnessing explicit CSK assertions for dialogue systems has been studied in
Kim et al. (2023), based on the ATOMIC resource (about social interactions).
NormDial Li et al. (2023) is a small collection of 267 human-written social
norms specific to America and China, used to generate a bilingual dialogue
dataset on social norms adherence or violation. In this work, we aim at a much
broader coverage of diverse cultures, and apply our large-scale Mango
collection to the task of intercultural dialogues.

##  3 Cultural Commonsense Knowledge Distillation Workflow

We propose Mango, a workflow for distilling and consolidating cultural
commonsense knowledge (CCSK) from large language models (LLMs).

######  Definition 1 (Cultural commonsense knowledge assertion).

A cultural commonsense knowledge (CCSK) assertion $a=(c;g;s)$ is a triple of a
concept $c$; a culture/cultural group $g$; and a natural-language statement
$s$ that represents a cultural belief, norm, or common practice about the
concept $c$ that applies to group $g$. An example CCSK assertion is: (tipping;
Japan; Not a common practice).

The goal of Mango is to generate CCSK for diverse cultures, covering a wide
variety of concepts. Moreover, by clustering similar assertions, we obtain
ranking signals for the assertions, which can be useful for downstream
applications.

Our workflow consists of 2 phases, each consisting of 2 steps: (1a) generating
CCSK for a given concept, (1b) generating CCSK for a given culture (Section
3.1), (2a) clustering similar CCSK assertions, and (2b) generating cluster
representatives (Section 3.2). An overview of our workflow is depicted in
Figure 1. We also provide input and output examples for each step in Table 1.

Figure 1: Mango’s CCSK distillation workflow. Examples for each step can be
found in Table 1.

###  3.1 Phase 1: Assertion Generation

People of different cultures may have different perspectives on certain
concepts. These differences are what we are interested in, as they are crucial
in situations where cross-cultural knowledge is required to understand one
another. One might ask LLMs to generate CCSK for a given pair of concept _and_
culture (e.g., prompting for perceptions of tipping in Japan). However, the
main drawback of this approach is that it requires concept and culture
pairings, which is problematic because of the large number of possible
combinations, and the fact that some combinations may not make sense.

Instead, we propose to use LLMs to generate CCSK for a given concept or a
given cultural group _separately_. This way we let the model decide which
concepts are relevant for a given cultural group and vice versa, which will
reduce the chance of nonsensical concept-culture combinations, hence reducing
costs. Example prompts and outputs can be seen in Table 1.

For each prompt, we provide the LLM with 5 pairs of example assertions
randomly drawn from a set of human-written CCSK assertions. Each example
consists of a concept, and 2 different perspectives on that concept associated
with 2 or more different cultures (more details on prompt templates can be
found in Appendix A.1). We implement our workflow using GPT-3.5. However, in
practice, other LLMs could be used. We also run each prompt several times at a
high temperature (i.e., high creativity), that can hopefully lead to different
output assertions given the same input.

#### Step 1a: Generating CCSK for a given concept

We seed this step with concepts from ConceptNet Speer et al. (2017), which is
a popular commonsense knowledge base constructed by human annotations and
consists of a wide range of everyday concepts. In addition, we also use
cultural concepts from Candle Nguyen et al. (2023b) as inputs for this step.
Candle is a cultural knowledge base constructed by extracting relevant
sentences from a cleaned web crawl.

#### Step 1b: Generating CCSK for a given culture

The seed cultures used for this step are taken from the Candle dataset, which
include geo-locations (countries, continents, geo-regions), and religions.

#### Iterative Generation

Step 1a and Step 1b are processed independently, and each step can generate
new cultural groups and concepts, respectively. These new concepts and
cultural groups can be fed back to the corresponding approach in order to
generate new CCSK assertions.

Step 1a: Generating CCSK for a given concept
---
Input concept: chopsticks
Prompt: You are a helpful assistant that writes culture-specific commonsense
assertions. Some examples assertions are listed below:
car | Important in US, Germany | Considered luxury item in poorer countries
<4 more examples...>
Please write assertions for the concept: chopsticks.
Parsed output:
• Concept: chopsticks. Culture: Japan. Statement: Standard eating utensils.
• Concept: chopsticks. Culture: Western countries. Statement: Considered
exotic and less commonly used for everyday meals.
Step 1b: Generating CCSK for a given culture
Input culture: Japan
Prompt: You are a helpful assistant that writes culture-specific commonsense
assertions. Some examples assertions are listed below:
rice | Staple food in East Asia | Side dish in European countries
<4 more examples...>
Please write assertions for the culture: Japan.
Parsed output:
• Concept: tipping. Culture: Japan. Statement: Not a common practice.
• Concept: tipping. Culture: USA. Statement: Common and expected practice in
the service industry.
Step 2a: CCSK assertion clustering
Input: >500K CCSK assertions
Sample output cluster:
• Concept: tipping. Culture: Japanese. Statement: Not a common practice.
(Frequency: 5)
• Concept: leaving tip. Culture: Japanese culture. Statement: Not a common
practice and may even be seen as rude. (Frequency: 2)
• Concept: tipping at restaurants. Culture: Japan. Statement: Tipping is not
commonly practiced and can even be considered rude as it implies that the
service is not already included in the price. (Frequency: 1)
• Concept: tipping service staff. Culture: Japan. Statement: Not a common
practice and can even be considered rude or disrespectful. (Frequency: 1)
Step 2b: Cluster representative generation
Prompt: Please generate a representative sentence for the following
assertions:
<the sample cluster above>
Output: Concept: tipping. Culture: Japan. Statement: Tipping is not a common
practice in Japan and can be considered rude or impolite. (Frequency: 9)
Table 1: Examples of the Mango workflow.

###  3.2 Phase 2: Assertion Consolidation

It is natural that our CCSK generation approaches produce similar assertions
that have very little or zero semantic differences. The repetitions can come
from the fact that there exist concepts with similar meanings (e.g., tea,
drinking tea, and tea drinking), and terms referring to the same groups (e.g.,
East Asia, East Asian cultures, and East Asian countries) in the input.
Furthermore, as we run each prompt several times, even at high output
randomness (temperature), repetitions are inevitable.

While untreated redundancy is undesirable, we propose to take advantage of
these redundancies in order to rank our assertions. Specifically, by grouping
together semantically similar assertions, we create frequency signals, which
can be useful for downstream applications which only look for a subset of
highest-significance assertions.

#### Step 2a: Assertion Clustering

As we generate hundreds of thousands of assertions in Phase 1, it is
prohibitively expensive to run a clustering algorithm on all assertions at
once. It would even be infeasible for algorithms such as the Hierarchical
Agglomerative Clustering (HAC) algorithm to process such a large amount of
data points. Instead, we propose a divide-and-conquer approach to clustering
this large set of assertions. Our approach consists of 3 substeps:

  1. 1.

Clustering similar concepts: The concepts in the assertions generated in Phase
1 are clustered into groups of similar concepts.

  2. 2.

Clustering similar cultures: Similarly to concept clustering, we group
together similar cultures.

  3. 3.

Clustering subsets of assertions: For each pair of concept cluster and culture
cluster, we only cluster the subset of assertions associated with any of the
concepts and any of the cultures in those clusters.

As the sizes of the entire concept and culture sets and the corresponding
assertion subsets are substantially smaller than that of the entire set of
generated assertions, standard clustering algorithms can process them
efficiently. In our experiment, we use SentenceBert embeddings Reimers and
Gurevych (2019) and the HAC algorithm for all 3 substeps. Nevertheless, in
practice, other text embedding models and clustering algorithms could be used.
An example assertion cluster can be found in Table 1, in which the respective
concept cluster includes tipping, leaving tip, tipping at restaurants, tipping
service staff, and the culture cluster includes Japan, Japanese, Japanese
culture.

#### Step 2b: Representative Generation

For each cluster of CCSK assertions, we generate a _full sentence_ as the
representative of the cluster. We also obtain the frequency of each cluster by
adding up all the frequencies of its member assertions.

For the final output, we store a set of CCSK cluster instances, each
containing the following information: _concept_ (the representative concept of
the CCSK cluster), _culture_ (the representative culture of the CCSK cluster),
_statement_ (the representative sentence of the CCSK cluster), _similar
statements_ (the set of the statements of the member assertions), and
_frequency_ (the frequency sum of the cluster).

##  4 Implementation of Mango

Step | Input | Output
---|---|---
| Step 1a
---
(2 runs)
31,196 concepts | 468,543 assertions
| Step 1b
---
(2 runs)
10,796 cultures | 115,220 assertions
Step 2a | 507,780 filtered assertions | 167,396 assertion clusters
Step 2b | 167,396 assertion clusters | 167,396 full CCSK sentences
Table 2: Input and output of each step in our implementation.

We implement our workflow using GPT-3.5222Model name: gpt-3.5-turbo-1106 . In
the generation phase, we run each prompt 5 times with a temperature of 1.0
(high creativity). We summarize the input and output of our implementation in
Table 2.

#### Input Concepts and Cultures:

We run each step in Phase 1 twice, whereas the first run is fed with seed
concepts and seed cultures from prior datasets, and the second run is fed with
new concepts and cultures generated in the first run.

  * •

Seed concepts: We take 8,357 concepts from Candle Nguyen et al. (2023b), which
have more than 1 assertion, and 16,480 concepts from ConceptNet Speer et al.
(2017), which have more than 3 assertions. We clean this set of concepts by
filtering out incomprehensible phrases using GPT-3.5, retaining a seed set of
19,940 concepts for the first run of Step 1a.

  * •

Seed cultures: We take 286 groups (272 geo-locations and 14 religions) from
Candle as seed cultures for the first run of Step 1b.

After the first run of Step 1a with the seed concepts, we obtain 10,510 new
cultures. After the first run of Step 1b with the 286 seed cultures, and the
second run with the new 10,510 cultures, we obtain 11,256 new concepts, which
are used for the second run of Step 1a.

#### Assertion Filtering:

After Phase 1, we obtain 581,563 distinct CCSK assertions. We perform various
simple filters to clean these assertions:

  * •

Removing too long or too short assertions: We restrict the length of assertion
to be between 2 and 25 words.

  * •

Removing assertions that have more than one sentence in the generated
statements.

  * •

Removing assertions whose cultures are too general or noisy: We construct a
dictionary of words that a valid culture should not contain. For example, we
filter out cultures such as “Other cultures” (context-dependent), “Non-
European countries”, “Some parts of Asia” (not specific enough), etc. More
details on this dictionary can be found in Appendix A.2.

After filtering, we obtain 507,780 assertions (i.e., 87% of the original set),
14,298 cultural groups, and 32,126 concepts.

#### Clustering:

For both concept, culture and assertion clustering, we use the HAC algorithm
combined with the SentenceBert embedding model all-MiniLM-L6-v2333Model
description: https://sbert.net/. We use point-wise Euclidean distance of
normalized embeddings, the Ward’s linkage Ward (1963), and the distance
threshold set to 1.5, which are adopted from the Candle method Nguyen et al.
(2023b).

We obtain 4,571 concept clusters and 1,610 culture clusters, with the largest
candidate set for assertion clustering containing 463 assertions. Finally, we
obtain 167,396 assertion clusters, where the largest cluster contains 141
assertions. Table 3 lists the top cultures and concepts in our dataset.

Concept | Count | Culture | Count
---|---|---|---
family | 372 | Countries
tea | 352 | United States | 9097
hospitality | 349 | Japan | 4597
personal space | 338 | India | 3670
marriage | 285 | Regions
family structure | 234 | Western countries | 5788
education | 228 | Eastern countries | 1849
gender roles | 200 | Middle Eastern countries | 1059
public transportation | 193 | Religions
music | 183 | Christianity | 142
traditional clothing | 180 | Islamic countries | 121
time | 174 | Hinduism | 106
food | 149 | Ethnic groups
spicy food | 148 | Amazonian tribes | 143
communication | 147 | Inuit communities | 101
fishing | 132 | Maori culture | 73
Table 3: Top concepts and cultures in Mango.

#### Costs:

The assertion generation steps costed $71. On average, each thousand generated
assertions costed 12 cents. The cluster representative generation costed $41.
On average, each thousand cluster representative generations costed 25 cents.

The API to the GPT-3.5 model we used in this implementation has limits at 1M
input tokens per minute, and 10K requests per minute. By making concurrent
requests, our workflow could be executed in less than 5 hours, including the
clustering steps which take less than 30 minutes.

##  5 Quality of Mango Assertions

We evaluate the assertion quality of Mango by comparison to several resources
of similar kind.

#### Compared Resources:

Our baseline resources are Quasimodo Romero et al. (2019), StereoKG Deshpande
et al. (2022) and Candle Nguyen et al. (2023b). StereoKG and Candle are
specialized in culture-specific knowledge. Quasimodo is a general commonsense
knowledge base, but for this comparison, we only consider Quasimodo assertions
that contain geo-locations or religions.

StereoKG and Candle store assertions in the form of natural-language
sentences, while Quasimodo assertions originally come in triple format
(subject-predicate-object). Therefore, for comparability, we verbalized the
Quasimodo assertions using GPT-3.5.

For our resource, in addition to the full assertion set
(Mango${}^{\textit{full}}$), we also evaluate Mango${}^{\textit{top}}$, which
contains the top-ranked assertions up to the same size as Candle (i.e., 60K
assertions).

#### Metrics:

CCSK assertions should satisfy a set of conditions, that are sometimes in
conflict. We employ three dimensions Bhatia and Shwartz (2023) to evaluate
their intrinsic quality:

  * 1\.

Cultural Relevance (CR) measures the plausibility of the assertion, i.e.,
whether the statement actually represents cultural knowledge.

  * 2\.

Stereotype Avoidance (SA) assesses if the assertion avoids reinforcing
cultural stereotypes and presenting offensive materials.

  * 3\.

Linguistic Accuracy (LA) checks if the assertion is grammatical, meaningful
and understandable as a standalone sentence.

#### Setup:

Our evaluation is conducted on the Amazon Mechanical Turk (MTurk) platform.
Specifically, we ask human annotators on MTurk to evaluate each assertion
along the 3 dimensions, each on a 3-point Likert scale: _negation_ (0),
_ambiguity_ (1) and _affirmation_ (2) (the evaluation questions can be found
in Appendix B and Figure 3). For each resource, we randomly sample 300
assertions for evaluation, each assessed by 3 different workers.

#### Results:

Resource |  Quality ([0..2]) | Size
---|---|---
CR | SA | LA | #C | #A
StereoKG | 0.75 | 0.90 | 1.11 | 10 | 4K
Quasimodo | 0.85 | 1.18 | 1.35 | 0.4K | 131K
Candle | 1.59 | 1.65 | 1.76 | 0.4K | 60K
Mango${}^{\textit{full}}$ | 1.65* | 1.71* | 1.88* | 11.1K | 167K
Mango${}^{\textit{top}}$ | 1.71* | 1.76* | 1.90* | 8.1K | 60K
Table 4: Results of _intrinsic evaluation_ via human annotations (metrics: CR
\- cultural relevance, SA \- stereotype avoidance, LA \- linguistic accuracy),
along with the coverage of the resources (#C \- number of cultures, #A \-
number of assertions). The (*) marker indicates results with statistically
significant gains over Candle ($p<0.05$ in the Student’s t-test).

We report averaged scores given by the annotators in Table 4. It can be seen
that Mango assertions have the highest quality compared to prior resources.
Notably, despite being nearly 3 times larger than the largest baseline,
Mango${}^{\textit{full}}$ has better quality than all baselines, on all
metrics.

Moreover, our top-ranked assertion subset, Mango${}^{\textit{top}}$, has the
same size as Candle, but it outperforms this resource on all 3 metrics by a
large margin. This affirms that the frequency signals we obtain in our
clustering step are helpful for pulling out the most significant assertions.

##  6 CCSK for Intercultural Dialogues

2(a) Vanilla LLM 2(a) LLM w/ explicit CCSK

NaturalnessConsistencySpecificityCultural Sensitivity*Overall Quality20%35%50%
(a) GPT

NaturalnessConsistencySpecificityCultural Sensitivity*Overall Quality20%35%50%
(b) Mistral

NaturalnessConsistencySpecificity*Cultural SensitivityOverall
Quality*20%35%50% (c) Bard

Figure 2:  Results of head-to-head comparison for the _next utterance
generation_ task via human evaluation. The y-axis represents the percentage of
samples preferred by the evaluators (the “Tie” cases are omitted from the
plots). The (*) marker indicates results with statistically significant
differences ($p<0.05$ in the Wilcoxon T-test).

Explicit knowledge has been used to improve LLM performance in downstream
tasks such as social dialogue generation Kim et al. (2023) and intra-cultural
dialogue synthesis Li et al. (2023). However, other important scenarios, which
involve _intercultural_ interactions, remain under-explored. To address this
gap, we introduce 2 new tasks concerning intercultural conversations. We will
show that explicit CCSK assertions from resources like Mango can improve LLM
responses in dialogue applications requiring cross-cultural knowledge.

###  6.1 Next Utterance Generation

The input of this task includes: (1) a narrative that involves interactions
between 2 people of different cultures, and (2) their ongoing dialogue. The
task is to generate the utterance of the next speaker. To excel in this task,
LLMs need to leverage cultural knowledge such that the generated responses are
natural, consistent, culturally sensitive and specific. We provide an example
of input and output for this task in Table 5. More examples and details of
prompting techniques can be found in Appendix C.

Input
---
Narrative
John, an American, is visiting his friend Kenji, who lives in Tokyo. They are
paying their bill for dinner at a restaurant.
Ongoing dialogue
John: That’s a great meal, Kenji. I really liked the sushi.
Kenji: My pleasure, John. I’m glad you enjoyed it.
John: Let me see the bill. It is 8,000 yen. I’m gonna leave 10,000 yen.
Output
Method 1: Vanilla GPT-3.5
Kenji: Thank you, John. You’re too kind. Next time, dinner is on me. It’s a
very generous tip too.
Method 2: GPT-3.5 with explicit CCSK
Injected CCSK: Tipping is not a common practice in Japan and can be considered
rude or impolite.
Kenji: Oh, no, John. You don’t need to leave a tip here in Japan. Just 8,000
yen is fine. Thank you for offering though.
Table 5: Example input and output for the next utterance generation task.

#### Input Construction:

First, using GPT-3.5 and a small set of few-shot examples, we generate short
narratives involving 2 people of different cultures, e.g., “Liz from England
is visiting her friend Qiang in China. They are preparing tea together.”.
Then, for each narrative, we ask the LLM to generate a possible dialogue
between the 2 participants in that situation. Finally, the first 3 utterances
of each generated dialogue are used to construct test samples. Prompt
templates and narrative examples can be found in Appendix C.1 and Table 8.

#### Methods:

We compare 2 methods, without and with explicit CCSK assertions in the
prompts. _Method 1 (Vanilla LLM)_ , prompts an LLM with the task description,
the input narrative, and the dialogue history. On the other hand, _Method 2
(LLM with explicit CCSK)_ , alters the prompts of _Method 1_ by augmenting
relevant CCSK. For that, we retrieve the top-2 assertions from Mango, based on
cosine similarity between embeddings of the input narrative and our CCSK
assertions. We provide more details on the retrieval technique in Appendix
C.2. The templates for prompting LLMs with this task can be found in Appendix
C.3.

#### Setup:

We experiment with 3 different LLMs from some of the most popular model
families: (i) GPT-3.5444Model name: gpt-3.5-turbo-1106, also known as ChatGPT,
by OpenAI, (ii) the strongest model of the Mistral family by MistralAI555Model
name: mistral-medium. Model description:
https://docs.mistral.ai/platform/endpoints/., and (iii) Google’s largest
globally accessible language model as of January 2024, Bard666Accessed via
https://bard.google.com/. For each LLM, we randomly draw 100 test samples and
use the 2 methods to generate 100 pairs of responses. We employ human
annotators on MTurk to evaluate the quality of the generated utterances.
Specifically, we show side-by-side the outputs of the 2 methods given the same
input narrative, and ask the evaluators to choose the better one based on the
following dimensions:

  * 1\.

Naturalness: The response does not sound awkward or unnatural.

  * 2\.

Consistency: The response does not contradict the narrative or previous
utterances.

  * 3\.

Specificity: The response contains specific details rather than vague/generic
information.

  * 4\.

Cultural Sensitivity: The response shows respect and understanding of the
cultures.

  * 5\.

Overall Quality: The overall satisfaction with the response.

Dimensions 1-3 and 5 are established criteria for evaluating dialogues Mehri
et al. (2022); Kim et al. (2023), dimension 4 is a dimension we introduce in
this evaluation, as per our focus on cross-cultural knowledge.

Each sample is evaluated by 3 different MTurk workers. To alleviate positional
bias, the orders of the outputs are randomly shuffled before being revealed to
the annotators. More details on the human evaluation can be found in Appendix
C.4.

#### Results:

The human evaluation results are demonstrated in Figure 2. It can be seen that
explicit CCSK assertions help all 3 LLMs to perform significantly better in
this task, as the _overall quality_ of the generated utterances are preferred
by the human annotators compared to the outputs of the vanilla LLMs. This is
attributed by the fact that the CCSK-enhanced utterances are more _specific_
and _culturally sensitive_ (for all 3 LLMs), and even more _natural_ and
_consistent_ (for Bard). This shows that even though LLMs inherently possess
cultural knowledge, they often fail to incorporate such knowledge into the
generated utterances, and that explicit CCSK injected in the prompts can
mitigate this problem. We provide some evaluated test samples in Table 12 in
Appendix C.4.

Additionally, we also compared using Mango vs. Candle Nguyen et al. (2023b)
assertions for augmenting prompts to GPT-3.5. We sample 100 test narratives
and use the same retrieval method for both resources in this comparison. Human
annotators preferred utterances generated with Mango assertions in terms of
naturalness, consistency and specificity. The head-to-head preferences for
each dimension are (Mango vs. Candle): Naturalness (32.7% vs. 30.7%);
Consistency (30.7% vs. 28.0%); Specificity (39.7% vs. 37.0%); Cultural
Sensitivity (34.3% vs. 34.3%); Overall Quality (46.0% vs. 46.0%).

###  6.2 Full Dialogue Generation

Metric | No CCSK | W/ CCSK
---|---|---
Naturalness | 39.3% | 38.7%
Consistency | 21.0% | 22.7%
Specificity | 36.7% | 43.0%
Cultural Sensitivity | 22.7% | 28.3%
Overall Quality | 40.7% | 44.7%
Table 6: Results of head-to-head human evaluation for the _full dialogue
generation_ task with GPT-3.5. The numbers present the percentage of samples
preferred by the evaluators.

In this task, instead of generating a single utterance, we ask LLMs to
generate a full dialogue between the 2 people in a given narrative. We
anticipate that this task is more difficult both for the LLMs to solve and for
humans to evaluate.

We randomly sample 100 test narratives and ask GPT-3.5 to generate dialogues.
We use the same prompting methods and evaluation setup as in the previous
task. The evaluation results can be found in Table 6. It can be seen that
injecting explicit CCSK in the prompts does not diminish the natural flow and
consistency of the generated dialogues, on the other hand, it provides more
specificity and cultural sensitivity into the intercultural interactions. As a
result, the annotators prefer the CCSK-enhanced dialogues on overall quality,
similar to the results of the next utterance generation task.

Along with the CCSK collection, we also release a dataset of 5,000
intercultural narratives and dialogues generated by GPT-3.5 with and without
CCSK augmented for further research, under the CC-BY-4.0 License.

##  7 Conclusion

We presented Mango, a methodology to distill and consolidate CCSK from LLMs.
We executed the Mango workflow using GPT-3.5, obtaining a collection of 167K
assertions covering 11K cultures and 30K concepts, which surpasses existing
resources in quality and coverage by a large margin. In the extrinsic
evaluation, we showed that by augmenting explicit assertions from Mango into
prompts, LLMs can perform better in intercultural dialogue generation tasks as
their responses were judged more specific, more culturally sensitive, and
better overall quality by human evaluators.

## Limitations

Although our method for CCSK distillation outperforms text extraction by a
large margin in terms of quality and size, there are three inherent
limitations when using GPT-3.5: (1) Since GPT-3.5 is a commercial product
provided via an API only, it cannot be guaranteed that our pipeline is long-
term reproducible. (2) Since the training process of GPT-3.5 is undocumented,
we do not know what corpus it has been trained on, and in particular, whether
there might be systematic gaps in its training corpus (know what you don’t
know). (3) Not specific to GPT-3.5, the usage of LLMs for CCSK distillation
means losing the ability to trace assertions to their source, compared with
text extraction.

## Ethics Statement

Adapting conversational AI to cultural contexts is important for opening
systems to diverse communities. At the same time, CCSK represents dual-use
technology, as it can also be used to reinforce stereotypes, and discriminate.

Our data represents the outputs of a research prototype. We recommend against
using our data in production systems without a careful evaluation of benefits
(of having a system that is more culturally adept) and associated challenges
and risks (of stereotype perpetuation etc.).

## References

  * Acharya et al. (2020) Anurag Acharya, Kartik Talamadupula, and Mark A. Finlayson. 2020.  An atlas of cultural commonsense for machine reasoning.  _CoRR_ , abs/2009.05664.
  * Anacleto et al. (2006) Junia Anacleto, Henry Lieberman, Marie Tsutsumi, Vânia Neris, Aparecido Carvalho, Jose Espinosa, Muriel Godoi, and Silvia Zem-Mascarenhas. 2006.  Can common sense uncover cultural differences in computer applications? In _Artificial Intelligence in Theory and Practice_ , pages 1–10, Boston, MA. Springer US.
  * Bhatia and Shwartz (2023) Mehar Bhatia and Vered Shwartz. 2023.  GD-COMET: A geo-diverse commonsense inference model.  In _Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing_ , pages 7993–8001, Singapore. Association for Computational Linguistics.
  * Bosselut et al. (2019) Antoine Bosselut, Hannah Rashkin, Maarten Sap, Chaitanya Malaviya, Asli Celikyilmaz, and Yejin Choi. 2019.  COMET: Commonsense transformers for automatic knowledge graph construction.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 4762–4779, Florence, Italy. Association for Computational Linguistics.
  * CH-Wang et al. (2023) Sky CH-Wang, Arkadiy Saakyan, Oliver Li, Zhou Yu, and Smaranda Muresan. 2023.  Sociocultural norm similarities and differences via situational alignment and explainable textual entailment.  In _Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing_ , pages 3548–3564, Singapore. Association for Computational Linguistics.
  * Choi (2022) Yejin Choi. 2022.  The Curious Case of Commonsense Intelligence.  _Daedalus_ , 151(2):139–155.
  * Cohen et al. (2023) Roi Cohen, Mor Geva, Jonathan Berant, and Amir Globerson. 2023.  Crawling the internal knowledge-base of language models.  In _Findings of the Association for Computational Linguistics: EACL 2023_ , pages 1856–1869, Dubrovnik, Croatia. Association for Computational Linguistics.
  * Deshpande et al. (2022) Awantee Deshpande, Dana Ruiter, Marius Mosbach, and Dietrich Klakow. 2022.  StereoKG: Data-driven knowledge graph construction for cultural knowledge and stereotypes.  In _Proceedings of the Sixth Workshop on Online Abuse and Harms (WOAH)_ , pages 67–78, Seattle, Washington (Hybrid). Association for Computational Linguistics.
  * Forbes et al. (2020) Maxwell Forbes, Jena D. Hwang, Vered Shwartz, Maarten Sap, and Yejin Choi. 2020\.  Social chemistry 101: Learning to reason about social and moral norms.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 653–670, Online. Association for Computational Linguistics.
  * Fung et al. (2024) Yi Fung, Ruining Zhao, Jae Doo, Chenkai Sun, and Heng Ji. 2024.  Massively multi-cultural knowledge acquisition & LM benchmarking.  _CoRR_ , abs/2402.09369.
  * Gordon et al. (2010) Jonathan Gordon, Benjamin Van Durme, and Lenhart K. Schubert. 2010.  Learning from the web: Extracting general world knowledge from noisy text.  In _Proceedings of the 2nd AAAI Conference on Collaboratively-Built Knowledge Sources and Artificial Intelligence_ , AAAIWS’10-02, page 10–15, Palo Alto, California, USA. AAAI Press.
  * Huang and Yang (2023) Jing Huang and Diyi Yang. 2023.  Culturally aware natural language inference.  In _Findings of the Association for Computational Linguistics: EMNLP 2023_ , pages 7591–7609, Singapore. Association for Computational Linguistics.
  * Hwang et al. (2021) Jena D. Hwang, Chandra Bhagavatula, Ronan Le Bras, Jeff Da, Keisuke Sakaguchi, Antoine Bosselut, and Yejin Choi. 2021.  (comet-)atomic 2020: On symbolic and neural commonsense knowledge graphs.  In _Thirty-Fifth AAAI Conference on Artificial Intelligence_ , AAAI’21, pages 6384–6392, Palo Alto, California, USA. AAAI Press.
  * Kim et al. (2023) Hyunwoo Kim, Jack Hessel, Liwei Jiang, Peter West, Ximing Lu, Youngjae Yu, Pei Zhou, Ronan Bras, Malihe Alikhani, Gunhee Kim, Maarten Sap, and Yejin Choi. 2023\.  SODA: Million-scale dialogue distillation with social commonsense contextualization.  In _Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing_ , pages 12930–12949, Singapore. Association for Computational Linguistics.
  * Lenat (1995) Douglas B. Lenat. 1995.  Cyc: A large-scale investment in knowledge infrastructure.  _Commun. ACM_ , 38(11):33–38.
  * Li et al. (2023) Oliver Li, Mallika Subramanian, Arkadiy Saakyan, Sky CH-Wang, and Smaranda Muresan. 2023.  NormDial: A comparable bilingual synthetic dialog dataset for modeling social norm adherence and violation.  In _Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing_ , pages 15732–15744, Singapore. Association for Computational Linguistics.
  * Li and Zhang (2023) Zhi Li and Yin Zhang. 2023.  Cultural concept adaptation on multimodal reasoning.  In _Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing_ , pages 262–276, Singapore. Association for Computational Linguistics.
  * Liu et al. (2021) Fangyu Liu, Emanuele Bugliarello, Edoardo Maria Ponti, Siva Reddy, Nigel Collier, and Desmond Elliott. 2021.  Visually grounded reasoning across languages and cultures.  In _Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing_ , pages 10467–10485, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.
  * Liu and Singh (2004) Hugo Liu and Push Singh. 2004.  Conceptnet — a practical commonsense reasoning tool-kit.  _BT Technology Journal_ , 22:211–226.
  * Mehri et al. (2022) Shikib Mehri, Jinho Choi, Luis Fernando D’Haro, Jan Deriu, Maxine Eskenazi, Milica Gasic, Kallirroi Georgila, Dilek Hakkani-Tur, Zekang Li, Verena Rieser, Samira Shaikh, David Traum, Yi-Ting Yeh, Zhou Yu, Yizhe Zhang, and Chen Zhang. 2022.  Report from the nsf future directions workshop on automatic evaluation of dialog: Research directions and challenges.
  * Nguyen et al. (2023a) Tuan-Phong Nguyen, Simon Razniewski, Julien Romero, and Gerhard Weikum. 2023a.  Refined commonsense knowledge from large-scale web contents.  _IEEE Transactions on Knowledge and Data Engineering_ , 35(8):8431–8447.
  * Nguyen et al. (2023b) Tuan-Phong Nguyen, Simon Razniewski, Aparna Varde, and Gerhard Weikum. 2023b.  Extracting cultural commonsense knowledge at scale.  In _Proceedings of the Web Conference 2023_ , WWW ’23, New York, NY, USA. Association for Computing Machinery.
  * Nguyen et al. (2021) Tuan-Phong Nguyen, Simon Razniewski, and Gerhard Weikum. 2021.  Advanced semantics for commonsense knowledge extraction.  In _Proceedings of the Web Conference 2021_ , WWW ’21, page 2636–2647, New York, NY, USA. Association for Computing Machinery.
  * Palta and Rudinger (2023) Shramay Palta and Rachel Rudinger. 2023.  FORK: A bite-sized test set for probing culinary cultural biases in commonsense reasoning models.  In _Findings of the Association for Computational Linguistics: ACL 2023_ , pages 9952–9962, Toronto, Canada. Association for Computational Linguistics.
  * Petroni et al. (2019) Fabio Petroni, Tim Rocktäschel, Sebastian Riedel, Patrick Lewis, Anton Bakhtin, Yuxiang Wu, and Alexander Miller. 2019.  Language models as knowledge bases? In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 2463–2473, Hong Kong, China. Association for Computational Linguistics.
  * Reimers and Gurevych (2019) Nils Reimers and Iryna Gurevych. 2019.  Sentence-BERT: Sentence embeddings using Siamese BERT-networks.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 3982–3992, Hong Kong, China. Association for Computational Linguistics.
  * Romero et al. (2019) Julien Romero, Simon Razniewski, Koninika Pal, Jeff Z. Pan, Archit Sakhadeo, and Gerhard Weikum. 2019.  Commonsense properties from query logs and question answering forums.  In _Proceedings of the 28th ACM International Conference on Information and Knowledge Management_ , CIKM ’19, page 1411–1420, New York, NY, USA. Association for Computing Machinery.
  * Sap et al. (2019) Maarten Sap, Ronan Le Bras, Emily Allaway, Chandra Bhagavatula, Nicholas Lourie, Hannah Rashkin, Brendan Roof, Noah A. Smith, and Yejin Choi. 2019.  Atomic: An atlas of machine commonsense for if-then reasoning.  In _Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence_ , AAAI’19, Palo Alto, California, USA. AAAI Press.
  * Shwartz (2022) Vered Shwartz. 2022.  Good night at 4 pm?! time expressions in different cultures.  In _Findings of the Association for Computational Linguistics: ACL 2022_ , pages 2842–2853, Dublin, Ireland. Association for Computational Linguistics.
  * Speer et al. (2017) Robyn Speer, Joshua Chin, and Catherine Havasi. 2017.  Conceptnet 5.5: An open multilingual graph of general knowledge.  In _Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence_ , AAAI’17, page 4444–4451, Palo Alto, California, USA. AAAI Press.
  * Speer and Havasi (2012) Robyn Speer and Catherine Havasi. 2012.  ConceptNet 5: A large semantic network for relational knowledge.  _Theory and Applications of Natural Language Processing_.
  * Tandon et al. (2014) Niket Tandon, Gerard de Melo, Fabian Suchanek, and Gerhard Weikum. 2014.  Webchild: Harvesting and organizing commonsense knowledge from the web.  In _Proceedings of the 7th ACM International Conference on Web Search and Data Mining_ , WSDM ’14, page 523–532, New York, NY, USA. Association for Computing Machinery.
  * Ward (1963) Joe H. Ward. 1963.  Hierarchical grouping to optimize an objective function.  _Journal of the American Statistical Association_ , 58:236–244.
  * West et al. (2022) Peter West, Chandra Bhagavatula, Jack Hessel, Jena Hwang, Liwei Jiang, Ronan Le Bras, Ximing Lu, Sean Welleck, and Yejin Choi. 2022.  Symbolic knowledge distillation: from general language models to commonsense models.  In _Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 4602–4625, Seattle, United States. Association for Computational Linguistics.
  * West et al. (2023) Peter West, Ronan Bras, Taylor Sorensen, Bill Lin, Liwei Jiang, Ximing Lu, Khyathi Chandu, Jack Hessel, Ashutosh Baheti, Chandra Bhagavatula, and Yejin Choi. 2023.  NovaCOMET: Open commonsense foundation models with symbolic knowledge distillation.  In _Findings of the Association for Computational Linguistics: EMNLP 2023_ , pages 1127–1149, Singapore. Association for Computational Linguistics.
  * Yin et al. (2022) Da Yin, Hritik Bansal, Masoud Monajatipoor, Liunian Harold Li, and Kai-Wei Chang. 2022.  GeoMLAMA: Geo-diverse commonsense probing on multilingual pre-trained language models.  In _Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing_ , pages 2039–2055, Abu Dhabi, United Arab Emirates. Association for Computational Linguistics.
  * Yin et al. (2021) Da Yin, Liunian Harold Li, Ziniu Hu, Nanyun Peng, and Kai-Wei Chang. 2021.  Broaden the vision: Geo-diverse visual commonsense reasoning.  In _Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing_ , pages 2115–2129, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.
  * Zhang et al. (2020) Hongming Zhang, Daniel Khashabi, Yangqiu Song, and Dan Roth. 2020.  Transomcs: From linguistic graphs to commonsense knowledge.  In _Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI-20_ , pages 4004–4010, California, USA. International Joint Conferences on Artificial Intelligence Organization.
  * Zhou et al. (2023) Li Zhou, Laura Cabello, Yong Cao, and Daniel Hershcovich. 2023.  Cross-cultural transfer learning for Chinese offensive language detection.  In _Proceedings of the First Workshop on Cross-Cultural Considerations in NLP (C3NLP)_ , pages 8–15, Dubrovnik, Croatia. Association for Computational Linguistics.

##  Appendix A Details of Assertion Generation

###  A.1 Prompt Templates

For assertion generation, we use the gpt-3.5-turbo-1106 model at its chat
completion endpoint777https://api.openai.com/v1/chat/completions which takes
as input a list of messages of 3 different roles: system, user, and assistant.
The system’s message at the beginning of the list contains detailed
instruction for the task being solved by the LLM. The user’s messages contain
the inputs of the task. Given a list of messages, the API will return an
assistant’s message, which is expected to contain the answers for the task.

For convenience, we ask GPT-3.5 to structure its responses into JSON
objects888https://platform.openai.com/docs/api-reference/chat/create#chat-
create-response_format. In each prompt, we provide 5 assertion pairs as few-
shot examples, which are randomly sampled from a pool of 10 examples written
by humans. The prompt templates can be found in Table 7.

System |  |  You are a helpful assistant who writes culture-specific commonsense assertions. You always respond in JSON format with the following fields:
---
\- “concept”: string
\- “commonsense”: list of two objects representing significantly different
common sense about the concept in different cultures:
\- “culture”: list of strings
\- “assertion”: string
Some examples of culture-specific commonsense assertions are listed below, in the format: * concept | commonsense assertion in culture 1 | commonsense assertion in culture 2.
car | Important in US, Germany | Considered luxury item in poorer countries
pig | Important farm animal in Europe, China | Considered dirty/shunned in Middle East
bread | Dark/full-grain in Germany | Fluffy/toast-bread in Indonesia
chopsticks | Standard eating utensils in East Asia | An exception in Europe
window | Used to keep heat inside in northern countries | Used to keep heat outside in tropical countries
Example 1: Generating CCSK for a given concept
User |  |  Write culture-specific commonsense assertions for the concept: feeding dogs.
---
⬇ { "concept": "feeding dogs", "commonsense": [ { "culture": ["United States",
"Europe"], "assertion": "Feeding dogs high-quality, specialized pet food is
common practice." }, { "culture": ["India", "Nepal"], "assertion": "Feeding
dogs leftovers or homemade food is a common and acceptable practice." } ] }
Example 2: Generating CCSK for a given culture
User |  |  Write culture-specific commonsense assertions where one of the cultures is: Vietnam.
---
⬇ { "concept": "motorbike", "commonsense": [ { "culture": ["Vietnam"],
"assertion": "Common mode of transportation for individuals and families" }, {
"culture": ["USA"], "assertion": "Often used as a recreational vehicle rather
than a primary mode of transportation" } ] }
Table 7: Examples of prompting GPT-3.5 to generate CCSK assertions.

###  A.2 Dictionary for Assertion Filtering

We have a small set of words to filter out low quality assertions.
Specifically, if the culture of an assertion contains any of the following
words, it will be rejected: other, general, 1, 2, (, ), and, ,, some, unknown,
parts of, few, /, non-, many, outside, part of, various, elsewhere, rest of,
certain.

##  Appendix B Details of Intrinsic Evaluation

For each competing resource, we sampled 300 assertions for evaluation. Each
MTurk HIT contained 5 assertions and was compensated $0.40. We estimate each
HIT takes 2 minutes to complete, hence an hourly wage of $12. The annotation
page can be found in Figure 3. Each HIT is done by 3 different annotators. The
annotators were required to be Master Workers with a lifetime approval rate
greater than 99%. There were totally 36 different workers who participated in
this task. We observed the following Krippendorff’s Alpha values for each of
the metrics: Cultural Relevance: 0.42, Stereotype Avoidance: 0.23, Linguistic
Accuracy: 0.41.

Figure 3: The (truncated) MTurk annotation page for CCSK assertion evaluation.
The page goes on with 4 other assertions.

##  Appendix C Details of Extrinsic Evaluation

In this section, we provide details on prompting and other techniques used in
the 2 extrinsic tasks (cf. Section 6).

###  C.1 Prompts for Narrative Generation

An example prompt for intercultural narrative generation can be seen in Table
8. In each prompt, we sample 3 narratives from a pool of 10 human-written
narratives as few-shot examples. We use the GPT-3.5 model with a temperature
of 1.0.

User |  |  You are a narrative generator. Your task is to generate short narratives of less than 5 sentences around a cultural concept that involves two people from two different cultures. The narrative should lead to an intercultural interaction where cultural differences play a significant role. You must not include the cultural differences, or cultural knowledge, or the resolution, or the consequences of the situation in the narrative.
---
Some examples:
\- Anna, an American, is visiting a remote village in Vietnam where Minh is a
local. Anna asks Minh where she can get food for her dog.
\- Erling from Norway is visiting Seoul. He and his new Korean friend,
Heungmin, are picking foods for their dinner at a traditional restaurant.
\- Liz and Qiang are two friends, who are currently in England. Qiang is from
China who is visiting the country. Liz is a local. They are preparing tea
together.
Please write 3 more narratives:
Assistant |  |  \- Maria, a Mexican, is visiting Japan and is shopping in a local market. She meets Yuki, a Japanese woman, and asks for help in choosing a traditional Japanese outfit for a festival.
---
\- Pablo, a Spaniard, is traveling in India and meets Rajesh, a local, at a
temple. They both want to participate in a religious ceremony, and Pablo asks
Rajesh for guidance on the proper etiquette.
\- Fatima, a Saudi Arabian, is studying in France and meets Pierre, a French
student, at a party. They both want to dance, and Fatima asks Pierre to teach
her a traditional French dance.
Table 8: An example of prompts used to generate intercultural narratives in
the 2 extrinsic tasks.

###  C.2 CCSK Retrieval

We use a simple embedding-based retrieval approach. First, we compute the
embeddings of all assertions in our Mango dataset using the SentenceBert model
all-MiniLM-L6-v2. Then, given a narrative, we replace the names of the people
with “X” and “Y” in order to reduce the distractions for the embedding model.
For each given narrative, we retrieve the top-2 most similar CCSK assertions
from Mango based on cosine similarity of the embeddings. We also restrict the
similarity to be better than 0.5. We only consider narratives that have
relevant CCSK assertions retrieved from Mango in the human evaluation.
Examples of CCSK retrieval can be seen in Table 9.

Example 1
---
Narrative: Carlos from Argentina is visiting Korea. He greets his new Korean
friend, Jihoon, by giving him a friendly pat on the back.
Query: X from Argentina is visiting Korea. He greets his new Korean friend, Y,
by giving him a friendly pat on the back.
Retrieval Results:
• In South Korea, beckoning with an open hand or palm facing downwards is
considered polite. (Similarity: 0.5216)
• In South Korean culture, it is common to gently pat someone on the shoulder
or back as a sign of encouragement or reassurance. (Similarity: 0.5201)
Example 2
Narrative: Maria, a woman from Spain, is visiting a Bedouin tribe in Jordan
upon an invitation from her new friend, Ahmed. They are preparing to have
dinner under the star-lit desert sky.
Query: X, a woman from Spain, is visiting a Bedouin tribe in Jordan upon an
invitation from her new friend, Y. They are preparing to have dinner under the
star-lit desert sky.
Retrieval Results:
• Bedouins, a Middle Eastern culture, are known for their nomadic lifestyle,
hospitality, and expertise in desert survival. (Similarity: 0.5217)
• Desert cultures highly value hospitality and express it through offering
food, drinks, and shelter to guests. (Similarity: 0.5207)
Table 9: Examples of retrieving Mango’s CCSK assertions relevant to given
narratives.

###  C.3 Prompts for Extrinsic Tasks

Example prompts for the next utterance generation and full dialogue generation
tasks can be found in Table 10 and Table 11 respectively.

User |  |  You will be generating the next response of a given dialogue between two people. Along with the dialogue, you’ll be given some context about the two participants of the dialogue, e.g., their relationship, situation, etc. Please make the response naturalistic, consistent, specific, interesting and culturally sensitive.
---
Context:
Erling from Norway is visiting Seoul. He and his new Korean friend, Heungmin,
are picking foods for their dinner at a traditional restaurant.
Dialog:
Erling: Wow, Heungmin, this place looks amazing! What do you recommend we try
for our dinner tonight?
Heungmin: I’m glad you like it, Erling! You should definitely try bulgogi,
it’s a Korean BBQ classic. And don’t miss out on kimchi, it’s a must-try side
dish.
|  You will be generating the next response of a given dialogue between two
people. Along with the dialogue, you’ll be given some context about the two
participants of the dialogue, e.g., their relationship, situation, etc. Please
make the response naturalistic, consistent, specific, interesting and
culturally sensitive.
---
Please make the next response more culturally realistic using the following
knowledge:
\- Spicy food is a staple in South Korean cuisine, widely enjoyed, and
considered an essential part of the diet.
\- In Scandinavian countries, spices are used sparingly, with a focus on
simplicity and natural flavors in traditional dishes.
Context:
Erling from Norway is visiting Seoul. He and his new Korean friend, Heungmin,
are picking foods for their dinner at a traditional restaurant.
Dialog:
Erling: Wow, Heungmin, this place looks amazing! What do you recommend we try
for our dinner tonight?
Heungmin: I’m glad you like it, Erling! You should definitely try bulgogi,
it’s a Korean BBQ classic. And don’t miss out on kimchi, it’s a must-try side
dish.
Assistant |  |  Erling: Bulgogi and kimchi sound great! I’ve heard so much about both of them. I’m really looking forward to trying them. Thank you for the recommendation, Heungmin. This is going to be an amazing dinner experience.
---
|  Erling: Sounds great, Heungmin! I’ve heard a lot about bulgogi and kimchi,
so I’m really looking forward to trying them. But I have to admit, I’m a
little nervous about the spice level. I’m not used to eating such spicy food.
---
Table 10: An example of prompts used in the next utterance generation task (cf. Section 6.1). System |  You are a dialog generator. You are given a narrative and related context such as the backgrounds of the speakers, and the situation of the interaction. Your task is to generate a short dialog between the two people involved in the narrative. The dialog is turn-by-turn which includes 6 utterances, each person has 3 utterances. Each person’s utterance should be 1 to 2 sentences. Please make the dialog naturalistic, consistent, specific, interesting and culturally sensitive.
---|---
User |  |  Narrative: Anna, an American, is visiting a remote village in Vietnam where Minh is a local. Anna asks Minh where she can get food for her dog.
---
|  Narrative: Anna, an American, is visiting a remote village in Vietnam where
Minh is a local. Anna asks Minh where she can get food for her dog.
---
Please make the dialog more culturally realistic using the following
knowledge:
\- In Vietnam, dogs are often fed traditional homemade food or scraps from
family meals, including rice and meat scraps.
First analyze if the provided knowledge is relevant to the narrative. Then
proceed by generating the dialog.
Assistant |  |  Anna: Hey Minh, I need to find some food for my dog. Do you know where I can get some pet food around here?
---
Minh: Hi Anna! Sure, you can try the small pet store down the road, it’s just
a 10-minute walk from here.
Anna: Great! Thanks, Minh. Is it easy to spot? I’m not familiar with the area.
Minh: Yes, you won’t miss it. It’s a little blue shop with a sign featuring a
dog and a cat.
Anna: Perfect, I’ll head there soon. Do you think they have a variety of
options?
Minh: They should have a decent selection, but don’t expect the same variety
as in the city. You’ll find some good options for your dog, though.
Anna: That’s good to know. I appreciate your help, Minh.
Minh: No problem, Anna. If you need anything else, just let me know. Enjoy
your time in the village!
|  The provided knowledge is relevant to the narrative as it helps in
understanding the cultural context of feeding dogs in Vietnam.
---
Anna: Hi Minh, I’m wondering where I can find some food for my dog around
here. Do you know if there’s a pet store nearby?
Minh: Oh, we don’t have pet stores here. But you can give your dog some rice
and meat scraps. Many people do that for their dogs here.
Anna: Oh, that’s interesting. I didn’t know that. Thank you for letting me
know. Do you know where I can find rice and meat scraps then?
Minh: You can check with the local market or some of the food vendors. They
usually have some leftovers they can give you for your dog.
Anna: Great, I’ll give that a try. Thank you for your help, Minh. It’s really
different from what I’m used to back home.
Table 11: An example of prompts used in the full dialogue generation task (cf.
Section 6.2).

###  C.4 Details of Human Evaluation for Extrinsic Tasks

The instruction and layout of our annotation pages used for MTurk evaluations
are influenced by the work of Kim et al. (2023). Instead of using “Definitely
A/B” and “Slightly A/B”, we narrow the option set down to “A is Better”, “B is
Better”, and introduce a third option which is “Tie”. The annotation pages can
be found in Figure 4 and Figure 5. For both tasks, we require the workers to
be Master Workers who have a lifetime approval rate of more than 99%.

#### Utterance Comparison

For the 300 pairs of evaluated utterances, there were 41 different MTurk
workers who participated in the evaluation. Each HIT was compensated $0.20. We
estimate each HIT takes 1 minute to complete, hence an hourly wage of $12. We
observed the following Krippendorff’s Alpha values for each of the metrics:
Naturalness: -0.06, Consistency: 0.06, Specificity: 0.20, Cultural
Sensitivity: 0.10, Overall Quality: 0.02.

#### Dialogue Comparison

For the 100 pairs of evaluated dialogues, there were 29 different MTurk
participants. Each HIT was compensated $0.30. We estimate each HIT takes 1.5
minutes to complete, hence an hourly wage of $12. We observed the following
Krippendorff’s Alpha values for each of the metrics: Natural Flow: 0.08,
Consistency: 0.15, Specificity: 0.30, Cultural Sensitivity: 0.13, Overall
Quality: 0.20.

We provide some samples evaluated by MTurk workers in Table 12 and Table 13.

Figure 4: The annotation page used for utterance evaluation on MTurk.
Instruction and layout are influenced by Kim et al. (2023). Figure 5: The
annotation page used for dialogue evaluation on MTurk. Instruction and layout
are influenced by Kim et al. (2023). Sample 1
---
Narrative
|  Ali from Tunisia is visiting Tokyo for the first time. He and his newly
made Japanese friend, Hiroshi, are deciding how to celebrate Ali’s birthday in
one of Tokyo’s iconic districts.
---
Dialogue
|  Ali: Hiroshi, I’m so excited to celebrate my birthday in Tokyo! What do you
think we should do?
---
Hiroshi: Happy birthday, Ali! I think we should start with a traditional
Japanese meal at a local izakaya.
Ali: That sounds great! I’ve been wanting to try authentic Japanese cuisine.
And then maybe we could check out the vibrant nightlife in Shibuya?
Vanilla GPT | GPT + CCSK
|  -
---
|  Injected CCSK:
---
• In Japan, birthdays are celebrated with symbolic rituals, special meals, and
a focus on traditional ceremonies and gift-giving.
|  Hiroshi: Absolutely, Ali! Shibuya is the perfect place to experience
Tokyo’s bustling nightlife. We could start with a few drinks at a traditional
Japanese izakaya and then explore the neon-lit streets and vibrant energy of
Shibuya. It’s going to be an unforgettable birthday celebration!
---
|  Hiroshi: That sounds like a fantastic plan, Ali! But I also think it would
be wonderful to incorporate some Japanese birthday traditions into our
celebration. How about we visit a shrine to make a prayer for good luck and
then participate in the Omikuji fortune-telling ritual? It’s a special way to
mark your birthday and immerse yourself in Japanese culture. And of course, we
can still enjoy the bustling nightlife in Shibuya afterwards.
---
Criterion |  Natural Flow |  Consistency |  Specificity |  Cultural Sensitivity |  Overall Quality
Annotator 1 |  GPT + CCSK |  Tie |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK
Annotator 2 |  Tie |  Tie |  GPT + CCSK |  Tie |  GPT + CCSK
Annotator 3 |  Vanilla GPT |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK
Sample 2
Narrative
|  Fiona, a woman from Scotland, is in Nairobi visiting her online friend
Makena. Makena is taking her to a traditional Kenyan hair salon for the first
time.
---
Dialogue
|  Makena: Welcome to the salon, Fiona! Are you excited to try out some Kenyan
hair styles?
---
Fiona: Oh, I am a bit nervous, but also curious to see what kind of styles are
popular here. It’s quite different from what I’m used to in Scotland.
Makena: Don’t worry, you’re going to love it! Kenyan hair stylists are really
talented and they have some unique techniques.
Vanilla GPT | GPT + CCSK
|  -
---
|  Injected CCSK:
---
• Hairdressing education in Kenya focuses on intricate braiding and natural
hair care techniques for diverse African hair types and textures.
• In Kenya, elaborate and intricate braided hairstyles are a significant
aspect of cultural identity.
|  Fiona: That’s good to hear! I can’t wait to see what they can do. I’ve
always admired African hairstyles from afar, so I’m really looking forward to
experiencing it firsthand.
---
|  Fiona: That sounds amazing! I’ve always admired the intricate braided
hairstyles I’ve seen here. I’ve never had the chance to experience it myself,
so I’m really looking forward to it.
---
Criterion |  Natural Flow |  Consistency |  Specificity |  Cultural Sensitivity |  Overall Quality
Annotator 1 |  Tie |  GPT + CCSK |  GPT + CCSK |  Tie |  GPT + CCSK
Annotator 2 |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK
Annotator 3 |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK
Table 12: Examples of generated utterances by GPT without and with CCSK, and
choices of MTurk workers in our evaluation. Note that in the evaluation, only
the narratives, the dialogues, and the utterance pairs (without explicit
method names) are shown to the annotators (cf. Figure 4). Sample 1
---
Narrative
|  Amara, an American studying in Japan, is invited by her Japanese friend
Haruki to his grandmother’s home for a traditional meal.
---
Vanilla GPT | GPT + CCSK
|  -
---
|  Injected CCSK:
---
• In Japan, the culture of consumption emphasizes moderation, shared meals,
traditional preparation, etiquette, and home-cooked meals.
• In Japan, there is a strong cultural expectation for adult children to care
for their elderly parents at home.
|  Amara: Wow, Haruki, your grandmother’s home is beautiful.
---
Haruki: Thank you, Amara. I’m glad you could come.
Amara: I’m so excited to try traditional Japanese food. Everything looks
amazing.
Haruki: My grandmother is a fantastic cook. She’s been preparing the meal all
day.
Amara: I really appreciate her effort. Itadakimasu!
Haruki: Enjoy your meal, Amara. I hope you like it.
|  Haruki: Amara, I’m really excited to bring you to my grandmother’s house
for a traditional meal today. She’s an amazing cook.
---
Amara: Thank you for inviting me, Haruki. I’m honored to experience a
traditional Japanese meal with your family.
Haruki: Just a heads up, at my grandmother’s place, we sit on the floor to
eat. It’s a more traditional way of dining.
Amara: I’ll remember to show respect and gratitude for the meal. I’ve read a
bit about Japanese dining etiquette, but it’s my first time experiencing it
firsthand.
Haruki: It’s important for us to take care of our elders in Japan, and having
meals together is a way to show our respect and appreciation.
Amara: I think it’s a beautiful tradition. In the US, we also value family,
but the idea of sharing home-cooked meals with multiple generations under the
same roof is not as common.
Criterion |  Natural Flow |  Consistency |  Specificity |  Cultural Sensitivity |  Overall Quality
Annotator 1 |  Tie |  Tie |  GPT + CCSK |  GPT + CCSK |  Tie
Annotator 2 |  GPT + CCSK |  Tie |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK
Annotator 3 |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK
Sample 2
Narrative
|  Omkar from India and Harry from Australia are coworkers. During their
break, Omkar starts preparing Dosa, an Indian dish, and offers to share some
with Harry.
---
Vanilla GPT | GPT + CCSK
|  -
---
|  Injected CCSK:
---
• Dosa is a specialty dish in Indian restaurants in the United States, less
commonly made at home.
• Dosa is a popular South Indian dish made from fermented rice and lentil
batter, often served with chutney and sambar.
|  Omkar: Hey Harry, I’m making some dosa for myself. Want to try some?
---
Harry: Dosa? What’s that? Is it spicy?
Omkar: It’s a type of crispy pancake made from fermented rice and lentil
batter. It can be spicy, but I can make it mild for you.
Harry: That sounds interesting! I’ll give it a try.
Omkar: Great! I’ll make a mild one for you. It’s a popular South Indian dish,
and I love sharing it with my friends.
|  Omkar: Hey, Harry, I’m making some Dosa. Want to try some?
---
Harry: Dosa? Is that the Indian dish with the crispy texture and served with
the coconut chutney?
Omkar: Yes, that’s right! It’s a popular South Indian dish made from fermented
rice and lentil batter.
Harry: I’ve only had it at Indian restaurants here. I’d love to try your
homemade version.
Omkar: Great! I also have some sambar and chutney to go with it. Here, have a
taste.
Harry: Mmm, this is fantastic! The flavors are so different from what I’ve had
before.
Omkar: I’m glad you like it. It’s a bit of a process to make, but it’s worth
it for the authentic taste.
Criterion |  Natural Flow |  Consistency |  Specificity |  Cultural Sensitivity |  Overall Quality
Annotator 1 |  GPT + CCSK |  Tie |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK
Annotator 2 |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK
Annotator 3 |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK |  GPT + CCSK
Table 13: Examples of generated dialogues by GPT without and with CCSK, and
choices of MTurk workers in our evaluation. Note that in the evaluation, only
the narratives and the dialogue pairs (without explicit method names) are
shown to the annotators (cf. Figure 5).

##  Appendix D Dataset Usage and License

We used Quasimodo (CC-BY-2.0; Romero et al. (2019)), StereoKG (MIT License;
Deshpande et al. (2022)), and Candle (CC-BY-4.0; Nguyen et al. (2023b)) for
comparing with our Mango dataset, which is compatible with their corresponding
license.


# Field-Induced Quantum Spin Nematic Liquid Phase in the S=1 Antiferromagnetic
Heisenberg Chain with Additional Interactions

Tôru Sakai1,2 Hiroki Nakano1 Rito Furuchi1 and Kiyomi Okamoto1 Graduate School
of Science, University of Hyogo, Hyogo 678-1297, Japan<EMAIL_ADDRESS>
###### Abstract

The magnetization process of the $S=1$ antiferromagnetic chain with the
single-ion anisotropy $D$ and the biquadratic interaction is investigated
using the numerical diagonalization. Both interactions stabilize the 2-magnon
Tomonaga-Luttinger liquid (TLL) phase in the magnetization process. Based on
several excitation gaps calculated by the numerical diagonalization, some
phase diagrams of the magnetization process are presented. These phase
diagrams reveal that the spin nematic dominant TLL phase appears at higher
magnetizations for sufficiently large negative $D$.

##  1 Introduction

The quantum spin nematic state is one of interesting topics in the field of
the strongly correlated electron systems. It was theoretically predicted to be
realized in several frustrated systems; the square-lattice model with the
ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor
interactions[1], the triangular-lattice antiferromagnetic with multi spin
exchange interactions[2], and the ferromagnetic and antiferromagnetic zigzag
chain[3, 4]. The high-magnetic field measurement[5] on the zigzag chain
compound LiCuVO4 detected an anomalous behavior of the magnetization curve
just below the saturation magnetization, which was supposed to be the spin
nematic phase. The quantum spin liquid like behavior of the $S=1$ triangular-
lattice compound NiGa2S4 was theoretically explained as the spin nematic
state[6]. A density matrix renormalization group (DMRG) analysis[7] indicated
that the field-induced spin nematic liquid phase appears in the $S=1$
antiferromagnetic chain with the biquadratic interaction. It was supported by
the numerical diagonalization study[8].

On the other hand, the 2-magnon bound state similar to the spin nematic state
was predicted to appear in the magnetization process of the $S=1$
antiferromagnetic chain with the easy axis anisotropy based on the numerical
diagonalization analysis[9]. It would possibly correspond to the spin nematic
state. In the present paper, we investigate the $S=1$ antiferromagnetic chain
with the easy axis anisotropy and the biquadratic interaction using the
numerical diagonalization, in order to consider the relation between this
2-magnon bound state and the spin nematic liquid phase.

##  2 Model

We consider the magnetization process of the $S=1$ antiferromagnetic chain
with the easy axis single ion anisotropy $D$ and the biquadratic interaction
$J_{\rm BQ}$. The system under the magnetic field is described by the
Hamiltonian

$\displaystyle{\cal H}$ $\displaystyle=$ $\displaystyle{\cal H}_{0}+{\cal
H}_{Z}$ (1) $\displaystyle{\cal H}_{0}$ $\displaystyle=$ $\displaystyle
J\sum_{j=1}^{L}\vec{S}_{j}\cdot\vec{S}_{j+1}+D\sum_{j=1}^{L}(S_{j}^{z})^{2}+J_{\rm
BQ}\sum_{j=1}^{L}(\vec{S}_{j}\cdot\vec{S}_{j+1})^{2}$ (2) $\displaystyle{\cal
H}_{Z}$ $\displaystyle=$ $\displaystyle-H\sum_{j=1}^{L}S_{j}^{z}.$ (3)

In this paper we consider the case of $J_{\rm BQ}<0$, $D<0$ and fix $J=1$. The
first term of ${\cal H}_{0}$ is the bilinear exchange interaction which
stabilizes the antiparallel configuration of the nearest neighbor spin pair.
On the other hand, the third term, the biquadratic interaction does not only
stabilize the antiparallel configuration, but also the parallel one. Thus the
spin nematic liquid phase would possibly occur for sufficiently large $|J_{\rm
BQ}|$. A numerical diagonalization and DMRG study indicated that the
biquadratic interaction stabilizes the spin nematic correlation[10]. If the
spin nematic liquid phase is realized, the four spin correlation function
would exhibit the power-law decay, while the two spin one decays
exponentially. Then in this phase the single magnon excitation should be
gapped, but the 2-magnon excitation should be gapless. Therefore the 2-magnon
bound state would be realized there. If the spin nematic liquid phase appears
in the magnetization process described by the Hamiltonian (3), each step of
the magnetization curve for the finite-size systems should be $\delta
S^{z}_{\rm total}=2$, while $\delta S^{z}_{\rm total}=1$ in the conventional
Tomonaga-Luttinger liquid (TLL) phase. The negative $D$ also yields a similar
2-magnon bound state, because the $S_{j}^{z}=\pm 1$ states are stabilized and
the $S_{j}^{z}=0$ state is skipped[9]. In order to clarify the feature of
these 2-magnon bound states, we investigate the model (3) using the numerical
diagonalization of finite clusters under the periodic boundary condition. The
calculated lowest energy for each magnetization $M=(\sum_{j=1}^{L}S_{j}^{z})$
and each momentum $k$ is denoted as $E_{k}(M)$ in the following sections.

##  3 Spin Nematic Liquid

The negative biquadratic interaction stabilizes the TLL phase where the
2-magnon bound state is realized, as well as the negative $D$. In this
2-magnon TLL phase the spin correlation functions are expected to have the
following asymptotic forms:

$\displaystyle\langle(S_{0}^{+})^{2}(S_{r}^{-})^{2}\rangle\sim
r^{-{\eta}_{2}},\quad\langle
S_{0}^{z}S_{r}^{z}\rangle\sim\cos(2k_{F}r)r^{-{\eta}_{z}}\quad(r\rightarrow\infty),$
(4)

where $2k_{F}$ is given by $2k_{F}=(1-M/M_{s})\pi$ and $M_{s}$ is the
saturation magnetization ($M_{s}=L$).
$\langle(S_{0}^{+})^{2}(S_{r}^{-})^{2}\rangle$ is the nematic (quadrapole)
correlation perpendicular to the magnetic field and $\langle
S_{0}^{z}S_{r}^{z}\rangle$ is the SDW correlation parallel to it. In a DMRG
work[7] the region with ${\eta}_{2}<{\eta}_{z}$ is called the nematic phase
and the region with ${\eta}_{2}>{\eta}_{z}$ is called the SDW phase, although
the boundary between them is just a crossover line. Thus in order to find the
spin nematic liquid phase, we should look for the parameter region where the
2-magnon TLL is realized and ${\eta}_{2}<{\eta}_{z}$ is satisfied.

##  4 Exciation Gaps

In order to determine the boundary between the 1-magnon (conventional) and
2-magnon TLL phases, we consider several excitation gaps. The 2-magnon
excitation gap $\Delta_{2}$ is gapless in both phases. The 1-magnon excitation
gap $\Delta_{1}$ (the $2k_{F}$ excitation gap of the 2-magnons
$\Delta_{2k_{F}}$) is gapless (gapped ) in the 1-magnon TLL phase, while
gapped (gapless) in the 2-magnon one. $D$ dependence of the scaled excitation
gaps $L\Delta_{1}$, $L\Delta_{2}$ and $L\Delta_{2k_{F}}$ at $M=M_{s}/2$ for
$J_{\rm BQ}=-0.2$ are shown in Fig. 1(a). Fig. 1(a) indicates the above
behaviors of these gaps. The cross point of $\Delta_{1}$ and $\Delta_{2k_{F}}$
is one of good estimations of the phase boundary between the 1-magon and
2-magon TLL phases. Our analysis of the $L$ dependence indicates that this
phase boundary converges faster than $1/L^{2}$ with respect to $L$. Thus we
adopt this method to determine the boundary between the 1-magnon and 2-magnon
TLL phases.

Figure 1:  (a)Scaled gaps $L\Delta_{1}$, $L\Delta_{2}$ and $L\Delta_{2k_{F}}$
at $M=M_{s}/2$ for $J_{\rm BQ}$=-0.2 are plotted versus $D$ for $L=12$ and 16,
(b)Exponents $\eta_{2}$ and $\eta_{z}$ estimated by (5) plotted versus
$M/M_{s}$ for $L=$14 and 16 ($J_{\rm BQ}$=-0.2, $D$=-1.5).
$\eta_{2}\eta_{z}=1$ is well satisfied around the cross of $\eta_{2}$ and
$\eta_{z}$. (c)Scaled gaps $L\Delta_{\pi}$ for $J_{\rm BQ}=-0.2$. It indicates
the phase boundary about $D\sim-0.1$.

##  5 Spin Correlation Exponents

According to the conformal field theory, the critical exponents $\eta_{2}$ and
$\eta_{z}$ can be estimated the forms

$\displaystyle\eta_{2}={{E_{0}(M+2)+E_{0}(M-2)-2E_{0}(M)}\over{E_{k_{1}}(M)-E_{0}(M)}},\quad\eta_{z}=2{{E_{2k_{F}}(M)-E_{0}(M)}\over{E_{k_{1}}(M)-E_{0}(M)}},$
(5)

for each magnetization $M$, where $k_{1}$ is defined as $k_{1}=L/2\pi$.
$\eta_{2}$ and $\eta_{z}$ estimated for $L$=14 and 16 are plotted versus
$M/M_{s}$ in Fig. 1 (b). It suggests that the SDW correlation is dominant for
small $M$, while the nematic one is for large $M$. Since the cross point of
$\eta_{2}$ and $\eta_{z}$ is not so strongly dependent of $L$, the cross point
of $L=16$ is used as the crossover point between the SDW and nematic TLL
phases in Fig. 2(a), (b) and (c), for $J_{\rm BQ}$=0, -0.2 and -0.5,
respectively. At least around the cross point the system well holds the
relation $\eta_{2}\eta_{z}=1$, which should be satisfied for TLL, as shown in
Fig. 1(b).

##  6 Phase diagrams

The phase diagrams on the $D$-$M/M_{s}$ plane are presented for $J_{\rm
BQ}$=0, -0.2, and -0.5 in Figs. 2 (a), (b), and (c), respectively. The phase
boundary at $M=0$ between the Haldane and Néel ordered phases, which is
denoted as the green triangle in Fig. 2, is determined by the phenomenological
renormalization using the excitation gap $\Delta_{\pi}$ with $k=\pi$ for
$L$=10, 12, 14, and 16. The scaled gap $L\Delta_{\pi}$ is plotted versus $D$
for $J_{\rm BQ}=-0.2$ in Fig. 1(c). The $L$ dependent critical point obtained
by $L\Delta_{\pi}(L,D_{c})=(L+2)\Delta_{\pi}(L+2,D_{c})$ can be easily
extrapolated to the infinite $L$ limit. The critical point at $M=M_{s}$ is
determined as the point where the 1-magnon and 2-magnon excitation gaps are
equal, which is the blue triangle in Fig. 2. Here, NTLL, SDWTLL and CTLL
denote the nematic TLL, the SDW TLL, and the conventional TLL, respectively.
Fig.2(a) indicates that the NTLL can appear even for $J_{\rm BQ}=0$. Figs.
2(b) and (c) suggest that the biquadratic interaction enhances both of NTLL
and SDWTLL phases. The crossover boundary between NTLL and SDWTLL is always
about the half the saturation magnetization. It is not so strongly dependent
on $J_{\rm BQ}$.

Figure 2:  Phase diagrams with respect to $D$ and $M/M_{s}$ for $J_{\rm
BQ}$=0(a), -0.2(b) and -0.5(c).

##  7 Summary

The magnetization process of the $S=1$ antiferromagnetic chain with the easy-
axis single-ion anisotropy and the biquadratic interaction is investigated by
the numerical diagonalization for finite-size systems. It is found that the
nematic TLL phase appears in higher magnetization region for sufficiently
large negative $D$, even for $J_{\rm BQ}=0$.

## Acknowledgments

This work was partly supported by JSPS KAKENHI, Grant Numbers JP20K03866,
JP18H04330 (J-Physics) and JP20H05274. A part of the computations was
performed using facilities of the Supercomputer Center, Institute for Solid
State Physics, University of Tokyo, and the Computer Room, Yukawa Institute
for Theoretical Physics, Kyoto University.

## References

## References

  * [1] N. Shannon, T. Momoi and P. Sindzingre, Phys. Rev. Lett. 96, 027213 (2006).
  * [2] T. Momoi, P. Sindzingre and N. Shannon, Phys. Rev. Lett. 97, 257204 (2006).
  * [3] A. V. Chubukov, Phys. Rev. B 44, R4693 (1991).
  * [4] T. Hikihara, L. Kecke, T. Momoi and A. Furusaki, Phys. Rev. B 78, 144404 (2008).
  * [5] N. Büttgen et al., Phys. Rev. B 90, 134401 (2014).
  * [6] S. Nakatsuji et al., Science 309, 1697 (2005).
  * [7] S. R. Manmana, A. M, Lauchli, F. H. L. Essler and F. Mila, Phys. Rev. B 83, 184433 (2011).
  * [8] T. Sakai, AIP Advances 11, 015306 (2021).
  * [9] T. Sakai, Phys. Rev. B 58, 6268 (1998).
  * [10] A. Lauchli, G. Schmid and S. Trebst, Phys. Rev. B 74, 144426 (2006).