# PHALM: Building a Knowledge Graph from Scratch
by Prompting Humans and a Language Model

Tatsuya Ide1 Eiki Murata1 Daisuke Kawahara1 Takato Yamazaki2 Shengzhe Li2
Kenta Shinzato2 Toshinori Sato2
1Waseda University 2LY Corporation
{t-ide@toki.,eiki.murata.1650-2951<EMAIL_ADDRESS>
<EMAIL_ADDRESS>
###### Abstract

Despite the remarkable progress in natural language understanding with
pretrained Transformers, neural language models often do not handle
commonsense knowledge well. Toward commonsense-aware models, there have been
attempts to obtain knowledge, ranging from automatic acquisition to
crowdsourcing. However, it is difficult to obtain a high-quality knowledge
base at a low cost, especially from scratch. In this paper, we propose PHALM,
a method of building a knowledge graph from scratch, by prompting both
crowdworkers and a large language model (LLM). We used this method to build a
Japanese event knowledge graph and trained Japanese commonsense generation
models. Experimental results revealed the acceptability of the built graph and
inferences generated by the trained models. We also report the difference in
prompting humans and an LLM. Our code, data, and models are available at
github.com/nlp-waseda/comet-atomic-ja.

##  1 Introduction

Since pretrained models (Radford and Narasimhan, 2018; Devlin et al., 2019;
Yang et al., 2019) based on Transformer (Vaswani et al., 2017) appeared,
natural language understanding has made remarkable progress. In some
benchmarks, the performance of natural language understanding models has
already exceeded that of humans. These models are applied to various
downstream tasks ranging from translation and question answering to narrative
understanding and dialogue response generation. In recent years, the number of
parameters in such models has continued to increase (Radford et al., 2019;
Brown et al., 2020), and so has their performance.

When we understand or reason, we usually rely on commonsense knowledge.
Computers also need such knowledge to answer open-domain questions and to
understand narratives and dialogues, for example. However, pretrained models
often do not handle commonsense knowledge well (Zhou et al., 2020; Hwang et
al., 2021).

There are many knowledge bases for commonsense inference. Some are built by
crowdsourcing (Speer et al., 2017; Sap et al., 2019; Hwang et al., 2021), but
acquiring a large-scale knowledge base is high-cost. Others are built by
automatic acquisition (Zhang et al., 2019, 2020), but it is difficult to
acquire high-quality commonsense knowledge. Recently, there have been some
methods using large language models (LLMs) for building knowledge bases (Yuan
et al., 2021; West et al., 2022; Liu et al., 2022). They often extend existing
datasets, but do not build new datasets from scratch. Furthermore, there are
not many non-English datasets, although the knowledge that is considered
commonsense varies by languages and cultures Lin et al. (2021); Nguyen et al.
(2023); Acharya et al. (2021).

Figure 1: An overview of our method. We build a knowledge graph step by step
from scratch, by prompting both humans and an LLM.

In this paper, we propose PHALM111Prompting Humans And a Language Model., a
method to build a knowledge graph from scratch with both crowdsourcing and an
LLM. Asking humans to describe knowledge using crowdsourcing and generating
knowledge using an LLM are essentially the same (as it were, the latter is an
analogy of the former), and both can be considered to be prompting. Therefore,
we consider prompting for both humans and an LLM and gradually acquire a
knowledge graph from a small scale to a large scale. Specifically, we acquire
a small-scale knowledge graph by asking crowdworkers to describe knowledge and
use them as a few shots for an LLM to generate a large-scale knowledge graph.
At each phase, we guarantee the quality of graphs by applying appropriate
filtering. In particular, we also propose a low-cost filtering method for the
commonsense inferences generated by the LLM.

We built a Japanese knowledge graph on events, considering prompts for both
humans and an LLM. With Yahoo!
Crowdsourcing222https://crowdsourcing.yahoo.co.jp/ and HyperCLOVA JP, a
Japanese variant of the LLMs built by Kim et al. (2021), we obtained a
knowledge graph that is not a simple translation, but unique to the culture.
Then, we compared inferences collected by crowdsourcing and generated by the
LLM. In addition to acquisition, we trained a Japanese commonsense generation
model based on the built knowledge graph. With the model, we verified the
acceptability of output inferences for unseen events. The resulting knowledge
graph and the commonsense model created in this paper will be released to the
public.

In summary, our contributions are (1) the proposal of a method to build a
large high-quality commonsense knowledge graph from scratch without existing
datasets, including a low-cost filtering method, (2) the comparison of
prompting for humans and an LLM, and (3) the publication of the resulting
Japanese commonsense knowledge graph and commonsense generation models.

##  2 Related Work

(a) Crowdsourcing interface to acquire inferences (xEffect)

(b) An example of prompts for generating inferences from HyperCLOVA. The
underlined parts are generated.

Figure 2: Comparison of prompting between for humans (Figure 2(a)) and for an
LLM (Figure 2(b)).

###  2.1 Commonsense Knowledge Datasets

There are several knowledge bases about commonsense, from what appears in the
text to what is tacit but not written in the text. ConceptNet (Speer et al.,
2017), for example, is a knowledge graph that connects words and phrases by
relations. GenericsKB (Bhakthavatsalam et al., 2020) is a corpus describing
knowledge of entities in natural language rather than in graph.

In some datasets, commonsense knowledge is collected in the form of question
answering. Roemmele et al. (2011) acquire plausible causes and effects for
premises as two-choice questions. Zellers et al. (2018) provide SWAG,
acquiring inferences about a situation from video captions as four-choice
questions. KUCI (Omura et al., 2020) is a dataset for commonsense inference in
Japanese, which is obtained by combining automatic extraction and
crowdsourcing. Talmor et al. (2019) build CommonsenseQA, which treats
commonsense on ConceptNet’s entities as question answering.

In contrast, we propose a method to construct a structural (not QA form) graph
based on events.

###  2.2 Knowledge Graphs on Events

Regarding commonsense knowledge bases, there are several graphs that focus on
events. ATOMIC (Sap et al., 2019) describes the relationship between events,
mental states (Rashkin et al., 2018), and personas. Hwang et al. (2021) merge
ATOMIC and ConceptNet, proposing ATOMIC-2020.

There are also studies for leveraging context. GLUCOSE (Mostafazadeh et al.,
2020) is a commonsense inference knowledge graph for short stories, built by
annotating ROCStories (Mostafazadeh et al., 2016). CIDER (Ghosal et al., 2021)
and CICERO (Ghosal et al., 2022) are the graphs for dialogues where
DailyDialog (Li et al., 2017) and other dialogue corpora are annotated with
inferences.

ASER (Zhang et al., 2019) is an event knowledge graph, automatically extracted
from text corpora by focusing on discourse. With ASER, TransOMCS (Zhang et
al., 2020) aims at bootstrapped knowledge graph acquisition by pattern
matching and ranking.

While ConceptNet and ATOMIC are acquired by crowdsourcing, ASER and TransOMCS
are automatically built. On one hand, a large-scale graph can be built easily
in an automatic way, but it is difficult to obtain knowledge not appearing in
the text. On the other hand, crowdsourcing can gather high-quality data, but
it is expensive in terms of both money and time.

There is a method that uses crowdsourcing and LLMs together to build an event
knowledge graph (West et al., 2022). Although it is possible to acquire a
large-scale and high-quality graph, they assume that an initial graph, ATOMIC
in this case, has already been available. As stated in Section 1, our proposal
is a method to build a commonsense knowledge graph from scratch without such
existing graphs.

###  2.3 Commonsense Generation Models

There have been studies on storing knowledge in a neural form rather than a
symbolic form. In particular, methods of considering neural language models as
knowledge bases (Petroni et al., 2019; AlKhamissi et al., 2022) have been
developed. Bosselut et al. (2019) train COMET by finetuning pretrained
Transformers on ATOMIC and ConceptNet, aiming at inference on unseen events
and concepts. Gabriel et al. (2021) point out that COMET ignores discourse,
introducing recurrent memory for paragraph-level information.

West et al. (2022) propose symbolic knowledge distillation where specific
knowledge in a general language model is distilled into a specific language
model via a symbolic one. They expand ATOMIC using GPT-3 (Brown et al., 2020),
filter the outputs using RoBERTa (Liu et al., 2019), and finetune GPT-2
(Radford et al., 2019) on the filtered ones. Training data for this filtering
was created through manual annotation, which is expensive.

##  3 Prompting Humans and an LLM

We propose a method to build a knowledge graph for commonsense inference from
scratch, with both crowdsourcing and an LLM. In our method, we first construct
a small-scale knowledge graph by crowdsourcing. Using the small-scale graph
for prompts, we then extract commonsense knowledge from an LLM. The flow of
our method is shown in Figure 1. Building a knowledge graph from scratch only
by crowdsourcing is expensive in terms of both money and time. Hence, the
combination of crowdsourcing and an LLM is expected to reduce the cost.

In other words, our method consists of the following two phases: (1)
collecting a small-scale graph by crowdsourcing and (2) generating a large-
scale graph by an LLM. While crowdsourcing elicits commonsense from people,
shots are used to extract knowledge from an LLM. At this point, these phases
are intrinsically the same, being considered as prompting (Fig 2). In the two
phases, namely, we prompt people and an LLM, respectively.

We build a commonsense inference knowledge graph in Japanese. We focus on an
event knowledge graph such as ATOMIC (Sap et al., 2019) and ASER (Zhang et
al., 2019). Handling commonsense on events and mental states would facilitate
understanding of narratives and dialogues. We use Yahoo! Crowdsourcing in the
first phase and HyperCLOVA JP (Kim et al., 2021), an LLM in Japanese, in the
second phase. We also propose a method to filter the triplets generated by the
LLM at a low cost.

###  3.1 Acquisition by Crowdsourcing

We first acquire a small-scale high-quality knowledge graph by crowdsourcing.
With Yahoo! Crowdsourcing, specifically, we ask crowdworkers to write events
and inferences. In a task, we provide them with 10 shots as a prompt for each
event and inference. Note that for inferences, the prompts differ for each
relation, as mentioned later. We obtain a graph by filtering the collected
inferences syntactically and semantically.

#### Events

We ask crowdworkers to write daily events related to at least one person
(PersonX). An example of the crowdsourcing task interface is shown in Figure
5(a). The task provides instructions and 10 examples, and each crowdworker is
asked to write at least one event. After all tasks are completed, we remove
duplicate events. As a result, 257 events were acquired from 200 crowdworkers.
We manually verified that all of the acquired events have sufficient quality.

#### Inferences

For the events collected above, we ask crowdworkers to write inferences about
what happens and how a person feels before and after the events. In this
paper, the relations for inference are based on ATOMIC.333The relations are
not exactly the same as those of ATOMIC. xIntent in this paper covers xIntent
and xWant in ATOMIC, and tails for our xIntent and xReact may contain not
mental states but events. The reason for the difference is that English and
Japanese have different linguistic characteristics, i.e., it is difficult to
collect knowledge in the same structure as the original. The following four
are adopted as our target relations.

  * •

xNeed: What would have happened before

  * •

xEffect: What would happen after

  * •

xIntent: What PersonX would have felt before

  * •

xReact: What PersonX would feel after

While xNeed and xEffect are inferences about events, xIntent and xReact are
inferences about mental states.

Three crowdworkers are hired per event. Given an instruction and 10 examples,
each crowdworker is asked to write one inference. An example of the
crowdsourcing task interface is shown in Figure 5(b). We remove duplicate
inferences as in the case of events and then apply syntactic filtering444KNP
determines if the subject is PersonX, if the tense is present, and if the
event is a single sentence. using the Japanese syntactic parser
KNP555https://nlp.ist.i.kyoto-u.ac.jp/?KNP.

| Inst # | Val # | Val % | IAA
---|---|---|---|---
Event | 257 | - | - | -
xNeed | 504 | 402 | 79.76 | 39.85
xEffect | 621 | 554 | 89.21 | 25.00
xIntent | 603 | 519 | 86.07 | 36.11
xReact | 639 | 550 | 86.07 | 31.82
Table 1: The statistics on events and inferences acquired by crowdsourcing. Val # and Val % represent the number and percentage of triplets considered valid by the crowdworkers, respectively. Head | Rel |  Tail | Eval
---|---|---|---
Xが顔を洗う (X washes X’s face) | xNeed |  Xが水道で水を出す (X runs water from the tap) | ✓
|  |  Xが歯を磨く (X brushes X’s teeth) |
| xEffect |  Xがタオルを準備する (X prepares a towel) | ✓
|  |  Xが鏡に映った自分の顔に覚えのない傷を見つける (X finds an unrecognizable scar on X’s face in the mirror) | ✓
|  |  Xが歯磨きをする (X brushes his teeth) | ✓
| xIntent |  スッキリしたい (Want to feel refreshed) | ✓
|  |  眠いのでしゃきっとしたい (Sleepy and Want to feel refreshed) | ✓
| xReact |  さっぱりして眠気覚ましになる (Feel refreshed and shake off X’s sleepiness) | ✓
|  |  きれいになる (Be clean) | ✓
|  |  さっぱりした (Felt refreshed) | ✓
Table 2: Examples of inferences acquired through crowdsourcing. Triplets with
✓ in the eval column were judged to be acceptable by the evaluation in Section
3.2.

The numbers of the acquired events and inferences are shown in the Inst #
column of Table 1. Examples of acquired inferences are shown in Table 2.

###  3.2 Evaluation and Filtering of Crowdsourced Triplets

To examine the qualities of the inferences acquired by crowdsourcing, we
crowdsource their evaluation. We ask three crowdworkers whether the inferences
are acceptable or not and judge their acceptability by majority voting. The
evaluation is crowdsourced independently for each relation. The inferences
judged to be unacceptable by majority voting are filtered out.

The inferences collected in Section 3.1 are evaluated and filtered as above.
The statistics are listed in the middle two columns of Table 1. We also
calculated Fleiss’s $\kappa$ 666As a reference, $\kappa\in[0,0.2]$ is
considered to be “slight” agreement, $(0.2,0.4]$ is “fair”, and $(0.4,0.6]$ is
“moderate” Landis and Koch (1977). as an inner-annotator agreement (IAA) in
the evaluation, which is shown in the rightmost column of Table 1. The IAAs
were “fair” to weak “moderate”. This is because commonsense is subjective and
depends on the individual.

There are several tendencies in the inferences filtered out, i.e., judged to
be unacceptable. In some inferences, the order is reversed, as in the triplet
$\langle$PersonX sleeps twice, xEffect, PersonX thinks that they are off work
today$\rangle$. Others are not plausible, as in $\langle$PersonX surfs the
Internet, xNeed, PersonX gets to the ocean$\rangle$.

###  3.3 Generation from an LLM

From a small-scale high-quality knowledge graph acquired in Sections 3.1 and
3.2, we generate a large-scale knowledge graph with an LLM. We use the Koya
39B model of HyperCLOVA JP as an LLM. Both events and inferences are generated
by providing 10 shots. The shots are randomly chosen from the small-scale
graph for each generation.

#### Events

New events are generated by HyperCLOVA JP, using the events acquired in
Section 3.2 as shots. An example prompt for event generation is shown in
Figure 6(a). We generate 10,000 events, remove duplicates, and apply the same
syntactic filtering as in Section 3.1.

#### Inferences

Rel |  Template
---|---
xNeed |  $h$ためには、$t$必要がある。 (To $h$, need to $t$.)
xEffect |  $h$。結果として、$t$。 ($h$. As a result, $t$.)
xIntent |  $h$のは、$t$と思ったから。 ($h$ because felt $t$.)
xReact |  $h$と、$t$と思う。 ($h$ then feel $t$.)
Table 3: The templates of shots for an LLM. $h$ and $t$ stand for head and
tail, respectively. When generating, $t$ is extracted.

As in event generation, the inferences acquired in Sections 3.1 and 3.2 are
used as shots. We generate 10 inferences for each event and remove duplicate
triplets. While we simply list the shots as a prompt in event generation,
different prompts are used for each relation in inference generation. An
example prompt for xEffect generation is shown in Figure 6(b). Shots are given
in natural language, and tails are extracted by pattern matching. Shot
templates for each relation are shown in Table 3. Finally, the syntactic
filtering is applied to obtain the graph.

| Inst # | Val % | IAA
---|---|---|---
Event | 1,429 | - | -
xNeed | 44,269 | 79.95 | 31.79
xEffect | 36,920 | 81.94 | 34.11
xIntent | 52,745 | 84.84 | 31.37
xReact | 60,616 | 89.20 | 19.06
Table 4: The statistics of events and inferences generated from an LLM. Val % and IAA are the evaluation results of randomly selected inferences. Head | Rel |  Tail
---|---|---
Xがコンビニへ行く (X goes to a convenience store) | xNeed |  Xが財布を持っている (X has X’s wallet), Xが外出する (X goes out), Xが外出着に着替える (X changes into going-out clothes), Xが財布を持って出かける (X goes out with X’s wallet), Xが外へ出る (X goes outside)
| xEffect |  Xが買い物をする (X goes shopping), Xが雑誌を立ち読みする (X browses through magazines), XがATMでお金をおろす (X withdraws money from ATM), Xが弁当を買う (X buys lunch), Xがアイスを買う (X buys ice cream)
| xIntent |  何か買いたいものがある (Want to buy something), 雑誌を買う (Buy a magazine), 飲み物を買おう (Going to buy a drink), 飲み物や食べ物を買いたい (Want to buy a drink or food), なんでもある (There is everything X wants)
| xReact |  何か買いたいものがある (Want to buy something), 何か買う (Buy something), 何か買おう (Going to buy something), 何か買いたくなる (Come to buy something), ついでに何か買ってしまう (Buy something incidentally)
Table 5: Examples of inferences generated from an LLM. For each relation, five
examples are displayed.

(a) xNeed

(b) xEffect

(c) xIntent

(d) xReact

Figure 3: The number of inferences passed for each threshold of probability by
the filter model (blue bars) and the percentage of valid inferences (red
lines).

###  3.4 Filtering of the Triplets Generated by LLM

Because we use an LLM, some of the generated inferences are invalid. In a
previous study, invalid inferences were removed by training and applying a
filtering model with RoBERTa. The training data for the filtering model was
made by manually annotating a portion of the large graph, which is expensive.
In this section, we propose a low-cost filtering method to train filters
without human annotation. This is consistent with our claim that a commonsense
knowledge graph should be built for each language.

The filtering model is a binary classification model that is given a triplet
and outputs whether it is valid or not. Both positive and negative examples
are required for training. Since the small-scale graph used as the LLM shots
was manually collected, we assume that all triplets in it are valid, and we
take them as positive examples. Negative examples are not included, but we
create pseudo-negative examples from the triplets in the small graph and adopt
them. Details of how to create negative examples are given in Appendix D. The
filtering model is constructed by finetuning Japanese
RoBERTa777https://huggingface.co/nlp-waseda/roberta-large-japanese on the
training data created without human annotation. We use a RoBERTa model
finetuned on an NLI task Kurihara et al. (2022) in advance, following the
previous study West et al. (2021). See Appendix D for further details on the
filtering model.

###  3.5 The Statistics of the Large Graph

We obtain a large, high-quality commonsense knowledge graph from scratch by
the four procedures described in the previous sections: crowdsourcing
acquisition, crowdsourcing filtering, LLM scaling, and filtering with RoBERTa.
The statistics of events and inferences generated by HyperCLOVA JP are shown
in Table 4. The results of the evaluation and the inter-annotator agreement
are also shown in Table 4. Since the filtering threshold is a hyperparameter,
we present unfiltered statistics here. A comparison with Table 1 indicates
that the quality is as good as those written by crowdworkers. Examples of
generated inferences are shown in Table 5.

The generated knowledge graph in Japanese reflects the culture of Japan, such
as $\langle$PersonX goes to the office, xNeed, PersonX takes a train$\rangle$
and $\langle$PersonX eats a meal, xNeed, PersonX presses the switch on the
rice cooker$\rangle$. This fact indicates the importance of building from
scratch for a specific language, rather than translating a similar dataset in
a different language, which emphasizes the value of our method proposed in
this paper.

##  4 Analysis on the Built Knowledge Graph

###  4.1 Effect of Filtering for the Small Graph

In this paper, a small-scale knowledge graph is collected as in Sections 3.1
and 3.2, and a large-scale knowledge graph is generated as in Section 3.3.
Here, we examine how effective the filtering for the small graph in Section
3.2 is. As an experiment, we use filtered and unfiltered small-scale graphs as
prompts to generate a large-scale graph. Then, we randomly select 500
generated triplets for each relation and evaluate them by crowdsourcing as in
Section 3.2. Note that the results for the filtered triplets are the same as
Section 3.3.

| xNeed | xEffect | xIntent | xReact
---|---|---|---|---
w/o Fltr | 81.62 | 82.42 | 83.84 | 89.29
w/ Fltr | 80.81 | 85.45 | 86.06 | 90.30
Table 6: The ratios of appropriate inferences generated by the LLM with
respect to filtering.

The ratios of appropriate inferences generated by the LLM with and without
filtering for the small graph are shown in Table 6. We experiment with a
subset of the graph. For all relations except xNeed, filtering improves the
quality of triplets.

###  4.2 Effect of Filtering for the Large Graph

To evaluate the filtering model in Section 3.4, 500 triplets in the large
graph are manually annotated. The results of applying the filter to the test
data are shown in the Figure 3. Since setting a high threshold increases the
ratio of valid triplets, it can be said that we have constructed an effective
filter at a low cost.

###  4.3 Comparison between Humans and an LLM

In Section 3.1, on one hand, we asked crowdworkers to describe events and
inferences. In Section 3.3, on the other hand, we had an LLM generate them.
Here, we compare a small-scale knowledge graph by crowdsourcing and a large-
scale one from an LLM, i.e., inferences generated by humans and a computer.
Because the relationships between events can be largely divided into
contingent and temporal relationships (Bethard et al., 2008), we adopt
contingency and time interval as metrics for comparison.

Of the four relations, we focus on xEffect as a representative, which is a
typical causal relation. For each head of the triplets acquired by
crowdsourcing in Sections 3.1 and 3.2, we generate three tails using the LLM
in Section 3.3 and compare them with the original tails. From the 554 heads
for xEffect in the small-scale graph, we obtained 586 unique inferences.

#### Contingency

One measure is how likely a given event is to be followed by a subsequent
event. Crowdworkers are given a pair of events in an xEffect relation and
asked to judge how likely the following event is to happen on a three-point
scale: “must happen,” “likely to happen,” and “does not happen.” We ask three
crowdworkers per inference and calculate the median of them.

#### Time Interval

The other measure is the time interval between the occurrence of an event and
that of a subsequent event. As in the evaluation of contingency, crowdworkers
are given a triplet on xEffect. We ask them to judge the time interval between
the two events in five levels: almost simultaneous, seconds to minutes, hours,
days to months, and longer. Finally, the median is calculated from the results
of three crowdworkers.

(a) Contingency

(b) Time interval

Figure 4: A comparison between crowdsourcing and LLM generation.

The comparison between humans and an LLM for each measure is shown in Figure
4. Figure 4(a) shows that the subsequent events by crowdsourcing, or humans,
are slightly more probable. In Figure 4(b), the inferences generated by an LLM
have a longer time interval. This result indicates a difference in the results
of prompting humans and an LLM; for xEffect, humans infer events that happen
relatively soon, while an LLM infers events that happen a bit later.

##  5 Japanese Commonsense Generation Models

To verify the quality of the graph constructed in Section 4 and to build a
neural knowledge base, we train Japanese commonsense generation models.
Japanese versions of GPT-2 (Radford et al., 2019) and T5 (Raffel et al., 2020)
are finetuned to generate inferences on unseen events. Since our preliminary
experiments showed better results with GPT-2 than with T5, we report the full
results with GPT-2 in this section. In preliminary experiments, the pretrained
models without finetuning performed poorly, which shows that the built graph
imparted commonsense reasoning ability to the models. See Appendix E for the
results including T5.

###  5.1 Training

Using the constructed knowledge graph, we finetune pretrained models to
construct Japanese commonsense generation models. To evaluate inferences on
unseen events, 150 triplets are randomly selected as the test set. For
pretrained models, we adopt Japanese GPT-2888https://huggingface.co/nlp-
waseda/gpt2-small-japanese of the Hugging Face implementation (Wolf et al.,
2020).

As GPT-2 predicts the next word, the head and the relation are given as an
input, and the model is trained to output the tail. Since the relations are
not included in the vocabulary of the pretrained models, they are added as
special tokens.

###  5.2 Evaluation

We generate inferences for the head events in the test set using the trained
Japanese commonsense generation models and evaluate the inferences manually.
Examples of the inference results are shown in Appendix E.

Using crowdsourcing, we evaluate how likely the generated inferences are. We
ask three crowdworkers how likely each triplet is and decide by majority vote
whether each triplet is valid or not. The result is shown in Table 7. Notably,
the performance of GPT-2 exceeds that of HyperCLOVA. Comparing Table 7 with
Table 4, which can be regarded as the performance of HyperCLOVA’s commonsense
generation, GPT-2 performs better for all relations. This represents the
quality of the built graphs and the effectiveness of storing commonsense in
the neural model.

Furthermore, as shown in Table 7, the ratio of valid triplets of xNeed and
xIntent are lower than xEffect and xReact, respectively. Given that xNeed is a
relation that infers past events, xEffect is a future event, xIntent is a past
mental state, and xReact is a future mental state, this can be attributed to
the fact that we used an autoregressive model, which makes it difficult to
infer in reverse order of time.

| xNeed | xEffect | xIntent | xReact | Total
---|---|---|---|---|---
Val % | 84.00 | 90.00 | 90.00 | 93.33 | 89.33
IAA | 54.56 | 25.00 | 25.59 | 19.52 | -
Table 7: Evaluation scores of the commonsense generation model.

##  6 Conclusion

We proposed a method for building a knowledge graph from scratch with both
crowdsourcing and an LLM. Based on our method, we built a knowledge graph on
events and mental states in Japanese using Yahoo! Crowdsourcing and HyperCLOVA
JP. Since designing tasks for having humans describe commonsense and
engineering prompts for having an LLM generate knowledge are similar to each
other, we compared their characteristics. We evaluated the graph generated by
HyperCLOVA JP and found that it was similar in quality to the graph written by
humans.

Furthermore, we trained a commonsense generation model for event inference
based on the built knowledge graph. We attempted inference generation for
unseen events by finetuning GPT-2 in Japanese on the built graph. The
experimental results showed that these models are able to generate acceptable
inferences for events and mental states.

We hope that our method for building a knowledge graph from scratch and the
acquired knowledge graph lead to further studies on commonsense inference,
especially in low-resource languages.

## Limitations

For acquiring a small-scale event knowledge graph and analyzing the built
graph, we crowdsource several tasks using Yahoo! Crowdsourcing. Specifically,
we collect the descriptions of commonsense, filter them, and explore the
characteristics of the graph by crowdsourcing. We obtained a consent from
crowdworkers on the platform of Yahoo! Crowdsourcing.

The event knowledge graph and the commonsense generation models built in this
paper help computers understand commonsense. A commonsense-aware computer, for
example, can answer open-domain questions by humans, interpret human
statements in detail, and converse with humans naturally. However, such graphs
and models may contain incorrect knowledge even with filtering, which leads
the applications to harmful behavior.

## Acknowledgements

This work was supported by a joint research grant from LINE Corporation.

## References

  * Acharya et al. (2021) A. Acharya, Kartik Talamadupula, and Mark A. Finlayson. 2021.  Toward an atlas of cultural commonsense for machine reasoning.  _Workshop on Common Sense Knowledge Graphs_.
  * AlKhamissi et al. (2022) Badr AlKhamissi, Millicent Li, Asli Celikyilmaz, Mona Diab, and Marjan Ghazvininejad. 2022.  A review on language models as knowledge bases.
  * Bethard et al. (2008) Steven Bethard, William Corvey, Sara Klingenstein, and James H. Martin. 2008.  Building a corpus of temporal-causal structure.  In _Proceedings of the Sixth International Conference on Language Resources and Evaluation (LREC’08)_ , Marrakech, Morocco. European Language Resources Association (ELRA).
  * Bhakthavatsalam et al. (2020) Sumithra Bhakthavatsalam, Chloe Anastasiades, and Peter Clark. 2020.  Genericskb: A knowledge base of generic statements.
  * 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.
  * Brown et al. (2020) Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D 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 Ziegler, Jeffrey Wu, Clemens Winter, Chris Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei. 2020.  Language models are few-shot learners.  In _Advances in Neural Information Processing Systems_ , volume 33, pages 1877–1901. Curran Associates, Inc.
  * Devlin et al. (2019) Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2019.  BERT: Pre-training of deep bidirectional transformers for language understanding.  In _Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers)_ , pages 4171–4186, Minneapolis, Minnesota. Association for Computational Linguistics.
  * Gabriel et al. (2021) Saadia Gabriel, Chandra Bhagavatula, Vered Shwartz, Ronan Le Bras, Maxwell Forbes, and Yejin Choi. 2021.  Paragraph-level commonsense transformers with recurrent memory.  _Proceedings of the AAAI Conference on Artificial Intelligence_ , 35(14):12857–12865.
  * Ghosal et al. (2021) Deepanway Ghosal, Pengfei Hong, Siqi Shen, Navonil Majumder, Rada Mihalcea, and Soujanya Poria. 2021.  CIDER: Commonsense inference for dialogue explanation and reasoning.  In _Proceedings of the 22nd Annual Meeting of the Special Interest Group on Discourse and Dialogue_ , pages 301–313, Singapore and Online. Association for Computational Linguistics.
  * Ghosal et al. (2022) Deepanway Ghosal, Siqi Shen, Navonil Majumder, Rada Mihalcea, and Soujanya Poria. 2022.  CICERO: A dataset for contextualized commonsense inference in dialogues.  In _Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 5010–5028, Dublin, Ireland. 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.  _Proceedings of the AAAI Conference on Artificial Intelligence_ , 35(7):6384–6392.
  * Kim et al. (2021) Boseop Kim, HyoungSeok Kim, Sang-Woo Lee, Gichang Lee, Donghyun Kwak, Jeon Dong Hyeon, Sunghyun Park, Sungju Kim, Seonhoon Kim, Dongpil Seo, Heungsub Lee, Minyoung Jeong, Sungjae Lee, Minsub Kim, Suk Hyun Ko, Seokhun Kim, Taeyong Park, Jinuk Kim, Soyoung Kang, Na-Hyeon Ryu, Kang Min Yoo, Minsuk Chang, Soobin Suh, Sookyo In, Jinseong Park, Kyungduk Kim, Hiun Kim, Jisu Jeong, Yong Goo Yeo, Donghoon Ham, Dongju Park, Min Young Lee, Jaewook Kang, Inho Kang, Jung-Woo Ha, Woomyoung Park, and Nako Sung. 2021.  What changes can large-scale language models bring? intensive study on HyperCLOVA: Billions-scale Korean generative pretrained transformers.  In _Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing_ , pages 3405–3424, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.
  * Kurihara et al. (2022) Kentaro Kurihara, Daisuke Kawahara, and Tomohide Shibata. 2022.  JGLUE: Japanese general language understanding evaluation.  In _Proceedings of the Thirteenth Language Resources and Evaluation Conference_ , pages 2957–2966, Marseille, France. European Language Resources Association.
  * Landis and Koch (1977) J. Richard Landis and Gary G. Koch. 1977.  The measurement of observer agreement for categorical data.  _Biometrics_ , 33(1):159–174.
  * Li et al. (2017) Yanran Li, Hui Su, Xiaoyu Shen, Wenjie Li, Ziqiang Cao, and Shuzi Niu. 2017.  DailyDialog: A manually labelled multi-turn dialogue dataset.  In _Proceedings of the Eighth International Joint Conference on Natural Language Processing (Volume 1: Long Papers)_ , pages 986–995, Taipei, Taiwan. Asian Federation of Natural Language Processing.
  * Lin et al. (2021) Bill Yuchen Lin, Seyeon Lee, Xiaoyang Qiao, and Xiang Ren. 2021.  Common sense beyond English: Evaluating and improving multilingual language models for commonsense reasoning.  In _Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)_ , pages 1274–1287, Online. Association for Computational Linguistics.
  * Liu et al. (2022) Alisa Liu, Swabha Swayamdipta, Noah A. Smith, and Yejin Choi. 2022.  Wanli: Worker and ai collaboration for natural language inference dataset creation.
  * Liu et al. (2019) Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. 2019.  Roberta: A robustly optimized bert pretraining approach.
  * Mostafazadeh et al. (2016) Nasrin Mostafazadeh, Nathanael Chambers, Xiaodong He, Devi Parikh, Dhruv Batra, Lucy Vanderwende, Pushmeet Kohli, and James Allen. 2016.  A corpus and cloze evaluation for deeper understanding of commonsense stories.  In _Proceedings of the 2016 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 839–849, San Diego, California. Association for Computational Linguistics.
  * Mostafazadeh et al. (2020) Nasrin Mostafazadeh, Aditya Kalyanpur, Lori Moon, David Buchanan, Lauren Berkowitz, Or Biran, and Jennifer Chu-Carroll. 2020.  GLUCOSE: GeneraLized and COntextualized story explanations.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 4569–4586, Online. Association for Computational Linguistics.
  * Nguyen et al. (2023) Tuan-Phong Nguyen, Simon Razniewski, Aparna Varde, and Gerhard Weikum. 2023.  Extracting cultural commonsense knowledge at scale.  In _Proceedings of the ACM Web Conference 2023_ , WWW ’23, page 1907–1917, New York, NY, USA. Association for Computing Machinery.
  * Omura et al. (2020) Kazumasa Omura, Daisuke Kawahara, and Sadao Kurohashi. 2020.  A method for building a commonsense inference dataset based on basic events.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)_ , pages 2450–2460, Online. Association for Computational Linguistics.
  * Papineni et al. (2002) Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu. 2002.  Bleu: a method for automatic evaluation of machine translation.  In _Proceedings of the 40th Annual Meeting of the Association for Computational Linguistics_ , pages 311–318, Philadelphia, Pennsylvania, USA. 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.
  * Radford and Narasimhan (2018) Alec Radford and Karthik Narasimhan. 2018.  Improving language understanding by generative pre-training.
  * Radford et al. (2019) Alec Radford, Jeff Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. 2019.  Language models are unsupervised multitask learners.
  * Raffel et al. (2020) Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu. 2020.  Exploring the limits of transfer learning with a unified text-to-text transformer.  _Journal of Machine Learning Research_ , 21(140):1–67.
  * Rashkin et al. (2018) Hannah Rashkin, Maarten Sap, Emily Allaway, Noah A. Smith, and Yejin Choi. 2018\.  Event2Mind: Commonsense inference on events, intents, and reactions.  In _Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 463–473, Melbourne, Australia. Association for Computational Linguistics.
  * Roemmele et al. (2011) Melissa Roemmele, Cosmin Adrian Bejan, and Andrew S. Gordon. 2011.  Choice of plausible alternatives: An evaluation of commonsense causal reasoning.  In _AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning_ , Stanford University.
  * 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.  _Proceedings of the AAAI Conference on Artificial Intelligence_ , 33(01):3027–3035.
  * Speer et al. (2017) Robyn Speer, Joshua Chin, and Catherine Havasi. 2017.  Conceptnet 5.5: An open multilingual graph of general knowledge.  _Proceedings of the AAAI Conference on Artificial Intelligence_ , 31(1).
  * Talmor et al. (2019) Alon Talmor, Jonathan Herzig, Nicholas Lourie, and Jonathan Berant. 2019.  CommonsenseQA: A question answering challenge targeting commonsense knowledge.  In _Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers)_ , pages 4149–4158, Minneapolis, Minnesota. Association for Computational Linguistics.
  * Vaswani et al. (2017) Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Ł ukasz Kaiser, and Illia Polosukhin. 2017.  Attention is all you need.  In _Advances in Neural Information Processing Systems_ , volume 30. Curran Associates, Inc.
  * 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. (2021) Peter West, Chandra Bhagavatula, Jack Hessel, Jena D. Hwang, Liwei Jiang, Ronan Le Bras, Ximing Lu, Sean Welleck, and Yejin Choi. 2021.  Symbolic knowledge distillation: from general language models to commonsense models.
  * Wolf et al. (2020) Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Remi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin Lhoest, and Alexander Rush. 2020.  Transformers: State-of-the-art natural language processing.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing: System Demonstrations_ , pages 38–45, Online. Association for Computational Linguistics.
  * Yang et al. (2019) Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Russ R Salakhutdinov, and Quoc V Le. 2019.  Xlnet: Generalized autoregressive pretraining for language understanding.  In _Advances in Neural Information Processing Systems_ , volume 32. Curran Associates, Inc.
  * Yuan et al. (2021) Ann Yuan, Daphne Ippolito, Vitaly Nikolaev, Chris Callison-Burch, Andy Coenen, and Sebastian Gehrmann. 2021.  Synthbio: A case study in faster curation of text datasets.  In _Proceedings of the Neural Information Processing Systems Track on Datasets and Benchmarks_ , volume 1.
  * Zellers et al. (2018) Rowan Zellers, Yonatan Bisk, Roy Schwartz, and Yejin Choi. 2018.  SWAG: A large-scale adversarial dataset for grounded commonsense inference.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing_ , pages 93–104, Brussels, Belgium. 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. International Joint Conferences on Artificial Intelligence Organization.  Main track.
  * Zhang et al. (2019) Hongming Zhang, Xin Liu, Haojie Pan, Yangqiu Song, and Cane Wing-Ki Leung. 2019\.  Aser: A large-scale eventuality knowledge graph.
  * Zhang* et al. (2020) Tianyi Zhang*, Varsha Kishore*, Felix Wu*, Kilian Q. Weinberger, and Yoav Artzi. 2020.  Bertscore: Evaluating text generation with bert.  In _International Conference on Learning Representations_.
  * Zhou et al. (2020) Xuhui Zhou, Yue Zhang, Leyang Cui, and Dandan Huang. 2020.  Evaluating commonsense in pre-trained language models.  _Proceedings of the AAAI Conference on Artificial Intelligence_ , 34(05):9733–9740.

##  Appendix A Examples of Prompting

Figure 5 and Figure 6 are examples of prompting both humans and an LLM,
respectively.

(a) For events

(b) For inferences (xEffect)

Figure 5: Examples of crowdsourcing interfaces. Crowdworkers are asked to
describe events and inferences.

(a) For events

(b) For inferences (xEffect)

Figure 6: Prompts for generating events and inferences from an LLM. The
underlined parts are generated.

##  Appendix B An Example of Crowdsourced Evaluation

Figure 7: An example of evaluation regarding xEffect relations. We ask three
crowdworkers whether a given inference is acceptable or not.

We evaluate and filter the inferences obtained in Sections 3.1 and 3.3 by
crowdsourcing. An example of the interface for evaluating an xEffect inference
is shown in Figure 7.

##  Appendix C Hyperparameter Details

Max tokens | 32
---|---
Temperature | 0.5
Top-P | 0.8
Top-K | 0
Repeat penalty | 5.0
Table 8: Hyperparameters for event and inference generation with HyperCLOVA JP. | T5 | GPT-2
---|---|---
Batch size | 64 | 64
Learning rate | 5e-5 | 5e-5
Weight decay | 0.0 | 0.0
Adam betas | (0.9, 0.999) | (0.9, 0.999)
Adam epsilon | 1e-8 | 1e-8
Max grad norm | 1.0 | 1.0
Num epochs | 30 | 3
LR scheduler type | Linear | Linear
Warmup steps | 0 | 0
Table 9: Hyperparameters for finetuning T5 and GPT-2 on the knowledge graph.

We generate a large-scale knowledge graph using HyperCLOVA JP in Section 3.3.
The hyperparameters for the generation is shown in Table 8.

With the built knowledge graph, we finetune Japanese T5 and GPT-2 on the task
of commonsense inference in Section 5. The hyperparameters for T5 and GPT-2
are shown in Table 9.

##  Appendix D Filtering Model Details

We show the details of the filtering model trained in Section 3.4.

###  D.1 Training Data

First, how to make negative samples is shown. We collect 1,401 samples for
xNeed, 1,750 for xEffect, 1,730 for xIntent, and 1,861 for xReact as training
data. Hereafter, $G_{\mathrm{small}}$ represents the small-scale graph.

#### Negative Sample Type 1

Pseudo-negative samples are adopted by incorrectly ordering the time series.
When a valid triplet $(h,r,t)\in G_{\mathrm{small}}$ is given, an
inappropriate inference can be obtained by considering $(t,r,h)$. Since the
head and tail need to be swapped, it is used only for inference between event
pairs.

#### Negative Sample Type 2

By considering $(h_{1},r,t_{2})$ or $(h_{2},r,t_{1})$ from two valid triplets
of the same relation $(h_{1},r,t_{1}),(h_{2},r,t_{2})\in G_{\mathrm{small}}$
where $(h_{1}\neq h_{2})$, an inappropriate inference can be obtained. Since
the context is different between the head and tail, it can be an easy sample
during training. For example, it is also possible to consider selecting events
with similar contexts by considering the similarity between sentences to make
them slightly more difficult.

#### Negative Sample Type 3

In CSKG, there are relationships that are temporally reversed, such as xIntent
and xReact. If we denote the reverse relationship for a relationship $r$ as
$\mathrm{inv}(r)$, for two valid triplets
$(h,r,t),(h,\mathrm{inv}(r),t^{\prime})\in G_{\mathrm{small}}$ with the same
head, $(h,r,t^{\prime})$ can be adopted as a negative sample. Unlike Type 2,
it is possible to obtain negative samples in the same context.

###  D.2 Results

The probabilities predicted by the model for each label of the test data are
shown in Table 10. The valid triplets yielded higher predictions, again
confirming the validity of the filter model.

Relation | valid(1) | invalid(2) | (1)-(2)
---|---|---|---
xNeed | 0.880$\pm$0.295 | 0.626$\pm$0.450 | +0.254
xEffect | 0.367$\pm$0.447 | 0.256$\pm$0.413 | +0.111
xIntent | 0.781$\pm$0.276 | 0.643$\pm$0.300 | +0.138
xReact | 0.759$\pm$0.348 | 0.519$\pm$0.426 | +0.240
Table 10: The average probabilities the filter model predicted for (1) the
inferences deemed appropriate by crowdsourcing and (2) the inferences deemed
inappropriate by crowdsourcing. Standard deviations are shown after
plus/minus. The rightmost column is the difference between them.

##  Appendix E Commonsense Generation Model Details

###  E.1 Training Details

To confirm the appropriate model and input format, we construct some
commonsense generation models with a subset of the built graph as a
preliminary experiment. For pretrained models, we adopt Japanese
T5999https://huggingface.co/megagonlabs/t5-base-japanese-web and Japanese
GPT-2.

The input format is shown in 11. Since T5 is a seq2seq model, the head and the
relation are given in the form of “$r:h$” as an input, and the tail is given
as the correct output. The relation for T5 is changed to a natural language
sentence. For example, “xNeed” is rewritten to “What event occurs before this
statement?” The instructions to T5 may not be the best; prompt-engineering
could improve the results. As GPT-2 predicts the next word, the head and the
relation are given as an input, and the model is trained to output the tail.
Since the relations are not included in the vocabulary of the pretrained
models, they are added as special tokens. In the constructed knowledge graph,
the subject of an event is generalized as “X,” but it would be better to
change it into a natural expression as the input to the pretrained models. We
randomly replace the subject with a personal pronoun during training and
inference. To confirm this effect, we also train GPT-2 with the subject
represented as “X.” We denote this as GPT-2X.

Model | Rel | Encoder Input | Decoder Input
---|---|---|---
T5 | xNeed | この文の前に起こるイベントは何ですか？: $h$ | $t$
|  | (What event occurs before this statement?: $h$) |
| xEffect | このイベントの次に発生する事象は何ですか？: $h$ | $t$
|  | (What is the next event to occur after this event?: $h$) |
| xIntent | 次の文の発生した理由は何ですか？: $h$ | $t$
|  | (What is the reason for the occurrence of the following statement?: $h$) |
| xReact | 次の文の後に感じることは何ですか？: $h$ | $t$
|  | (What will be felt after the following statement?: $h$) |
GPT-2 | xNeed | - |  $h$ xNeed $t$
| xEffect | - |  $h$ xEffect $t$
| xIntent | - |  $h$ xIntent $t$
| xReact | - |  $h$ xReact $t$
Table 11: The input formats for training. Note that $h$ and $t$ denote a head
and a tail.

###  E.2 Evaluation

#### Automatic Evaluation

We calculate BLEU (Papineni et al., 2002) and BERTScore (Zhang* et al., 2020)
as automatic metrics. Table 12 shows these results. GPT-2X and GPT-2 performed
the best in BLEU and BERTScore, respectively. Table 14 shows the average
output length and the number of unique words for each model. The average
output length of T5 is longer than those of GPT-2s, but GPT-2s have the
greater numbers of unique words than T5.

#### Manual Evaluation

Using crowdsourcing, we evaluate how likely the generated inferences are.
Following the previous study (West et al., 2022), we show crowdworkers two
events (a head and a tail) and a relation. Then, we ask them to evaluate the
appropriateness of the inference by choosing from the following options:
“always,” “often,” “sometimes,” and “never.” The choices are displayed with an
appropriate verb for each relation (e.g., “always happens” for xEffect). For
each inference, the numbers of crowdworkers who choose “never” and other than
“never” (i.e., at least “sometimes”) are used to determine the majority vote.
The acceptance rate (AR) is the proportion of inferences in which more
crowdworkers choose other than “never.” By assigning 0 to 3 points each to
“never,” “sometimes,” “often,” and “always,” we also calculate the mean point
(MP) as the average score of all the inferences. Table 12 shows these results.
AR is higher than 85% for all models, indicating that the inferences for
unseen events are almost correct. GPT-2 obtained the highest scores for both
AR and MP.

Although the replacement of subjects did not make a difference in AR, there is
a difference in the distributions of MP as shown in Figure 8. The number of
crowdworkers who chose “never” for the inference of GPT-2 is less than half of
that for GPT-2X. This result indicates that it is better for the model to
replace subjects “X” with personal pronouns.

Table 15 shows the correlation coefficients between the manual and automatic
evaluation metrics. The correlation coefficients between the manual metrics
(AR and MP) and BERTScore are positive, while those between the manual metrics
and BLEU are negative or have no correlation. It seems that BERTScore, which
uses vector representations, can evaluate equivalent sentences with different
expressions, but BLEU, which is based on n-gram agreement, cannot correctly
judge the equivalence. One of the reasons for the negative correlation in BLEU
is that many inferences of the mental state consist of a single word in
Japanese, such as “tired” and “bored,” for both the gold answer and the
generated result. In this case, BLEU tends to be low because the words are
rarely matched, but the shorter the sentences are, the easier it is for the
model to generate appropriate results.

Examples of outputs are shown in Table 13. We can see that the obtained
outputs are acceptable to humans. The outputs vary for each model.

Model | AR | MP | BS | BLEU
---|---|---|---|---
T5 | 87.5 | 1.64 | 90.26 | 18.57
GPT-2 | 91.0 | 1.73 | 92.31 | 18.26
GPT-2X | 91.0 | 1.68 | 92.03 | 18.99
T5freeze | - | - | 68.20 | 3.19
GPT-2freeze | - | - | 69.36 | 7.33
Table 12: Total evaluation scores. AR, MP, and BS indicate the acceptance rate, the mean point, and BERTScore, respectively. The bottom two columns show the baselines, which are not finetuned, just pretrained. Model |  Input |  Output
---|---|---
T5 |  この文の前に起こるイベントは何ですか？:あなたが友人たちと旅行に出かける (What event occurs before this statement?: You go on a trip with your friends) |  あなたが車を運転する (You drive a car)
|  このイベントの次に発生する事象は何ですか？:あなたが友人たちと旅行に出かける (What is the next event to occur after this event?: You go on a trip with your friends) |  あなたが楽しい時間を過ごす (You have a good time)
|  次の文の発生した理由は何ですか？:あなたが友人たちと旅行に出かける (What is the reason for the occurrence of the following statement?: You go on a trip with your friends) |  楽しい (Have fun)
|  次の文の後に感じることは何ですか？:あなたが友人たちと旅行に出かける (What will be felt after the following statement?: You go on a trip with your friends) |  楽しい (Have fun)
GPT-2 |  僕が友人たちと旅行に出かけるxNeed (I go on a trip with your friends xNeed) |  僕がパスポートを取得する (I get my passport)
|  僕が友人たちと旅行に出かけるxEffect (I go on a trip with your friends xEffect) |  僕が楽しい時間を過ごす (I have a good time)
|  僕が友人たちと旅行に出かけるxIntent (I go on a trip with your friends xIntent) |  楽しいことがしたい (Want to have fun)
|  僕が友人たちと旅行に出かけるxReact (I go on a trip with your friends xReact) |  楽しい (Feel fun)
Table 13: Examples of the inferences generated by T5 and GPT-2. Model | Avg Out Len | Uniq Word #
---|---|---
T5 | 5.29 | 392
GPT-2 | 5.03 | 451
GPT-2X | 5.03 | 436
Table 14: Average output length and the number of unique words. Figure 8: The number of inferences for each MP. | AR | MP | BS | BLEU
---|---|---|---|---
AR | 1.00 | 0.75 | 0.59 | -0.11
MP | - | 1.00 | 0.43 | -0.46
BS | - | - | 1.00 | 0.30
BLEU | - | - | - | 1.00
Table 15: Correlation coefficients between automatic and manual evaluation
metrics.


# Optical superradiance of a pair of color centers in an integrated silicon-
carbide-on-insulator microresonator

Daniil M. Lukin∗1, Melissa A. Guidry∗1, Joshua Yang1, Misagh Ghezellou2,
Sattwik Deb Mishra1, Hiroshi Abe3, Takeshi Ohshima3, Jawad Ul-Hassan2, and
Jelena Vučković†,1
1E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA.
2Department of Physics, Chemistry and Biology, Linköping University, SE-58183,
Linköping, Sweden
3National Institutes for Quantum Science and Technology, Takasaki, Gunma 370-
1292, Japan

###### Abstract

An outstanding challenge for color center-based quantum information processing
technologies is the integration of optically-coherent emitters into scalable
thin-film photonics. Here, we report on the integration of near-transform-
limited silicon vacancy (VSi) defects into microdisk resonators fabricated in
a CMOS-compatible 4H-Silicon Carbide-on-Insulator platform. We demonstrate a
single-emitter cooperativity of up to 0.8 as well as optical superradiance
from a pair of color centers coupled to the same cavity mode. We investigate
the effect of multimode interference on the photon scattering dynamics from
this multi-emitter cavity quantum electrodynamics system. These results are
crucial for the development of quantum networks in silicon carbide and bridge
the classical-quantum photonics gap by uniting optically-coherent spin defects
with wafer-scalable, state-of-the-art photonics.

Color centersatature2018material ; awschalom2018quantum ; wolfowicz2021quantum
are among the leading contenders for the realization of distributed quantum
information processing, including communicationpompili2021realization ;
bhaskar2020experimental  and computationnickerson2014freely , combining a
long-lived multi-qubit spin registerbradley2019ten  with a photonic interface
in the solid state. To continue scaling up quantum networks while maintaining
high entanglement generation rates, the intrinsically weak interaction between
photons and color centers must be enhanced via integration into photonic
resonatorssipahigil2016integrated ; evans2018photon ; lukin20204h ;
bhaskar2020experimental ; crook2020purcell ; rugar2021quantum ;
kuruma2021coupling . Efforts in cavity integration have already enabled
milestone demonstrations such as cavity-mediated coherent interaction between
two emitters evans2018photon , single-emitter cooperativity exceeding 100 and
spin-memory-assisted quantum communicationbhaskar2020experimental . The
ultimate goal of quantum computation and error-protected
communicationmuralidharan2016optimal  requires the realization of photonic
circuits with high complexity and minimal inter-node loss, and will require
bringing together all integrated photonics expertise developed in the past two
decades.pelucchi2021potential

Yet color center technologies cannot at present take advantage of the state of
the art in integrated photonics, due to two central challenges. First, thin-
film-on-insulator photonics technologies have been incompatible with high-
quality color centers: this motivated the focus on bulk-crystal-carving
methodskhanaliloo2015high ; sipahigil2016integrated ; dory2019inverse ;
wan2020large ; babin2021fabrication , suitable for fabrication of individual
devices but restrictive in terms of large-scale monolithic photonic circuits.
Second, inversion symmetry, which protects optical transitions from electric
fields (to first orderaghaeimeibodi2021electrical ; de2021investigation ), had
been widely considered to be a prerequisite for color centers to maintain
optical coherence in nanophotonic structures. This notion motivates the
dominant focus on group-IV color centers in diamond (SiV, SnV,
GeV)bradac2019quantum , and eliminates from consideration an entire class of
materials that lack crystal inversion symmetry. Among these materials is
silicon carbide (SiC)lukin2020integrated , which has otherwise emerged as the
top contender for wafer-scale integration of color centers with excellent
spin-optical properties (such as the silicon vacancy (VSi)soykal2016silicon ;
banks2019resonant ; morioka2020spin ; nagy2021narrow ; babin2021fabrication
and the divacancyanderson2019electrical ; bourassa2020entanglement ). This
inversion symmetry requirement has only recently been challenged in a
demonstration of optically-coherent VSi in bulk-carved SiC
nanobeamsbabin2021fabrication .

In this work, we demonstrate the integration of optically-coherent non-
inversion-symmetric color centers into scalable thin-film SiC nanophotonics.
We demonstrate cavity cooperativity of a single VSi color center of up to 0.8,
allowing for the observation of dipole-induced transparencywaks2006dipole  in
SiC. We achieve a photon detection rate of up to 0.4 MHz from a single defect
into the zero-phonon-line (ZPL), limited by the population shelving in the
metastable state. We use this platform to demonstrate superradiant emission of
two SiC color centers, and highlight the unique applications of the two-
emitter whispering-gallery-mode (WGM) resonator system for quantum information
processing architectures. Our work challenges the notion that inversion
symmetry is a prerequisite for nanophotonic integration of optically-coherent
spin defects, and bridges the classical-quantum photonics gap by uniting color
centers with CMOS compatible, wafer-scalable, state-of-the-art
photonicssong2019ultrahigh ; guidry2020optical ; guidry2022quantum .

Figure 1: Spectrally-stable VSi emitters in integrated 4H-SiCOI photonics. (a)
Scanning electron micrograph of the device. A waveguide, which wraps around
the disk (seen in the optical microscope image, inset), is coupled to the
resonator. A microscope objective is used to couple light to and from the flat
facets of the waveguide. (b) A cavity photoluminescence spectrum (emitter PLE
spectrum) in black (green), taken with a scanning resonant laser with 1.5 µW
(0.5 pW) of power in the waveguide. We extract a loaded cavity quality factor
of Q $=1.3\cdot 10^{5}$. The prominent peaks at 2.7 and 4.5 GHz detuning are
the A2 transitions of the two emitters. The corresponding A1 transitions are
labelled with arrows. Ịn this figure and henceforth, laser detuning is
relative to 327.113 THz ($916.5$ nm). (c) Lifetime measurements for emitter A
(blue) and emitter B (red) on- and off-resonance with the cavity. The gray
region represents the excitation pulse. (d) A 1-hour PLE scan of each emitter
(while the other is selectively ionized into the dark state), with the cavity
positioned on-resonance with the emitter.

The photonic device consists of a microdisk resonator integrated with a
waveguide (Fig. 1(a)), fabricated in 4H-Silicon Carbide-on-Insulator
(4H-SiCOI)lukin20204h . The high-Q transverse-magnetic (TM) modes of the
resonator optimally align with the dipole moment of the VSi in a c-cut
wafersoykal2016silicon . The coupling waveguide terminates in a flat facet on
both ends to allow for efficient single-mode free-space coupling. Details of
the fabrication process are presented in the Supplementary Information. We
observe a total coupling efficiency from the waveguide to the single-mode
fiber of up to 24%, which includes all setup losses. The experiments are
performed at 4.3 K in a closed-cycle cryostat (Montana Instruments). The
microresonator modes are tuned spectrally via argon gas condensation. A pulsed
femtosecond laser centered at 740 nm is used to uniformly excite the emitters
in the disk: it couples to all resonator modes simultaneously, owing to its
broad spectrum. As the microresonator is gas-tuned, an enhancement of emission
at the VSi ZPL wavelength of 916.5 nm (as observed via a spectrometer)
indicates Purcell enhancement of one or more VSi. With a resonator mode parked
at the Purcell enhancement condition, we measure the absorption lines of the
coupled emitters via photoluminescence excitation (PLE), where a weak (0.5 pW
in the waveguide) continuous-wave resonant laser is scanned across the ZPL
while detecting the phonon sideband (PSB) of the emitters. A PLE scan shows
that in this device, two emitters are coupled to the cavity (Fig. 1b),
henceforth labeled emitters A and B. The VSi is known to feature two spin-
preserving optical transitions, A1 and A2, split by 1 GHz banks2019resonant .
We perform experiments with a weak off-axis external magnetic field that mixes
the ground-state spins and eliminates resonant-laser-induced spin-
polarization. We focus our study on the A2 transition of each emitter, which
is brighter due to its higher quantum efficiencybanks2019resonant . We
optimize the magnetic field orientation to reduce the relative intensity of
the A1 transition upon resonant driving through coherent population trapping
of the spin-$\frac{3}{2}$ sublevels. Through the absence of a cavity
transmission dip, we conclude that the resonator mode is strongly undercoupled
to the waveguide. To observe the cavity lineshape, we measure the cavity
photoluminescence noise by scanning across the resonance with higher laser
power (1.5 µW in the waveguide) and extract a loaded quality factor of
$1.3\cdot 10^{5}$ (Fig. 1b).

Figure 2: Dipole induced transparency (DIT) in SiC. (a) A wide laser scan
across the cavity resonance, showing the transmission spectrum through the
device (black). The VSi phonon sideband emission is simultaneously detected
(green, multiplied by 50x). Excitation of the resonator mode is performed
through a scattering imperfection on the disk edge and transmission through
the waveguide is detected. (b) Close-up scan at the cavity center for
different emitter detunings. Orange and green traces are offset by +0.1 and
+0.2 MHz, respectively.

The emitter-cavity coupling rate is a key metric for cavity quantum
electrodynamics systems. We determine coupling strength of each emitter to the
cavity by measuring the emitter lifetime reduction on resonance, known as
Purcell enhancement. First, we selectively ionize one emitter into the dark
state via strong resonant excitation, and tune the cavity on-resonance with
the remaining bright emitter. We then excite the emitter with 150 ps resonant
pulses (obtained via pulse-shaping a mode-locked Ti:Sapphire laser) through
the cavity mode and detect the transient ZPL emission using temporal
filtering. As shown in Fig. 1(c), the on-resonance lifetime for emitter A (B)
is measured to be 4.2 ns (3.5 ns), which corresponds to a lifetime reduction
of 2.7 (3.2) from the bulk lifetime of 11.3 ns di2021InPreparation , and a
Purcell enhancement $F$ of 28 (37) (see Supplementary Information). From the
simulated mode volume of $128(\frac{\lambda}{n})^{3}$ for the fundamental TM00
mode, we find the theoretical maximum Purcell enhancement of 77 in this
device. The observed Purcell enhancement is comparable to that achieved in the
first integrations of the diamond silicon vacancysipahigil2016integrated ;
zhang2018strongly  and tin vacancyrugar2021quantum ; kuruma2021coupling  into
photonic crystal nanobeam cavities, despite the much stronger mode confinement
of those devices. We attribute this to the optimal dipole overlap of the VSi
with the cavity TM mode and the less stringent emitter positioning
requirements of the microdisks. Via resonant pulsed excitation with 1 ns long
pulses (generated from a continuous-wave laser using electro-optic amplitude
modulation) and detection of the PSB emission with the cavity detuned by $-80$
GHz, we measure the off-resonant lifetime of emitter A (B) to be 10.7 ns (11.1
ns). The minor discrepancy between the off-resonant lifetimes and the bulk
lifetime (11.3 ns) is attributed to the coupling of the emitters to other
modes of the microdisk.

Although Purcell enhancement has been observed in several color center
platformscrook2020purcell ; bracher2017selective ; sipahigil2016integrated ;
zhang2018strongly ; rugar2021quantum , including thin-film
diamondfaraon2011resonant  and SiClukin20204h , to date cavity-coupled color
centers that retain their optical coherence have only been demonstrated in
bulk-carved diamondsipahigil2016integrated ; evans2018photon . To quantify the
optical coherence and the spectral stability of the VSi in 4H-SiCOI
microdisks, we perform continuous PLE scans on each emitter while on- and off-
resonance with the cavity. The on-resonance PLE scans are shown in Fig. 1(d).
Emitters A and B were measured at different times, and the cavity has been
centered on the measured emitter before the start of each one-hour
acquisition. Over the course of one hour, no emitter ionization is observed,
and spectral wandering is below 500 MHz. The average single-scan optical
transition linewidth for emitter A (B) is found to be 54.3(3) MHz (63.4(3)
MHz), which corresponds to 17 MHz (18 MHz) of spectral diffusion beyond the
transform limit. Repeating the measurement off-resonance, we find the emitter
A (B) linewidth to be 37.8(8) MHz (38.5(8) MHz), which corresponds to 24 MHz
of spectral diffusion beyond the transform limit (see Supplementary
Information). The reduced spectral diffusion on-resonance may be due to a
decreased rate of excitation of surface-related defects, because the well-
confined TM cavity mode is efficiently excited with low laser power. These
results indicate excellent spectral stability of the nanophotonics-integrated
VSi.

Figure 3: Superradiant emission of two VSi color centers. (a) Second-order
correlation of the photon emission along one waveguide direction displays
bunching at zero time delay, a signature of superradiance. Inset: zoom-in of
the superradiance feature. (b) The relative phase $\phi$ of the emitters
impacts the cross-correlation photon statistics between the opposite waveguide
directions and can produce anti-bunched emission. The solid line in a,b is the
numerical fit based on a five-level modeldi2021InPreparation  of the VSi. (c)
The level structure representing the pair of two-level-system emitters
decaying into degenerate clockwise (red arrows) and counterclockwise (blue
arrows) optical modes. The corresponding transition rates are indicated next
to the arrows, where $\Gamma$ is the unmodified single-emitter decay rate into
a propagating mode. (d) Theoretically-predicted phase-dependent cross-
correlation between clockwise and counterclockwise modes for a pair of ideal
two-level emitters.

From the measured Purcell enhancement and off-resonant emitter linewidths, we
calculate the emitter-cavity cooperativity $C=\frac{4g^{2}}{\kappa\gamma}$ to
be 0.6 and 0.8 for emitter A and B, respectively (see Supplementary
Information). This regime enables the observation of dipoled-induced
transparency (DIT)waks2006dipole , where the VSi scatter photons from an input
coherent state. Because the device studied here is strongly under-coupled to
the bus waveguide, DIT is difficult to observe through waveguide transmission.
We instead excite the disk through a scattering point on its edge, and detect
emission into the waveguide, thus in effect performing the measurement in a
drop-port configurationwaks2006dipole  (see Supplementary Information).
Scanning the continuous-wave laser across the disk resonance, DIT dips for
both emitters are clearly observed, shown in Fig. 2(a,b). The slow spectral
drift of the emitters allows us to measure DIT for different relative
detunings. Looking forward, spin initialization, targeted emitter placement,
and cavities with a larger $Q/V$ metric lukin20204h ; song2019ultrahigh  will
enable stronger transmission contrast in DIT for the realization of spin-
photon entanglement and spin-readout via the modification of cavity
reflectivity evans2018photon ; bhaskar2020experimental .

Photon interference between two color centers, a prerequisite for the
generation of remote spin-spin entanglement, has been an outstanding challenge
in silicon carbide. Here, we demonstrate two-photon interference between two
microdisk-integrated emitters, which arises from their collective coupling to
the same cavity mode. To observe photon interference in the continuous wave
regime, an above-resonant laser is coupled to a resonator mode around 730 nm
to excite both emitters. We note that while above-resonant excitation in bulk
crystal has been used to obtain nearly transform-limited photon emission from
the VSimorioka2020spin , we observe that in nanostructures it induces rapid
spectral diffusion due to disturbance of the surface charge environment,
broadening the optical linewidths to approximately 0.5 GHz. This spectral
instability reduces the rate of superradiant emission (however, optical
coherence may be preserved using resonant excitation, as shown later in the
work). Fig. 3(a) shows the second-order auto-correlation $g^{(2)}(\tau)$ of
the color centers’ collective emission in the Hanbury Brown and Twiss
configuration, where emission into the waveguide is split between two
detectors via a beamsplitter. The sharp peak at zero time delay is a signature
of superradiant emission and the probabilistic generation of entanglement
between the two color centers. This feature has also been observed with up to
three waveguide-integrated quantum dots kim2018super ; grim2019scalable  and a
pair of waveguide-integrated silicon vacancy centers in
diamondsipahigil2016integrated ; machielse2019quantum . In contrast, for
cross-correlations between the two waveguide propagation directions, an anti-
bunching interference dip is observed (Fig. 3(b)). This feature is indicative
of photon pairs preferentially leaving the resonator in the same direction.

Figure 4: Manipulating the single-photon emission of a pair of emitters. (a)
Weakly exciting the emitters with a resonant pulse (grey) through the CW mode
will prepare the system in the superposition
$(e^{i\phi}\ket{eg}+\ket{ge})/\sqrt{2}$, which will result in asymmetric
emission rates. (b) By independently controlling the excitation phase of the
two emitters positioned such that $\phi=\pi/2$, the microresonator
incorporates the functionality of a single-photon router. The phase of the
free-space excitation pulse is represented by the color, where green, grey,
and orange correspond to $\pi/2$, $0$, and $-\pi/2$, respectively.

The experimentally-observed photon statistics are explained by the out-of-
phase coupling of the two emitters to a pair of degenerate clockwise and
counterclockwise optical modes of the resonator. The interaction Hamiltonian
for this system can be written as

$H_{I}=g_{A}\sigma_{A}^{\dagger}S_{A}+g_{B}\sigma_{B}^{\dagger}S_{B}+\text{h.c.},$
(1)

where $\sigma_{A}$ and $\sigma_{B}$ are the lowering operators for emitters A
and B, respectively, and $g_{A}$ and $g_{B}$ are the emitter-cavity coupling
strengths; each emitter couples to its own standing wave supermode
$S_{A}=(a_{\text{CW}}+a_{\text{CCW}})/\sqrt{2}$ and
$S_{B}=(e^{-i\phi}a_{\text{CW}}+e^{i\phi}a_{\text{CCW}})/\sqrt{2}$, where
$a_{\text{CW}}$ ($a_{\text{CCW}}$) is the clockwise (counterclockwise)
resonator propagating mode, and phase $\phi$ corresponds to the emitters’
azimuthal separation in the resonator. Consider two special cases: (i) for
$\phi=(0\mod\pi)$, $S_{A}=\pm S_{B}$ and the two emitters couple to the same
standing wave mode, resulting in a single-mode interactionevans2018photon ;
(ii) for $\phi=(\pi/2\mod\pi)$, $S_{A}$ and $S_{B}$ are orthogonal, and in the
standing wave basis the emitters are de-coupled. However, because the
measurement is performed in the propagating mode basis
$\\{a_{\text{CW}},a_{\text{CCW}}\\}$ (corresponding to emission to the right
and to the left, respectively), the pair of emitters exhibits interference for
all values of $\phi$. For $(\phi\mod\pi)\neq 0$, the cross-correlation between
the two waveguide propagation directions will reveal interference features
unique to a multi-mode, multi-emitter system.

The collective emission behavior can be understood via a cascaded decay
diagram shown in Fig. 3(c). Starting with the two-emitter excited state
$\ket{ee}$, emission into the clockwise mode projects the emitters into the
superposition state $(e^{i\phi}\ket{eg}+\ket{ge})/\sqrt{2}$. From this state,
decay via clockwise emission proceeds with the superradiant rate $2\Gamma$,
where $\Gamma$ is the unmodified single-emitter decay rate into a propagating
mode. In contrast, the rate of counterclockwise emission is modified by
$\cos^{2}\phi$, as follows from the transition amplitude
${\bra{gg}(e^{i\phi}\sigma_{A}+\sigma_{B})(e^{i\phi}\ket{eg}+\ket{ge})/\sqrt{2}}$.
When $\cos^{2}\phi=0$, photons leave the resonator always in the same
direction, which corresponds to perfect antibunching in the cross-correlation.
For $\cos^{2}\phi=\pm 1$, the cross-correlation is identical to the
autocorrelation on a single waveguide direction. These cases are illustrated
in Fig. 3(d). The correlation measurements (Fig. 3(a,b)) are fit to a reduced
five-level emitter modeldi2021InPreparation  with free parameters of
excitation power, $\phi$, cavity detuning, and background noise. The presence
of background noise from the above-resonant excitation reduces the
interference contrast.

Figure 5: Chiral single-photon scattering from a pair of emitters in a WGM
resonator (a) The emitter pair is excited through the CW mode. Photons
scattered into the CW (red) and CCW (blue) mode are time-correlated to the
excitation pulse, tracing out the temporal shape of the emitted single-photon
wavepacket. The solid red and blue lines represent the simulated expectation
values $\langle a^{\dagger}_{\text{CW}}a_{\text{CW}}\rangle$ and $\langle
a^{\dagger}_{\text{CCW}}a_{\text{CCW}}\rangle$, respectively. The asymmetric
CW and CCW emission arises from non-trivial emitter phase difference, inferred
to be $(0.34\pi\mod\pi)$. The simulated case where ${\phi=0}$ is shown as a
grey dotted curve, in which case the emission is symmetric. (b) The PLE
spectrum of the two emitters shows frequency separation of 0.44 GHz, which is
used as a fixed parameter in the simulation of the wavepacket in (a). (c,d)
Same as panels (a,b) but for emitter frequency separation of 0.19 GHz, with
inferred phase $\phi=(0.28\pi\mod\pi)$.

Excitation of emitters via above-resonant optical fields increases spectral
diffusion and is compatible neither with spin-selective excitation nor optical
coherent control. To overcome this, we use resonant excitation to coherently
manipulate the two-emitter superposition in the single photon subspace, a
regime which has enabled pioneering quantum network experiments with NV
centers in diamond humphreys2018deterministic ; pompili2021realization .
Consider exciting the two emitters through the waveguide via fast resonant
pulses in the clockwise direction (Fig. 4(a)). In the bad-cavity regime
($\kappa\gg\gamma$) and with resonator finesse $\mathcal{F}\gg 1$, if the two
emitters are initially in the ground state $\ket{gg}$, a pulse instantaneously
prepares the system into a superposition state

$\ket{\psi}=(1-P_{e})\ket{gg}\\\
+\sqrt{P_{e}(1-P_{e})}(e^{i\phi}\ket{eg}+\ket{ge})+P_{e}e^{i\phi}\ket{ee},$
(2)

where $P_{e}$ is the single-emitter excitation probability. In the weak
excitation limit ($P_{e}\ll 1$), the probability of double-excitation is
negligible, and the system is prepared in the superposition
$(e^{i\phi}\ket{eg}+\ket{ge})/\sqrt{2}$ conditioned on the detection of a
scattered photon. This corresponds to the preparation of the two-emitter
system into the intermediate level of the diagram in Fig. 3(c). The emission
from this state will proceed superradiantly in the clockwise direction
independent of $\phi$, but the back-scattering rate will be modified by
$\cos^{2}\phi$ (Fig. 4(a)). For $\phi=\pi/2$, complete directionality is
achieved. This is analogous to classical chiral scattering observed in WGM
resonators coupled to a pair of dielectricpeng2016chiral  and
plasmoniccognee2019cooperative  nanostructures. The $\phi=\pi/2$ condition can
be used to implement routing of single photons from an emitter pair (Fig.
4(b)) and, as shown in the Supplementary Information, enables efficient spin-
spin entanglement protocols. We note that due to the cavity-mediated coupling
of emitters, collective scattering of input light is strengthened in the high-
cooperativity regime, whereas in a waveguide system high-cooperativity
emitters will act as individual strong scatterers.

The combination of preserved optical coherence and spectral stability enables
the experimental realization of single-photon interference between two VSi
emitters, shown in Fig. 5. Because the emitters’ transitions are not
degenerate, their relative phase will precess at the rate equal to their
frequency difference, which is observed as an oscillation in the single-photon
wavepacket. Notably, the phase difference in the oscillations of CW and CCW
emission originates from the relative emitter phase $\phi$. As described in
the Supplementary Information, the non-unity contrast of the oscillations is
due to the distribution of the spin population across the bright
spin-$\frac{1}{2}$ and dark spin-$\frac{3}{2}$ manifolds (corresponding to the
optical transitions A2 and A1, respectively). The oscillations persist
throughout the entire wavepacket, confirming nearly transform-limited photon
emission, essential for interference-based entanglement
generationhumphreys2018deterministic . The smaller amplitude oscillation with
a 1 ns period is due to incomplete suppression of the A1 emission line of the
VSi (Fig. 1(b)). The free parameters in the numerical model are cavity
detuning, $\phi$, and the population of the spin-$\frac{1}{2}$ manifold. From
the numerical fit, the spin population is inferred to be unpolarized, as
expected in an off-axis magnetic field. The relative emitter phase inferred
from the data in Fig. 5(a) and 5(c) is $\phi=(0.34\pi\mod\pi)$ and
$\phi=(0.28\pi\mod\pi)$, respectively. We note that $\phi$ was observed to
drift in time, attributed to nonuniform deposition of water ice on the
resonator as a result of the asymmetric resonator undercut geometry. This
explanation is consistent with the observed slow systematic drift of emitter
spectral separation by approximately 1 GHz per day due to strain from the ice.

The present study of the cavity quantum electrodynamics of a color center pair
in a microdisk resonator suggests that despite a typically lower quality
factor-to-mode volume ratio (Q/V) than high-confinement photonic crystal
cavities, WGM resonators may offer unique capabilities and warrant further
consideration for applications in chip-integrated quantum information
processing. As we show in the Supplementary Information, the two-emitter
chiral scattering at the $\phi=\pi/2$ condition enables efficient entanglement
generation via single-photon interference. Through integration with a color
center that exhibits two orthogonal circularly polarized transitions such as
the divacancy in silicon carbide, the microdisk could be used to realize
single-emitter chiral light-matter interactionscheucher2016quantum ;
lodahl2017chiral . Furthermore, the microdisk is a promising platform for
near-term many-body quantum optics demonstrations with solid state spins, as
many individually-addressable and spectrally-tunable emitters may be
integrated into a single resonatorlukin2020integrated .

In conclusion, we have demonstrated near-unity cooperativity between a color
center and a microresonator fabricated in a wafer-scalable, CMOS-compatible
semiconductor photonics platform. Additionally, we observe two-photon
superradiance and single-photon interference between two SiC color centers.
The integration of VSi into state-of-the-art microring
resonatorsguidry2022quantum  and high-confinement photonic crystal
cavitiessong2019ultrahigh  would enable deterministic emitter-photon
interactions in SiC. Taken together with the recent demonstrations of nuclear
spin controlbourassa2020entanglement ; babin2021fabrication , wide spectral
tuning via electric fieldsanderson2019electrical ; lukin2020spectrally  and
single-shot readoutanderson2021five , silicon carbide satisfies the
prerequisites to implement a fully-monolithic quantum photonic processor. The
maintained spin-optical coherence of the VSi at elevated temperatures of up to
20 K babin2021fabrication ; udvarhelyi2020vibronic  offers an additional
degree of flexibility for operation with low-cost cryogenic systems. Finally,
the spectral stability of the VSi, despite its substantial dipole
momentlukin2020spectrally , suggests that a first-order insensitivity to
electric fields is not a prerequisite for color center compatibility with
nanostructures; this result motivates a continued effort toward the
integration of other SiC color centers, such as the
divacancyanderson2019electrical , the nitrogen-vacancy centervon2016nv , the
vanadium centerspindlberger2019optical ; wolfowicz2020vanadium , and the
chromium iondiler2020coherent , into nanophotonics.

∗These authors contributed equally

†<EMAIL_ADDRESS>

Acknowledgments We gratefully acknowledge discussions with Florian Kaiser,
Charles Babin, Di Liu, Jörg Wrachtrup, Öney O. Soykal, Daniel Riedel,
Christopher P. Anderson, Ki Youl Yang, Shahriar Aghaeimeibodi, Alexander D.
White. This work is funded in part by the U.S. Department of Energy (DoE),
Office of Science, under Awards DE-SC0019174, DE-Ac02-76SF00515, and the
National Quantum Information Science Research Centers. D.M.L. acknowledges the
J. Hewes Crispin and Marjorie Holmes Crispin Stanford Graduate Fellowship
(SGF) and the National Defense Science and Engineering Graduate (NDSEG)
Fellowship. M.A.G. acknowledges the Albion Hewlett SGF and the NSF Graduate
Research Fellowship. J.Y. acknowledges the NDSEG. J.U.H. acknowledges support
from Swedish Research Council (grant No. 2020-05444), Knut and Alice
Wallenberg Foundation (grant No. KAW 2018-0071), and the EU H2020 project
QuanTELCO (grant No. 862721). T.O. acknowledges grants JSPS KAKENHI 20H00355
and 21H04553. Part of this work was performed at the Stanford Nanofabrication
Facility (SNF) and the Stanford Nano Shared Facilities (SNSF).

## References

  * (1) Atatüre, M., Englund, D., Vamivakas, N., Lee, S.-Y. & Wrachtrup, J.  Material platforms for spin-based photonic quantum technologies.  _Nature Reviews Materials_ 3, 38–51 (2018).
  * (2) Awschalom, D. D., Hanson, R., Wrachtrup, J. & Zhou, B. B.  Quantum technologies with optically interfaced solid-state spins.  _Nature Photonics_ 12, 516–527 (2018).
  * (3) Wolfowicz, G. _et al._ Quantum guidelines for solid-state spin defects.  _Nature Reviews Materials_ 906–925 (2021).
  * (4) Pompili, M. _et al._ Realization of a multinode quantum network of remote solid-state qubits.  _Science_ 372, 259–264 (2021).
  * (5) Bhaskar, M. K. _et al._ Experimental demonstration of memory-enhanced quantum communication.  _Nature_ 580, 60–64 (2020).
  * (6) Nickerson, N. H., Fitzsimons, J. F. & Benjamin, S. C.  Freely scalable quantum technologies using cells of 5-to-50 qubits with very lossy and noisy photonic links.  _Physical Review X_ 4, 041041 (2014).
  * (7) Bradley, C. E. _et al._ A ten-qubit solid-state spin register with quantum memory up to one minute.  _Physical Review X_ 9, 031045 (2019).
  * (8) Sipahigil, A. _et al._ An integrated diamond nanophotonics platform for quantum-optical networks.  _Science_ 354, 847–850 (2016).
  * (9) Evans, R. E. _et al._ Photon-mediated interactions between quantum emitters in a diamond nanocavity.  _Science_ 362, 662–665 (2018).
  * (10) Lukin, D. M. _et al._ 4H-silicon-carbide-on-insulator for integrated quantum and nonlinear photonics.  _Nature Photonics_ 14, 330–334 (2020).
  * (11) Crook, A. L. _et al._ Purcell enhancement of a single silicon carbide color center with coherent spin control.  _Nano Letters_ 20, 3427–3434 (2020).
  * (12) Rugar, A. E. _et al._ A quantum photonic interface for tin-vacancy centers in diamond.  _Physical Review X_ 11, 031021 (2021).
  * (13) Kuruma, K. _et al._ Coupling of a single tin-vacancy center to a photonic crystal cavity in diamond.  _Applied Physics Letters_ 118, 230601 (2021).
  * (14) Muralidharan, S. _et al._ Optimal architectures for long distance quantum communication.  _Scientific reports_ 6, 1–10 (2016).
  * (15) Pelucchi, E. _et al._ The potential and global outlook of integrated photonics for quantum technologies.  _Nature Reviews Physics_ 1–15 (2021).
  * (16) Khanaliloo, B., Mitchell, M., Hryciw, A. C. & Barclay, P. E.  High-Q/V monolithic diamond microdisks fabricated with quasi-isotropic etching.  _Nano Letters_ 15, 5131–5136 (2015).
  * (17) Dory, C. _et al._ Inverse-designed diamond photonics.  _Nature Communications_ 10, 3309 (2019).
  * (18) Wan, N. H. _et al._ Large-scale integration of artificial atoms in hybrid photonic circuits.  _Nature_ 583, 226–231 (2020).
  * (19) Babin, C. _et al._ Fabrication and nanophotonic waveguide integration of silicon carbide colour centres with preserved spin-optical coherence.  _Nature Materials_ 67–73 (2022).
  * (20) Aghaeimeibodi, S., Riedel, D., Rugar, A. E., Dory, C. & Vučković, J.  Electrical tuning of tin-vacancy centers in diamond.  _Physical Review Applied_ 15, 064010 (2021).
  * (21) De Santis, L., Trusheim, M., Chen, K. & Englund, D.  Investigation of the Stark effect on a centrosymmetric quantum emitter in diamond.  _Physical Review Letters_ 127, 147402 (2021).
  * (22) Bradac, C., Gao, W., Forneris, J., Trusheim, M. E. & Aharonovich, I.  Quantum nanophotonics with group IV defects in diamond.  _Nature Communications_ 10, 5625 (2019).
  * (23) Lukin, D. M., Guidry, M. A. & Vučković, J.  Integrated quantum photonics with silicon carbide: challenges and prospects.  _PRX Quantum_ 1, 020102 (2020).
  * (24) Soykal, Ö., Dev, P. & Economou, S. E.  Silicon vacancy center in 4H-SiC: Electronic structure and spin-photon interfaces.  _Physical Review B_ 93, 081207 (2016).
  * (25) Banks, H. B. _et al._ Resonant Optical Spin Initialization and Readout of Single Silicon Vacancies in 4H-SiC.  _Physical Review Applied_ 11, 024013 (2019).
  * (26) Morioka, N. _et al._ Spin-controlled generation of indistinguishable and distinguishable photons from silicon vacancy centres in silicon carbide.  _Nature Communications_ 11, 2516 (2020).
  * (27) Nagy, R. _et al._ Narrow inhomogeneous distribution of spin-active emitters in silicon carbide.  _Applied Physics Letters_ 118, 144003 (2021).
  * (28) Anderson, C. P. _et al._ Electrical and optical control of single spins integrated in scalable semiconductor devices.  _Science_ 366, 1225–1230 (2019).
  * (29) Bourassa, A. _et al._ Entanglement and control of single nuclear spins in isotopically engineered silicon carbide.  _Nature Materials_ 19, 1319–1325 (2020).
  * (30) Waks, E. & Vuckovic, J.  Dipole induced transparency in drop-filter cavity-waveguide systems.  _Physical Review Letters_ 96, 153601 (2006).
  * (31) Song, B.-S. _et al._ Ultrahigh-Q photonic crystal nanocavities based on 4H silicon carbide.  _Optica_ 6, 991–995 (2019).
  * (32) Guidry, M. A. _et al._ Optical parametric oscillation in silicon carbide nanophotonics.  _Optica_ 7, 1139–1142 (2020).
  * (33) Guidry, M. A., Lukin, D. M., Yang, K. Y., Trivedi, R. & Vučković, J.  Quantum optics of soliton microcombs.  _Nature Photonics_ 16, 52–58 (2022).
  * (34) Liu, D. _et al._ (manuscript in preparation).  _(in preparation)_ (2021).
  * (35) Zhang, J. L. _et al._ Strongly cavity-enhanced spontaneous emission from silicon-vacancy centers in diamond.  _Nano Letters_ 18, 1360–1365 (2018).
  * (36) Bracher, D. O., Zhang, X. & Hu, E. L.  Selective Purcell enhancement of two closely linked zero-phonon transitions of a silicon carbide color center.  _Proceedings of the National Academy of Sciences_ 114, 4060–4065 (2017).
  * (37) Faraon, A., Barclay, P. E., Santori, C., Fu, K.-M. C. & Beausoleil, R. G.  Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity.  _Nature Photonics_ 5, 301–305 (2011).
  * (38) Kim, J.-H., Aghaeimeibodi, S., Richardson, C. J., Leavitt, R. P. & Waks, E.  Super-radiant emission from quantum dots in a nanophotonic waveguide.  _Nano Letters_ 18, 4734–4740 (2018).
  * (39) Grim, J. Q. _et al._ Scalable in operando strain tuning in nanophotonic waveguides enabling three-quantum-dot superradiance.  _Nature materials_ 18, 963–969 (2019).
  * (40) Machielse, B. _et al._ Quantum interference of electromechanically stabilized emitters in nanophotonic devices.  _Physical Review X_ 9, 031022 (2019).
  * (41) Humphreys, P. C. _et al._ Deterministic delivery of remote entanglement on a quantum network.  _Nature_ 558, 268–273 (2018).
  * (42) Peng, B. _et al._ Chiral modes and directional lasing at exceptional points.  _Proceedings of the National Academy of Sciences_ 113, 6845–6850 (2016).
  * (43) Cognée, K. G., Doeleman, H. M., Lalanne, P. & Koenderink, A.  Cooperative interactions between nano-antennas in a high-Q cavity for unidirectional light sources.  _Light: Science & Applications_ 8, 115 (2019).
  * (44) Scheucher, M., Hilico, A., Will, E., Volz, J. & Rauschenbeutel, A.  Quantum optical circulator controlled by a single chirally coupled atom.  _Science_ 354, 1577–1580 (2016).
  * (45) Lodahl, P. _et al._ Chiral quantum optics.  _Nature_ 541, 473–480 (2017).
  * (46) Lukin, D. M. _et al._ Spectrally reconfigurable quantum emitters enabled by optimized fast modulation.  _npj Quantum Information_ 6, 80 (2020).
  * (47) Anderson, C. P. _et al._ Five-second coherence of a single spin with single-shot readout in silicon carbide.  _Science Advances_ 8, eabm5912 (2022).
  * (48) Udvarhelyi, P. _et al._ Vibronic states and their effect on the temperature and strain dependence of silicon-vacancy qubits in 4H-SiC.  _Physical Review Applied_ 13, 054017 (2020).
  * (49) Von Bardeleben, H. _et al._ NV centers in 3C, 4H, and 6H silicon carbide: A variable platform for solid-state qubits and nanosensors.  _Physical Review B_ 94, 121202 (2016).
  * (50) Spindlberger, L. _et al._ Optical properties of vanadium in 4H silicon carbide for quantum technology.  _Physical Review Applied_ 12, 014015 (2019).
  * (51) Wolfowicz, G. _et al._ Vanadium spin qubits as telecom quantum emitters in silicon carbide.  _Science Advances_ 6, eaaz1192 (2020).
  * (52) Diler, B. _et al._ Coherent control and high-fidelity readout of chromium ions in commercial silicon carbide.  _npj Quantum Information_ 6, 1–6 (2020).