# GNOME: Generating Negotiations through Open-Domain Mapping of Exchanges

Darshan Deshpande∗,1 Shambhavi Sinha∗,1 Anirudh Ravi Kumar∗,1
Debaditya Pal∗,1 Jonathan May1,2
1Thomas Lord Department of Computer Science, University of Southern California
2 Information Sciences Institute, University of Southern California
{darshang, sinhasha, ar16847<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Language Models have previously shown strong negotiation capabilities in
closed domains where the negotiation strategy prediction scope is constrained
to a specific setup. In this paper, we first show that these models are not
generalizable beyond their original training domain despite their wide-scale
pretraining. Following this, we propose an automated framework called GNOME,
which processes existing human-annotated, closed-domain datasets using Large
Language Models and produces synthetic open-domain dialogues for negotiation.
GNOME improves the generalizability of negotiation systems while reducing the
expensive and subjective task of manual data curation. Through our
experimental setup, we create a benchmark comparing encoder and decoder models
trained on existing datasets against datasets created through GNOME. Our
results show that models trained on our dataset not only perform better than
previous state of the art models on domain specific strategy prediction, but
also generalize better to previously unseen domains.

**footnotetext: These authors contributed equally to this work

##  1 Introduction

Negotiation is a key component of modern dialogue systems and has significant
applications from bargaining Lewicki (1981) to gaming Hausken (1997), and
business transactions Filzmoser (2010); Mumpower (1991). Negotiation agents
powered by language models (LMs) are increasingly being used to conduct
automated negotiations in a variety of contexts, including game theory
Boritchev and Amblard (2021); Peskov and Cheng (2020), multi-issue bargaining
Chawla et al. (2021); Yamaguchi et al. (2021) and pyschotherapy Tanana et al.
(2016).

Figure 1: GNOME generated negotiation dialogue Figure 2: Generalizability test
for existing datasets

Previous works have explored models trained for negotiation strategy
prediction that aim to label each utterance in a dialogue with the appropriate
negotiation strategies to enable the negotiator to understand the opponent’s
motive effectively. These studies include development of strategy prediction
models for tasks such as commodity price bargaining Ahmad et al. (2023a); He
et al. (2018) and item negotiation in a barter setting Lewis et al. (2017);
Chawla et al. (2021) while limiting the scope of the negotiation to a specific
selection of items (closed-domain). However, to facilitate the wider adoption
and domain-agnostic negotiation understanding, the training datasets must be
as varied and open as possible He et al. (2018). Additionally, closed-domain
settings have been shown to affect out-of-domain task performance, which
remains an unsolved challenge for modern negotiation agents Li and Murray
(2023).

Recently, Large Language Models (LLMs) have shown excellent generalization
capabilities in zero and few-shot settings across multiple benchmarks Bubeck
et al. (2023); Chang et al. (2023); Kojima et al. (2022); Hou et al. (2024);
Ahmed and Devanbu (2022); Dai et al. (2022). As a preliminary experiment to
our study, we show that this generalization capability is impacted when LLMs
are fine-tuned on closed-domain negotiation strategy prediction tasks. For our
experiments, we selected four popular datasets, trained models on these
individually, and evaluated their performance on out-of-domain data from other
datasets. These datasets included CaSiNo Chawla et al. (2021), which consists
of negotiations involving campfire resources like firewood, water, and food;
Job Interview Yamaguchi et al. (2021), containing simulated job interview
negotiations for salary and responsibilities; Craigslist Bargain He et al.
(2018), focused on negotiations for items on the Craigslist platform; and
Persuasion For Good Wang et al. (2019), where participants are persuaded to
donate to social causes. These datasets present a varied set of negotiation
strategies that were manually mapped to a more general set of labels to allow
for cross-comparison (more details about this mapping can be found in Appendix
A).

Our results presented in Figure 2 demonstrate that existing encoders and LLMs
trained on individual datasets show poor generalization when tested on
datasets with different negotiation scenarios. Furthermore, we observed that
domain-restricted training, for example, on item exchange-based CaSiNo, poorly
generalizes on monetary negotiations, as found in the Job Interview and
Craigslist Bargain datasets. This highlights the need for diverse, cross-
domain training data.

To address this generalizability problem, we introduce a novel framework for
Generating Negotiations through Open Domain Mapping of Exchanges, or GNOME,
that utilizes existing human-annotated closed-domain datasets to produce
synthetic open-domain datasets for strategy prediction for negotiation. An
example of this is shown in Figure 1 where the original dialogue for a bike
sale is translated to a negotiation for a Victorian armchair while maintaining
the consistency of the original dialogue.

Figure 3: GNOME Framework

In this work, we show that:

  1. 1.

Models trained and fine-tuned on open-domain data exhibit improved performance
in domain-specific strategy prediction tasks.

  2. 2.

Open-domain training and fine-tuning enhances a model’s ability to generalize
to novel, unseen domains.

  3. 3.

High-quality synthetic data, derived from human annotations, can effectively
substitute for costly additional human-annotated data.

##  2 GNOME as a Framework

The GNOME framework has three distinct stages: pre-processing, domain mapping
and post-processing, as illustrated in Figure 3. This section describes the
framework and methodology employed for the curation of the GNOME generated
dataset or the GNOME dataset.

#### Pre-processing:

The pre-processing stage consists of three sub-stages.

First, we filter out incomplete dialogues as we believe they do not contain
enough strategic information for accurate strategy prediction.

The second sub-stage involves creating common label mappings for strategies
across datasets in order to evaluate GNOME’s out-of-domain performance and
generalizability. In order to do so, we group similar labels according to
their definition. The labels for these groups then become the new labels. The
label mapping ensures that our analysis is both inclusive of the specific
nuances within the datasets and broadly applicable to different negotiation
settings. A few instances of the common mappings are provided in Table 1.
Here, we present examples of semantically similar utterances that demonstrate
coordination among negotiators. Despite having different labels in their
respective datasets, these utterances are mapped to a common Coordination
strategy during our label-mapping stage. A detailed breakdown of the mapped
label instances can be found in Appendix A.

Dataset Utterance Original Label Mapped Label Craigslist Bargain The wheels
seem nice on it, but they could be a beter quality. Would you accept 100 for
the board? propose Coordination CaSiNo We need some firewood too, though!
Let’s try to make a deal that benefits us both! Could I have 1 firewood, 3
food, and 3 waters? Coordination Coordination Job Interview you have something
for 5 days per week any job with above average salary ? inquire Coordination
Persuasion for Good Thank you.Can we make it $1.50?These children really need
the assistance. Negotiate-Price-Increase Coordination

Table 1: Example of Label Mapping

The final sub-stage involves skew correction of the dataset where we aim to
counter the imbalance in the distribution that results from the combination of
the datasets. This is necessary to ensure that equal importance is assigned to
all negotiation strategies. Each dialogue in the dataset consists of multiple
turns and has multiple labels associated with each turn. Since we need to
sample entire dialogues, we must consider the label distribution of entire
dialogue as opposed to individual utterances. To achieve this, we employ a
frequency-based sampling approach where each label is assigned a score
inversely proportional to its frequency within the dataset. The score for each
utterance is then computed as the sum of the individual label scores. Finally,
the score for each dialogue instance is derived by summing the scores of its
constituent utterances. After scoring the datasets, we select the top $k$
highest-scoring dialogue instances from each dataset and combine them to form
the seed dataset for our experiments.

#### Domain Mapping:

Domain mapping refers to changing the negotiation setting of dialogues to a
more diverse and unique scenario. This adaptation is achieved by feeding
individual dialogues to a Large Language Model in a zero-shot manner. We map
the entire dialogue with a random seed and a temperature of one at every
generation step to maximize diversity and discourage repetition. For
completeness, we experimented with generating utterances individually by
feeding the dialogue till the current turn. However, this approach resulted in
decreased generation quality and consistency across utterances. We attribute
this inconsistency to the restricted context window accessible to LLM. Hence,
we map the entire dialogue at once.
The prompt used for this task is defined in Appendix B. Our proposed prompt
incorporates several constraints to promote diversity and contextual coherence
in the target domain. Firstly, we ensure that the generated dialogue adheres
to the style established in the original dialogue and maintains fluency. To
preserve the labels between the original and domain-mapped utterance, we
assert that the length of the generated dialogue must equal the length of the
original dialogue. Further, we instruct the model to append an [EOS] token to
each generated utterance, making it convenient for automated parsing and label
transfer to the newly generated dialogue. Finally, as an optional step to ease
the qualitative analysis, we prompt the model to generate the topic of the new
domain. We repeat the above process $n$ times over the seed dataset to produce
approximately the same number of dialogues as all original datasets combined.

#### Post-processing:

To refine the generated data, we remove the dialogues shorter than the
original instances, which indicate the LLM’s failure to generate the
designated [EOS] token. Furthermore, we identify and remove any potential
duplicate dialogues produced during generation. We also ensure that the
dataset does not contain instances from the seed dataset to prevent data
leakage.

##  3 GNOME Dataset

In this section, we describe the curation parameters and characteristics of
the open-domain synthetic dataset we created using GNOME. We select four
manually annotated negotiation datasets: the CaSiNo corpus Chawla et al.
(2021), the Craigslist Bargain Dataset He et al. (2018), the Job Interview
Dataset Yamaguchi et al. (2021) and the Persuasion for Good corpus Wang et al.
(2019). These datasets were chosen as they cover a wide range of negotiation
settings like multi-item bargaining, price negotiation, integrative
negotiation and persuasion. The number of dialogues in each dataset is
presented in table 2.

Dataset # of Dialogues CaSiNo 396 Craigslist Bargain 6555 Job Interview 2577
Persuasion for Good 300

Table 2: Number of dialogues in each dataset before seed dataset creation

After selecting the datasets, the next step is to map them to a common set of
labels so that the same strategy prediction model can be trained and evaluated
on all of them. The process of label mapping is carried out manually in order
to ensure good quality labels that covers all of the different strategies in
these datasets. After manual review, we find that the various labels can be
mapped to a common set of five labels, which are: Rapport, Assessment, Self-
Interest, Coordination and Non-Strategic. These labels were chosen because
they accurately cover the diverse range of strategy labels present in the
datasets used and are comprehensive enough to potentially represent the
strategies used in any negotiation setting. After the label mapping procedure,
we observe a significant skew in the combined dataset prior to forming the
seed dataset (Figure 4(a)). Hence, we use the skew correction method described
in Figure 3 in an effort to balance the label distributions. We then sample
$k=250$ dialogues from each of the four datasets to curate the seed dataset.
The observed skew in the seed dataset is reported in 4(b).

For the domain mapping stage, we choose Llama-3-70B AI@Meta (2024) as it is
the leading open-source LLM in its size category AI@Meta (2024). We then map
the seed dataset $n=10$ times to generate approximately the same number of
dialogues as all original datasets combined (Table 2). The resulting dataset
contains 288 duplicates, which are removed in the post-processing step. We
also observe inconsistencies in instruction following, resulting in misplaced
[EOS] tokens in the generated dialogue. This misplacement causes errors in
dialogue extraction and label assignment during post-processing, and hence, we
remove these instances. We report the total number of misplaced tokens in
Table 3.

Dataset # of misplaced [EOS] tokens CaSiNo 236 Craigslist Bargain 247 Job
Interview 30 Persuasion for Good 227

Table 3: Number of misplaced [EOS] tokens after domain-mapping

In order to discover the overall number of domains we utilized clustering
analysis on the SentenceTransformer embeddings Reimers and Gurevych (2019) of
the generated domain titles. Through the analysis, we observed the presence of
472 distinct domains, which were additionally verified through manual
inspection for overlap.

###  3.1 Human Evaluations

The human evaluation study analyzes the outputs of the domain mapping stage.
We take a random sample (without replacement) of 100 dialogue pairs,
consisting of the original dialogue and the domain-mapped dialogue, with
uniform probability and use it for the study. The dialogue pairs consist of
the original dialogue as well as the domain mapped dialogue. We crowdsourced
four annotators for this study (Appendix C) who were shown the pairs one at a
time. The annotators are asked to rate the dialogue pair in terms of
structural similarity and coherence. Structural similarity refers to how
similar the domain-mapped dialogue is compared to the original dialogue. This
is an important evaluation metric as we plan to utilize the same labels from
the original dialogue for the domain-mapped one. Coherence is defined as the
overall understandability, congruity and consistency of the domain mapped
dialogue. The annotators are asked to rate both of these metrics on a Likert
scale ranging from 1 to 5. After the annotation process, we calculate
Krippendorff’s alpha to measure inter-annotator reliability. We further
present the average metric values and percentage agreement from the
annotations to indicate dataset quality in Table 6.

##  4 Experimental Setup

In this section, we present our experimental setup for evaluating the impact
of GNOME on the generalization capabilities of various models for the strategy
prediction task. We focus on the
DeBERTa-v3111https://huggingface.co/microsoft/deberta-v3-base and
ELECTRA222https://huggingface.co/google/electra-base-discriminator for encoder
models, and Llama-3-8B333https://huggingface.co/meta-llama/Meta-Llama-3-8B and
Mistral444https://huggingface.co/mistralai/Mistral-7B-v0.1Jiang et al. (2023)
for decoder LLM models as they are strong baselines for their respective
categories He et al. (2023); Clark et al. (2020); AI@Meta (2024); Jiang et al.
(2023). We fine-tune our models on a single NVIDIA A100 GPU using a weighted
cross-entropy loss to address data imbalance in the multi-label text
classification task.

For DeBERTa and ELECTRA, the fine-tuning process involves 3 epochs, a batch
size of 16, and a cosine learning rate scheduler with a learning rate of 8e-4
for DeBERTa and a learning rate of 4e-4 for ELECTRA. For Llama-3-8B and
Mistral, we apply 4-bit quantization using bitsandbytes Dettmers et al. (2022)
to reduce the model size. Additionally, we use LoRA (Low-Rank Adaptation)
fine-tuning Hu et al. (2021) with Flash Attention 2 Dao (2023) for faster
training. The LoRA fine-tuning is performed with a rank and alpha of 16 over 3
epochs. We set the batch size to 16, the gradient accumulation steps to 8 and
the learning rate to 5e-4 for Llama and 6e-4 for Mistral using the last token
for classification. The hyperparameters for these models were exhaustively
searched to optimize performance.

We contrast the performance of a model fine-tuned on GNOME-augmented data
(GNOME A) against the original data A when tested on A to demonstrate that
training in a general setting improves task-specific performance. We call
these experiments synthetic-in-domain and in-domain experiments respectively.
We then evaluate if a model trained on GNOME A can generalize well to an
unseen dataset (B), which we refer to as synthetic-out-of-domain test.
Additionally, we evaluate the generalization performance of the models by
training the models on combined datasets (A + B + C) and testing them on an
unseen dataset (D) as a leave-one-out experiment. Here (A, B, C, D) are the
datasets mentioned in section 3. All the datasets have a 60-40 train-
validation split. For evaluation, we calculated weighted F1 scores and class-
wise joint accuracy to measure performance on the imbalanced dataset. Class-
wise joint accuracy measures the overall correctness of predictions per class
in a multi-label classification setting.

##  5 Results

Experiment Fine-tune $\rightarrow$ Test DeBERTa ELECTRA Llama-3-8B Mistral-7B
In-domain A $\rightarrow$ A 0.5918 0.4454 0.6306 0.5435 Synthetic-in-domain
GNOME A $\rightarrow$ A 0.8910 0.8747 0.7213 0.7487 Out-of-domain A
$\rightarrow$ B 0.2539 0.1169 0.2223 0.2244 Synthetic-out-of-domain GNOME A
$\rightarrow$ B 0.3438 0.3483 0.3333 0.3397 Leave-one-out A + B + C
$\rightarrow$ D 0.3405 0.3365 0.2139 0.1705 Synthetic-leave-one-out GNOME (A +
B + C) $\rightarrow$ D 0.3892 0.4000 0.3406 0.3633

Table 4: Average F1 scores reported on corresponding experiments. A,B,C,D
$\in$ {CaSiNo, Craigslist Bargain, Job Interview, Persuasion for Good}. The
individiual F1 scores are taken from the respective experiments and then
averaged. 666All reported results are statistically significant across 3 runs.
For detailed results, refer to Appendix E.

We evaluate the effectiveness of the GNOME framework in addressing our
research questions: Do models fine-tuned on open-domain data show improved
performance in domain-specific strategy prediction? (RQ1), Does open-domain
training and fine-tuning improve a model’s generalizability? (RQ2) and Can
GNOME data substitute human-annotated data? (RQ3)

#### Do models fine-tuned on open-domain data show improved performance in
domain-specific strategy prediction? (RQ1)

The first block in Table 4 represents the results of in-domain ad synthetic-
in-domain experiments. We observe that DeBERTa, ELECTRA, Llama-3-8B, and
Mistral-7B exhibit absolute increase in F1 scores of 29.91%, 42.93% , 9.07%,
and 20.52%, respectively, when trained on GNOME datasets compared to their
performance when trained on their original versions. Due to the wide range of
domains covered by GNOME data, the models are exposed to more nuanced
representations and various linguistic patterns, which make them perform
better on domain-specific test sets. Hence, we conclude that the model trained
on GNOME A significantly enhances task-specific performance compared to fine-
tuning on the corresponding original dataset (A). Additionally, we perform a
Qualitative analysis to confirm that the improvements in F1 score is due to
added diversity in section 6.

#### Does open-domain training and finetuning improve a model’s
generalizability? (RQ2)

The second block in Table 4 shows the results from the out-of-domain and
synthetic-out-of-domain experiments. We observe that DeBERTa, ELECTRA,
Llama-3-8B, and Mistral-7B exhibit absolute increase in F1 scores of 8.9%,
23.14% , 12.67%, and 11.53%, respectively, when trained on GNOME datasets
compared to their performance when trained on original datasets. An
interesting observation is that Mistral-7B displays better generalization than
Llama-3-8B on both the original and GNOME-augmented datasets despite
Llama-3-8B’s larger pre-training. This suggests that the size of the pre-
training corpus is independent of downstream performance on strategy
prediction.

Furthermore, the third block in Table 4 represents the results of the leave-
one-out and synthetic-leave-one-out experiments. We see that DeBERTa, ELECTRA,
Llama-3-8B, and Mistral-7B exhibit absolute increase in F1 scores of 4.87%,
6.35% , 11.11%, and 19.28%, respectively, when trained on GNOME datasets
compared to their performance when trained on a combination of original
datasets. We also observe that encoder models generalize better than the
decoder models when trained on GNOME (A + B + C).

Concluding from the above two experiments, we can see that the models fine-
tuned on GNOME datasets generalize better to an unseen domain than the ones
trained on domain-specific datasets.

Utterance |  True
Label |  GNOME Model
Label |  Original Dataset Model Label
---|---|---|---
HI! Are you excited to launch our new fashion line?
I am
…
_What sort of rare fabrics are you looking for?_ |  Coordination |  Coordination |  Self-Interest
Hello
Do you have a preference for any extra amenities for your flight?
Yes. I need 2 extra legroom seats, 2 lounge passes, and 1 meal upgrade
…
_Thank you for your time_ |  Rapport |  Assessment |  Rapport
Hello
I was wondering if I can rent the luxury sedan and the SUV
…
_I am an avid traveler. i can afford to give you the luxury sedan for 2 days for the SUV for 3 days though_ |  Coordination |  Coordination |  Coordination
Table 5: Qualitative Analysis of model performance on GNOME dataset. The
utterance for which the label is defined is italicized.

#### Can GNOME data substitute human-annotated data for negotiations? (RQ3)

Metric Structural Similarity Coherence Krippendorf’s alpha 0.6819 0.5557
Average Value 4.808 4.615 Percentage Agreement 85% 55%

Table 6: The table shows the annotator reliability metrics for the GNOME
dataset. Average values calculated on a scale of 1-5.

Table 6 describes metrics from the human evaluation studies performed on the
GNOME dataset. We observe that the average coherence and structural similarity
annotation values are greater than 4.5 out of 5, indicating that the generated
responses are logical, congruent, and grounded in real-life negotiation
dialogues in structure. We noticed some instances with high structural
similarity but low coherence scores, which indicates that the domain mapping
step was able to follow the original dialogue structurally, but the original
dialogue was of poor quality. We found the Job Interview dataset to contain
the majority of such incoherent dialogues while randomly sampling for human
evaluations.

van der Lee et al. (2021) present a survey of observed annotator reliability
metrics for automatically generated texts where the authors find that most of
the reported alpha values fall in the range of 0.3 - 0.5 for such approaches.
Li et al. (2023) also report similar trends and show that the alpha values
decrease with an increase in the subjectivity of the datasets. Our calculated
alpha values are higher than this range, which indicates a better agreement
compared to other synthetic datasets. To further assess the level of
agreement, we calculate the percentage agreement of the Likert scale
annotations. The coherence and structural similarity metrics have a percentage
agreement of 55% and 85%, respectively, which indicates that the annotators
have high agreement considering the incoherence introduced by the Job
Interview dataset. Considering the three reported values in Table 6, we
believe that we have a strong inter-annotator agreement. Furthermore, based on
the high average annotation values, we can claim that GNOME data can
effectively substitute human-annotated data.

Referring to our research questions, the results discussed above, confirm that
GNOME datasets help improve performance on domain-specific negotiations while
promoting generalizability across domains. Finally, we show that GNOME data is
an effective substitute for human-annotated data.

##  6 Qualitative Analysis

Table 5 displays example utterances from the GNOME dataset, the true labels,
and the predicted labels from a model fine-tuned on the GNOME dataset and a
model trained on the original dataset. The first row contains a dialogue that
was mapped from the CaSiNo dataset. During domain mapping, the items being
negotiated were changed from the scope of the CaSiNo dataset to rare fabrics
and other fashion accessories. The model trained on the original CaSiNo
dataset was not exposed to any examples involving such items and, therefore,
makes a mistake in classifying the utterance. The model trained on the GNOME
dataset was introduced to a variety of negotiation scenarios, and it can
generalize better to previously unseen items. It can, thus, correctly classify
this utterance.

The second example highlights a unique condition where the label of the
utterance is not dependent on the context of the negotiation. Utterances like
"Hello" and "Thank you" are examples of rapport building, irrespective of how
the rest of the dialogue continues. The model trained on the original dataset
accurately identifies this condition and correctly classifies this utterance.
The model trained on the GNOME dataset is exposed to a greater variety of
negotiation scenarios, and a significant portion of them contain assessment
utterances that start with a polite refusal of a previously made offer. For
example, "Thank you, but I cannot accept this deal" leads to confusion and
incorrect classification.

The final example shows how the structure of the utterance can help both
models provide accurate results. Usually, during negotiations, numbers only
come up while the participants are trying to coordinate a bargain. For
example: "I can pay $20 for this tshirt". In such examples, the model can
simply recognize multiple numbers as a pattern to accurately classify them as
"Coordination" utterances.

##  7 Relevant Work

#### Negotiation Datasets

The ability to engage in effective negotiations is an important skill for
intelligent agents, enabling them to reach agreeable outcomes through
persuasive dialogue across various contexts Zhan et al. (2024). Through the
domain of in-game negotiation settings, Lewis et al. (2017) were among the
first to explore end-to-end learning of negotiation dialogues. They trained
models directly from human-human negotiations without annotated dialogue
states, creating the Deal Or No Deal dataset with 5,808 dialogues. Following
this, in an effort to decouple strategy prediction and negotiation generation
He et al. (2018) released the Craigslist Bargain dataset, which includes
multiple buyer-seller negotiation scenarios from Craigslist Bargain and human-
annotated negotiation strategy labels, expanding the scope of negotiation
research to include strategic elements and grounding it in real-world
concepts. Extending the work on datasets grounded in real-world concepts, Wang
et al. (2019) introduced Persuasion for Good, a dataset aimed at developing
personalized persuasive dialogue systems for social good, such as charitable
donations. This dataset highlights the potential of negotiation dialogue
systems to contribute to socially beneficial outcomes.

In an effort to shift the focus of negotiation datasets from single-issue to
multi-issue bargaining Chawla et al. (2021) introduced CaSiNo, a corpus of
1,030 negotiation dialogues set in a camping scenario and Yamaguchi et al.
(2021) released a corpus of job interviews dealing with negotiations regarding
salary and responsibilities. More recently, Ahmad et al. (2023b) developed an
Integrative Negotiation Agent (INA) by prompting GPT-J. This agent is designed
for integrative negotiations, dynamically adjusting prices and negotiating the
inclusion or exclusion of items in a bundle deal, showcasing advanced
negotiation capabilities.

The datasets discussed above focused solely on bilateral dialogue. To
introduce a different negotiation setting, Boritchev and Amblard (2021)
introduced DinG, a French corpus capturing multi-party negotiations during
Settlers of Catan gameplay.

#### Synthetic Datasets

Previous work involving the use of LLM-generated synthetic data includes Li et
al. (2023), where the authors attempted to benchmark text classification
models trained on synthetic data. However, they found that using synthetic
data lead to instability in model performance depending on the subjectivity of
the classification problem. Higher subjectivity at both the task and instance
level was negatively correlated with model performance. Liu et al. (2024) and
Bao et al. (2023) describe synthetic data generation pipelines to generate
high-quality domain-specific data. The authors further show that high-quality
synthetic data grounded in human-annotated datasets can significantly improve
model performance.

With GNOME, we combine different types of negotiation (e.g., multi-issue
bargaining, persuasion, price negotiation) from multiple datasets while
creating diverse negotiation scenarios through domain mapping. As observed by
Shu et al. (2021), open-domain training can improve model generalizability on
previously unseen datasets. Furthermore, by grounding the synthetic data in
human-annotated datasets, we ensure high-quality generations.

#### Large Language Models (LLMs) for Negotiation

With the recent emergence of Large Language Models (LLMs) like Meta’s Llama
AI@Meta (2024) and OpenAI’s ChatGPT OpenAI (2024), there have been several
studies that experiment with the negotiation capabilities of such models Zhan
et al. (2022). Fu et al. (2023) uses LLMs in a self-play setting where the
models negotiate with and improve each other in a game setting. The authors
find that only a subset of LLMs can improve in a self-play setting with
minimal human intervention. Xu et al. (2024) analyze the performance of LLMs
in the context of the negotiation based communication game "Werewolf" and show
that the models are effectively able to play the game without the need for
fine-tuning. Chen et al. (2024) created an evaluation suite to test the
negotiation capabilities of LLMs in an auction setting and reported that the
models possess key skills for auction negotiation which can further be
improved using adaptive strategies. However, the authors find that
occasionally the LLMs would be outperformed by simpler methods indicating
opportunities for further advancement.

##  8 Conclusion

In this work, we introduce GNOME, a framework designed to generate synthetic
open-domain negotiation dialogues from existing human-annotated closed-domain
datasets. GNOME demonstrates that it is possible to generate diverse and
domain-independent datasets, which in turn enhances the performance and
generalization abilities of negotiation models. This approach addresses the
limitations of current negotiation models, which often fail to generalize
beyond the specific contexts of their training data. Our benchmarking compares
encoder and decoder models trained on traditional datasets versus those
generated by GNOME, revealing significant improvements in the ability of
models to generalize to new negotiation scenarios. This demonstrates the
efficacy of synthetic data in reducing reliance on extensive human annotation,
which is often subjective and labor-intensive. In the future, we aim to focus
on expanding the variety of negotiation scenarios and further refining the
synthetic data generation process to enhance the realism and applicability of
the dialogues produced. Additionally, we encourage research on replacing
GNOME’s dependency on manual mapping of labels with an automated labeling
procedure. This extension will further validate the flexibility and utility of
GNOME in creating high-quality synthetic data across a wide range of
applications. We also hope to extend GNOME beyond negotiations, exploring its
potential applications in other dialogue-driven domains and tasks.

## Limitations

Although GNOME aims to produce diverse and high-quality synthetic dialogues,
the quality of generated data is inherently dependent on the original closed-
domain datasets and the large language models (LLMs) used. Any biases or
limitations present in the source datasets can propagate into the synthetic
data, potentially affecting the performance and generalizability of the
trained models. Even though GNOME automates the generation of negotiation
dialogues, the quality of synthetic data can vary. The generated dialogues
might not always capture the nuances and subtleties of human negotiations,
potentially affecting the performance of models trained on this data.

## Ethics Statement

We only use openly available datasets (CaSiNo: CC-BY-4.0, Job Interview,
Craigslist Bargain: MIT License, Persuasion For Good: Apache 2.0) and
encourage users of GNOME to strictly adhere to the licensing of the datasets
used. We do not collect any personally identifiable data during the creation
of the GNOME dataset. Instead, we relied on publicly accessible datasets that
were previously annotated for negotiation scenarios. In the qualitative
evaluation of the data, all human annotations were obtained with appropriate
consent and we ensured that the use of these annotations complied with ethical
standards and data protection regulations. The above study was exempted from
the IRB review (UP-24-00493). Further, due to the automated nature of the
generation process, there remains a possibility that offensive content could
be inadvertently generated. We encourage users to utilize safety tools like
Llama Guard (Inan et al., 2023) to ensure safer generations. By addressing
these considerations, we aim to promote the ethical use of GNOME and
contribute to the development of fair and responsible negotiation models.

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##  Appendix A Dataset Label Mappings

###  A.1 Casino Dataset

⬇

"Small-Talk":"Rapport",

"Empathy":"Rapport",

"Coordination":"Coordination",

"No-Need":"Self-Interest",

"Elicit-Pref":"Coordination",

"Undervalue- Partner": "Assessment",

"Vouch-Fairness": "Assessment",

"Other-Need":"Self-Interest",

"Non-strategic": "Non-strategic"

###  A.2 Craigslist Bargain Dataset

⬇

"intro":"Rapport",

propose": "Coordination",

"vague-price":"Coordination",

"counter":: "Coordination",

"inform": "Assessment"

###  A.3 Persuasion for Good Dataset

⬇

"Negotiate-Price-NoChange":"Coordination",

"Ask_Clarification-Y":"Self-Interest",

"Provide_Clarification-Y":"Self-Interest",

"tell_price":"Coordination",

"Negotiate-Remove-delivery":"Coordination",

"Ask_Price":"Coordination",

"Negotiate-Price-Decrease":"Coordination",

"Negotiate-Price-Increase":"Coordination",

"Acknowledge acceptance":"Assessment",

"Accept":"Assessment",

"Negotiate-Remove-X":"Coordination",

"Negotiate-Remove-X_Negotiate-Price-Decrease":"Coordination",

"Negotiate-Price-Remove-X":"Coordination",

"Negotiate-Add-X":"Coordination",

"Reject":"Assessment",

"Greet-Inform":"Rapport",

"Greet-Ask":"Rapport",

"Greet-Ask_Negotiate-Price-Decrease":"Rapport,Self-Interest",

"Greet-Inform_Negotiate-Price-Increase":"Rapport,Self-Interest",

"Greet-Inform_Negotiate-Price-NoChange":"Rapport,Self-Interest",

"Greet-Inform_Negotiate-Price-NoChange":"Rapport,Self-Interest",

"avoid_rejection":"Coordination"

###  A.4 Job Interview Dataset

⬇

"greet":"Rapport",

"disagree":"Asessment",

"agree":"Asessment",

"inquire":"Coordination",

"propose":"Coordination",

"inform":"Asessment",

##  Appendix B Domain Adaptation Prompt

The following prompt was used to change the domain of the negotiation dialogs:

System: You are an assistant that can produce accurate and contextually
grounded dialogues. You are tasked with changing the domain of the input
dialogue. In doing so, ONLY output the new domain in the format of
NEW_DOMAIN{{name_of_new_domain}} followed by the domain-changed dialogue.

Prompt: Change the domain for this negotiation setting. Make sure to be as
diverse but contextually grounded as possible when picking the new domain and
add a [EOS] token at the end of every utterance. Make sure to have same number
of utterances in the output as there were in the given dialogue and DO NOT
output any text other than the mapped dialogue: {dialogue}

##  Appendix C Annotator Recruitment

We recruited four annotators for our human evaluation studies from Amazon
MTurk, a popular crowd-sourcing platform. The eligibility criteria were:

  * •

The individual must be over 18 years of age.

  * •

The individual must be fluent in English.

For each survey completion, the participant was paid $0.02. The requisite
conditions are that they complete the survey. The payment and disbursement are
handled internally by Amazon Mechanical Turk. The maximum allowed amount spent
from discretionary on the annotation of all data points is $10.

##  Appendix D Skew Correction

(a) Observed skew before seed dataset creation

(b) Observed skew after seed dataset creation

##  Appendix E Results

Figure 5: DeBERTa Results Figure 6: ELECTRA Results Figure 7: Llama-3-8B
Results Figure 8: Mistral-7B Results


# Higher-order, quantum magnetic inductions in chiral topological materials

Yizhou Liu<EMAIL_ADDRESS>Hengxin Tan  Binghai Yan  Department of
Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001,
Israel

###### Abstract

The classic magnetic induction effect is usually considered in electric
circuits or conductor coils. In this work, we propose quantum induction
effects induced by the Berry curvature in homogenous solids. Two different
types of quantum inductions are identified in the higher order of a magnetic
field. They are closely related to the magnetic-field-induced anomalous
velocity proportional to the Berry curvature so that both quantum inductions
become significantly enhanced near Weyl points. Further, we propose an ac-
magnetic-field measurement to detect quantum induction effects and distinguish
them from classical induction.

Introduction.—Faraday’s law of induction, which describes the current
generated by a varying magnetic field, is usually considered in the coil
geometry. But it also exists in uniform gyrotropic materials as the low
frequency limit of optical gyrotropyLandau  _et al._ (2013) and gains renewed
interest in recent studies of topological materials.

In Weyl semimetalsArmitage  _et al._ (2018); Yan and Felser (2017), the chiral
magnetic effect (CME) known previously in particle physicsFukushima  _et al._
(2008) can lead to a nonequilibrium current in the presence of a nonorthogonal
electric field and magnetic field ($\boldsymbol{B}$)Son and Yamamoto (2012).
The CME roots in the chiral anomaly and the Berry curvature of Weyl
fermionsNielsen and Ninomiya (1983); Son and Spivak (2013). A similar effect
was also proposed to generate current by a varying magnetic field
($\boldsymbol{\dot{B}}$) rather than the static $\boldsymbol{B}$ Zyuzin  _et
al._ (2012); Vazifeh and Franz (2013); Jian-Hui  _et al._ (2013); Başar  _et
al._ (2014); Goswami  _et al._ (2015). This dynamical effect was later
recognized as a gyrotropic magnetic effect (GME)Zhong  _et al._ (2016). It is
equivalently a Faraday induction effect and not governed by the chiral anomaly
or Berry curvature.

In this work, we find that the Faraday induction includes quantum
contributions in the higher order in addition to GME. The quantum induction
(QI) effects are intimately induced by the Berry curvature in general and
related to the chiral anomaly for a Weyl semimetal. They can be significantly
enhanced near Berry curvature monopoles such as Weyl points or multiply-
degenerate points. We have calculated QIs in chiral topological semimetals
CoSi and MnSi and proposed experiments to distinguish QIs from the coexisting
classical induction (CI).

Semiclassical theory of induction.—According to the semiclassical equation of
motion of electrons Chang and Niu (1996); Sundaram and Niu (1999); Xiao  _et
al._ (2010) the electronic velocity $\dot{\boldsymbol{r}}$ under external
magnetic field $\boldsymbol{B}(t)$ can be derived as,

$\displaystyle
D_{\boldsymbol{k}}\dot{\boldsymbol{r}}=\tilde{\boldsymbol{v}}_{\boldsymbol{k}}+\frac{e}{\hbar}(\tilde{\boldsymbol{v}}_{\boldsymbol{k}}\cdot\boldsymbol{\Omega_{k}})\boldsymbol{B},$
(1)
$\displaystyle\tilde{\boldsymbol{v}}_{\boldsymbol{k}}=\boldsymbol{v_{k}}-\frac{1}{\hbar}\nabla_{\boldsymbol{k}}(\boldsymbol{m_{k}}\cdot\boldsymbol{B}),$
(2)

with
$D_{\boldsymbol{k}}=1+\frac{e}{\hbar}\boldsymbol{\Omega_{k}}\cdot\boldsymbol{B}$
being the modified density of states Xiao  _et al._ (2005),
$\boldsymbol{v}_{\boldsymbol{k}}$ refers to the ordinary band velocity
$\boldsymbol{v_{k}}=\frac{1}{\hbar}\nabla_{\boldsymbol{k}}\varepsilon_{\boldsymbol{k}}$,
and $\boldsymbol{\Omega_{k}}$ and $\boldsymbol{m_{k}}$ are the Berry curvature
and orbital magnetic moment, respectively. The second term on the right-hand
side of Eq. (1) is the magnetic-field-induced anomalous velocity which gives
rise to the chiral anomaly in the presence of an extra electric field Son and
Spivak (2013).

In this work, we focus on the effect of magnetic-field-induced current. The
electric current is expressed as

$\boldsymbol{j}=-e\int\frac{\text{d}\boldsymbol{k}}{(2\pi)^{3}}D_{\boldsymbol{k}}\dot{\boldsymbol{r}}f,$
(3)

with $f$ being the nonequilibrium distribution function of electrons which the
Boltzmann transport equation can determine in the relaxation time
approximation:

$-\frac{f-f_{0}}{\tau}=\dot{\boldsymbol{k}}\cdot\nabla_{\boldsymbol{k}}f+\dot{\boldsymbol{r}}\cdot\nabla_{\boldsymbol{r}}f+\partial_{t}f,$
(4)

where $f_{0}=\frac{1}{e^{(\varepsilon-\varepsilon_{F})/k_{B}T}+1}$ is the
equilibrium Fermi-Dirac distribution function with $\varepsilon_{F}$ being the
Fermi energy. For uniform but time-dependent magnetic field
$\boldsymbol{B}(t)$, the nonequilibrium distribution function $f$ up to the
first order of relaxation time $\tau$ can be derived as

$f=f_{0}+\tau(\boldsymbol{m_{k}}\cdot\dot{\boldsymbol{B}})\left.\frac{\partial
f_{0}}{\partial\varepsilon}\right|_{\varepsilon=\varepsilon_{\boldsymbol{k}}}+O(\tau^{2}),$
(5)

where
$\boldsymbol{m_{k}}\equiv-\frac{\partial\varepsilon}{\partial\boldsymbol{B}}$.
By substituting Eqs. (1), (2), and (5) into (3), we get the final expression
of the induction current as

$\displaystyle\boldsymbol{j}=$
$\displaystyle\boldsymbol{j}^{c}+\boldsymbol{j}^{q},$ (6)
$\displaystyle\boldsymbol{j}^{c}=$
$\displaystyle-e\tau\int\frac{\text{d}\boldsymbol{k}}{(2\pi)^{3}}(\boldsymbol{m_{k}}\cdot\dot{\boldsymbol{B}})\boldsymbol{v_{k}}\left.\frac{\partial
f_{0}}{\partial\varepsilon}\right|_{\varepsilon=\varepsilon_{\boldsymbol{k}}}=\sum_{\alpha,\beta=x,y,z}C_{\alpha\beta}\dot{B}_{\beta}\boldsymbol{e}_{\alpha},$
(7) $\displaystyle\boldsymbol{j}^{q}=$
$\displaystyle-\frac{e^{2}\tau}{\hbar}\boldsymbol{B}\int\frac{\text{d}\boldsymbol{k}}{(2\pi)^{3}}(\tilde{\boldsymbol{v}}_{\boldsymbol{k}}\cdot\boldsymbol{\Omega_{k}})(\boldsymbol{m_{k}}\cdot\dot{\boldsymbol{B}})\left.\frac{\partial
f_{0}}{\partial\varepsilon}\right|_{\varepsilon=\varepsilon_{\boldsymbol{k}}}$
(8) $\displaystyle=$
$\displaystyle\left(\boldsymbol{Q}^{(1)}\cdot\boldsymbol{\dot{B}}\right)\boldsymbol{B}+\left(\sum_{\alpha,\beta=x,y,z}Q^{(2)}_{\alpha\beta}\dot{B}_{\alpha}B_{\beta}\right)\boldsymbol{B}.$
(9)

Equations (6)–(9) are the central results of this work. The total induction
current $\boldsymbol{j}$ can be divided into two parts, $\boldsymbol{j}^{c}$
and $\boldsymbol{j}^{q}$, to represent the classical induction and quantum
induction, respectively. Here, $\boldsymbol{j}^{q}$ explicitly contains the
Planck constant $\hbar$ and also the Berry curvature
$\boldsymbol{\Omega}_{\boldsymbol{k}}$. The classical term can be rewritten
into a compact form of
$j^{c}_{\alpha}=\sum_{\beta}C_{\alpha\beta}\dot{B}_{\beta}$
($\alpha,\beta=x,y,z$) describing conventional Faraday electromagnetic
induction in materials. The coefficients are

$C_{\alpha\beta}=-e\tau\int\frac{\text{d}\boldsymbol{k}}{(2\pi)^{3}}v_{\alpha}m_{\beta}\left.\frac{\partial
f_{0}}{\partial\varepsilon}\right|_{\varepsilon=\varepsilon_{\boldsymbol{k}}},$
(10)

which was consistent with previous formulations as the low-frequency limit of
natural optical activity, or natural gyrotropyGoswami  _et al._ (2015); Zhong
_et al._ (2016). Corresponding inverse effect is the current-induced
magnetization is described by $\boldsymbol{M}=C^{T}\boldsymbol{E}$ ($T$ stands
for matrix transpose) Zhong  _et al._ (2016); Yoda  _et al._ (2018) with
$\boldsymbol{E}$ and $\boldsymbol{M}$ being the electric field and induced
magnetization, respectively. According to Eq. (10), the diagonal coefficients
($C_{\alpha\alpha}$) vanish in the presence of inversion symmetry or mirror
symmetry. Therefore, the ordinary induction can only occur in chiral systems
Yoda  _et al._ (2015) or solenoids Yoda  _et al._ (2018).

The quantum induction current $\boldsymbol{j}^{q}$ is higher order in
$\boldsymbol{B}$ and $\boldsymbol{\dot{B}}$. Up to our knowledge, it is not
discussed in literature so far. It can be further divided into two parts as:
$\boldsymbol{j}^{q}=\left(\boldsymbol{Q}^{(1)}\cdot\dot{\boldsymbol{B}}\right)\boldsymbol{B}+\left(\sum_{\alpha\beta}Q^{(2)}_{\alpha\beta}\dot{B}_{\alpha}B_{\beta}\right)\boldsymbol{B}$
with $\boldsymbol{Q}^{(1)}=(Q^{(1)}_{x},Q^{(1)}_{y},Q^{(1)}_{z})$ and
$Q^{(2)}_{\alpha\beta}$ being the response coefficients of QIs whose
expressions are given by:

$\begin{split}Q^{(1)}_{\alpha}=&-\frac{e^{2}\tau}{\hbar}\int\frac{\text{d}\boldsymbol{k}}{(2\pi)^{3}}(\boldsymbol{v_{k}}\cdot\boldsymbol{\Omega_{k}})m_{\alpha}\left.\frac{\partial
f_{0}}{\partial\varepsilon}\right|_{\varepsilon=\varepsilon_{\boldsymbol{k}}}\\\
Q^{(2)}_{\alpha\beta}=&-\frac{e^{2}\tau}{\hbar^{2}}\int\frac{\text{d}\boldsymbol{k}}{(2\pi)^{3}}m_{\alpha}\left(\boldsymbol{\Omega_{k}}\cdot\nabla_{\boldsymbol{k}}\right)m_{\beta}\left.\frac{\partial
f_{0}}{\partial\varepsilon}\right|_{\varepsilon=\varepsilon_{\boldsymbol{k}}}.\end{split}$
(11)

Recall $\boldsymbol{v_{k}}$ and $\nabla_{\boldsymbol{k}}$ are odd under
inversion symmetry ($\mathcal{P}$) or time-reversal symmetry ($\mathcal{T}$)
while $\boldsymbol{\Omega_{k}}$ and $\boldsymbol{m_{k}}$ are even under
$\mathcal{P}$ but odd under $\mathcal{T}$. $Q^{(1)}_{\alpha}$ exists when both
$\mathcal{P}$ and $\mathcal{T}$ are broken. $Q^{(2)}_{\alpha\beta}$ only
requires $\mathcal{P}$-breaking, similar to $C_{\alpha\beta}$. Because
$\boldsymbol{j}^{q}$ is proportional to the Berry curvature
$\boldsymbol{\Omega_{k}}$, it is naturally expected that the quantum induction
is enhanced in $\mathcal{P}$-breaking topological semimetals such as the Weyl
semimetal or triple-point semimetal. The Berry curvature contribution in
Eq.(10) has the same origin as the chiral anomaly effect.

Weyl semimetal.—Take the Weyl semimetal as an example. We can estimate the
magnitudes of the coefficients $C$, $Q^{(1)}$, and $Q^{(2)}$. Near the Weyl
point, the group velocity $v$ is a constant while the Berry curvature and the
orbital magnetic moment scale as $\Omega\propto\frac{1}{k^{2}_{F}}$ and
$m\propto\frac{1}{k_{F}}$, respectively, where
$k_{F}=\frac{\varepsilon_{F}-\varepsilon_{W}}{\hbar v_{F}}$ is the Fermi wave
vector with $\varepsilon_{W}$ and $v_{F}$ being the energy of Weyl point and
Fermi velocity, respectively. Therefore, we obtain $C\propto k_{F}$ for a
single Weyl point and
$C\propto(\varepsilon_{F}-\varepsilon_{W1})-(\varepsilon_{F}-\varepsilon_{W2})=\varepsilon_{W2}-\varepsilon_{W1}$
for a pair of Weyl points. Here $C$ depends on the energy separation of Weyl
points but less sensitive to $\varepsilon_{F}$. In contrast,
$Q^{(1)}\propto\frac{1}{k_{F}}$ and $Q^{(2)}\propto\frac{1}{k^{3}_{F}}$ become
divergent when the Fermi energy approaches Weyl points.

Figure 1:  CI and QI in CoSi. (a) Chiral crystal structure of CoSi with cubic
point group symmetry $T$. (b) Brillouin zone (BZ) and high-symmetry lines. (c)
Bulk band structure and CI of CoSi. (d) $C_{\alpha\alpha}$ as function of
Fermi energy $\varepsilon_{F}$. (e) Bulk band structure and second QI of CoSi.
(f) $Q^{(2)}_{\alpha\alpha}$ as function of $\varepsilon_{F}$. The first QI
$Q^{(1)}_{\alpha}=0$ due to TRS.

We consider a minimal model of a Weyl semimetal without $\mathcal{P}$ or
$\mathcal{T}$. A minimal model of Weyl Hamiltonian without $\mathcal{T}$ has
one pair of Weyl points. The inversion (and any mirror) symmetry is naturally
broken if the energies of two Weyl points are different, which motivates us to
consider the following two-band model:

$\begin{split}&H_{\boldsymbol{k}}=\varepsilon_{0}+d_{x}\sigma_{x}+d_{y}\sigma_{y}+d_{z}\sigma_{z},\\\
&\varepsilon_{0}=A_{0}\sin k_{z},~{}~{}~{}d_{x}=A\sin
k_{x},~{}~{}~{}d_{y}=A\sin k_{y},\\\ &d_{z}=M-B_{1}(\cos k_{x}+\cos
k_{y})-B_{2}\cos k_{z},\end{split}$ (12)

with $A_{0}$, $A$, $B_{1}$, $B_{2}$, and $M$ being constants. $\sigma_{x,y,z}$
refer to Pauli matrix. The band structure of such model is given by
$\varepsilon_{s\boldsymbol{k}}=\varepsilon_{0}+s\sqrt{d^{2}_{x}+d^{2}_{y}+d^{2}_{z}}$
($s=\pm 1$ refers to the upper or lower band) with the band crossing happens
when $d_{x}=d_{y}=d_{z}=0$. Within the parameters range
$|M-2B_{1}|<|B_{2}|<|M|$, $|B_{2}|<|M+2B_{1}|$, the band structure has a pair
of Weyl points with opposite chiralities on the $k_{z}$-axis which are
determined by $M-B_{2}\cos k_{z}=0$. The energies of the two Weyl points
become different when $A_{0}\neq 0$, and the low energy effective Hamiltonian
near the Weyl points become:

$H_{\chi}=\hbar(v_{1}k_{x}\sigma_{x}+v_{1}k_{y}\sigma_{y}+\chi
v_{2}k_{z}\sigma_{z})+\varepsilon_{\chi}+\chi\hbar v^{\prime}k_{z}.$ (13)

with $v_{1}$ being the group velocity along $k_{x}$ and $k_{y}$ axis and
$v_{2}$ the group velocity along $k_{z}$; $v^{\prime}$ represents a tilting
parameter of the Weyl cone along $k_{z}$ axis; $\chi=\pm$ refers the Weyl cone
with positive (negative) chirality; $\varepsilon_{+}$ and $\varepsilon_{-}$
are the energies of Weyl points. Based on the approximation
$\left.\frac{\partial
f_{0}}{\partial\varepsilon}\right|_{\varepsilon=\varepsilon_{\boldsymbol{k}}}\approx-\delta(\varepsilon_{\boldsymbol{k}}-\varepsilon_{F})$,
the classical coefficients are calculated (for small tilted parameter
$v^{\prime}$) as SM :

$C_{\alpha\alpha}\approx\frac{e^{2}\tau\Delta\varepsilon}{12\pi^{2}\hbar^{2}},~{}~{}~{}\alpha=x,y,z$
(14)

which depends only on the relaxation time $\tau$ and the energy difference
between two Weyl points $\Delta\varepsilon=\varepsilon_{+}-\varepsilon_{-}$.
Since $\Delta\varepsilon$ changes sign under inversion or mirror operations,
the CI can only exist in chiral systems, consistent with our previous
discussion.

Unlike CI $C_{\alpha\beta}$ which depends only on the energy difference
between two Weyl points but independent on the Fermi energy $\varepsilon_{F}$,
the QIs $Q^{(1)}_{\alpha}$ and $Q^{(2)}_{\alpha\beta}$ significantly depends
on $\varepsilon_{F}$ according to our previous discussion. The QIs of the
effective model is calculated as SM :

$\displaystyle Q^{(1)}_{z}=-\frac{e^{3}\tau
v^{2}_{1}v^{\prime}}{24\pi^{2}\hbar
v_{2}}\left(\frac{1}{\varepsilon_{F}-\varepsilon_{+}}-\frac{1}{\varepsilon_{F}-\varepsilon_{-}}\right),~{}~{}~{}Q^{(1)}_{x,y}=0,$
(15) $\displaystyle
Q^{(2)}_{xx}=Q^{(2)}_{yy}\approx\frac{e^{4}v^{2}_{1}v^{2}_{2}\tau}{48\pi^{2}}\left[\frac{1}{(\varepsilon_{F}-\varepsilon_{+})^{3}}-\frac{1}{(\varepsilon_{F}-\varepsilon_{-})^{3}}\right],$
(16) $\displaystyle
Q^{(2)}_{zz}\approx\frac{e^{4}v^{4}_{1}\tau}{48\pi^{2}}\left[\frac{1}{(\varepsilon_{F}-\varepsilon_{+})^{3}}-\frac{1}{(\varepsilon_{F}-\varepsilon_{-})^{3}}\right].$
(17)

The quantum coefficients $Q^{(1)}$ and $Q^{(2)}$ become zero when
$\varepsilon_{+}=\varepsilon_{-}$, i.e. when the inversion symmetry
$\mathcal{P}$ is restored. Remarkably, according to Eqs. (15)–(17), the
quantum coefficients get maximized when $\varepsilon_{F}$ approaches one of
the Weyl points. Numerical results of the full lattice model in Eqs.
(LABEL:Toy_model) is shown in Ref.SM,  which is consistent with the analytical
results.

Figure 2:  CI and QIs in MnSi. (a) Crystal and ferromagnetic structure of MnSi
under external magnetic field $\boldsymbol{B}$. (b) Bulk band structure and CI
of ferromagnetic MnSi. (c) $C_{\alpha\alpha}$ as function of
$\varepsilon_{F}$. (d), (f) Bulk band structure and the first (d) and second
(f) QI of MnSi. (e), (g) $Q^{(1)}_{\alpha}$ and $Q^{(2)}_{\alpha\alpha}$ as
functions of $\varepsilon_{F}$. $Q^{(1)}_{x,y}=0$ due to the two-fold (skew)
rotation symmetry along $z$-axis.

Material candidates.—In the following, we demonstrate the quantum induction
effect in inversion-breaking topological materials, among which the chiral
topological materials has attracted much research of interest because of the
multifold fermion Chang  _et al._ (2017, 2018); Rao  _et al._ (2019); Sanchez
_et al._ (2019); Takane  _et al._ (2019) and the quantized photogalvanic
responses de Juan  _et al._ (2017). The transition-metal monosilicides family
$X$Si ($X=\text{Rh},\text{Co}$, etc.) with a chiral cubic crystal structure
(Figs. 1(a)-(b)) exhibit a pair of chiral Weyl fermions with large Chern
numbers. They have been mostly investigated because the Weyl points’ energy is
very close to the Fermi level and has long Fermi arcs observed by the angle-
resolved photoemission spectroscopy (ARPES). The band structure of CoSi is
shown in Fig. 1(c) (see calculation details in Ref. SM, ) with multiple Weyl
cones located at $\Gamma$ and R near the Fermi level Chang  _et al._ (2017).

Because of the cubic symmetry all the off-diagonal components of
$C_{\alpha\beta}$ and $Q^{(2)}_{\alpha\beta}$ vanish, and the diagonal
coefficients are equal, i.e. $C_{xx}=C_{yy}=C_{zz}$,
$Q^{(2)}_{xx}=Q^{(2)}_{yy}=Q^{(2)}_{zz}$ and
$C_{\alpha\beta}=Q^{(2)}_{\alpha\beta}=0$ ($\alpha\neq\beta$). Figures
1(c)-(d) and 1(e)-(f) show the numerically calculated $C_{\alpha\alpha}$ and
$Q^{(2)}_{\alpha\alpha}$, respectively, for a relaxation time $\tau\approx
6.6\times 10^{-15}$s (see details of the calculation methods in Ref. SM, ). As
is shown $Q^{(2)}_{\alpha\alpha}$ get significantly enhanced at the multiple
Weyl points, which is different from $C_{\alpha\alpha}$ of the two-band Weyl
Hamiltonian.

In the presence of TRS or cubic symmetry, quantum response $Q^{(1)}$ vanishes.
However, both TRS and cubic symmetry can be broken by the magnetization
induced by the external magnetic field (Fig. 2(a)). Previous experimental
studies have reported ferromagnetic order in the ground state of MnSi at
extremely low temperatures Williams  _et al._ (1966); Shinoda and Asanabe
(1966); Wernick  _et al._ (1972); Ishikawa  _et al._ (1977). In the
ferromagnetic state, both the TRS and cubic symmetries are naturally broken so
that the $Q^{(1)}_{\alpha}$ can be nonzero. Figures 2(b)-(g) show the band
structure and coefficients $C_{\alpha\beta}$, $Q^{(1)}_{\alpha}$, and
$Q^{(2)}_{\alpha\beta}$ of ferromagnetic MnSi (see calculation details in SM
SM ). It should be noted that the $x$\- and $y$-components of
$Q^{(1)}_{\alpha}$ vanish because of the two-fold (skew) rotation symmetry
along the $z$-axis.

Figure 3:  Different signatures of CI and QIs in an external ac magnetic
field. (a)-(b) Schematic setup of a sample (red) under an external ac magnetic
field $B(\omega_{1}t)=B_{0}+B_{1}\sin(\omega_{1}t)$ having a frequency
dependent output electrical current $I(\omega)$. (c)-(e) Schematic of the
output signals of classical and quantum induction current $I^{c}(\omega)$,
$I^{q}_{1}(\omega)$, and $I^{q}_{2}(\omega)$ as function of frequency,
respectively. The estimated typical orders of each peak is given in Tab. 1.

Discussion.—The coexisting classical and quantum induction current can be
differentiated in an external ac magnetic field. We consider an ac magnetic
field $B(t)=B_{0}+B_{1}\sin(\omega_{1}t)$ as schematically shown in Figs.
3(a)-(b). The constant field $B_{0}$ is used to fix the magnetization of the
sample and the time-dependent $B_{1}\sin(\omega_{1}t)$ to generate the
induction effect. The currents of CI and QIs over a sample with cross-section
area $A$, i.e. $I^{c}=C\dot{B}$, $I^{q}_{1}=Q^{(1)}\dot{B}B$, and
$I^{q}_{2}=Q^{(2)}\dot{B}B^{2}$, is given by:

$\begin{split}I^{c}=&I^{c}_{\omega_{1}}\cos(\omega_{1}t),\\\
I^{q}_{1}=&I^{q1}_{\omega_{1}}\cos(\omega_{1}t)+I^{q1}_{2\omega_{1}}\sin(2\omega_{1}t),\\\
I^{q}_{2}=&I^{q2}_{\omega_{1}}\cos(\omega_{1}t)+I^{q2}_{2\omega_{1}}\sin(2\omega_{1}t)+I^{q2}_{3\omega_{1}}\cos(3\omega_{1}t),\end{split}$
(18)

with the expressions of $I^{c}_{\omega_{1}}$,
$I^{q1}_{\omega_{1}/2\omega_{1}}$, and
$I^{q2}_{\omega_{1}/2\omega_{1}/3\omega_{1}}$ shown in Tab. 1. Figures
3(c)-(e) show the schematic output of the signals in the frequency domain, but
the signals of CI and QIs show different numbers of peaks. We can roughly
estimate the orders of magnitude of these peaks in a $\mathcal{T}$-broken
chiral Weyl semimetal from Eqs. (14), (15)–(17). The scales of energies and
velocities are of the order $\sim 0.1$eV and $\sim 10^{5}$ m/s, respectively,
so that for a typical relaxation time $\tau\sim 10^{-14}$ s, and external
magnetic field with experimentally achievable parameters $B_{0}\sim 1$ T,
$B_{1}\sim 0.1$ T, and $\omega_{1}\sim 100$ kHz Ma  _et al._ (2004); Jordan
_et al._ (1999), the current signals are of several orders of pA for $A\sim 1$
cm2 as is shown in the last column of Tab. 1. The classical signal dominates
at $\omega_{1}$ but is absent at higher frequencies. Remarkably, the strength
of the quantum signal $I^{q1}_{2\omega_{1}}$ is comparable with the circular
photogalvanic effect (CPGE) at low frequency, which is of the order 10–100 pA
de Juan  _et al._ (2017). Therefore we believe the QIs can be experimentally
observed with currently available techniques.

Table 1:  Expresions and typical orders of magnitudes of $I^{c}_{\omega_{1}}$, $I^{q1}_{\omega_{1}/2\omega_{1}}$, and $I^{q2}_{\omega_{1}/2\omega_{1}/3\omega_{1}}$ in Eq. (18) and Figs. 3(c)-(e) under an external ac magnetic field $B(t)=B_{0}+B_{1}\sin\omega_{1}t$. Parameters $B_{0}=1$ T, $B_{1}=0.1$ T, $\omega_{1}=100$ kHz are used Ma  _et al._ (2004); Jordan  _et al._ (1999). The cross-sectional area is taken as $A=1$ cm2.  |  Expression |  Typical order (pA)
---|---|---
$I^{c}_{\omega_{1}}$ |  $\omega_{1}CB_{1}A$ |  $10^{6}\sim 10^{7}$
$I^{q1}_{\omega_{1}}$ |  $\omega_{1}Q^{(1)}B_{0}B_{1}A$ |  103
$I^{q1}_{2\omega_{1}}$ |  $\frac{\omega_{1}}{2}Q^{(1)}B^{2}_{1}A$ |  10$\sim$100
$I^{q2}_{\omega_{1}}$ |  $\omega_{1}Q^{(2)}(B^{2}_{0}+B^{2}_{1}/4)B_{1}$ |  0.1$\sim$1
$I^{q2}_{2\omega_{1}}$ |  $\omega_{1}Q^{(2)}B_{0}B^{2}_{1}A$ |  0.01$\sim$0.1
$I^{q2}_{3\omega_{1}}$ |  $-\frac{\omega_{1}}{4}Q^{(2)}B^{3}_{1}A$ |  10${}^{-3}\sim 10^{-4}$

Reference Yoda  _et al._ , 2018 introduced a dimensionless $\xi$ parameter to
describe how “chiral” the crystal is based on the inverse GME. It is defined
as $\xi=\frac{C_{zz}}{\sigma_{zz}}\frac{c}{S_{xy}}$ where $\sigma_{zz}$ is the
electrical conductivity, and $c$ and $S_{xy}$ refer to the length and cross-
sectional area of the unit cell along $z$-axis. $\xi$ has the physical meaning
of the effective number of helical “turns” within a unit cell. Since both
$C_{zz}$ and $\sigma_{zz}$ are proportional to relaxation time $\tau$, $\xi$
is an intrinsic material parameter that is independent of $\tau$. For CoSi,
the parameter $\xi$ is about 0.3 at the Fermi level and can reach 0.8 by fine-
tuning $\varepsilon_{F}$ SM . Reference Nagaosa, 2019 predicted a principle
for giant inductance based on the emergent electromagnetic field (EEMF) in a
spiral magnet and is recently confirmed by an experimental study Yokouchi  _et
al._ (2020). Our theory is based on the general band structure and does not
necessarily require a spiral magnetic structure. Interestingly, MnSi supports
helical magnetic structure at low-temperature and low- (magnetic-) field
regimes, but ferromagnetic order at higher field strength Ishikawa  _et al._
(1977); Ishikawa and Arai (1984) which makes the material an ideal platform to
study different QI effects.

In summary, we proposed two kinds of quantum induction effects in
noncentrosymmetric topological materials, proportional to the Berry curvature
on the Fermi surface. We illustrate the principle of our theory by studying
two chiral topological materials CoSi and MnSi. Furthermore, we propose to
observe the quantum induction effect in an ac magnetic field to differentiate
it from the classical induction effect. Our findings provide another
topological quantum effect induced by the Berry phase in solid-state
materials.

###### Acknowledgements.

We thank Tobias Holder and Daniel Kaplan for their helpful discussions. B.Y.
acknowledges the financial support by the Willner Family Leadership Institute
for the Weizmann Institute of Science, the Benoziyo Endowment Fund for the
Advancement of Science, Ruth and Herman Albert Scholars Program for New
Scientists, and the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation program (Grant No. 815869).

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