# Towards Lexical Gender Inference: A Scalable Methodology using Online
Databases

Marion Bartl
Insight SFI Research Centre
for Data Analytics
School of ICS
University College Dublin
<EMAIL_ADDRESS>
Susan Leavy
Insight SFI Research Centre
for Data Analytics
School of ICS
University College Dublin
<EMAIL_ADDRESS>

###### Abstract

This paper presents a new method for automatically detecting words with
lexical gender in large-scale language datasets. Currently, the evaluation of
gender bias in natural language processing relies on manually compiled
lexicons of gendered expressions, such as pronouns (he, she, etc.) and nouns
with lexical gender (mother, boyfriend, policewoman, etc.). However, manual
compilation of such lists can lead to static information if they are not
periodically updated and often involve value judgements by individual
annotators and researchers. Moreover, terms not included in the list fall out
of the range of analysis. To address these issues, we devised a scalable,
dictionary-based method to automatically detect lexical gender that can
provide a dynamic, up-to-date analysis with high coverage. Our approach
reaches over 80% accuracy in determining the lexical gender of nouns retrieved
randomly from a Wikipedia sample and when testing on a list of gendered words
used in previous research.

##  1 Introduction

There is a growing body of research on gender bias embedded in trained
language models as well as on allocational and representational harms caused
by the deployment of these models. There have moreover been increasing calls
for early and thorough data description and curation in order to gain insights
into how, for instance, gender stereotyping or quality of service bias is
propagated from data into a language model. What both of these strands of
research have in common is their reliance on pre-defined lexicons of terms
related to gender.

In English, gendered words most commonly include pronouns (he, she, they,
etc.), and also words that carry lexical gender, such as boyfriend,
policewoman, or prince. Previous works on gender bias in language technologies
often use manually compiled lists of words carrying lexical gender to, for
example, mitigate gender stereotyping through data augmentation (Lu et al.,
2020), assess trans-exclusionary bias in co-reference annotations (Cao and
Daumé III, 2020) or evaluate gender inequalities in Wikipedia article titles
(Falenska and Çetinoğlu, 2021). However, curated lists are limited in their
coverage of terms that contain lexical gender and can become outdated if not
maintained.

To address this issue, we present a scalable algorithmic method to determine
lexical gender by querying a word’s dictionary definitions for a small subset
of definitively gendered words. Our method allows for high-coverage,
instantaneous detection of words carrying lexical gender, which eliminates the
need to manually compile and maintain static lists of gendered words. This not
only facilitates the extension of previous work on gender bias in NLP, but can
also be used for a more detailed analysis on the representation of gender in
large-scale language datasets used to train large language models like BERT
(Devlin et al., 2018) or GPT-2 (Radford et al., 2019).

By combining the gender labels obtained from Merriam Webster Online (Merriam-
Webster, 2022), WordNet® (Princeton University, 2010) and Dictionary.com
(Dictionary.com, LLC, 2022), our method reaches an accuracy of 84% in
determining the lexical gender of words in a random sample of 1,000 Wikipedia
articles and 87% accuracy on a list of words carrying lexical gender adapted
from previous research. The code for the algorithm, evaluation methods and
datasets are available111https://github.com/marionbartl/lexical-gender.

In the following section we first outline the conceptions of linguistic gender
used in this research and secondly present an overview of research on gender
in language technology that relies on curated lists of gendered words.
Thirdly, we discuss prior approaches to algorithmic gender inference. Section
3 gives a detailed overview of the algorithm and Section 4 introduces the
datasets used to assess our gender detection algorithm. We present
quantitative and qualitative results in Section 5 and discuss limitations as
well as avenues for future development.

##  2 Background

When dealing with the category of gender in language technology, it is
important to make a distinction between the social category of gender and
gender in a linguistic sense. While social gender relates to the complex
property, performance and experience of one’s own and others’ gender within
society (Ackerman, 2019), linguistic gender describes the expression of gender
within grammar and language. In English, linguistic gender mainly encompasses
ways to express gender as female, male or gender-indefinite (Fuertes-Olivera,
2007). Social gender, as an extra-linguistic category, includes a more fluid
view of gender aside from male and female categories. This includes
transgender, genderqueer and other non-binary experiences and expressions of
gender (Darwin, 2017). As Bucholtz (1999) and Cao and Daumé III (2020) point
out, there is no “one-to-one” mapping between social and linguistic gender.
However, the two are influenced by each other: on one hand, expressions of
gender in language are subject to changing norms in society (Fuertes-Olivera,
2007), on the other hand, the way gender is represented in language influences
the conception of gender within society (Butler, 1990). Thus, being able to
evaluate gendered expressions in language provides insights into societal
conceptualisations of gender.

Since this research explicitly focuses on lexical gender in English, which is
a linguistic category, we give an overview of linguistic gender in English in
Section 2.1. Section 2.2 explores the role lexical gender information plays in
different areas of research on gender bias in NLP, which simultaneously
present possible areas of application for our method of lexical gender
inference. Section 2.3 discusses two prior algorithmic systems for lexical
gender inference in English.

###  2.1 Linguistic gender in English

The taxonomy of linguistic gender in this work builds upon the approach
developed by Cao and Daumé III (2020) and incorporates work by Corbett (1991),
Hellinger and Bussmann (2003) and Fuertes-Olivera (2007).

Within linguistic gender, Cao and Daumé III (2020) differentiate between
grammatical, referential, and lexical gender. Grammatical gender refers to the
distinction of noun classes based on agreement between nouns and their
dependants. English, as a natural or notional gender language (McConnell-
Ginet, 2013), does not have grammatical gender, but it has referential and
lexical gender. Referential gender is used to refer to the social gender of a
specified extra-linguistic entity. Thus, it “relates linguistic expressions to
extra-linguistic reality, typically identifying referents as ‘female’, ‘male’,
or ‘gender-indefinite.’ ” (Cao and Daumé III, 2020). In English, pronouns fall
under the category of referential gender. Lexical gender, which this work
focuses on, is non-referential but a semantic property of a given linguistic
unit, which can be either masculine, feminine222We use the terms masculine and
feminine instead of male and female here in order to underline the purely
linguistic, i.e. semantic, property of lexical gender or gender-
indefinite/gender-neutral. Ackerman (2019) calls these words “definitionally
gendered”. Words that carry lexical gender can require semantic agreement in
related forms, such as, for instance, using the pronoun his in connection with
the word stuntman in the sentence ‘Every stuntman needs to rehearse his
stunts.’ Fuertes-Olivera (2007). In English, lexical gender is usually not
morphologically marked. Exceptions to this rule include e.g. the suffixes -man
to denote masculine gender, such as in policeman, or -ess to denote feminine
gender, such as in waitress. It should moreover be noted that lexical gender
is exclusively a linguistic property. However, words containing lexical gender
can be used to express referential gender if a concrete referent is specified
(Cao and Daumé III, 2020).

###  2.2 Lexical gender in gender bias research

The evaluation and mitigation of gender biases in language datasets and models
relies on referential expressions of gender, such as pronouns, but also words
that carry lexical gender. These pieces of research vary in application, as
well as the number of gendered expressions considered, which varies from two
to around 120 words. Most works assess binary differences between male and
female gender. However, an emergent strand of NLP research also focuses on
non-binary gender expressions (Cao and Daumé III, 2020) and creating gender-
neutral datasets and systems (Vanmassenhove et al., 2021). The following
considers example use-cases of lexicons of lexically gendered words. These
simultaneously represent a variety of applications for our lexical gender
detection algorithm.

#### Dataset evaluation

The most straightforward form of using gendered words is to assess the
distribution of gendered words in a corpus. Zhao et al. (2019) counted he/she
pronouns in the One Billion Word Benchmark (Chelba et al., 2013) to show male
skew in the training data for the ELMo language model (Peters et al., 2018),
which is the primary focus of their analysis. This analysis addressed calls
for better data evaluation (Bender et al., 2021; Rogers, 2021) prior to or
alongside model bias analyses.

#### Retrieval for analysis

Limited-scope lists of words that carry lexical gender were used by Caliskan
et al. (2017) to retrieve Word2Vec embeddings (Mikolov et al., 2013) and
perform the Word Embedding Association Test (WEAT). This test measured
stereotyping by calculating implicit associations between eight male/female
word pairs and words related to maths or science and arts. Guo and Caliskan
(2021) used an adapted version of the WEAT, the CEAT, to asses intersectional
biases in contextualized word embeddings (ELMo (Peters et al., 2018), BERT
(Devlin et al., 2018), OpenAI GPT (Radford et al., 2019; Brown et al., 2020)).
Another use-case in which gendered words were used for retrieval is research
by Falenska and Çetinoğlu (2021), who assessed gender bias in Wikipedia
articles. As a first step, they filtered the article titles for a limited
number of words that carry lexical gender.

#### Creation of synthetic evaluation data

In sentence-based analyses of gender-bias, lists of words with lexical gender
can also be used to fill placeholders in sentence templates and thus create
synthetic sentences with different gendered entities. For example, Kiritchenko
and Mohammad (2018) created the Equity Evaluation Corpus (EEC) to analyse
gender stereotyping in sentiment analysis systems. The EEC inspired the
creation of the Bias Evaluation Corpus with Professions (BEC-Pro), which was
used to analyse associations between gendered entities and professions in BERT
(Bartl et al., 2020). Similarly, Sheng et al. (2019) used the word pair the
man/the woman as fillers within sentence-start prompts for open-ended natural
language generation (NLG) and the subsequent analysis of gender biases in the
generated sentences.

In a rare instance of research on non-binary representations of gender in NLP,
Cao and Daumé III (2020) used gendered lists of words to find and hide lexical
gender in the GAP dataset (Webster et al., 2018). The dataset created in this
way was used to measure gender- and trans-exclusionary biases in coreference
resolution performed by both humans and machine-learning models.

#### Data manipulation

Extensive lists of gendered words were used in the context of Counterfactual
Data Augmentation (CDA), which replaces words with masculine lexical gender
with their feminine variants and vice versa in a corpus. This is done in order
to create training or fine-tuning data for gender bias mitigation. For
instance, Lu et al. (2020) ‘hand-picked’ gender pairs to swap in CDA and
Maudslay et al. (2019) added first names to the list of words to be swapped.

Another kind of data manipulation, this time aiming for neutral gender, was
performed by Vanmassenhove et al. (2021). They used lists of unnecessarily
gendered job titles (e.g. mailman/mailwoman) and feminine forms (e.g.
actress), as well as generic uses of the suffix -man (such as in freshman) in
the extended version of their Neutral Rewriter, which re-writes explicit
mentions of gender into their gender-neutral variants (mail carrier, actor,
first-year student).

###  2.3 Lexical gender inference

Previous approaches to automatic lexical gender inference used unsupervised
and semi-supervised learning, drawing on the presence of gendered pronouns in
the context of a given noun (Bergsma and Lin, 2006; Bergsma et al., 2009).
While Bergsma and Lin (2006) created a large dataset of probabilistic noun
gender labels, Bergsma et al. (2009) used these as basis for creating training
examples for a statistical model that uses context and morphological features
to infer lexical gender.

One major point of criticism here lies in the probabilistic determination of
noun gender, which has the risk of mislabelling lexically neutral nouns, such
as professions, as being gendered due to contextual distributions that are
representative of stereotypes or the number of men and women holding the
profession instead of the linguistic category of lexical gender. For example,
since there are more female than male nurses (Bureau of Labor Statistics
(2022), BLS) and thus most nurses are referred to with female pronouns in
text, the algorithm might infer that the term nurse has female lexical gender,
when in fact it is neutral.

Figure 1: Simplified exemplary flowchart of gender detection algorithm

##  3 Method: Automatic Detection of Lexical Gender

The main goal of this work is to produce a dynamic, high coverage, scalable
method to determine the lexical gender of a target word in order to replace
previously used manually compiled lexicons. For this purpose, we leveraged the
fact that the definition of a lexically gendered word includes words from a
small set of definitively gendered words that carry the same lexical gender.
In the following, we describe the main algorithm setup, additional parameters
and heuristics, as well as the method to combine lexical gender labels from
different databases. A schematic, exemplary overview of the algorithm is
presented in Figure 1.

$w$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
---|---|---|---|---|---|---|---|---
feminine | woman | female | wife | daughter | mother | girl | sister | aunt
masculine | man | male | husband | son | father | boy | brother | uncle

Table 1: Words carrying explicit lexical gender; $w$ = number of pairs used
for experiments

###  3.1 Algorithm construction

The method we outline utilises the increasing availability of machine-readable
dictionaries, such as Merriam Webster Online, Dictionary.com, and the lexical
database WordNet, in order to identify gendered terms. Examples (1) and (2)
illustrate how lexical gender is captured within Merriam-Webster’s (2022)
definitions of nun and monk:

  1. (1)

nun: a woman belonging to a religious order

  2. (2)

monk: a man who is a member of a religious order and lives in a monastery

Both definitions mention the lexical gender of the referent through a gendered
word, in this case man and woman. Initial analyses showed that gendered words
are more likely to occur at the beginning of a definition and definitions
often used the words female/male or woman/man to specify lexical gender. In
identifying gendered terms, we thus considered the presence and amount of up
to eight definitively gendered words, such as male/female, man/woman etc., in
the target word’s definitions to draw inferences about its lexical gender.

For retrieval of the definitions, we accessed WordNet through the Natural
Language Toolkit (NLTK, Bird et al., 2009) and Merriam Webster Online as well
as Dictionary.com through HTTP requests.

Once the definitions for a given target word were retrieved, the process of
obtaining lexical gender was the same for either dictionary. We determined
whether a word has masculine, feminine, or neutral lexical gender by counting
occurrences of a number of word pairs which have clearly defined feminine or
masculine lexical gender, which are displayed in Table 1. If the combined
definition texts contain more masculine than feminine terms, the word was
labelled with masculine lexical gender, and vice versa. If the same number of
masculine and feminine words was found within a set of definitions, which
includes the case in which none of the pre-defined gendered terms can be
found, the word was labelled with neutral lexical gender. We additionally
obtained a combined label through a majority vote over the individual
dictionaries’ gender labels. In cases in which words could not be found in one
dictionary and querying each of the other dictionaries returned different
labels, a neutral gender label was assigned.

###  3.2 Parameters

Three variable parameters were used to limit the number of definitions and
word tokens queried, as well as the number of definitively gendered words to
use for the query. In order to determine the best combination of values for
our parameters, we performed a grid search using our gold standard data (see
Section 4.1) and combined labels to test performance.

#### Number of definitions $d$

We limited the number of definitions, because definitions that occur early on
have a higher likelihood of describing a more general sense of the word, while
later definitions relate to very specific word senses. Therefore, we retrieved
only the first $d$ definitions that the dictionary lists for the word. During
grid search, we tested integer values in the range $d=[2..10]$, and the best
value was determined to be $d=4$.

#### Number of tokens $t$

We also experimented with limiting the number of tokens within a given
definition to see whether definitively gendered terms were more likely to be
mentioned earlier in a given definition. The definitions were tokenized using
NLTK (Bird et al., 2009). We took the first $t$ tokens of each definition.
Regarding the number of tokens in a definition, we tested the algorithm with
$t=\\{5,10,15,20,25,30,35\\}$ in our experiments and found $t=20$ to produce
optimal results.

#### Number of gendered word pairs $w$

The word pairs used during experiments are listed in Table 1. The first two
word pairs, woman/man and female/male, as well as the pair girl/boy, are most
commonly used to describe the gender of a person or animal, while the rest of
the words describes gendered family relations. The latter were chosen in order
to account for cases in which the lexical gender of a person is described in
relation to another person by using family terms. This is for example the case
in the definition of baroness in Merriam Webster: “the wife or widow of a
baron” (Merriam-Webster, 2022). The grid search was performed for integer
values in the range $w=[2..8]$ and best performance was obtained for $w=5$
word pairs. Moreover, if a target word was included in the definitively
gendered pairs or their plural forms, it was automatically classified with the
respective lexical gender.

|  | gold
---
(N=134)
| Wiki1000-sample
---
(N=515)
| Wiki1000 dataset
---
(N=12,643)
POS | NN | NN | NNS | all | NN | NNS | all
masc | 53 | 82 | 43 | 125 | 100 | 46 | 146
fem | 53 | 51 | 29 | 80 | 60 | 28 | 88
neut | 28 | 212 | 98 | 310 | 7,679 | 3,880 | 11,559
not found | - | - | - | - | 618 | 232 | 850
all | 134 | 345 | 170 | 515 | 8,457 | 4,186 | 12,643
Table 2: Composition of evaluation corpora for lexical gender detection
algorithm.
Note: for Wiki1000 full, combined predicted labels were used, because no gold
labels exist for this dataset

###  3.3 Morphological Heuristics

Aside from the lexical database method described above, we additionally
applied heuristics relating to suffix-morphology and punctuation.
Morphological heuristics were applied before querying the dictionaries, while
the punctuation-related heuristic was applied when a word could not be found
in a dictionary.

The first heuristic was applied in order to handle gender-neutral definitions
of words that carry gender-explicit markers, such as the word businessman,
which carries the masculine suffix -man. Its definition in WordNet (Princeton
University, 2010) is shown in (3).

  1. (3)

businessman: a person engaged in commercial or industrial business (especially
an owner or executive)

Even though businessman contains a masculine suffix, its definition is
generic, most likely due to the fact that businessman was once used for
business people of all genders. However, since feminine or neutral equivalents
(business woman, business person) are widely used nowadays, the word
businessman has become gender specific and defining it generically represents
an outdated, male-as-norm viewpoint (Fuertes-Olivera, 2007).

We thus classified words containing the suffixes -man and -boy or -woman and
-girl into masculine and feminine lexical gender, respectively. Regular
expressions were used to ensure that feminine or neutral words ending in -man
such as woman or human, as well as words that have the suffix -woman, were not
classified as masculine.

Another heuristic was applied in order to account for spellings that differ in
punctuation, e.g. grandfather vs. grand-father. We check for and subsequently
remove punctuation within a word if it cannot be found within a dictionary.
This also applies to the cases in which non-detection is caused by a
whitespace character.

##  4 Data

We used two test datasets to evaluate and run the algorithm. The first
dataset, which we call gold standard hereafter, contains nouns that have a
clear lexical gender and were mainly sourced from previous research on gender
bias. The second dataset contains 1,000 randomly sampled Wikipedia articles,
which we used to extract gendered nouns. The following describes both datasets
in detail.

###  4.1 Gold Standard

In order to gain insights into the performance of the dictionary-based
algorithm for lexical gender retrieval, we compiled a list of words that have
a nearly unambiguous lexical gender, which acts as the gold standard. The gold
standard list was developed based on a lexical gender list by Cao and Daumé
III (2020) with the addition of more words retrieved from online lists for
learners of English333 www.vocabularypage.com/2017/03/gender-specific-
nouns.html4447esl.com/gender-of-nouns/555learnhatkey.com/what-is-gender-in-
english-grammar/ . Nouns retrieved from prior research and online sources were
subsequently filtered for explicitness of lexical gender. For example, the
pair actor/actress would not be considered since the word actor is nowadays
used for both male and female referents. We moreover added neutral gender
replacements for word pairs for which such an alternative exists. An example
would be the triplet headmaster-masc, headmistress-fem, headteacher-neut. The
final list is comprised of 53 masculine, 53 feminine, and 28 neutral words
(see Table 4 in the Appendix).

|  | gold standard
---
(N=134)
| Wiki1000-sample
---
(N=515)
measure | P | R | F1 | Acc | P | R | F1 | Acc
WordNet | 0.91 | 0.83 | 0.85 | 0.83 | 0.73 | 0.63 | 0.63 | 0.63
Merriam Webster | 0.89 | 0.77 | 0.8 | 0.77 | 0.83 | 0.82 | 0.82 | 0.82
Dictionary.com | 0.93 | 0.87 | 0.89 | 0.87 | 0.76 | 0.61 | 0.59 | 0.61
Combined | 0.92 | 0.87 | 0.89 | 0.87 | 0.85 | 0.84 | 0.84 | 0.84
Table 3: Quantitative results for lexical gender detection of gold standard
and Wiki1000-sample

###  4.2 Wikipedia Sample

This research aims at providing a flexible, scalable, and high-coverage method
for lexical gender detection. Therefore we additionally tested the approach on
more naturalistic data, namely a random sample of 1,000 articles from English
Wikipedia obtained through the wikipedia python
library666https://pypi.org/project/wikipedia/. We will abbreviate this sample
corpus as Wiki1000 hereafter.

The articles were then cleaned and tokenized into sentences using NLTK (Bird
et al., 2009) and subsequently processed with SpaCy to obtain part-of-speech
(POS) tags for each word. All singular and plural nouns (POS-tags: NN, NNS)
were then extracted and analysed for lexical gender. Nouns that contained
special characters due to cleaning and tokenization errors were dropped. This
method provided us with 12,643 nouns, as illustrated under Wiki1000 in Table
2.

In order to test the performance of the algorithm, the instances of the
Wiki1000 dataset needed true labels. A corpus size of 12,643 instances,
however, was beyond the scope of this research to manually label. In fact, it
represents the kind of corpus size that we aim to label automatically. We
therefore filtered Wiki1000 for nouns that were labelled as either masculine
or feminine by Merriam Webster Online, Dictionary.com, or WordNet. Like this,
we specifically target gendered nouns and obtain a corpus similar to the gold
standard corpus, but sourced from naturally occurring text. The resulting
corpus of 515 nouns, which we call Wiki1000-sample, was subsequently labelled
for ‘true’ lexical gender by members of the research team (Fleiss’s
$\kappa\approx 0.87$). The labels used for evaluation were determined by
majority vote. The specifications of the Wiki1000-sample dataset can be found
in Table 2.

In line with previous research on gender bias in Wikipedia Wagner et al.
(2015); Falenska and Çetinoğlu (2021), which found an over-representation of
male entities in the encyclopedia, Table 2 shows that there are approximately
1.5 times as many mentions of distinct entities with masculine lexical gender
in our 1,000-article Wikipedia sample than there of entities with feminine
lexical gender.

##  5 Results and Discussion

###  5.1 Quantitative analysis

An overview of algorithm performance on the gold standard dataset and the
reduced Wiki1000 sample can be found in Table 3. We report the weighted
average of precision, recall, and F1-measure due to unbalanced classes in our
test data.

As seen in Table 3, our best performing approach on both the gold dataset (87%
accuracy) as well as the sample of Wiki1000 (84% accuracy) was combining
labels from all three sources by majority vote. Keeping in mind that the
Wiki1000 sample is approximately three times the size of the gold standard,
the relative consistency in performance here indicates robustness for our
approach. It should also be noted that only querying Dictionary.com reached
the same performance on the gold standard dataset (87% accuracy) while on the
Wiki1000 sample, using only Merriam Webster reached a comparable accuracy
score to the combined model (82%).

Table 3 moreover shows that on the gold standard dataset, which was used to
fine-tune our parameter values using grid search, our method reached an
accuracy of 77% or higher in each experiment configuration. Using the same
parameter values for experiments on the Wiki1000 sample, only the combined
approach as well as using only Merriam Webster reaches an accuracy of >77%.
When using only WordNet or Dictionary.com, the performance drops from 84% to
63% and 61% accuracy, respectively. This shows that parameter configurations
can be adapted to specific dictionaries and dataset sizes.

Figure 2 shows confusion matrices for the combined approach on both the gold
standard dataset (2(a)) and the Wiki1000-sample (2(b)). Figure 2(a) shows that
on the gold standard, the combined classifier mislabelled four feminine and 11
masculine instances as neutral, but did not mislabel any of the neutral
instances as either masculine or feminine. In contrast, both these
classification mistakes can be found on the Wiki1000 sample (Figure 2(b)).
Here, the algorithm classifies more lexically neutral words as gendered than
vice versa.

Cases in which lexically neutral words are classified as gendered include
words that are traditionally related to specific genders, such as bikini or
soprano, as well as patriarchy or testes. It is likely that dictionary
definitions reflect this traditional gender association, leading to
misclassification. Conversely, classifications of gendered words as neutral
can e.g. be caused by definitions that do not mention gender, either because
of presumed knowledge (pope) or because a lexically specific word was formerly
used for all genders (landlord). Another reason for gendered-as-neutral
misclassification can be the definition of one gendered term by using another,
which ‘cancel each other out’. For example, WordNet defines widow as “a woman
whose husband is dead especially one who has not remarried” (Princeton
University, 2010).

(a) gold standard

(b) Wiki1000-sample

Figure 2: Confusion matrices for combined labels
words that were not found in (a): single person, child-in-law

Another issue, which only occurred when testing on the gold standard dataset,
concerns words that could not be found. The first is single person, which we
chose as gender-neutral alternative for bachelor/spinster. The fact that it
was not found could be due to the term single person being more of a composite
phrase than a joined expression. Moreover, single people are often described
using the adjective single in a predicative way, such as in the sentence ‘He
is single.’, instead of ‘He is a single person.’ The other word that could not
be found is child-in-law, which is the gender-neutral variant of son/daughter-
in-law. Here, the issue could be frequency of use, since child-in-law is less
established than its gender-specific variants.

###  5.2 Qualitative analysis

The following section discusses some classification errors in more detail. We
focus on errors that occur due to gender-exclusive definitions in the lexical
databases caused by historically close associations of words to a single
gender.

In our first example, an outdated definition in WordNet (Princeton University,
2010) causes the misclassification of the word crew, a neutral term, as
masculine. We show the first and fourth definitions in Example (4) in order to
illustrate how the masculine label was obtained.

  1. (4)

crew

     * 1.

the men and women who man a vehicle (ship, aircraft, etc.)

     * 4.

the team of men manning a racing shell

In the first definition, the words men and women are used to define the crew
of any vehicle while in the fourth definition, which describes the crew of a
racing shell (a type of rowing boat), only the word men is used. This leads to
a masculine lexical gender label, since the definitions taken together contain
more masculine than feminine words. However, the fourth definition could have
been worded like the first, or used the word people, since racing shells can
be crewed by people of any gender.

A similar classification error occurred for the words soprano, menopause and
nurse, which were all classified as feminine by the combined model, even
though they have neutral lexical gender. These terms are all closely
associated with female social gender due to anatomical and hormonal
differences between sexes (soprano and menopause), historical biases of women
performing care-work, as well as current gender distributions in certain
professions (nurse; Bureau of Labor Statistics (2022), BLS). While using
gender-exclusive wording to define lexically neutral terms could inform
readers of a word’s traditional relation to social gender, it can also
reproduce gender stereotypes and exclude those who do not identify as female
but still sing in soprano voice or work as a nurse. Moreover, using feminine
words in the definition of words like menopause can be seen as a form of
trans-exclusionary bias, since people assigned female at birth, whose body can
cease to menstruate, might not identify as female.

###  5.3 Limitations and Future Developments

We have selected dictionaries to obtain the lexical gender of a word, because
they represent a relatively objective resource that is expected to list
neutral and non-stereotypical definitions of words. However, as shown in
Section 5.2, dictionaries are after all a human-curated resource and as such
still carry human biases and outdated definitions, which in turn lead to
biased or outdated results.

We would moreover like to point out that we are explicitly working with
English, which does not mark gender grammatically. In languages that mark
grammatical gender, our method would most likely be obsolete, because here
gender can e.g. be inferred from formal features such as morphology or
agreement for most nouns Corbett (1991). What is more, English, as a lingua
franca and the language most focused on by the NLP community (Bender et al.,
2021), has a plethora of high-quality and high-coverage resources available.
Since our method is reliant on lexical resources, adapting the method to low-
resource languages could prove challenging. However, while more complex
lexical resources like WordNet might not yet exist for some languages, it is
likely that online dictionaries do exist. Therefore, we still believe that our
method can be adapted to other notional gender languages (McConnell-Ginet,
2013).

Another limitation of the present work concerns word sense disambiguation,
since the presence of lexical gender depends on the word’s sense in context.
As an example, the word colt, can either mean a young male horse or a brand of
pistol. In the sense of a male horse, the lexical gender of colt is clearly
masculine while in the sense of the pistol, it is neutral. Differences in the
lexical gender of word senses can also be caused by semantic shifts, such as
for the word master, which traditionally refers to a man who is in control of
e.g. servants or a household. However, in an academic context its meaning has
shifted and now refers to an academic degree, or more broadly to a person of
undefined gender who has reached a high level of skill in a given discipline.
Therefore, future work will integrate word sense disambiguation within the
algorithm.

##  6 Conclusion

We have presented a method to automatically determine the lexical gender of a
given word by querying its dictionary definitions. The performance of the
algorithm on a gold standard dataset of gendered nouns based on related
literature, as well as a set of nouns sampled from 1,000 randomly selected
Wikipedia articles, reached up to 87% accuracy. Previous research on gender
bias in NLP used manually compiled lists of gendered words for data
evaluation, retrieval, manipulation, and the synthetic creation of data. In
contrast, our method is scalable and has a high, dynamic coverage, which gives
it a variety of applications within past and future research on gender bias in
NLP. These include e.g. the assessment of gender representations in large-
scale corpora, the retrieval of gendered words for which gender-neutral
replacements need to be found, as well as determining whether male-centric
language such as epicene he is used in coreference resolution clusters.

## Acknowledgements

This publication has emanated from research conducted with the financial
support of Science Foundation Ireland under Grant number 12/RC/2289_P2. For
the purpose of Open Access, the author has applied a CC BY public copyright
licence to any Author Accepted Manuscript version arising from this
submission.

We would like to thank Ryan O’Connor for his help in annotating the nouns in
our Wikipedia corpus for lexical gender.

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## Appendix

category | masculine | feminine | neutral
---|---|---|---
family | brother | sister | sibling
dad | mum |
dad | mom |
daddy | mummy |
daddy | mommy |
father | mother | parent
father-in-law | mother-in-law | parent-in-law
fiance | fiancee | betrothed
grandfather | grandmother | grandparent
grandson | granddaughter | grandchild
husband | wife | spouse
nephew | niece |
son | daughter | child
son-in-law | daughter-in-law | child-in-law
step-father | step-mother | step-parent
stepfather | stepmother | stepparent
uncle | aunt |
widower | widow |
misc | bachelor | spinster | single person
boy | girl | child
boyfriend | girlfriend | partner
gentleman | lady |
groom | bride |
lad | lass |
male | female |
man | woman | person
manservant | maidservant | servant
steward | stewardess | attendant
swain | nymph | spirit
wizard | witch |
occupation | businessman | businesswoman | business person
chairman | chairwoman | chairperson
fireman | firewoman | fire fighter
headmaster | headmistress | head teacher
landlord | landlady | renter
milkman | milkmaid |
policeman | policewoman | police officer
salesman | saleswoman | salesperson
waiter | waitress | server
religion | friar | nun |
monk | nun |
title | Mr. | Mrs. | Mx.
baron | baroness |
count | countess |
czar | czarina |
duke | duchess |
earl | countess |
emperor | empress | ruler
king | queen |
prince | princess |
signor | signora |
sir | madam |
viscount | viscountess |

Table 4: Masculine, feminine and neutral nouns of the gold standard dataset


# Polarization-selective magneto-optical modulation

Banoj Kumar Nayak  Andrew and Erna Viterbi Department of Electrical
Engineering, Technion, Haifa 32000 Israel  Eyal Buks  Andrew and Erna Viterbi
Department of Electrical Engineering, Technion, Haifa 32000 Israel

(August 27, 2024)

###### Abstract

We study magneto-optical coupling in a ferrimagnetic sphere resonator made of
Yttrium iron garnet. We find that the resonator can be operated in the telecom
band as a polarization-selective optical modulator. Intermodulation gain can
be employed in the nonlinear regime for amplification.

Information is commonly transmitted by modulating a monochromatic carrier
wave. The method of single sideband modulation (SSM) allows reducing both
transmission power and bandwidth, in comparison with simpler methods such as
amplitude, frequency and phase modulation lazzarini2008asymmetric . In the
radio frequency band SSM can be implemented using electronic circuits,
however, SSM implementation in the optical band is challenging, since it
requires that different out of phase modulation methods are simultaneously
applied Li_1 .

Magneto-optical (MO) coupling Rameshti_1 ; Kusminskiy_299 ; Zhu_2012_11119 ;
Juraschek_094407 ; Bittencourt_014409 ; Zhang_123605 ; Stancil_Spin  in
ferrimagnetic sphere resonators (FSR) can be used for optical modulation of
signals in the microwave band. Such a modulation has been demonstrated before
Haigh_133602 ; Osada_103018 ; Osada_223601 ; Sharma_094412 ; Almpanis_184406 ;
Zivieri_165406 ; Desormiere_379 ; Liu_3698 ; Chai_820  by exciting individual
whispering gallery FSR optical modes using either a tapered optical fiber or a
prism. Here we employed a modified experimental setup, in which light in the
telecom band is transmitted through the FSR bulk. Driving the FSR near its
resonance generates sidebands in the transmitted optical spectrum. We find
that the FSR can be used as a polarization-selective SSM. The polarization
selectivity is attributed to angular momentum conservation in photon-magnon
scattering Wettling_211 ; cottam1986light ; Liu_060405 ; Haigh_143601 ;
Hisatomi_207401 ; Hisatomi_174427 . We demonstrate that intermodulation (IMD)
gain can be exploited in the nonlinear regime for amplification.

Figure 1: Experimental setup. Optical fibers are installed on both sides of
the FSR for transmission of light through the sphere. Optical components [TL
(tunable laser), Att (optical attenuator), PC (polarization controller) and
PBS (polarization beam splitter)] and fibers are red colored, and MW
components [MWA (microwave loop antenna), S (splitter), C (circulator), VNA
(vector network analyzer), SA (spectrum analyzer) and SG (signal generator)]
and coaxial cables are blue colored. TL2 together with two PBSs (labelled as
PBS1 and PBS2) and two differential photo detectors (labelled as DPD1 and
DPD2) operate as a polarization-selective optical spectrum analyzer (OSA)
Baney_355 . A power amplifier is serially connected to the SG. The MWA is
weakly coupled to the FSR-LGR system.

The experimental setup is schematically shown in Fig. 1. Optical components
and fibers are red colored, whereas blue color is used to label microwave (MW)
components and coaxial cables. A MW cavity made of a loop gap resonator (LGR)
allows achieving a relatively large coupling between magnons and MW photons
Goryachev_054002 ; Zhang_205003 ; Mathai_054428 ; Nayak_062404 . The LGR is
fabricated from a hollow concentric aluminium tube. A sapphire (S) strip of
$260\operatorname{\mu m}$ thickness is inserted into the gap in order to
increase its capacitance, which in turn reduces the frequency $f_{\mathrm{c}}$
of the LGR fundamental mode. An FSR made of Yttrium iron garnet (YIG) having
radius of $R_{\mathrm{s}}=125\operatorname{\mu m}$ is held by two ceramic
ferrules (CF) inside the LGR. The angular frequency of the Kittel mode
$\omega_{\mathrm{m}}$ is approximately given by
$\omega_{\mathrm{m}}=\mu_{0}\gamma_{\mathrm{e}}H_{\mathrm{s}}$, where
$H_{\mathrm{s}}$ is the static magnetic field, $\mu_{0}$ is the free space
permeability, and
$\gamma_{\mathrm{e}}/2\pi=28\operatorname{GHz}\operatorname{T}^{-1}$ is the
gyromagnetic ratio Stancil_Spin .

The applied static magnetic field $\mathbf{H}_{\mathrm{s}}$ is controlled by
adjusting the relative position of a magnetized Neodymium using a motorized
stage. The static magnetic field is normal to the light propagation direction
$\mathbf{k}$, and the magnetic field of MW drive is nearly parallel to
$\mathbf{k}$. The LGR-FSR coupled system is encapsulated inside a metallic
rectangular shield made of aluminum. The LGR is weakly coupled to a microwave
loop antenna (MWA).

The plot in Fig. 2 exhibits a vector network analyzer (VNA) reflectivity
measurement of the LGR-FSR coupled system. The static applied magnetic field
$H_{\mathrm{s}}$ in this measurement is varied near the value corresponding to
avoided-crossing between the FSR and LGR resonances.

Figure 2: VNA reflectivity in dB units as a function of magnetic field
$H_{\mathrm{s}}$ at applied microwave power of $-30$ dBm.

Optical side bands are observed in the transmission spectrum when the driving
microwave frequency $\omega_{\mathrm{p}}/\left(2\pi\right)$ is tuned close to
the FSR resonance at $\omega_{\mathrm{m}}/\left(2\pi\right)$. The plot shown
in Fig. 3 exhibits the measured total optical intensity
$I_{\mathrm{T}}=I_{\mathrm{DPD1}}+I_{\mathrm{DPD2}}$ as a function of the
wavelength $\lambda_{2}$ of TL2, where $I_{\mathrm{DPD1}}$ and
$I_{\mathrm{DPD2}}$ are the intensities measured by the two differential
photodetectors (labelled as DPD1 and DPD2 in Fig. 1). The primary wavelength
$\lambda_{\mathrm{L}}$ of TL1, which is related to the TL1 frequency
$\omega_{\mathrm{L}}/\left(2\pi\right)$ by $\omega_{\mathrm{L}}=2\pi
c/\lambda_{\mathrm{L}}$, where $c$ is the speed of light, is separated from
optical side bands by
$\lambda_{\mathrm{SB}}\simeq\lambda_{\mathrm{L}}^{2}\omega_{\mathrm{p}}/\left(2\pi
c\right)$ (about $30.0\operatorname{pm}$ for laser wavelength of
$\lambda_{\mathrm{L}}=1539\operatorname{nm}$, and FSR driving frequency of
$\omega_{\mathrm{p}}/\left(2\pi\right)=3.79\operatorname{GHz}$).

Figure 3: The transmitted optical spectrum. For this measurement the TL1 is
set at optical power of $31\operatorname{mW}$ and wavelength
$\lambda_{\mathrm{L}}$ of $1538.887\operatorname{nm}$, and the driving
microwave is set at frequency $\omega_{\mathrm{p}}/\left(2\pi\right)$ of
$3.79\operatorname{GHz}$ and power $P_{\mathrm{p}}$ of $20$ dBm.

Both motorized polarization controllers (labelled as PC1 and PC2 in Fig. 1)
have three optomechanical components (paddles), which act as either quarter or
half wave plates. The paddles’ angles of PC1 (PC2) are denoted by
$\theta_{1\mathrm{A}}$, $\theta_{1\mathrm{B}}$ and $\theta_{1\mathrm{C}}$
($\theta_{2\mathrm{A}}$, $\theta_{2\mathrm{B}}$ and $\theta_{2\mathrm{C}}$).
The incident light state of polarization (SOP) can be manipulated using PC1.
We observe that intensity of lower wavelength
$\lambda_{\mathrm{L}}-\lambda_{\mathrm{SB}}$ anti-Stokes sideband and higher
wavelength $\lambda_{\mathrm{L}}+\lambda_{\mathrm{SB}}$ Stokes side band
depend on the input SOP. SSM in the transmission spectrum, with either single
anti-Stokes side band, or with single Stokes side band, can be obtained by
adjusting PC1. The plot shown in Fig. 4(a) exhibits the measured anti-Stokes
side band intensity as a function of microwave driving frequency
$f_{\mathrm{p}}=\omega_{\mathrm{p}}/\left(2\pi\right)$ and PC1 angle
$\theta_{1\mathrm{C}}$ near the avoided-crossing region. The plot shown in
Fig. 4(c) exhibits simultaneously measured Stokes side band intensity in the
same region. We clearly observe appreciable anti-Stokes and Stokes intensity
in Fig. 4 (a) and (c), respectively, when driving frequency
$\omega_{\mathrm{p}}/\left(2\pi\right)$ becomes close to FSR resonance
$\omega_{\mathrm{m}}/\left(2\pi\right)$. However, they are asymmetric. For a
certain range of PC1 position, SSM is obtained, i.e. only one side band,
either anti-Stokes or Stokes, is observed. Contrary to other experimental
setups, in which the FSR is optically coupled by either a tapered optical
fiber or a prism, for our setup, for which the measured optical transmission
weakly depends on the input wavelength $\lambda_{\mathrm{L}}$, SSM can be
obtained in wide range of $\lambda_{\mathrm{L}}$.

Figure 4: Side bands. (a) anti-Stokes intensity as a function of PC1 angle
$\theta_{1\mathrm{C}}$. (b) anti-Stokes intensity as a function of magnetic
field $H_{\mathrm{s}}$. (c) Stokes intensity as a function of
$\theta_{1\mathrm{C}}$. (d) Stokes intensity as a function of
$H_{\mathrm{s}}$. The magnetic field $H_{\mathrm{s}}$ in (a) and (c) is tuned
near avoided-crossing regime. TL1 is set at optical power of
$31\operatorname{mW}$ and wavelength $\lambda_{\mathrm{L}}$ of
$1537.7\operatorname{nm}$, and the driving microwave power is set at
$P_{\mathrm{p}}=20$ dBm. In (a) and (c), $\theta_{1\mathrm{A}}=170^{\circ}$
and $\theta_{1\mathrm{B}}=85^{\circ}$, and $\theta_{1\mathrm{C}}$ is varied
from $0^{\circ}$ to $170^{\circ}$, whereas in (b) and (d)
$\left(\theta_{1\mathrm{A}},\theta_{1\mathrm{B}},\theta_{1\mathrm{C}}\right)=\left(170^{\circ},85^{\circ},60^{\circ}\right)$
(for this setting both Stokes and anti-Stokes peaks are clearly visible near
the FSR resonance).

The plots shown in Fig. 4 (b) and (d) exhibit anti-Stokes and Stokes
intensity, respectively, as a function of microwave driving frequency
$f_{\mathrm{p}}$ and static magnetic field $H_{\mathrm{s}}$. The FSR resonance
changes as we vary the static magnetic field $H_{\mathrm{s}}$. Accordingly,
from Fig. 4(b) and (d), we see that both anti-Stokes and Stokes intensity gets
pronounced when driving frequency $\omega_{\mathrm{p}}/\left(2\pi\right)$ is
within the bandwidth of FSR resonance and disappear when driving frequency is
away from FSR frequency at $\omega_{\mathrm{m}}/\left(2\pi\right)$.

Our experimental setup (see Fig. 1) allows measuring the SOP of both
sidebands. While the plots shown in Fig. 4 display the total optical intensity
$I_{\mathrm{T}}=I_{\mathrm{DPD1}}+I_{\mathrm{DPD2}}$, the intensity
$I_{\mathrm{DPD1}}$ ($I_{\mathrm{DPD2}}$) is separately displayed in the top
(bottom) row plots shown in Fig. 5. These two intensities $I_{\mathrm{DPD1}}$
and $I_{\mathrm{DPD2}}$ represent two orthogonal SOP, which can be set by
adjusting PC2 (see Fig. 1). The left (right) column plots in Fig. 5 display
the measured intensity of the left anti-Stokes (right Stokes) sideband at
wavelength $\lambda_{\mathrm{L}}-\lambda_{\mathrm{SB}}$
($\lambda_{\mathrm{L}}+\lambda_{\mathrm{SB}}$), whereas the intensity at the
central wavelength $\lambda_{\mathrm{L}}$ is displayed by the central column
plots in Fig. 5. For the measurements shown in Fig. 5, PC1 is set to a nearly
SSM state. By varying the setting of PC2, we find that the central peak at
wavelength $\lambda_{\mathrm{L}}$ is maximized (minimized) in the same region
where the sidebands at wavelength
$\lambda_{\mathrm{L}}\pm\lambda_{\mathrm{SB}}$ are minimized (maximized). This
observation implies that in the region of SSM, the SOP of the sidebands is
nearly orthogonal to the SOP of the incident light. This orthogonality can be
exploited at the receiver end of a data transmission system based on our
proposed MO modulation, since it allows demodulation by polarization
filtering-out of the carrier at wavelength $\lambda_{\mathrm{L}}$.

Figure 5: Sideband SOP. The measured intensity $I_{\mathrm{DPD1}}$
($I_{\mathrm{DPD2}}$) is shown (in dBm units) in the plots labeled by the
letter ’a’ (’b’). The intensity at wavelengths
$\lambda_{\mathrm{L}}-\lambda_{\mathrm{SB}}$, $\lambda_{\mathrm{L}}$ and
$\lambda_{\mathrm{L}}+\lambda_{\mathrm{SB}}$ is shown in the plots labelled by
the numbers ’1’, ’2’ and ’3’, respectively. The TL1 is set at optical power of
$31\operatorname{mW}$ and wavelength $\lambda_{\mathrm{L}}$ of
$1538.9\operatorname{nm}$, the driving microwave is set at power
$P_{\mathrm{p}}$ of $20$ dBm.

Magnetic anisotropy gives rise to Kerr nonlinearity in the FSR response
Wang_224410 . The nonlinearity can be exploited for modulation amplification
Mathai_67001 . Modulation measurements in the nonlinear regime are shown in
Fig. 6. The results indicate that the Kerr coefficient is negative (giving
rise to softening). For the plots shown in the top (bottom) row of Fig. 6, the
microwave driving frequency is swept upwards (downwards). The dependency on
sweeping direction is attributed to nonlinearity-induced hysteresis.

Figure 6: Spectral peaks (in dBm units) in the nonlinear regime as a function
of MW driving power $P_{\mathrm{p}}$. The intensity of the left (right)
sideband at wavelength $\lambda_{\mathrm{L}}-\lambda_{\mathrm{SB}}$
($\lambda_{\mathrm{L}}+\lambda_{\mathrm{SB}}$) is shown in the plots in the
left (right) column, whereas the plots in the central column show the
intensity of the central optical peak (at TL1 wavelength
$\lambda_{\mathrm{L}}$). For the plots shown in the top (bottom) row, the
frequency $f_{\mathrm{p}}$ is swept upwards (downwards).

In summary, polarization-selective SSM in the telecom band is achieved using
an FSR strongly coupled to an LGR. Such a modulator can be integrated with
superconducting circuits, and can be employed for quantum state readout.

This work was supported by the Israeli science foundation, the Israeli
ministry of science, and by the Technion security research foundation.

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