2021 [1]Elnaz Shafaei-Bajestan 1]Eberhard Karls Universität Tübingen, Germany
2]Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

# Making sense of spoken plurals

*<EMAIL_ADDRESS>Peter Uhrig<EMAIL_ADDRESS>R. Harald Baayen<EMAIL_ADDRESS>[  [

###### Abstract

Distributional semantics offers new ways to study the semantics of morphology.
This study focuses on the semantics of noun singulars and their plural
inflectional variants in English. Our goal is to compare two models for the
conceptualization of plurality. One model (FRACSS) proposes that all singular-
plural pairs should be taken into account when predicting plural semantics
from singular semantics. The other model (CCA) argues that conceptualization
for plurality depends primarily on the semantic class of the base word. We
compare the two models on the basis of how well the speech signal of plural
tokens in a large corpus of spoken American English aligns with the semantic
vectors predicted by the two models. Two measures are employed: the
performance of a form-to-meaning mapping and the correlations between form
distances and meaning distances. Results converge on a superior alignment for
CCA. Our results suggest that usage-based approaches to pluralization in which
a given word’s own semantic neighborhood is given priority outperform theories
according to which pluralization is conceptualized as a process building on
high-level abstraction. We see that what has often been conceived of as a
highly abstract concept, [+plural], is better captured via a family of mid-
level partial generalizations.

###### keywords:

Plural semantics, Distributional semantics, FRACSS, Cosine Class Average,
Sound-meaning mapping, Spoken word recognition

##  1 Introduction

Distributional semantics (Landauer Dumais, 1997; Firth, 1968; Harris, 1954;
Mikolov ., 2013; Wang ., 2019; Günther ., 2019; Boleda, 2020) offers new
opportunities for understanding the semantics of word formation (see, e.g.
Marelli Baroni, 2015; Kisselew ., 2015) and inflection (see, e.g., Baayen
Moscoso del Prado Martín, 2005). Given corpus-based semantic vectors (known as
embeddings in computational linguistics and natural language processing) for
pairs of base words and corresponding complex words, several methods have been
proposed that take as input the semantic vector of the base word, and that
produce as output the vector of the complex word. One such method is
illustrated in Figure 1. Given the semantic vectors for two pairs of singulars
and plurals (table/tables and pen/pens), and given the semantic vector for
banana but no semantic vector for its plural, the semantic vector for bananas
is obtained by first calculating the vectors that start at a singular and
point to the corresponding plural (represented by blue vectors), and average
these, resulting in an average shift vector (in red). This shift vector can
then be applied to the vector of banana, resulting in the semantic vector for
bananas (lower panel). Kisselew . (2015) calculated the average shift vector
for each of a large set of German derivational affixes, and showed that this
results in high-quality estimates of the meanings of derived complex words.
Marelli Baroni (2015) used a method based on matrix multiplication to obtain
predicted semantic vectors for derived words, and showed that this method
generated quantitative predictors that help explain variance in measures of
lexical processing such as reaction times in visual lexical decision.

Figure 1: The average of the shift vectors for given singular-plural pairs
(table/tables, pen/pens) is used to calculate the semantic vector of the
unknown plural vector of banana.

The abovementioned studies associate each derivational exponent with one
conceptualization function that predicts the complex word from its base word.
Recent research on plural inflection has clarified that the semantics of
plurality can be too complex semantically to be represented by a single shift
vector. Chuang . (2022) observed that for Russian, a fusional language, the
shift vector for a singular to a plural noun embedding varies systematically
by each of the six cases. Nikolaev . (2022) report that also for Finnish, an
agglutinative language, plural shift vectors are different for each of the 14
cases. Furthermore, Shafaei-Bajestan . (2022) report that in English, shift
vectors are conditioned on the semantic class of the base word.

Figure 2: A projection of shift vectors (calculated from word2vec embeddings,
Mikolov ., 2013) onto a two-dimensional plane using the t-SNE dimension
reduction algorithm reveals semantic clustering ($N=11749$).  Each dot
represents a shift vector, one for each singular-plural pair. Three semantic
classes (based on WordNet) are highlighted: animals (red), persons (blue), and
communication words (green). If the semantics of pluralization would be
identical for all words, a single cluster with its centroid at a distance from
the origin would have emerged from the analysis. An interactive version of
this plot can be found here.

Figure 2 illustrates this phenomenon, highlighting three clusters of shift
vectors in a two-dimensional plane constructed with the t-SNE dimension
reduction technique (van der Maaten Hinton, 2008). T-SNE is designed such that
if observations cluster in a high-dimensional space, these clusters are (with
high probability) optimally visible and distinct in its two-dimensional re-
representation of this space. In Figure 2, words denoting people (e.g.,
president) are found predominantly in the lower right (in blue), words for
communication (e.g., language) cluster in the center-left (in green), and
words for animals (e.g., rabbit) are found in the upper right of the t-SNE
plane (in red). The grey dots represent nouns that belong to other semantic
classes.  Shafaei-Bajestan . (2022) propose to break down the set of nouns
into some 400 semantic classes, derived from WordNet (Miller, 1995). In this
way, overlap between clusters is reduced, and plural vectors constructed by
adding a class-specific shift vector to the vector of the singular are more
similar to the empirical vectors. Class-specific average vectors are
visualized with arrows in Figure 1 for the three example clusters.

We note here that in a t-SNE plane constructed for singular and plural
embeddings, plurals tend to occur very close to their singulars, and
semantically similar words tend to be relatively close together. What the
t-SNE analysis of the shift vector clarifies is that how plural vectors are
positioned with respect to their singular vectors varies considerably and
systematically by semantic class.

In English, words belonging to a semantic class are not overtly marked by a
specific exponent. Interestingly, there are languages that have
grammaticalized class-conditional plural semantics. Swahili, a Bantu language,
makes use of a large number of noun classes, many of which are semantically
motivated (Polomé, 1967). For instance, the m-wa class is used for persons,
the ma-ji class comprises words for objects that occur in clusters such as
fruits, and the ki-vi class covers artifacts and tools.  The Kiowa language
from the Tanoan language family, has nine semantically motivated noun classes
Harbour (2008, 2011). In contrast to English, Swahili and Kiowa have
grammaticalized interactions of semantic class and plurality, indicating that
speakers of these languages have made explicit in their grammars some
perceived differences in what it means to be a plural.

Further evidence for the grammaticalization of number by semantic class is
provided by languages with classifiers such as Mandarin Chinese (see, e.g. Yip
Rimmington, 2006). Constructions with numerals such as ‘two snakes’ require a
classifier before the noun, as in èr tíao shé, ‘two classifier snake’. The
classifier tiao is often found preceding long and flexible objects, such as
snakes and rivers. Mandarin classifiers thus group multiples of objects
together by their shape, size, or classes of artifacts (such as vehicles),
among many others.

Grammaticalization of number by semantic class is perhaps unsurprising as for
many concrete plural nouns, referents tend to occur in markedly different
configurations. This is illustrated in Figure 3. Oranges and apples appear in
groupings that are entirely different from the configurations in which cats
and dogs are typically found. It is remarkable that configurational properties
of multiples of objects are so well captured by word embeddings.

Figure 3: Multiples of different kinds of objects typically occur in different
configurations. The images for oranges and dogs are obtained without
modification from Vyagov (2021) and Gallice (2012). The images for apples and
cats, obtained from Khursheed (2014) and Park (2013), have been cropped.

The Kiowa noun system led Harbour (2008, 2011) to argue for a morphosemantic
theory of number. The studies by Nikolaev . (2022), Chuang . (2022), and
Shafaei-Bajestan . (2022) provide first steps in the formulation of such a
theory. Focusing on noun inflection in English, the finding that plural
semantics vary systematically by semantic class raises the question of how to
formalize the conceptualization process that underlies the use of singular and
plural nouns in English. Given a semantic vector $\bm{v}_{\text{sg}}$ for the
singular of a given lexeme, we can ask what kind of conceptualization
operation $\Phi$ is needed to map this singular onto the corresponding plural
$\bm{v}_{\text{pl}}$:

$\Phi(\bm{v}_{\text{sg}})=\bm{v}_{\text{pl}}.$ (1)

Shafaei-Bajestan . (2022) investigated two alternative implementations of
$\Phi$. The first implementation straightforwardly builds on the observed
clustering in the shift vector space.

$\Phi(\bm{v}_{\text{sg}})=\bm{v}_{\text{sg}}+\bm{v}_{\text{shift}\mid\text{semantic
class}}.$ (2)

For plurals that are ‘known’ and for which semantic vectors are available, a
plural vector is semantically decomposed in the following way:

$\bm{v}_{\textsc{pl}}=\bm{v}_{\text{sg}}+\bm{v}_{\text{shift}\mid\text{semantic
class}}+\bm{\epsilon}.$ (3)

In other words, known plurals are composed of the singular semantic vector, a
shift vector appropriate to the semantic class of their base words, and a
residual error vector that specifies the semantics that are specific to a
given plural form. As first pointed out by Sinclair (1991), regular inflected
words often have their own collocational profiles, which are part of native
speakers’ knowledge of the lexis of their language (see also Milin ., 2009;
Moscoso del Prado Martín ., 2004). In (3), this word specific knowledge that
is not predictable from the semantic class is represented by the error vector
$\bm{\epsilon}$.

For ‘out-of-vocabulary’ plurals, there is no error vector, and the semantic
vector predicted for these plurals simplifies to:

$\bm{v}_{\textsc{pl}}=\bm{v}_{\text{sg}}+\bm{v}_{\text{shift}\mid\text{semantic
class}}.$ (4)

This equation can also be used when evaluating how well the conceptualization
function $\Phi$ generalizes to data it has not been trained on. This approach,
which applies the approach to derivation of Kisselew . (2015) and extends it
to the English plural, was laid out in Shafaei-Bajestan . (2022). Following
their terminology, we henceforth refer to this method as Cosine Class Average
(CCA).

An alternative approach to plural conceptualization builds on the FRACSS model
of Marelli Baroni (2015), which was originally developed for derivational
morphology. When all singular semantic vectors are brought together as the row
vectors of a matrix $\bm{S}$, and all corresponding plural vectors are bundled
together as the row vectors of a matrix $\bm{P}$, a linear mapping $\bm{M}$
can be obtained by solving

$\bm{S}\bm{M}=\bm{P}.$

Given $\bm{M}$, the conceptualization function $\Phi$ is given by

$\Phi(\bm{v}_{\textsc{sg}})=\bm{v}_{\textsc{sg}}\bm{M},$ (5)

the embedding of a plural is decomposed as

$\bm{v}_{\textsc{pl}}=\bm{v}_{\textsc{sg}}\bm{M}+\bm{\epsilon},$ (6)

and for plurals for which an embedding is not available, the plural vector is
estimated by

$\bm{v}_{\textsc{pl}}=\bm{v}_{\textsc{sg}}\bm{M}.$ (7)

The conceptualization functions $\Phi_{\textsc{cca}}$ and
$\Phi_{\textsc{fracss}}$ implement two different ways of thinking about the
conceptualization of plural nouns. The perspective taken by
$\Phi_{\textsc{fracss}}$ is global in nature: to predict a plural meaning, one
needs to take into account the systematicities that govern all singular and
plural pairs. By contrast, the perspective taken by $\Phi_{\textsc{cca}}$ is
local in nature, the hypothesis being that it is only the systematicities
between singulars and plurals within the semantic class to which the lexeme
belongs that are relevant.

However, although $\Phi_{\textsc{cca}}$ straightforwardly implements the
structure that is revealed by the t-SNE analysis to be present in the high-
dimensional space of embeddings, precisely because it builds on semantic
classes, it is actually a complex theory: semantic classes are not
straightforward to define. FRACSS, by contrast, is a theory that takes as its
point of departure that there is a single plural operation. Because linear
transformations are quite powerful, it is possible that the linear
transformation of FRACSS will actually capture in its stride the semantic
conditioning that is revealed by the t-SNE analysis.

Shafaei-Bajestan . (2022) observed that the plural vectors predicted by
$\Phi_{\textsc{fracss}}$ and $\Phi_{\textsc{cca}}$ are in general very
similar. The former plural vectors were somewhat more similar to the word2vec
gold standard plural vectors in terms of angle, the latter vectors were
somewhat more similar in terms of vector length.  In order to assess the
relative merits of the two conceptualization functions, Shafaei-Bajestan .
(2022) therefore investigated the relation between plurals’ semantics and
their forms. Different approaches to clarifying this relation have been
proposed in the literature. Tamariz (2008); Shillcock . (2001); Monaghan .
(2014) compared distances in the form space to distances in a distributional
semantic space. Levy . (2021) employed methods from network science to build a
multi-layer network that connects a phonological network to a semantic
network. Lexical measures such as orthography-semantics consistency (Marelli
., 2015; Siegelman ., 2022) and phonology-semantics consistency (Amenta .,
2017) are now available for capturing the effects of form-meaning associations
on lexical processing.

Shafaei-Bajestan . (2022) addressed the systematicities between form and
meaning of English plural nouns using the Discriminative Lexicon Model (DLM)
proposed by Baayen . (2019). This computational model approximates
comprehension with a linear mapping from numeric form representations to
semantic vectors. A core assumption of the DLM is that the form space and the
semantic space are so similar and well calibrated to each other that simple
linear mappings are sufficient for obtaining high-quality (albeit not perfect)
predictions for meanings given forms (in comprehension), and for forms given
meanings (in production). Given that according to this model the mappings
between form and meaning are extremely simple, the quality of the model’s
predictions is critically dependent on the representations of form and of
meaning. Within this modeling framework, it is therefore essential to clarify
whether the semantic vectors of plurals are better aligned with words forms
when generated with FRACSS, or when generated with CCA.  Using form
representations that encode which triphones are present in a word’s form,
Shafaei-Bajestan . (2022) found that plural vectors obtained with
$\Phi_{\textsc{cca}}$ could be predicted more precisely from their forms than
plural vectors obtained with $\Phi_{\textsc{fracss}}$, especially when the
model was tested on held-out data.

A drawback of using form vectors that are derived from (tri)phones is that
phone-based representations do not do justice to both the richness and the
enormous variability of spoken words. The goal of the present study is to
clarify how well $\Phi_{\textsc{cca}}$ and $\Phi_{\textsc{fracss}}$ are
aligned with the audio signal.

In what follows, we report two experiments addressing this issue. The first
experiment follows Shafaei-Bajestan . (2021) and makes use of a version of the
Discriminative Lexicon Model that was developed specifically for auditory
comprehension: the LDL-AURIS model (Shafaei-Bajestan ., 2021). As this model
derives form vectors for word tokens from the audio files of these tokens, it
is well-suited to address the relation between specifically words’ speech
audio and their meanings.

The second experiment follows in the footsteps of Tamariz (2008); Shillcock .
(2001); Monaghan . (2014). These studies make use of distance measures, which
for words’ forms are based on orthographic or phone-based representations. In
section 3.1, we study the distances of form vectors that we extracted from the
audio files of word tokens, and compare these with the distances of semantic
vectors. Our question of interest is whether distances in ‘audio space’ are
more similar to distances in semantic space when plural meanings are estimated
with $\Phi_{\textsc{fracss}}$ or with $\Phi_{\textsc{cca}}$.

In what follows, we first introduce the dataset on which our analysis is
based. We then report the study using LDL-AURIS (section 3), followed by the
study using distances (section 4). We conclude with a discussion in section 5.

##  2 Data

Our data are taken from the NewsScape English Corpus 2016 (Uhrig, 2018, 2021).
This corpus is based on the US-American English-language recordings in the
UCLA Library Broadcast NewsScape. The corpus contains TV news, including
traditional newscasts and political talk shows as well as late-night shows and
daytime talk shows. The vast majority of the language recorded can thus be
assumed to be Standard English with a Network English accent. Overall, male
speakers contribute much more than half of the words. In a sample of shows
from broadcaster CNN for which transcripts were available online, even 80% of
the words were uttered by male speakers (Uhrig, 2021). In terms of age
distribution, younger speakers, especially children and teenagers, are
underrepresented. The initial audio quality is usually quite good because much
of the audio comes from recording studios, but the corpus also includes
footage from outside reporters. There are also programs with audiences, who
cheer and applaud, all reducing the quality of the audio signal.

For the year 2016, these recordings amount to more than 35,000 hours with
around 269 million tokens of subtitles. Directly after subtitle extraction,
the recordings are compressed to 240 MB/hour, using H.264 for the video stream
and the Fraunhofer FDK library to produce an AAC audio stream at 96 kbit/sec.
The subtitles were processed with Stanford CoreNLP (Manning ., 2014) version
3.7.0, i.e. annotated for part of speech with the Penn Treebank tagset using
CoreNLP’s caseless model.

Subtitles are not intended to be accurate transcripts of the words spoken. For
the sake of readability, they usually omit false starts, often leave out words
and phrases — in particular in fast dialogue — and are not designed to cope
with overlaps. Commercials often do not have subtitles at all. We thus expect
a certain error in the forced alignment, which is designed to align a
transcript with the corresponding audio recording. Due to the transcript
quality and the length of the recordings, most forced alignment systems are
not suitable for this use case. A slightly modified version of Gentle
(Ochshorn Hawkins, 2015), which markets itself as a “robust yet lenient forced
aligner built on Kaldi”111https://lowerquality.com/gentle/, was deployed on
the corpus. While the software reported a success rate of somewhere between
90% and 95% on average, we were able to select for inclusion only those files
where Gentle’s self-reported success rate was at least 97% because we only
needed a much smaller dataset than the entire corpus.

From this well-aligned part of the corpus, we selected 500 hours of programs
and extracted a total of 750,816 singular and plural audio word tokens of all
2062 orthographic word form types. The types were selected with the
constraints that their frequency was at least 70 in the 500-hour corpus and
that a word2vec semantic vector was available. Proper names, plurals endings
with anything other than an -s, plural-singular pairs with the same word form,
and named entities were excluded from the dataset.

The phonemic transcriptions that are provided in the NewsScape English Corpus
2016 were obtained with the Gentle forced aligner (Ochshorn Hawkins, 2015).
Gentle runs an automatic speech recognition process with a bigram language
model created from the transcript in the background. It is based on Kaldi ASR
(Povey ., 2011), which uses a purpose-built version of the CMUDict machine-
readable pronunciation dictionary (https://github.com/cmusphinx/cmudict) that
comes without stress information. Note that our dataset inherits the
pronunciation variants offered by CMUDict, i.e. the word either will be
represented either as [aðr] or as [i:ðr], depending on the pronunciation of
the speaker. However, not all pronunciation variants typically found in
American English are listed in the version of CMUDict used here. Thus don’t is
transcribed as [dont] or as [don], but vowel reductions that are typical of
fast speech in combinations such as don’t know, often rendered
orthographically as dunno, are not covered. Thus we have to be aware that
while our dataset offers some variation in pronunciation, which makes it more
ecologically valid than purely dictionary-based approaches without speech
recognition, it will contain instances where the transcript does not
correspond to the spoken form because the transcription of the spoken form was
not available in CMUDict.

##  3 Study 1: assessing the isomorphy of form and meaning with LDL-AURIS

###  3.1 Representations

For our investigations into the relation between spoken noun singulars and
plurals and their semantics, we set up three sets of 300-dimensional semantic
vectors. The first set of vectors based on pre-trained word2vec (Mikolov .,
2013) embeddings (for both singulars and plurals) was retrieved from Mikolov
(2013, Jul 30).222 In this study, we accept the embeddings of word2vec as
ground truth. A question we leave to further research is whether multi-modal
embeddings (see, e.g., Shahmohammadi ., 2021; Kiela Clark, 2017; Kiela .,
2015, for olfactory, auditory, and visual grounding of embeddings) will help
enhance the modeling of the conceptualization of plurality in English. For the
compilation of the other two sets, the vectors for singular words are
identical to those of the first set. For set 2, the plural vectors were
calculated according to $\Phi_{\textsc{cca}}$, and for set 3, according to
$\Phi_{\textsc{fracss}}$. The semantic classes used by the
$\Phi_{\textsc{cca}}$ conceptualization function are taken from WordNet
(Ciaramita Johnson, 2003; Fellbaum, 1998; Miller, 1995). For further details
on the granularity of the conceptual classes used, see Shafaei-Bajestan .
(2022).

For representing the speech signal of singular and plural nouns, we made use
of the Continuous Frequency Band Summary Features (C-FBSF) developed by
Shafaei-Bajestan . (2021). Figure 4 illustrates, for one example audio token
which can be accessed through the QR link in the upper right of the figure,
how these features are calculated. The algorithm takes the digital signal of a
word as input (top panel) and divides it into chunks based on the maxima of
the periodic parts of the signal. The MEL spectrogram (middle panel) for each
chunk is divided into 21 frequency bands, mirroring the frequency bands of the
cochlea. For each frequency band, an order-preserving random sample of length
20 is taken, and correlation coefficients of the values at the current
frequency band with those of the following bands are calculated and included.
These numeric vectors are concatenated first within chunks and then between
chunks (lower panel).

[hyperlink,height=1.5cm]http://go.redhenlab.org/pgu/0120

Figure 4: C-FBSF extraction for the audio of rendition of the word apple
(duration of $0.32\text{\,}\mathrm{s}$). Click here or scan the QR code to
listen to the audio. The top panel presents the waveform in dark gray, and the
smoothed Hilbert amplitude envelope of the signal in orange. The red vertical
lines indicate chunk boundaries, located at the local maxima of the Hilbert
envelope at $0.07\text{\,}\mathrm{s}$ and $0.23\text{\,}\mathrm{s}$. The mid
panel presents the corresponding log MEL spectrogram (using an FFT window size
of $0.005\text{\,}\mathrm{s}$) that depicts log energy values as colors over
time (shown on the x-axis) split at 21 auditory filter banks according to the
MEL scale (shown on the y-axis). The upper and mid panels are time-aligned.
Lower panel: a segment of the output C-FBSF vector that corresponds to the
first 7 sampled energy values from the 17th frequency band of the first chunk.
The length of the C-FBSF vector compiled from all three chunks and 21
frequency bands before zero-padding is 1953.

The dimensionality of the auditory space is determined by the number of chunks
in the longest word in the dataset, which is 4 for the present data. As a
consequence, the auditory space is 8,463-dimensional. All C-FBSF vectors are
zero-padded to match the 8,463 dimensions. For the audio token apple portrayed
in Figure 4, which has a duration of 0.32 seconds, an initial 1953-dimensional
vector is thus padded with 6510 trailing zeros.

###  3.2 Mapping audio vectors onto semantic vectors

The form vectors derived from the audio files were brought together as the row
vectors of a form matrix $\bm{C}$. The corresponding semantic vectors were
bundled as the row vectors of three semantic matrices $\bm{S}$: one with the
word2vec gold standard vectors, one replacing word2vec plural vectors with
FRACSS vectors, and one replacing word2vec plural vectors with CCA plural
vectors.

LDL-AURIS calculates a mapping $\bm{F}$ from the form matrix $\bm{C}$ to a
semantic matrix $\bm{S}$ by solving

$\bm{CF}=\bm{S}.$

We used the normal equations (Faraway, 2005) for the multivariate multiple
regression model to estimate $\bm{F}$, using the Moore-Penrose algorithm
(Moore, 1920) for matrix inversion. Once $\bm{F}$ has been estimated, we
obtain the predicted semantic matrix $\hat{\bm{S}}$ as follows:

$\hat{\bm{S}}=\bm{C}\bm{F}.$ (8)

We write $\hat{\bm{S}}$ rather than $\bm{S}$ because, as in regression, the
predicted row vectors $\hat{\bm{s}}$ of $\hat{\bm{S}}$ are not identical to
the gold standard row vectors $\bm{s}$ of $\bm{S}$. A specific predicted
semantic vector $\hat{\bm{s}}_{i}$ is judged to be accurate when it is closer
to the corresponding gold-standard vector $\bm{s}_{i}$ than to any other
semantic vector $\bm{s}_{j},j\neq i$. As a measure of semantic proximity, LDL-
AURIS uses the Pearson correlation.

###  3.3 Training data and test data

For evaluating the quality of a mapping $\bm{F}$, we split the data into
training and test sets using a stratified 10-fold cross-validation design with
respect to the word types. Cross-validation is a standard procedure in machine
learning for model evaluation. In 10-fold cross-validation, the dataset is
split into 10 parts (henceforth folds). Ten models are fitted on nine of the
folds, and are tested on the remaining fold. Stratification ensures that each
fold is appropriately representative of the whole dataset. We made sure that
all word types appear in every training and test set and that the relative
frequencies of audio tokens for each word type are preserved across training
and testing. Table 1 reports the number of types and the number of tokens
averaged over the 10 folds for singular and plural words, broken down by
whether the corresponding plural or the corresponding singular appears in the
training set.

Table 1: The number of word form types and the average number of audio tokens (and standard deviation) across 10 stratified folds. Dataset | Word form types | Average audio tokens (SD)
---|---|---
Train | 2062 | 675734 (1.26)
singular with plural | 475 | 273893 (6.26)
singular without plural | 979 | 243630 (9.10)
plural with singular | 499 | 141214 (7.95)
plural without singular | 109 | 16996 (4.81)
Test | 2062 | 75082 (1.26)
singular with plural | 475 | 30433 (6.26)
singular without plural | 979 | 27070 (9.10)
plural with singular | 499 | 15690 (7.95)
plural without singular | 109 | 1888 (4.81)

###  3.4 Procedure

For evaluating the three k ! LaTeX Error: File ‘algorithm.sty’ not found.inds
of predicted plural semantic vectors, we constructed the gold standard
semantic matrices $\bm{S}_{\text{\tiny{CCA}}}$,
$\bm{S}_{\text{\tiny{FRACSS}}}$, and $\bm{S}_{\text{\tiny{word2vec}}}$, each
of which contains row vectors for both singulars and plurals. The CCA and
FRACSS vectors for plurals were estimated with equations (4) and (7)
respectively. Using the form matrix $\bm{C}$, we calculated three mappings
$\bm{F}_{\text{\tiny{CCA}}}$, $\bm{F}_{\text{\tiny{FRACSS}}}$, and
$\bm{F}_{\text{\tiny{word2vec}}}$. Applying (8), we then obtained the
estimated vectors $\hat{\bm{S}}_{\text{\tiny{CCA}}}$,
$\hat{\bm{S}}_{\text{\tiny{FRACSS}}}$, and
$\hat{\bm{S}}_{\text{\tiny{word2vec}}}$.

It is worth keeping in mind that the rows of the form matrix $\bm{C}$ are all
distinct, and that the total number of rows in the $\bm{C}$ matrix equals the
number of audio tokens in our dataset. By contrast, many rows of the semantic
matrix $\bm{S}$ are duplicated, with as many duplicates for a given noun type
as there are tokens for that noun type. As the estimated semantic vectors are
estimates, the row vectors of $\hat{\bm{S}}$ are again all unique. However, if
the mappings are of good quality, the estimated semantic vectors for the audio
vectors of the same word type are expected to be highly similar.

We also note that because mappings are estimated for singulars and plurals
jointly, changing the semantic vectors of plurals will affect the semantic
vectors predicted for singulars. In other words, even though the form and
meaning vectors of singulars are identical across the three datasets, the
estimated singular vectors will be somewhat different, depending on the
quantitative properties of the plural semantic vectors.

We evaluated the quality of the estimated semantic vectors in two ways. First,
we calculated accuracy on both the training data and the test data. The
top-$N$ accuracy of the model is defined as the percentage of the test items
for which we find the predicted vector among the top-$N$ vectors with the
strongest correlations with the targeted output vector.

Since the word types have highly unequal frequencies with a Zipf-like
probability distribution, we also used the $F_{1}$ score (the harmonic mean of
precision and recall) to gauge the quality of the mappings $\bm{F}$ and the
different semantic vectors for plurals that these mappings predict.

###  3.5 Results

####  3.5.1 Recognitions

! LaTeX Error: File ‘algorithm.sty’ not found.

Figure 5 presents top-$N$ accuracy (for $N=1,2,\ldots,5$) for training data
(dark blue) and test data (light blue), for $\Phi_{\textsc{cca}}$ (left) and
$\Phi_{\textsc{fracss}}$ (right). Unsurprisingly, accuracy increases as the
criterion for accuracy is relaxed by increasing $N$. For $N=5$,
$\Phi_{\textsc{cca}}$ is successful for up to 25% of the training tokens and
22% of the test tokens. For $N=1$, accuracy on training is 15% and around 13%
for held-out data. The drop in accuracy for test data as compared to training
data is as expected. What is important is that the reduction in accuracy is
relatively small, an indication that the mappings are not severely overfitting
the data.

Figure 5: Top-$N$ accuracy of word recognition on the training set (dark blue)
and on the test set (light blue) for CCA (left) and FRACSS (right). The small
$1\mathrm{SE}$ error bars indicate that there is very little variability
across the 10 cross-validation folds.

Recognition accuracies are low. This is unsurprising, for various reasons.
First, it is worth noting that standard deep-learning speech recognition
systems do not perform well either on the task of isolated word
recognition.333Comparing the performance of LDL-AURIS with the performance of
two Automatic Speech Recognition (ASR) systems, DeepSpeech2 and Kaldi, on
98,883 audio tokens from the NewsScape 2016 corpus, Shafaei-Bajestan . (2021)
found that pre-trained Kaldi and pre-trained DeepSpeech2 performed at 22% and
20%, respectively, while LDL-AURIS trained on far fewer data performed at 12%.
It is for the recognition of connected speech that deep learning models show
truly impressive performance.

Second, the audio tokens used in the present study have all been cut
automatically based on the word boundaries identified during the forced
alignment process (see section 2). There are many instances in which these
cut-points do not coincide with the exact word boundaries, even if the
identification of such boundaries was possible at all.

Third, the models are trained and tested on auditory data spoken by numerous
speakers, with no prior speaker normalization. The speakers come from
different age groups and genders in diverse environments, some of which have
background noise.

For the purposes of the present study, the relative performance for plural
semantic vectors of the $\Phi_{\text{{fracss}}}$ and $\Phi_{\text{{cca}}}$ is
at the center of interest. A comparison of the left and right panels of Figure
5 clarifies that $\Phi_{\textsc{cca}}$ outperforms $\Phi_{\textsc{fracss}}$
for both training and test data.

Figure 6 spotlights the top 1 accuracy measure across 10 cross-validation
folds evaluated on the training sets and on the test sets for the three
mappings $\bm{F}_{\text{\tiny{CCA}}}$, $\bm{F}_{\text{\tiny{FRACSS}}}$, and
$\bm{F}_{\text{\tiny{word2vec}}}$, using box and whiskers plots. The mapping
using CCA reaches a median accuracy of 14.91% on the training sets and 12.95%
on the test sets, very close to the mapping that uses the semantic vectors
provided by word2vec for plurals (15.05% and 12.95% for training and test
respectively). The mapping using FRACSS plural vectors falls behind the CCA
plural vectors by a 4.34 and a 3.83 percentage-point difference in median
accuracy on the training and the test sets, respectively.

Figure 6: Comparison of the accuracy of CCA (blue), word2vec (red), and FRACSS
(green), evaluated with a stratified 10-fold cross-validation design on the
training and the test sets. The left panel shows the box plots for all
datasets crossed by methods. The panels on the right zoom in on individual
plots for improved readability. Each data point represents one fold.

As shown in Figure 7, when the performance of the mappings is evaluated with
weighted average $F_{1}$ scores,444A weighted averaged $F_{1}$ score is the
average of the $F_{1}$ scores for all word types weighted by the number of
true instances for each word type. the mapping using CCA outperforms the
mapping using word2vec, which in turn outperforms mappings based on FRACSS on
the training and the test sets of all folds.

Figure 7: Comparison between the weighted average $F_{1}$ scores for the
mappings using CCA (blue), word2vec (red), and FRACSS (green), evaluated with
a stratified 10-fold cross-validation design on the training and the test
sets.

We also compared the accuracy of these mappings with mappings that were set up
with semantic matrices for which the row vectors were randomly permuted,
breaking the relationship between words’ forms and meanings. As variability in
model performance turned out to be very small (see Figure 5), models were
trained and tested on just the first fold. The reduction in accuracy and
$F_{1}$ scores on the training and the test sets are reported in Table 2.
Consistent with the previous results, the reduction in performance under
random permutation is larger for CCA as compared to FRACSS for all dataset-
metric pairs.

Table 2: Reduction in accuracy and in weighted averaged $F_{1}$ score of LDL-AURIS on one cross-validation fold when the relation between form and meaning is broken by randomly permuting the rows of the semantic matrix. Model | Reduction in accuracy | Reduction in $F_{1}$ score
---|---|---
| training | test | training | test
FRACSS | 0.091 | 0.088 | 0.074 | 0.073
CCA | 0.135 | 0.126 | 0.093 | 0.088

As a final check on the quality of the two implementations of plural
conceptualization, we examined accuracy for four subsets of the data, defined
by the combinations of the singular and plural forms that were available to
the model for training. Figure 8 clarifies that accuracy was highest for
singular tokens the plural token of which also was encountered during
training. The group with the second-highest accuracy comprises plural tokens
that have a singular token in the training set. Accuracies are substantially
lower for singular and plural tokens that were not accompanied by a
corresponding plural or singular token during training. (For the counts of
auditory tokens within each group, see Table 1 above). For both
conceptualization methods, recognition accuracy benefits from training on
tokens of both numbers. Comparing CCA (left panel) with FRACSS (right panel),
we can conclude that CCA accuracies are greater than those for FRACSS, except
for held-out plurals that have no corresponding singulars in the training
dataset.

Figure 8: Within-group accuracy for different word groups. In group names, sg
stands for singular, pl for plural, w for with and w/o for without. A word in
the sg w/o pl group is a singular word whose plural form is not in the
training set. CCA accuracies are greater than those for FRACSS, except for
held-out plurals that have no corresponding singulars in the training dataset.

In summary, higher accuracies and higher higher average $F_{1}$ scores were
obtained with CCA compared to FRACSS, across both training and test data.

####  3.5.2 Errors

The confusion matrices in Figure 9 summarize the predictions of the models for
the items in the training set.555The results on the test set are very similar
and reported in the supplementary materials. Rows correspond to the number
feature for the target word: singular words are counted in the first row and
plural words in the second row of each matrix. The columns group words by the
four combinations of number and whether the lexeme is properly predicted.
Errors are highlighted in red and correct recognitions are highlighted in
blue. In addition to the absolute number of tokens, the percentage with regard
to the sum of the row is given in each cell. Training with plural vectors
obtained with CCA gives rise to larger numbers of correctly predicted target
words in the plural as well as in the singular group.

Figure 9: Confusion matrices for the performance of LDL-AURIS with CCA (top)
and FRACSS (bottom) vectors on the training set. Correct predictions appear in
blue and wrong predictions appear in red. Percentages are normalized to the
sum of rows. $N_{\text{SG}}=517,529$, $N_{\text{PL}}=158,204$ for both
matrices.

The two models rarely confuse number when they correctly predict the lexeme.
However, when a lexeme is not recovered correctly, the two models make
remarkably different kinds of errors. For plural vectors generated with CCA,
the predicted and targeted word types tend to match in terms of number. By
contrast, when plural vectors are generated using FRACSS, the mapping mostly
predicts plural forms irrespective of the target word’s number.

Overall, 81% of the predictions of the mapping using CCA match the target in
terms of number. This percentage reduces to only 50% for models with plurals
generated by FRACSS.666The estimated difference in proportions between groups
at 0.308 is supported by a proportions test (95% confidence interval of 0.306
and 0.309, $\chi^{2}(1)=140897$, $p\ll.0001$). Apparently, FRACSS introduces a
bias for plural semantics. This bias may arise due to FRACSS predicting all
plurals to be more similar in their semantics, resulting in a strong attractor
not only for plurals but also for singulars. From a methodological
perspective, these findings point to the importance of considering predicted
plural vectors not just in isolation, but within the full noun system that in
addition to plurals also contains singulars.

Apparently, plural vectors generated by $\Phi_{\text{{cca}}}$ are better
aligned with information about number in the audio signal than is the case for
plural vectors generated by $\Phi_{\text{{fracss}}}$. This suggests that the
global perspective of FRACSS, which takes all singular-plural pairs into
account, rather than just those singular-plural pairs that belong to a
conceptual class and that share a shift vector, is suboptimal.

It is surprising that the FRACSS method, which is quite powerful as the
underlying linear algebra allows for various geometric modifications such as
scaling (stretching or shrinking) and rotation, performs somewhat less well
than CCA, a method that from a geometric perspective only implements shifts
between vectors. On the other hand, CCA needs to be informed about semantic
classes and assumes that these are given, but setting up these classes is not
trivial.

###  3.6 An alternative approach

The models so far were built on the assumption that error vectors
$\bm{\epsilon}$ in Equations 3 and 6 are all measurement noise and reducible.
Thus, audio-to-semantic mappings were trained and evaluated using predicted
plurals by the CCA or the FRACSS conceptualization methods, which build plural
vectors without the error term.

Alternatively, one might assume that error vectors in Equations 3 and 6 are
entirely word-specific semantic information and irreducible. Although we
believe, avoiding both of these extremes, the error term comprises measurement
noise and word-specific knowledge, the second extreme approach is taken in the
following for empirical reasons. Therefore, audio-to-semantic mappings can be
trained using the predicted plurals by CCA or FRACSS but they should be
evaluated using the corpus-extracted vectors, which contain the error term.

Accordingly, we evaluated the two conceptualization methods by employing the
corpus-extracted word2vec embeddings as gold standard, and comparing the gold
standard with semantic vectors predicted by the previously obtained form-to-
meaning mappings $\bm{F}_{\text{\tiny{CCA}}}$ and
$\bm{F}_{\text{\tiny{FRACSS}}}$. For this evaluation, we used the data of the
previous cross-validation study. The word2vec vectors are brought together as
the rows of a matrix $\bm{S}_{\text{\tiny word2vec}}$. We estimated plural
vectors for the test set, and defined a plural vector to be accurate if it was
most correlated with the corresponding vector of $\bm{S}_{\text{\tiny
word2vec}}$.

Accuracies obtained from the second evaluation approach are reported in Figure
10. They are slightly higher for FRACSS for Top 1 evaluation, and slightly
higher for CCA for Top 2–5 evaluation. Both of the trained mappings get
approximately equally close to the empirical word2vec plural vectors. This
suggests that neither CCA nor FRACSS plural vectors are very different from
word2vec plural vectors. The results provide further evidence for the
observation by Shafaei-Bajestan . (2022) that CCA and FRACSS vectors are
generally similar to word2vec vectors. In their study, predicted plural
vectors by CCA and FRACSS were compared with corpus-extracted plurals using
cosine similarity as the measure (a median cosine similarity of 0.71 for CCA
and 0.75 for FRACSS).

These accuracies are within the range of accuracies observed in Figure 5,
which were obtained with CCA and FRACSS vectors as gold standard for
evaluation. From this analysis, we conclude that the CCA, FRACSS, and
empirical vectors are of very similar quality, and that the low word
recognition accuracy is not due to low quality of these vectors, but to the
enormous variability in the speech signal and the noise in our data.

Figure 10: Top-$N$ accuracy (%) of mappings from audio to semantics, trained
either with CCA or FRACSS vectors, but evaluated with word2vec vectors as gold
standard. The small $1\mathrm{SE}$ error bars indicate that there is very
little variability across the 10 cross-validation folds.

##  4 Study 2: assessing the isomorphy of form and meaning with distance
measures

We have seen that within the framework of the DLM, semantic vectors
conceptualized with $\Phi_{\text{{cca}}}$ enable a better mapping between
words’ audio and their meanings compared to $\Phi_{\text{{fracss}}}$. In this
section, we compare the two conceptualization functions with a method that
does not depend on the assumptions of the DLM, such as that the form space and
the semantic space can be transformed into each other simply using linear
mappings.

In what follows, we follow in the footsteps of Monaghan . (2014), and
investigate possible parallelism between the form space and the meaning space
using distance measures. Monaghan . (2014) reported that phone-based form
similarity (gauged with Euclidean distance and edit-distance measures)
correlated weakly ($r\approx 0.03$) yet significantly with semantic similarity
(gauged with the cosine similarity measure between contextual co-occurrence
vectors). They observed correlations for monosyllabic words, uninflected
lemmas, and monomorphemic polysyllabic words.

We calculated, for all pairs of words, both phone-based and audio-based
measures of their form similarity. In parallel, we calculate the semantic
similarity for these pairs of words, using both the original word2vec vectors
for plural nouns, as well as plural vectors generated with FRACSS and
generated with CCA. For the calculations, the audio tokens from the test set
of the first fold of the data (see section 3.3) for which phonemic information
was also available were used ($N=60206$, $V=2057$).

First, we calculated the Damerau–Levenshtein edit distance for all pairs of
word types in our dataset, which unlike the dataset of Monaghan et al., is
restricted to singular and plural nouns. We then calculated the Pearson
correlations between these phone-based edit distances on the one hand, and the
cosine distances777The cosine distance zooms in on the angle between two
vectors, ignoring differences in length. The greater the angle between two
vectors, the greater their cosine distance is. between the semantic vectors of
these word pairs on the other hand, using three different semantic vectors for
plurals: the word2vec plural vectors, the plural vectors obtained with FRACSS,
and the plural vectors obtained with CCA.

The upper part of Table 3 presents the correlation $r$ between the form and
meaning distances for all word pairs. These correlations are smallest for
FRACSS, intermediate for word2vec, and greatest for CCA (all $p<.0001$). The
correlations observed for vectors are of the same order of magnitude as the
correlations reported by Monaghan . (2014). For a random permutation of the
word2vec vectors, the correlation was reduced by a factor of 10 to 0.004. Our
replication study shows, first, that there is indeed some isomorphism between
the form space and the semantic space; and second, that the observations of
Monaghan . (2014), which were based on uninflected words, generalize to plural
inflection. Importantly, this analysis shows that, consistent with the results
reported in the previous section, CCA-based semantic vectors provide stronger
correlations between form distances and semantic distances than FRACSS-based
semantic vectors.

Table 3: Correlations between phone-based and audio-based form distances and semantic distances for three different semantic spaces: CCA, word2vec, and FRACSS. For the audio-based analysis correlations averaged over many samples of audio tokens are reported, with $\mathrm{SD}$ and the number of trials $N$ in which the correlation was significant at $\alpha=0.05$. Form distances | statistic | CCA | word2vec | FRACSS
---|---|---|---|---
phone-based | $r$ | 0.061 | 0.041 | 0.038
audio-based | $\bar{r}$ | 0.019 | 0.015 | 0.007
| $\mathrm{SD}$ | 0.003 | 0.003 | 0.005
| $N$ | 1000 | 1000 | 908

For assessing the isomorphy between the form space and the semantic space
using the speech signal instead of phone-based representations, we again
compared all pairs of words, assessing their semantic distance with the cosine
distance, and evaluated the dissimilarity of their speech signals by means of
the Euclidean distance between their C-FBSF form vectors, which were
calculated from the speech signal as described above in section 3.1.888By way
of example, the list of the top 10 nearest neighbors of an audio token of the
word positions includes two other audio renditions of the same word form
positions, one audio token of the singular form position, four tokens with
similar word-initial phones (protester, process, procedures, and perspective),
and three tokens with similar sounding word-final syllables (information and
conditions). As can be seen in Figure 11, audio-based distance increases with
phone-based edit distance ($r(1,812,351,113)=0.3$, $p<.0001$). As expected,
the variability in the audio-based distance as a function of phone-based
distance is huge.

Figure 11: Auditory Euclidean distance as a function of phone-based edit
distance.

To avoid comparing audio tokens of the same inflectional word type, which is
likely to inflate similarity compared to a phone-based analysis in which types
do not have non-identical replicates, we randomly sampled for each word type
one audio token and then calculated the form distance for each pair of the
selected tokens. Subsequently, the correlation between the form distances and
the semantic distances of all pairs of inflectional word types was computed.
This procedure was repeated 1000 times. The lower part of Table 3 presents
summary statistics for the audio-based comparisons of form and meaning. The
average correlations across trials $\bar{r}$, the standard deviations
$\mathrm{SD}$, and the number of trials $N$ for which the correlation was
significant at $\alpha=0.05$ are reported.

Correlations are greatest when semantic vectors are estimated with CCA, and
weakest when they are estimated with FRACSS. Randomization of the word2vec
semantic vectors resulted in reduced correlations ($M=0.003$,
$\mathrm{SD}=0.003$). The number of trials in which a significant correlation
was observed decreased from 1000 to 744.

The audio-based correlations are substantially lower than the phone-based
correlations. This is unsurprising, as the phone-based analysis do not take
into account the huge variability in the speech signal and the highly reduced
forms that speakers use in daily speech (see, e.g., Johnson, 2004). The small
magnitudes of these correlations clarify that evaluations of the similarities
between form and meaning run the risk of overestimating these similarities
when based on letter-based or phone-based representations. At the same time,
it is surprising that significant correlations, however small, can be detected
with this method for real, highly diverse, and noisy speech.

Importantly, our audio-based evaluation of the isomorphism between form and
meaning provides further support for the possibility that plural vectors
conceptualized with $\Phi_{\text{{cca}}}$ provide a better match with plural
forms compared to $\Phi_{\text{{fracss}}}$. Above, we showed that
$\Phi_{\textsc{cca}}$ is optimal for predicting meaning from form, using a
linear mapping within the framework of the DLM. The present observations
clarify that this result is unlikely to be an artifact of this linear mapping.
Plural vectors created with $\Phi_{\textsc{cca}}$ better mirror similarities
that exist in the form space.

##  5 General Discussion

Shafaei-Bajestan . (2022) showed that shift vectors, which represent the
change in meaning when going from a noun’s singular to its plural, cluster by
the semantic class of the base word. Apparently, modeling the semantics of
plurality in English with a single shift vector in semantic space, does not do
justice to the intricacies of the English noun plural. Likewise, formal
accounts of plurality based on abstract features such as [+plural] lack
precision. From a typological perspective, languages such as Swahili and Kiowa
have grammaticalized semantic-class-based differences in their noun classes,
languages such as Mandarin Chinese, Japanese and Korean make use of
classifiers that are often linked to semantic classes, whereas in English,
systematic differences between words’ referents are present only in the
semantics as ‘soft constraints’ (see also Corbett, 2000).

The dependence on semantic class that characterizes the English noun plurals
raises the question of how to account for the conceptualization of plurals. Do
we have to construct different plural shift vectors for each semantic class
(CCA)? Or is it possible to predict a noun’s plural meaning from a general
rule that is informed by all singular and plural nouns in the language
(FRACSS)?

Shafaei-Bajestan . (2022) addressed this question using the Discriminative
Lexicon Model, and observed that semantic vectors for plurals generated with
CCA were better aligned with triphone-based form vectors than plural vectors
generated using FRACSS. The present study investigated whether this result
generalizes to spoken language. Using the form vectors calculated from the
speech signal of a large number of audio tokens extracted from the NewsScape
resource, we observed that the semantic vectors generated by CCA can be
predicted with greater precision from their audio than is possible for plural
vectors generated by FRACSS. This holds both for training data and test data.
Furthermore, randomly pairing of form and meaning vectors degrades accuracy
more for CCA than for FRACSS.

The superior alignment of the CCA vectors with the form space, compared to
FRACSS, received further support from a series of analyses that do not depend
on the linear mappings of the Discriminative Lexicon model, and instead
follows up on a study by Monaghan . (2014). For each possible pairing of words
in our dataset of singular and plural nouns, we calculated their distance in
semantic space as well as their distance in form space (using both phone-based
and audio-based distance measures). Correlations of the distances in form and
meaning were stronger for plural vectors obtained with CCA compared to plural
vectors obtained with FRACSS. Considered jointly, we can conclude that
approximating the conceptualization of noun plurals in English with CCA likely
offers a more precise window on the processing of English noun singulars and
plurals in the mental lexicon, the reason being that a better alignment of
form and meaning implies greater regularity and hence facilitation of lexical
processing.

It is surprising that FRACSS does not perform as well as CCA, as the linear
mapping that FRACSS makes use of is more powerful than the simple vector
addition that CCA employs. In fact, given the common assumption that
pluralization is a unitary operation, a linear mapping as proposed by FRACSS
makes sense: A global singular-meaning-to-plural-meaning mapping is informed
by all the singular and plural nouns experienced by the language user, and can
be expected to make optimal use of the shared semantic similarities that are
supposed to exist between all singular and plural nouns. However, careful
inspection of the distributional semantics of English noun plurals shows that
in this language, the semantics of pluralization is not as uniform as
previously supposed. Conceptualization of English plurals is much more locally
determined. As a consequence, taking into account how nouns in distant
semantic classes are pluralized appears to be detrimental to prediction
accuracy.

When comparing FRACSS with CCA, however, it should be noted that CCA takes for
granted that information is available about which semantic class a lexeme
belongs to. As semantic classes are not straightforward to induce in a bottom-
up manner — we made use of WordNet — CCA is given much more refined
information to work with compared to FRACSS. In terms of model complexity, CCA
is therefore likely to be the more complex model. But this increased
complexity appears to be justified by greater prediction accuracy.

We conclude with placing the present study in the wider context of research on
spoken morphology. The data considered in our study are restricted to lexemes
that take {S} as the exponent for plurality. Recent studies on English word-
final /s/ have clarified that the acoustic duration of /s/ varies
systematically with the semantics realized with the /s/ (Plag ., 2017;
Tomaschek ., 2019). In other words, an exponent that in standard theories is
assumed to be realized in exactly the same way, independent of its function,
is now known to be articulated in ways that reflect its function. One of the
functions of /s/ considered in these investigations is the realization of
plurality on nouns. The present study provides evidence that pluralization for
English nouns is not a monolithic and general semantic operation, but varies
with the semantic class of the base word. Importantly, we have shown that
these differentiated plural semantics are aligned with words’ audio signal.
The way in which plurals are articulated therefore depends on the semantics of
their base words. All that we have accomplished in the present study is
demonstrate this fact. In what way these different class-specific semantics
are realized in the speech signal is at present unknown, and is a topic for
further research. A better understanding of the phonetic realization of
English plurals may further our understanding of why deep learning models in
natural language processing and artificial intelligence, which are superbly
tuned to the distributional statistics of language use, are so successful.
This, in turn, may contribute to enhancing models of lexical processing in the
mental lexicon.

### Acknowledgments

This research was made possible by funding from the ERC, project WIDE-742545,
awarded to RHB, and by funding from the Competence Network for Scientific High
Performance Computing in Bavaria to PU. The authors are indebted to two
anonymous reviewers, Jessica Nieder, and Melanie Bell for their critical and
constructive feedback on our manuscript.

### Authors’ contributions

ESB and RHB conceptualized and designed the study. PU collected and processed
the NewsScape data. ESB created the materials in consultation with PU. ESB
implemented the simulations. All authors were involved in the data analyses
and interpretation. All authors were involved in drafting the manuscript.

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