Seeing through the mess: evolutionary dynamics of lexical polysemy
Authors: Andreas Baumann
Andreas Stephan
Benjamin Roth
Venue: EMNLP 2023 Main (2023)
Keywords: polysemy
language change
mathematical modeling
adaptive dynamics
senses
frequency
non-conformism
discriminability

Abstract: Evidently, words can have multiple senses. For example, the word mess refers to a place to have food or to a confusing situation. How exactly multiple senses emerge is less clear. In this work, we propose and analyze a mathematical model of the evolution of lexical meaning to investigate mechanisms leading to polysemy. 

This model features factors that have been discussed to impact the semantic processing and transmission of words: word frequency, non-conformism, and semantic discriminability. We formally derive conditions under which a sense of a word tends to diversify itself into multiple senses that coexist stably.

The model predicts that diversification is promoted by low frequency, a strong bias for non-conformist usage, and high semantic discriminability. We statistically validate these predictions with historical language data covering semantic developments of a set of English words. Multiple alternative measures are used to operationalize each variable involved, and we confirm the predicted tendencies for twelve combinations of measures.

Seeing through the mess: evolutionary dynamics of lexical polysemy
Andreas Baumann', Andreas Stephan Benjamin Roth
Faculty of Philological and Cultural Studies, FFaculty of Computer Science, Uni Vie Doctoral School Computer Science DoCS
University of Vienna, Austria
(andreas, baumann, andreas. attreas. innrraaassttppaaae..aaniinnnnn roth]nnnivieeee at
benjamin.
Abstract
a
building noon providng
Evidently, words can have multiple senses. For example, the word refers place to have food or to a confusing situation. How exactly multiple senses emerge is less clear. this work, propose and analyze mathematical model of the evolution of lexical meaning to investigate mechanisms leading polysemy.
company of people wiiling logedher
senses mess
A quaniiyy milicooodd
A large amount or quantity sarnaiing.
Meros unilyty diny.
Arrry uniley state thanga place.
misanalle enterprionn
This model features factors that have been dis- cussed impact the semantic processing and transmission of words: word frequency, non-
time first attestation in OED
sentiment value miss in 1850
conformism, and semantic discriminability. We formally derive conditions under which of a word tends to diversify itself into multiple senses that coexist stably.
senses mess
X
nag
pos
'portion soup'
erobitonsyy time
X X1850
X
(disgusting) portion of soup"
X1900
The model predicts that diversification is pro- moted by low frequency, strong bias for non- conformist usage, and high semantic discrim- inability. We statistically validate these pre- dictions with historical language data cover- ing semantic developments of a set of English words. Multiple altermative measures are used operationalize each variable involved, and we confirm the predicted tendencies for twelve combinations measures.
X
stable stance
(disgusting) portion of soup
1050
X1950
'contusing situation
sentiment dimension
Figure I: (a) Evolutionary tree of the senses of mess based on first dates of attestation as documented in the Oxford English Dictionary (OED). (b) Schematic sketch of the diversification of mess in the semantic dimension of sentiment (negative to positive).
time and diversifies itself as additional senses are established in the population speakers (Trau- gott, 1985; Deane, 1988; Sagi et al., 2011; Mitra et al., 2014; Hamilton et al., 2016; Hu et al., 2019; Schlechtweg et al., 2020). Figure la displays the evolutionary tree of the semantics of the word mess.
1 Introduction
In natural language, lexical polysemy, i.e., the pres- ence of multiple senses for single word form, is the rule rather than the exception. The word mess, for instance, can denote, among other things, room in which food served, semi-liquid food, confusing situation, or physical state of disorder. From a communicative point of view, the fact that one form refers to multiple senses is, at first sight, sub-optimal given that ambiguity acts against suc- cessful communication. Yet, populations of speak- ers sustain multitude of polysemous words in their communicative systems, viz, languages.
The goal of this paper is to identify conditions under which semantic diversity is enforced with the help of analytic models of the population dy- namics of words. More specifically, we define model of the spread of words through popu- lation of speakers in which word transmission is governed by social and cognitive factors that have been suggested to be relevant to semantic change: word frequency, non-conformism, and semantic discriminability. An analytical assessment of our model shows that these factors indeed affect the
Where does this semantic diversity come from? Evidently, multiple senses a word do not just simply appear. Rather, word meaning evolves over

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tendency to establish additional senses in speaker populations. The predictions of the model are sub- sequently tested against empirical language data.'
that defines the short-term dynamics of lexical us- age in speaker population. In combination, the model lets us show that diversification of meaning is encouraged for words subject to low frequency, high non-conformism biases, and high semantic discriminability (cf. Table 1).
2 Approach
We consider three factors that have been suggested to be relevant to lexical transmission, semantic pro- cessing, and change (frequency, non-conformism, discriminabillty;; see Background section below). The question is if and how these factors impact the diversification of a word's meaning, and, more importantly, what the potential mechanisms lead- ing to diversification might be. Our approach to tackle these questions involves two parts, namely a theoretical and an empirical part.
Note that although the model would, provided all necessary historical information, theoretically allow us to obtain semantic trees for single words and single semantic dimensions (like 'sentiment', "edibility", "objectness") similar to the one in Figure la, this is not what we do. We also do not need to focus on the linguistic behavior of individual speak- ers. Rather, the strength of our model is that we can use it to predict more generally under which conditions semantic diversification the population level. Thus, our model reveals po- tential mechanisms governing the establishment of multiple coexisting senses.
On the theoretical level, we model the evolution of word's meaning over time and analyze under which conditions a word's 's meaning split into two separate and stably coexisting senses. This model captures the population dynamics of the semantic variants of a word, that is, we investigate how word variants spread through a population of speakers. Interactions among speakers and how they transmit word variants are governed by effects of frequency. non-conformism, and discriminability that we as- sume beforehand.
occur
On the empirical level, we measure the impact of frequency, non-conformism, and discriminabilityy on the tendency to diversify meaning. We base our analysis on historical language data covering about 3000 English words (Hu al., 2019). Based on this data set, we show that the predictions of the theoretical model are also supported on empirical grounds.
More concretely, we assume (i) that the success- ful transmission of a word variant from one individ- ual to another is more likely if it is used frequently, (ii) that rare linguistic behavior can have an ad- vantage during interactions as it stands out, and (iii) that the cognitive ability to discriminate be- tween senses impacts what is actually perceived as the same or different linguistic behavior in inter- actions. Table shows more details about these assumptions. Note, crucially, that none of these assumptions is about semantic long-term evolution per se. All of them are exclusively about how in- dividuals communicate and process language in short-term interactions.
In what follows, motivate our choice of fac- tors in semantic evolution, present an outline of the evolutionary model, its underlying population dynamics, and its predictions of how long-term evolution unfolds. After that, we describe the setup and outcome of our empirical account. The discus- sion section links both parts of this study.
Background
We adopt the established definition of polysemy as a one-to-many form-meaning mapping that comes about via changes on the meaning side. The key cri- terion here is historical relatedness (Leecch, 1974; McMahon, 1994). This contrasts with the phe- nomenon of homophony (e.g., steak vs. stake), which results from changes on the form side (see Valera, 2020, for more recent discussion).
Based on the model, we deduce the evolutionary dynamics of word's meaning and we derive which effects of frequency, non-conformism, and discrim- inability on the tendency to diversify meaning the model would predict.
Multiple factors have been suggested to impact semantic change and the evolution of polysemy. In this research, we consider three of them that have been discussed in the linguistic, cognitive, and computational literature.
Mathematically, our model consists of two stacked dynamical systems defined by ordinary differential equations: one that defines the long- term evolutionary dynamics of meaning, and one
The most prominent factor that was suggested to impact lexical semantics is the word frequency.
"oode and data available at https: httpps//gitlab..oo com/ andreas. baumam/eevolutioo_lexiieee _polsseeyyyyyy

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Frequency 9
Non-conformism bias 8
Discriminability 6
Definition
Number of occurrences of a word variant
Tendency at which a word vari- ant is used non-conformist vs. conformist settings Fraction of frequency in non- conformist genres vs. fre- quency in conformist genres
Ability to distinguish between two semantic uses of word
Empirical measure- ment
Normalized token frequency of a word (contemporary vs. his- torical)
Lexical concreteness ratings and average correlation be- tween sentence embeddings of all sense descriptions of word Modulates effects of (non-) con- formist behavior in interactions among individuals using differ- ent variants of word T ~ 8 v
Model assumptions about interactions
High
exposure increases chance of successful adoption in interactions
Imposes advantage in the propa- gation of the word variant when rare (common strategies lose their distinctive status)
Prediction
T~1 1/p V
''' ~ 5
Table Overview of the main model parameters, how they are defined and measured, and their respective impact the tendency to diversify meaning T as predicted by the model. A check-mark (v) indicates whether the predictions are empirically supported.
their seminal contribution, Hamilton et al. (2016)
itive connotation (this particularly holds true for slang with its function to signal out-group mem- bership) (Fajardo, 2019). The initial salience of these words, however, becomes weaker the more abundantly they are used.
have demonstrated that high-frequency words are,
the historical time scale, more stable than low- frequency words (but see Dubossarsky et al. (2017) for criticism).
The negative relationship between semantic change and frequency was suggested to be an effect of entrenchment (Hamilton et al., 2016; Cassani et al., 2021; Baumann et al., 2023). Frequent words are typically learned early, and this leads cogni- tive entrenchment, i.e., routinization of their pro- cessing and usage (Bybee, 2006). By consequence, it is less likely for feguffrey words to change their semantic profile than this might be the case for low-frequency words that could be, perhaps erroneously, used in novel contexts.
Non Non-conformisse is counteracted by conformism, i.e., the disproportionally high tendency to behave just like the majority does (Henrich and Boyd, 2002). Conformism functions stabilizing mecha- nism in the transmission of communicative systems. Intuitively, conformism biases should prevent se- mantic ambiguity since the introduction of novel senses is discouraged.
The third factor, discriminability. refers to in- dividual's ability to discriminate between two con- textual uses of a word (Miller and Charles, 1991; Miller, 1999). Intuitively, if discriminability is high then individuals are less likely to view two different uses a word as belonging to the same sense (for instance, if individuals can discriminate well, they would suggest the word mess to have two different senses in the utterances I see through the mess and I have burger in the mess). There is much less search on the effect of semantic discriminability on language change than for the other two factors dis- cussed above, but modeling and simulation results suggest that high discriminability entails more com- plex signaling inventories (Chaabouni et al., 2021; Imel, 2023). From a cognitive point of view, inter- dependencies among word utterances are weaker if they are (perceived being) diffferent from each other, i.e., in the case of high discriminability (den Heyer and Briand, 1986). This also extends interdependencies imposed by (non-)conformism pressures in interactions among individuals (Kim and Hommel, 2015).
The second factor that was suggested to in- crease diversity in the domain of cultural evolu- tion is that of non-conformist behavior, i.e., to behave differently than the majority does. Non- conformist behavior entails what referred to as negative frequency dependence (Efferson et al., 2008; Boyd and Richerson, 1988; Doebeli and Is- polatov, 2010a). That is, behavioral strategies are particularly successful if they are rarely employed. Non-conformist behavior is present in the lin- guistic domain as well. For one, several phenom- ena of linguistic innovations have been discussed under the notion of linguistic extravagance. Speak- ers have been argued to choose unorthodox lin- guistic strategies to stand out, get recognized, and in turn to promote the transmission of their mes- sage (Ungerer and Hartmann, 2020; Detges and Waltereit, 2002: Petré, 2017: Hein, 2017: Haspel- math, 2000). Often, extravagant linguistic behavior extends to the semantic domain. So, originally negative words like awesome have gained a pos-

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4 Theoretical analysis
In our context, the canonical equation of adaptive dynamies models change in a semantic property. More specifically, defines the rate of change of x in the semantic subspace X as a function of (a) the number of users of the word variant characterized by z, and (b) the fitness of the word variant relative to another variant:
Our model has the following components: We as- sume that words are transmitted through popula- tions of speakers. At any point in time, each word has set of one or more senses that we take to constitute word's meaning. We assume that each word sense can be represented as real value on a semantic dimension.
0f(z. dy y=
i - C. (x))
(1)
More specifically, we assume that x takes a value on a continuous scale so that x E X where X C R is a real-valued interval representing the range of possible values the semantic dimension. For instance, X could represent the word's sentiment ranging from 0 (negative) to 1 (positive). Then, sense of a word like mess might have had a rather positive sentiment of about x = 0.8 in the middle of the 19th century.
Here, C. > 0 is a constant defined by the rate and variance of semantic innovations that is in- dependent of the semantic property 2. Further- more, (xx) denotes the number of users U of the word sense characterized by the value x on the semantic dimension at population dynamic equilib- rium. 3 Intuitively, this means that a higher number of users facilitate larger amounts of change (be- cause each user could introduce an innovation). Finally, fx, v) denotes the fitness, i.e., the growth rate of a word variant with slightly different value of the semantic property y E X in population of individuals mainly using the word variant char- acterized by value x. This quantity referred to as invasion funess because determines whether or not a new variant can successfully invade to be used by the speaker population (for a visualiza- tion of f, see Figure 4 in Appendix 1.1.2). The term af v) u)/0yly- determines the direction of evolution.
Speakers might introduce a new variant of an already existing word sense. This happens, for in- stance, when someone starts using word sense in slightly different context (e.g., 'potentially disgusting soup' rather than just 'soup'). When this innovative behavior is adopted by the speaker population, the semantic value æ of a word sense changes within X.
Note that this only means that a certain semantic property of a sense changes. The introduction of an innovative variant of an already existing vari- ant does not automatically entail that both of them coexist stably in the speaker population. Stable coexistence would mean that the semantic value representing one sense splits into two variants de- fined by two values 21 and x2 within X that now represent two separate senses (i.e., a more posi- tive and a more negative sense of mess) that are both sustained by the speaker population. Such a scenario is schematically visualized in Figure 1b. The crucial question is under which conditions are splits like this possible?
Equation (1) can exhibit different types of long- term behavior (Metz et al., 1995). Two relevant scenarios are (a) convergence to a steady-state i.e., the existence of an attracting evolutionarily sta- ble strategy in X and (b) diversification, i.e., the existence of an evolutionary branching point in X (Geritz et al., 1997). The latter case implies the sta- ble coexistence of two different variants (formally, two stable equilibria of equation (1)). In the follow- ing, we investigate conditions for the existence of a branching point, as this relates to polysemy.
To shed light on this question, we use the canon- ical equation of adaptive dynamics which models the evolution of continuous properties in popula- tions of individuals (Metz et al., 1995; Dieckmann and Metz, 2006; Dercole and Rinaldi, 2008; Doe- shown
Whether or not such points exist in X for equa- tion (1) depends on the quantities (xx) and f(r, y)- Both of them are determined by the underlying pop- ulation dynamics of word variants. The population dynamics of single word variant characterized
beli, 10. Theoretically, the equation be linked to other well-studied models of evolu- tion such as replicator dynamics (from evolution- ary game theory) or the Price equation (Page and Nowak, 2002: Meszena et al., 2002).2
fectious diseases (Dieckmann al., 2002), economics to examine technological change leading to efficiency gains (Der- cole et al., 2008), or in cultural studies to model evolution of religious behavior (Docbeli and Ispolatov. 2010b).
"This equilibrium is reached when the variant has success- fully spread through the speaker population, i.c., when its number of users stops growing. See Appendix A.I.I.
"This equation has found applications in biology to study the evolution of phenotypic traits like drug resistance in in-

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by value x are defined by an ordinary differential equation (ODE) tracing the change in the number of users (x) of that variant. The change in the number of users is influenced by the factors out- lined in Section 3. The dynamics are based on the following assumptions:
dynamics in (1) shows an evolutionary branching point if
(i) frequency ip is sufficiently low,
(ū) non-conformism bias 3 is sufficiently high,
(I) Population structure: Individuals either use or do not use word variant. We assume ho- mogeneous mixing of users U and individuals not using the word variant, i.c., non-users N.
(ii) and discriminability is sufficiently high.
A proof is shown in Appendix A.1. In short, the model predicts the tendency diversify meaning to be (i) negatively associated with frequency, (ii) positively associated with non-conformism biases and (iii) positively associated with discrininability.
(II) Transmission:
and non- user meet, successful transmission of a word variant depends on word frequency yp and an adoption rate a. Adoption rate a is assumed to be a smooth function of x. We assume that there exists a value Zi within X maximizing a (arguably, adoption is not independent from semantic properties).
Whenever
5 Empirical analysis
We test if predictions (i-iii) resulting from the- oretical analysis are supported empirically, To do so, we investigate a sample of words and check if (i) frequency, (ii) non-conformism biases, and (iii) discriminability are associated with the ten- dency to diversify meaning in this sample. That is, our model would predict words with high non- conformism biases, high discriminability between senses, and low frequency to become more polyse- mous over time.
(III Negative frequency dependence: Whenever user meets another user of the same word variant they abandon it rate 3, the non- conformism bias. This bias is reduced by propensity to behave in conformist way. When a user meets another user with slightly different variant, non-conformism biases ap- ply as well but they are reduced by the per- ceived distance between the two variants. This distance depends on discriminability 8.
We base our analysis on a set of 3358 words compiled by Hu et al. (2019) containing informa- tion about the semantic development of words. In this data set, each word is accompanied by (i) a list of the descriptions of all of its senses taken from the Oxford English Dictionary (OED), and (ii) for each decade in the 19th and 20th century, the estimated probabilities for all senses of that word, originally derived from the Corpus of Historical American English (COHA) (Davies, 2010) through SentenceBERT embeddings. The development of the distribution of senses of the word mess is shown in Figure 2a.
The ODE modeling the change in the number of users U given assumptions (I-III) reads
Ú U= + <(A OYUU u(A OJUU, (2)
with a conformism rate <(A)
Ko exp(-1/2 2 a non-conformism rate (() cxp 1/2 A2 and Kg =: B. Here, A y denotes the difference between two semantic property values and y. A detailed description of this ODE can be found in Appendix A.1.1.
After only considering words with subjective concreteness ratings in Brysbaert et al. (2014) (see 5.3 below), we ended up with set of 3165 words. We restrict our analysis to all decades between 1850 and 2000 since earlier subcorpora of COHA relatively small and display different distribu- tion of genres. 5
This leads us to the following
Proposition 1. Consider a semantic dimension X. Assume that innovations in X. occur in relatively small steps and that new innovations occur only after a previous innovation has either spread suc- cessfully or disappeared.
"Note, also. that the observation period does not cover major sound shifts in history English that might have resulted in substantial increase of homophones.
Given the population dynamics of single word variants characterized by a single value in X as defined in (2), the canonical equation of adaptive
'Conducting the analysis with all decades from 1800 to 2000 does not substantially change the results, though.

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recepdion
office
Lenl
gutti
Jownsttnir
distribution of senses of mess over time
lycch
kinchen
busy
1.0
0.8
closet
@
semantic network of mess in the 1950s
yash
pol
bottle
fraicion of senses
mess
fish
gloin
0.6
get
smart
Pecity
carthoard
0.4
gitty
Jumn
yourself
hunch
Sice
domncg
Diy
0.2
Junny
hell
jot
thing
0.0
etvatoon then conl uned and problens
tu lding mone prosoding mests and recronioral belllitee for menttwee the smmd
1850
1900
1950
2000
unt soin thining
place
portis semsiiccus food
time
Hove con's medts with partoise panton rxpeddity an member srmeed meee unllyy and
three ways measuring the tendency mess diversify meaning
number of senses
sense diversity
0.40
Intransidnl
CO CODOOO
0.36
0.054
0.013
0.0003
0.32
1250
1250
2000
1850
1900
2000
time
Figure 2: (a) The evolution of the probability distribution over all senses of the word mess from 1850 to 2000. In 1850, mess has had mainly the meaning 'room for meals'. The distribution of senses becomes more diverse over time. (b) Eggonnetorr representing the semantic neighborhood of mess in 1950 (for this visualization, only cosine similarities above 0.25 are displayed as edges). At least two clusters can be identified. Nodes are color-coded with respect to their senses. (c) Developments of sense diversity, number senses, and network intransitivity (see 5. of the word mess over time (7 denotes the respective slopes). All three developments indicate that mess became more polysemous.
5.1 Diversification tendency
pute the effective number of senses the number N of all senses with p; > 0.05 (see Section 7 for discussion). That is, we ignore marginal senses when computing polysemy. We refer to this mea- sure as the nunber of senses.
The tendency to diversify meaning measures the extent to which a word becomes more polysemous over time. Crucially, this depends on how the de- gree of polysemy measured for a given word at a given point in time. We operationalize the degree of polysemy in three ways.
Third, we operationalize polysemy as in Hamil- ton et al. (2016) through the semantic neighbor- hood of word. We base our analysis the pre- trained SNGS embeddings used in that paper. For each decade, we compute network in which two words in our data set are connected they are semantically close. We compute pairwise cosine similarity for all word pairs and add an edge when- ever cosine similarity is greater than the median of all pairwise similarities in the data set. An ex- ample is shown in Figure 2b. For each word, we then compute its local clustering coefficient& C (i.e.,
the decade-wise probability distri- bution (p4) over all n senses of given word provided by Hu al. (2019). flat distribution in- dicates high diversity (i.c., high polysemy), while a distribution with, say, only a single dominant sense indicates low diversity. Hence, we derive an index of diversity given by D exp(H) where H Di = In(p;) is the Shannon entropy of the distribution (Hill, 1973). We refer to this as sense diversity.
First,
Second, for a word in a given decade, we com-
htt thwp://b.tttu...mem thub. com/wi

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transitivity), and define intransitivity = C. As in Hamilton al. (2016), we take intransitivity to measure polysemy (words tightly interconnected neighborhoods have few senses; words with star- like network topologies have many senses).
semantic variants of word as similar. If discrim- inability is high, two semantic variants are more likely perceived as different senses of the word. Discriminability cannot be easily measured based on corpus data, hence we rely on two dif- ferent proxies in our analysis. We demonstrate in the appendix that both proxies correlate signif-
We compute sense diversity, the number of senses, and intransitivity for every word in every decade. For every word we fit three Gaussian lin- ear regression models, one for each measure, i.e., D(t) = bpt + cD + E, (t)
icantly with measure that is closer to what intuitively understands as semantic discriminability in a small set of words.
bxt + eN + E, and (t) = byt + с₁ + E, where is time. We take the respective slopes 0,D bp. 0,N = bn and 0, I = to function as measures of the tendency diversify meaning (see Figure 2c).
The first discriminability measure that we em- ploy is lexical concreteness. Lexical concreteness is defined as the extent to which the content of a word can be grasped by the senses. It was shown that concreteness is subject to semantic prosody, i.e., concrete words likely surface in concrete contexts, and abstract words are likely to surface in abstract contexts (Snefjella and Kuperman, 2016). Under the assumption that this also extends to extra- linguistic contexts, we argue that concrete words (like mess) are more likely to be used in situations that let individuals differentiate between meanings than this holds true for abstract words (like space). We use crowd-sourced subjective ratings from Brys- baert al. (2014) to measure concreteness.
5.2
Non-conformism bias
A word's non-conformism bias measures to what extent that word is used a non-conformist way. We study the usage of words across more and less conformist genres to obtain empirical esti- mates of non-conformism biases. Six different (sub-)corpora used for this purpose. English Wikipedia?, and sub-corpora from the Corpus of Contemporary American English (COCA)$ cover- ing magazines, news, and academic texts are se- lected as representing conformist genres, as they feature language obeying linguistic norms. The fiction sub-corpus of COCA, as well as corpus of song lyrics", represent non-conformist genres in that the language therein is expected to be less constrained and more open to creative linguistic behavior.
The second discriminability measure is based on the sense descriptions from OED as provided by Hu et al. (2019) for all words. For each word, we computed embeddings using SentenceBERT (Reimers and Gurevych, 2019) for all sense descrip- tions of that word, a standard approach to represent text. We then compute all pairwise correlations among all senses of the word (Pearson's 's r). Dis- criminability is defined as the mean of all corre- lation coefficients. Thus, discriminability low, if all senses are relatively close to each other, and high if, on average, senses differ from each other. We find that the correlation between both measures (concreteness based vs. description- embedding based) is statistically robust at 0.25 (C (0.22, 0.29)). For additional support of the validity of these proxies see Appendix A.2.
For each word, we compute the mean per-million normalized frequency across all conformist cor- pora, fe, and the mean per-minnee ver-million normalized fre- quency across all non-conformist corpora, fne- We define the strength of the non-conformism bias as B = log(fne/ fe), so that is positive if word has relatively high frequencies in non-conformist genres as opposed to conformist genres.
5.3 Discriminability
Discriminability measures how well an individual discriminate between two senses of a word. If discriminability is low, individuals perceive two
5.4 Frequency
Two different ways to assess word frequency are used. For measuring frequency synchronically, use contemporary frequency information from Brysbaert et al. (2014). For measuring frequency
hhttps://uuggi ace. wo..datassets//iiipeeiaaa sample of 70 million tokens.
list from https: //www. noglish-corpora .rg/ cog//oca/: about 120 million tokens per genre.
"Word-frequency
10 111-MiniLM--6-v2
"200,000 Fnglish songs from htttps://ggnius.com 32
11 Note that the correlation coefficient is equivalent with cosine similarity for centered data.
million tokens.

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diachronically, we compute per million normalized token frequencies for each decade in COHA and av- erage across all decades in the observation period. In both cases, frequency was bog-transformed. Syn- chronic/contemporary and diachronic/historical fre- quencies correlate strongly and significantly with Pearson's ' 0.76 (C19.95 (0.75, 0.77)).
8,1
SF
0,N
SH
0,7
SE
diachronic yp and concreteness-
be
0.06
0.02
0.06
0.02
0.07
0.01
by
0.23
0.02
0.15
0.02
0.03
0.01
by
-0.10
0.02
-0.12
0.02
-020
0.01
diachronic yp and description
by
0.08
0.02
0.07
0.02
-0.00
0.02
by
0.08
0.02
0.04
0.02
0.06
0.02
b
-0.05
0.02
-0.09
0.02
-0.48
0.02
synchronie yp and concreteness bassnessss------dee based
bR 0.08
0.02
0.08
0.02
40.00
0.02
5.5 Statistical analysis and results We need to measure the effects of (i) non- conformism bias 8. (ii) discriminability 6, and (iii) frequency oo on the tendency to diversify meaning T. We have derived three measures for the depen- dent variable T (0,D, 0,N, and 0,1), two measures for bias B (concreteness vs. description based) and two measures for frequency yp (synchronic vs. di- achronic), resulting in 12 different configurations of dependent and independent variables.
by 0.08
0.02
0.06
0.02
0.12
0.02
bi
-0.02
0.02
-0.06
0.02
-0.22
0.02
synchromic yp and description-aase based
bp
0.08
0.02
0.09
0.02
0.09
0.01
by 0.23
0.02
0.16
0.02
0.03
0.01
b2
-0.08
0.02
-0.10 0.02
-0.13 0.01
Table Regression coefficients with standard errors for all models. Within each block, each column stands for one model configuration. Bold indicates statistically non-trivial effects at 95% confidence level.
As slopes, estimates of the tendency to diversify meaning are not theoretically constrained to a par- ticular interval, and none of the three measures of the independent variable shows a strongly skewed distribution. Hence, we fit Gaussian linear models of the form T = b + bgō + bpip + + to our data. All variables were centered and normalized with respect their standard deviation before en- tering the models in order standardize regression coefficients b,, bg. and byg.
dynamics of word variants; second, through an em- pirical analysis covering the factors implemented in the apulation-dynamin model. The approaches yield converging outcomes.
results As far as frequency is concerned, are in line with Hamilton et al.'s (2016) observa- tion that frequency interacts with semantic change, namely in such way that frequency in fact im- pedes change and fosters semantic stability. In a similar vein, Pagel et al. (2007) have shown that frequent concepts resist change more easily. Note that our way of conceptualizing semantic change subtly differs from that in Hamilton et al. (2016) who measured the impact of frequency on any type of change in word meaning. In contrast, the focus of our analysis is on a word's tendency to become more polysemous over time. Note, though, that our model not only predicts that low frequency entails, under certain circumstances, semantic di- versification but also that high frequeney Icads to the existence of an attracting evolutionarily stable strategy in the semantic space, hence eventually de- moting semantic change for high-frequency words altogether. That is, our model provides a mechanis- tic explanation for the empirical observation made in the literature: feequeryy words are more likely to adopt stable states in the semantic trait space that optimize ease of adoption." 12
The estimated regression coefficients are shown in Table 2. It can be seen, first, that almost all effects turn out to be statistically significant, and, second, that all significant effects have the sign predicted by the theoretical analysis. That is, all configurations (i) effects of non-conformism biases are positive, (ii) effects of discriminability are posi- tive, and (iii) effects of frequency are negative when predicting the tendency of diversification, and this holds true across all measures of the dependent variable. The one measure that stands out in this regard is 0,I, i.e., diversification tendency derived through lexical networks, which shows statisti- cally robust associations with non-conformism bias in two configurations. Most effects are within the weak to medium range (Cohen, 1992). Visualiza- tions for all model configurations can be found in Appendix A.3.
This explanation is an interesting alternative
6 Discussion and conclusion
In this paper, we have analyzed the evolution of lexical polysemy in two ways: first, by means of a mathematical model that captures the population
Similarly, our model and the empirical account implic- itly capture sense loss: multiple equilibria in the semantic trait space could lose their stable status if conditions (i-iii) in Proposition were not fulfilled anymore.

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the predominant account, which traces the posi- tive relationship between frequency and semantic stability back to the mechanism of cognitive en- trenchment (Bybee, 2006; Ellis et al., 2016). Here, the argument is that frequent words are strongly entrenched, i.c., subject to routinized perception, processing, and production so that they can resist change more easily (Schmid, 2020; Baumann et al., 2023). 13 Importantly, our account is agnostic with respect to mechanisms of entrenchment. In our model, the observed evolutionary behavior emerges from the assumption that frequent words are ac- quired more easily.
tion of meaning only if discriminability is high. If discriminability is low then semantic innovations that are close to an established sense will be ef- fectively perceived as coinciding with that sense. Consequently, they will suffer from the same dis- ad advantage imposed by negative frequency depen- dence that all common types are subject to, even though these innovations are initially rare.
We consider as a main strength of our approach that we do not only support (hypothesized) relation- ships between factors in semantic change and pol- ysemy on empirical grounds, but that we can also point at the mechanisms driving semantic change based on our theoretical analysis. This is so, in particular, due to the two-level architecture of the mathematical model, which combines short-term population dynamics driven by linguistic interac- tions that are subject to assumed biases with evo- lutionary long-term dynamics of lexical semantics. In that sense, our work goes beyond correlational accounts of polysemy.
As final note the effect of frequency, it is worth mentioning that Hamilton et al.'s (2016) result was criticized as being methodological artifact that arises from effects of frequency on cosine-similarities between word embeddings (Du- bossarsky et al., 2017). While we do acknowledge this criticism is important to emphasize that, from a methodological point of view, neither the theoret- ical nor the empirical account in our approach can be invalidated by these effects. Hence, our research provides independent evidence for Hamilton et al. 's (2016) findings.
7 Limitations
Our approach is subject multiple limitations, the most prominent of which are grounded in the ab- stract nature of our theoretical account. Our model is based on a set of simplifying assumptions. First, we assume that speakers in the population are ho- mogeneously mixed (and no further population structure, e.g., with respect to age, gender, or so- cial status). This is a standard assumption in many mathematical accounts ecology (Hofbauer et al., 1998). In line with linguistic research (Hopper and Traugott, 2003) lexical change assumed to be a gradual phenomenon, i.e., that innovative steps are relatively small. Furthermore, we assume innova- tions to spread fast, namely so fast that they reach their population-dynamme cquilibrium (or vanish) before the next innovation is introduced. From a mathematical point of view, the latter two assump- tions are necessary model semantic change by means of an ODE continuous time (i.e., equation (I)) (Dercole and Rinaldi, 2008).
In addition to the effect of frequency. our model predicts a positive relationship between non- conformism biases and the tendency of word to establish more senses supported by our empirical account in ten out of twelve configurations. In the model, the mecha- nism that promotes the stable coexistence of two semantic senses is that of negative frequency de- pendence, i.e., an advantage of lexical variants and as long as they are rare.
time. The prediction is
The prediction that this mechanism promotes polysemy is intuitive, and not very surprising for that matter. If rare variants have an advantage in their proliferation then this facilitates the estab- lishment of innovative uses. This resembles the argument that is brought forth in the discussion about the role that extravagant usage plays in lex- ical change (Ungerer and Hartmann, 2020; Petré, 2017; Haspelmath, 2000).
Note, also, that we assume every speaker to use only one semantic variant at time, according to our formulation of the model. That is, the stable coexistence of multiple senses, say A and B, in fact corresponds to the presence of two coexist- ing aobppopulations, one using A and one using B. However, the model can casily be reinterpreted such a way that the units in the population are not
We have also shown empirically and theoret- ically (in line with Baumann and Mühlenbernd (2022)) that non-conformism leads to diversifica-
OOn the other hand, however, frequency was argued to drive semantic bleaching together with formal reduction (Hop- per and Traugott, 2003), as evident in grammaticalization processes (e.g., the development of French pas from a noun to a negation particle).

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individuals, but rather usage events of individuals. Not all of the model's parameters and quantities can be measured empirically. Clearly, for example, there is no available historical data of the number of users of a word and its multiple senses. Like- wise, we do not specify what the shape of adoption rate a looks like exactly. Importantly, however, we do not need to have this information for making predictions about the expected long-term evolution of the semantic property. This is because we are in- terested in qualitative assertions (does a branching point exist?) rather than quantitative ones (when did a certain word obtain a new sense?). The fact that we can derive analytical predictions is one of the main strengths of our approach.
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A Appendix
ogy, 219(1))33-98
A.1 Proof of Proposition 1
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In this section, we derive conditions under which equation (1) shows an evolutionary branching point (resulting in the stable coexistence of two semantic variants). Before that, need to derive the pop- ulation dynamics of single word variants given by (2) based on the assumptions (I-III) Section 4. This done in the following subsection.
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A.1.1 Population dynamics
In order to derive the cquilibrium number of users of a word characterized by value x, i.e., (x)) we need to define the underlying population dynamics of the word. We will do so by setting out with a simple and well-studied model of lexical change that accounts for learning and frequency, and sub- sequently expand cover conformism and non- conformism biases.
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First, we assume that for every individual word variant, the population of linguistic individuals can be split into users that know and use the word and non-users that do not use it. Let us denote the respective numbers of individuals as U and N, re- spectively. Furthermore, tions are large and set U + N Non-users can adopt word variant (like mess with a positive con- notation) and switch to the user class at an adoption rate a whenever they encounter the word interact- ing with a user, which occurs at frequency şo. In
Eyal Sagi, Stefan Kaufmann, and Brady Clark. 2011. Tracing semantic change with latent semantic analy- sis. Current methods in historical semantics, 73:161- 183.
assume that popula-
Dominik Schlechtweg, Barbara McGillivray, Simon Hengchen, Haim Dubossarsky, and Nina Tahmasebi. 2020. Semeval-2020 task I: Unsupervised lexical semantic change detection. CoRR, abs/2007. 1464.

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this simple scenario and under the assumption of homogeneous mixing of users and non-users, word dynamies are defined by the ordinary differential equation
and
(Aa) = Po exp(-1/2 228²),
(5)
with variance 1/6, so that (non-Jconformism rates are highest if æ and y coincide (obtaining the max- ima Ko and vo, respectively). Let us define non- conformism bias as 3 : vD - Ko- The Gaus- sian dependency of (non-Jconformism rate on A is motivated by the assumption that individuals are influenced to a lesser extent by other individuals that display substantially different linguistic behav- ior (Dercole and Rinaldi, 2008; Kim and Hommel, 2015). 14 For instance, non-conformism rates (i.e., the need to abandon one's own behavior) is as- sumed to be highest if the linguistic behaviors of two individuals meeting each other coincide.
Ü= =pUu U.
This model is equivalent to previously studied mod- els of cultural change (Cavalli-Sforre and Feldman, 1981) and lexical dynamics (Nowak, 2000; Nowak et al., 2000; Solé, 2011). This equation models how words spread through a speaker population in an S-shaped manner; a pattern often encountered in diachronic linguistics (Denison, 2003). Note that, apart from variants of the same word (such positive and negative variants of mess), we do not model any interactions between different word types (like hypothetical co-devclopments and inter- actions of mess and banana).
non-conformism V
We assume that is real-valued smooth func- tion of the value of the semantic property and that there is a value ro for which (xx) obtains a maximum within X. Sentiment, for instance, was shown to influence lexical processing, which in turn arguably impacts a word's adoption rate. Note, importantly, that a does not only cover word acqui- sition by children but also adoption of words and their variants by adults.
0.6
0.4
0.2
conformism K
difference x
Let us integrate conformism and non- conformism rates into the model. As discussed above, conformism rates represent effects of positive frequency dependence in addition to frequency dependent word adoption. When two users meet, we assume that word usage is strengthened a conformism rate k. Similarly, a user of word meets another user of that word, they will abandon that word (or word variant) due at a non-conformism rate v. In that case they switch back to the non-user class.
Figure 3: Conformism rate k(A) and non-conformism
rate v<( (A). both with å 4. Maxima ni 0.4 and V/ = 0.8, so that the curvature of v is higher than that of x at A 0.
In both functions, ô can be interpreted to mea- sure the users' ability to discriminate between us- age variants within X. Lee., ö measures the users' discriminability. We assume, for simplicity, that for any given word, 8 is constant across the whole speaker population. If individuals are equipped with fine-grained semantic perception (high 8), they can easily distinguish between, say, positive and negative variants of the word mess. In that case, (non-)conformism rates are reduced faster as A increases. If, in contrast, individuals can not so easily distinguish between different usage variants (low d), they are more likely to treat these variants as the very same item which in turn yields high mooffroonfommssm rates. See Figure 3. In total, for a single variant characterized by x,
is plausible that, whenever two users of slightly different variants x and y in X of the word meet, conformism and non-conformism rates depend on the difference between those two variants. This is because if both variants are very dissimilar then these two items not so likely to be seen as two variants of the same word in the first place. In that case, conformism and non-conformism biases are expected to vanish. We model this behavior by letting rates k and / depend on the difference = x - y in a Gaussian manner as in
"Similar functions were used to model perceptual similar- ity (Nosofsky, 1986; Jäger, 2006) and communicative vague- ness (Franke and Corrcia, 2018)
x ()) = Kg exp(-1112 22)2)
(4)

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evalutionary time
30.03
changing fitness landscape
25:00-
innovation
negative fitness
15000
10003
branching at singularity Xo
0.4
0.2
direction of attraction
0.0
sasses (8xy)
semontic property
0.0
0.5
singularity X
positive fitness
0.10
0.5
resident x
014
0.8
Invastion
fitness landscape at singularity X
10.00
Figure 4: Evolutionary dynamics x in the semantic subspace X undergoing branching. In this setup, the adoption defined as concave function axx) -(x xg)² with Zy = 0.3 and 0.5. Discriminability is set to 8 = 4, and frequency is &p 1. Left: changing fitness landscape defined by invasion fitness f(z, v). Every resident x defines a different fitness landscape that innovations y must cope with. Purple (dark) denotes areas where innovations invade (positive f) the resident variant. Through multiple invasion-subsiitttion events, semantic property r approaches the singularity zo (direction of evolution shown by white arrows). This is because for every resident, innovations closer to mig have positive invasion fitness f (purple area). Bottom right: fitness landscape za (i.e., the slice represented by the dark line in the changing fitness landscape). Here, zg is local minimum of its own landscape so that it can be invaded by innovations on both sides. Top right: evolutionary trajectory of x given equation (1). Property x first approaches 2p, where it splits into two variants that converge towards stably coexisting variants Thigh and Nlows i.e., instance of evolutionary branching.
defined by singularity
the population dynamic systems then reads
A.1.2 Invasion fitness
We still need derive invasion fitness far y) equation (1). Invasion fitness is defined as the growth rate an initially rare innovation character- ized by y in a population of speakers that predom- inantly use x (i.e., the resident population) (Metz et al., 1995; Dercole and Rinaldi, 2008; Doebeli, 2011 1). That is, the number of users of the variant with value y is assumed to be close to and the resident population characterized by value æ rests at its population dynamic equilibrium Ö (x). That is, in the beginning y users only interact with x users but not with other users. Hence,
U==p(())UN+ae = 00U OJUU.
This ODE is extension of the model of re- ligious change in Doebeli and Ispolatov (2010b) and that of lexical change in Baumann and Mühlen- bernd (2022) in that it features both, conformism and non-conformism effects, as well as a parameter measuring frequency (as does the model by Nowak et al. (2000); see (3) above). It does also not feature a term that logistically regulates population growth, in contrast to the model in Doebeli and Ispolatov (2010b).
[(x, v) x a1))) ((x)) + kly x)((x)
The system above shows non-trivial equilib- rium at (z) = y (((z) Ko mb) > 0. It exists and stable long axx) pa(x) 10 Kg. which can be seen by lineariz- ing around (xx) in (2) (Hofbauer et al., 1998). That is, words must be adoptable and conformism rates must not be too strong.
- -vy - x))
(7)
and
For every resident variant x, invasion fitness f(x v) defines fitness landscape that users of innovative variants characterized by value y must cope with. f( y) > then an innovation characterized by

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y can successfully invade the resident population characterized by z. Furthermore, if is not close to an evolutionary singularity (see below), the inno- vation will, if it successfully invades, also replace the resident. Thus, invasion fitness determines the direction of the evolutionary dynamics of z. More specifically, evolutionary progress is determined by the fitness gradient D(r)
interpret Tro as measure of the tendency di- versify meaning. In particular, we see that Two depends on a word's frequency i,, non-conformism bias B = 20 - No, and discriminability 6. By taking the derivatives Tap with respect to yp, B, and 6, we see that
OT zo (4, 3.6) de
af(.y) in (1). by
a" (10) - ((xo) 0, (9)
y=
An evolutionary singularity then is point è E X where ( 0, i... an equilibrium of equation (I). That is, invasion fitness lets us identify the long-term evolutionary dynamics of semantic prop- erty x.
because a is locally concave around zo by assump- tion,
A2
a (,, 03
de
Ú
0,
8 A
A.1.3 Conditions for diversification
A=0
Let us now study the long-term dynamics of equa- tion (I) given the quantities derived in the previous sections. We have seen that for identifying evo- lutionary singularities in this equation it is suffi- cient to analyze the fitness gradient D(=). Since K. and y obtain maxima if x y. we have that ((x) = pa'(()) By assumption, adoption rate a obtains a maximum at zg (see definition of a above). This entails, first, that zp is an evolution- ary singularity and, second, that the dynamics of æ given by equation (1) approach zy- Hence, To is an evolutionary attractor.
<0
(10)
since exp(-1/2- is concave at its maximum,
and
A2
aT (P,8.6)
de
= 13
(
06
05
82A
A=0
= -3 08
-88h ( >
0,
>0
(11)
The question now is this: what happens if the se- mantic property x comes close to zn? For this, we need to analyze the fitness landscape (ro, y) de- fined by zg that nearby innovations y are exposed to. 2g is a maximum of this fitness landscape then nearby innovations cannot invade. In this case, To is evolutionarily stable. If, however, is minimum of this fitness landscape, then nearby innovations both sides of æo invade and co- exist. In that case, 2i is an evolutionary branching this evolutionary
as long as = 1/ Kg > 0.
Hence, an evolutionary branching point exists if o is sufficiently low, and if ,3 and 8 are sufficiently high.
A.2 Robustness check for discriminability
In this section, we test to what extent both measures of discriminability (concreteness based; sense- description based) correlate with more direct esti- mates of diseriminability. For this, we use the WiC data set (Pilehvar and Camacho-Collados, 2019), which contains for a set of target words several sen- tence pairs together with ratings indicating whether the target word has the same sense in both sen- tences or not (1 for same sense vs. 0 for different sense). We used the whole data set (train, dev, test). For each target word, we computed the mean rating (mean sameness) of all sentence pairs for (8) that word, thereby only considering words with 20 or more sentence pairs to avoid inaccurate mean estimates. This leaves us with 50 different target words that also show up in our set of 3165 words. Arguably, a high mean sameness rating indicates that different contextual uses of a single word are
point (Geritz et al., 1997). scenario which leads diversification of semantic propertics and hence to polysemy.
Whether zo is minimum of this fitness land- scape is given by the local curvature of f(zo, y). that is,
82 f w)
Tap =
0y²
1=z0
=pa"(ro) - (xxo)
+ (k) ((())(()))))))))))
If If, > 0 then Zo is a minimum of fxo. y) (and a maximum Tr, < 0). In other words, we can

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easy discriminate, while low mean same- ness rating indicates high discriminability. Conse- quently, we would expect mean sameness to neg- atively correlate with both of our discriminability proxies.
The correlogram in Figure shows that both discriminabiliity proxies correlate negatively with mean sameness expected. While this supports assumption that concreteness and average cor- relation among sense-description embeddings func- tion as good proxies for discriminability, we do need to emphasize that this robustness check is based on a relatively small number of words all of which show high utterance frequency. Future research would need to consider a larger and more representative set of words.
--0.336
dicctiinsbilily
0.0093
discriminabilly
p= 0.004
0.01.
r 0.32
rm 0.62
rm 00072 82
frequency
0.022
1. 56-08
Figure 5: Correlogram of mean sameness, frequency, and both discriminability proxies (Pearson's 's r together with p-values).
A.3 Visualization of statistical models
Figures 6 and 7 show the effects v, 8, and yo on the tendency to diversify meaning (three different measures) for all twelve configurations (rows). The shaded areas represent 95% confidence boundaries. Each point (gray) represents single word.

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a number senses a sense diversity
0.-
0.5
0,5
-04
4.5
-0.
0.5
0.5
4.5
4.5
-0.5
8 intransitivvity
0.5
46
0.5
-05
discriminabiiity
frequency (contemporary)
non-conformism bias
(sense-description based)
intransibivity a number senses sense diversity
0.0
0.0
-2
6.0
0.0
5.0
0.0
0.0
0.0
discriminability (concreteness based)
frequency (contemporary)
non-conformism blas
Figure 6: Model configurations employing contemporary word frequency.

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intramsitivity number senses sense diversity
0,
05
-05
4.5
0.-
0.5
0.5
0.5
0.5
405
discriminability (sense-description based)
frequency
non-conformism bias
(diachroniichistoriiaa)
diversity
05
00
.0.
.05
intransitivity number senses
0.5
0.0
-2
05
0.0
0.0
discriminability (concreteness based)
frequency (diachronic/historicaal)
non-conformism blas
Figure 7: Model configurations employing diachronicchistorical word frequency.


Reviews:
[{"review_id": "wwfYiQnK1p", "reviewer": "Reviewer_VVLs", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": 4, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank the reviewer for their positive feedback. It is good to see that our approach was presented in a clear way. \n\nIt seems that the only substantial criticism is that we have opted for an analytical (mathematical) modeling approach over one that employs simulations, i.e., in the present context, agent-based simulation models. We do acknowledge the usefulness of simulation models in the study of language change. In particular, we see that, as argued by Steels (2016, *Philos. Trans. R. Soc. B*, 371), agent-based accounts allow for a causal assessment of mechanisms that drive language change (as do mathematical models like the ones employed here), and it is evident that simulation models can integrate a larger number of parameters and factors than is possible for mathematical models. \n\nThe clear advantage of mathematical models, however, is that they let us examine relationships among parameters and outcomes analytically, i.e., by means of a mathematical expression, rather than statistically. We argue that this has benefits for the study of language, too (clearly, ours is by far not the first account to study language change with the help of mathematical models, let alone the study of biological evolution): our theoretical analysis yields deterministic and, crucially, testable predictions and we do not need to bother about issues like sample size, number and duration of simulation runs. We will elaborate on these advantages in the discussion section of the revised manuscript.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "The theoretical- formal - approach is very clearly defined, and the topics (diachronic lexical change and polysemy) are important for a better understanding of language structure and use.\nResults are very clearly and convincingly presented.", "reasons_to_reject": "I am not completely sure that a formal approach, rather than a simulative one, would be of interest for the nlp community.", "questions_to_authors": "", "paper_topic_and_main_contributions": "The paper proposes a formalisation, and related data analysis, of the diachronic phenomenon of lexical polysemy.\nThe noun “mess” is taken as example to show how the lexical change is (inversely) related to frequency (i.e. word usage by speakers), non-conformism, which in turn is related to high discriminability.", "excitement": 3, "reproducibility": 3, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"Missing_References": "In the list there are examples from the most relevant references on the topics. "}, "extra_text": {}}, {"review_id": "E43gbPoRoy", "reviewer": "Reviewer_SeWs", "summary": "", "questions": "", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank the reviewer for their feedback and time invested into carefully going through the manuscript. The review addresses the following three points:\n\n**(1) Polysemy and homonymy/homophony:** \nThis is an important point and we will delimit the phenomenon under investigation (polysemy) from homonymy in the revision. \nWe follow the mainstream distinction between polysemy and homonymy in linguistics. In short, the phenomenon that we look at is polysemy, i.e., one-to-many form-meaning mappings that come about via changes on the meaning side. The key criterion is that polysemy involves historical or psychological relatedness (cf. Leech, 1974, *Semantics*. Penguin Books; McMahon, 1994, *Understanding language change*. CUP). This is exactly what is modeled in our theoretical account (innovative steps in a semantic dimension originating from one variant). \n\nIn contrast, homonymy (a rarer phenomenon) comes about via changes on the form side. Note that the historical information that our empirical analysis uses (Hu et al. 2019) excludes homonyms as listed in the OED as well so that the theoretical and the empirical account are consistent, and we will point this out more clearly in the final version of the paper. \nNote also that major sound changes leading to homophony (e.g., *steak* vs. *stake*) took place in the transition from the Middle to the Early Modern English period, ca. 15th century, and the data used in our empirical analysis stemming from after 1850 is relatively stable with regard to large-scale sound changes that could lead to new homophones.\n\nAs to sense loss: yes, this is a relevant phenomenon that is explicitly treated in the empirical part and implicitly in the theoretical model (shifts in the model parameters can render multiple equilibria of eqn (1) unstable as per eqn (8)). We will add this point to the discussion section.\n\n**(2) Distinguishable causes of polysemy:** \nWe agree that polysemy can have different causes and our research provides an account for how potential causes can be linked via a plausible population dynamic model, and we show that the predictions of the model are in agreement with empirical data. The main objective of our research is exactly to investigate a selection of them that is theoretically and empirically motivated. \n\nWe are not aware of other research that attempts to mathematically model dynamics of polysemy linking individual behavior with phenomena on the population level, *and* for which results are tested against empirical observations. This does not mean that no alternative theory could account for the observed phenomena in principle, but it would not be adequate to characterize our approach as arbitrary.\n\nOur approach is not to derive “unique explanations on its own right” as the reviewer puts it. Quite to the contrary: our model shows that polysemy results from a well-motivated *combination* of different factors (e.g., non-conformism promotes diversification but only if discriminability is high enough). \n\n**(3) Causal vs. correlational analysis:** \nOur theoretical (mathematical) account allows for a causal assessment in that we start with mechanisms that apply to short-term interactions of speakers and rigorously analyze the evolutionary long-term consequences that follow from said mechanisms. The mathematical model (in fact, two stacked models) is far from representing a correlational analysis. Rather, we test its implications by showing that factors correlate as predicted.\n\nThe reviewer argues that the “model mathematically combines a number of factors suggested to correlate with the growth of polysemy”. However, this is not exactly what we do. In fact, the first model combines factors that have an impact on linguistic *interactions*, and only in a subsequent step we check, in a second model, what their impact on growth in polysemy is. Crucially, the first model integrates the factors in a plausible way (Table 1). Extant (statistical) correlational studies, in contrast, *directly* relate factors to (dynamics in) polysemy. The strength of our account, we think, is that it adds a theory to these relationships. We will elaborate on these points in the revised version to make this clear.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "The paper is generally well-structured and the topic (while not traditionally in the purview of NLP) may be of interest to audience at the conference.", "reasons_to_reject": "As noted above I have concerns about the status of the phenomenon (polysemy) being modeled. About how distinguishable different causes of polysemy really are from one another, and whether the present work is really separable from the kind of correlational analysis they mention.", "questions_to_authors": "", "paper_topic_and_main_contributions": "This submission presents a model attempting to predict the growth of polysemy for individual word forms diachronically. Why or how do some words gain many additional senses throughout the lifetime while others may not. Two big issues limit the effectiveness of the work however.\n\nFirstly, the real theoretical status of polysemy is potentially in doubt; at the very least there is a fuzzy boundary between polysemy and homophony. When sound change causes new homophones to occur in a language, some of those will inevitably have similar meanings while others won't -- do we want to count those cases as one or the other, or rather distinguish accidental from intentional (extended) polysemy? How about when words lose senses over time?\n\nSecond, the issue in my opinion is whether this question falls into a class of problems with so many potential answers that it may prove impossible to distinguish them. i.e. there are so many potential underlying mechanisms which lead to polysemy that the mere existence of polysemy is not something that is capable of distinguishing theories of language development and change -- let alone support unique explanations on its own right.\n\nFinally, despite the authors claims I don't see how The model mathematically combines a number of factors suggested to correlate with the growth of polysemy into a single implementation but none of these form a causal whole, so the work does not seem fundamentally different from a kind of correlational analysis.", "excitement": 2, "reproducibility": 3, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "wxTynY8PoU", "reviewer": "Reviewer_gMYd", "summary": "", "questions": "at page 2 you mention that none of the assumptions _immediately_ relates to semantic long term evolution. What do you mean by immediately? I agree they model short-term interactions, but it's hard for me to think of a scenario where long-term change does not depend on short-term interactions. Could you add a footnote outlining one such scenario that would make the non-trivial link more explicit?\n\nat page 5 you mention that early subcorpora from the coha are relatively small: what is relatively? would your analysis change if you include those decades as well?\n\npage 7, top: you mention corpus of historical american english but abbreviate it as coca, which is which? from context I guess you use the coca here, but not sure. \n\nYou interpret a correlation of 0.25 as reasonably strong: I agree that it's nothing worrying in the context of this work, considering the degree of noise involved in quantifying such complex phenomena, but that correlation is hardly strong: could you clarify what leads you to dub it as such?\n\npage 8, top: what is t? the previous formula includes T, but not t. Maybe I'm missing something obvious, but I'm missing it nonetheless.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 5, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We want to express our gratitude to the reviewer for their thorough, detailed, and reassuring feedback. We are excited to read that the reviewer considers our work as “springboard for future studies” and we are glad that the reviewer liked the way in which we presented our analysis.\n\nThe main criticism is that the discussion section deserves a more in depth assessment of our results. We agree and we will gladly expand that section. In particular, the reviewer has addressed our account of the mismatch between the obtained results regarding the role of frequency (essentially confirming Hamilton et al. 2016) and Zipf’s meaning-frequency law. It seems that our discussion in this regard was more prominent than we intended it to be. In fact, the suggested causal chain (more senses lead to higher frequency) is rather a conjecture than something that can be derived directly from our theoretical or empirical analysis (this is, because frequency is an input parameter in the model and not the outcome). Indeed, to address said conjecture one would need to parametrize *growth* in frequency. This would entail an entirely different analysis, and we will make clear in the revision that answering this question is subject to future research.\n\nWhat we will do, anyway, is to expand the Discussion by carefully addressing the role of the parameters as integrated in the model. More specifically, we will move the discussion of frequency that is currently in the Limitations section (lines 690-696) to the Discussion section. Here, we show why our model predicts high-frequency words to be less prone to diversification: high-frequency words are more likely to adopt stable states in the semantic space. We will relate this (as we think interesting) observation to extant research (e.g., Pagel et al. 2007, *Nature*, 449).\n\nOther comments:\n* page 2, “immediately”: What we mean is that these factors influence long-term evolution only indirectly via multiple small-scale interactions (just as the reviewer correctly writes). We will rephrase this to make our point clear. \n* page 5, “relatively small” subcorpora: We need to be specify more clearly. In addition to a smaller corpus size (e.g., the sub-corpus of the first decade is only about half as big as that of the 1850s), the first decades of the 19th century also lack a newspaper subcorpus, hence early sub-corpora are less representative. That said, to be on the safe side we now ran the analysis with the whole time span and did not find any substantial differences in our results. We will put this information into a footnote.\n* page 7, “reasonably strong”: Yes, good point, we will change that to “medium strength” (as suggested by Cohen 1992). We actually wanted to express that it is “not weak”, but “medium” is more accurate.\n* page 8, “where *t* is time”: This was an editing error (actually, this phrase belongs to the model formulas in the end of section 5.1). Thanks for spotting this!", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "The paper is thorough, upfront about the assumptions it needs to make, why they need to be made, and what consequences they may have on results. The mathematical specifications are dense but overall clear also to a non-specialist like me. The results are interesting and contribute to present the methodology as an interesting tool to study diachronic phenomena in language, potentially offering other researchers an interesting springboard for future studies. The limitations section is very thorough and insightful, complementing the results presented in the main paper in important ways.", "reasons_to_reject": "The paper is very dense in its presentation of the methodology and goes over the results rather quickly. The discussion is also not particularly insightful, and does not offer a very strong explanation for the tension between the observation that frequency is positively correlated with polysemy under a synchronic perspective and the empirical finding that sense differentiation tends to be stronger for low frequency words. The account offered by the authors (low frequency words from the past may become more frequent because of sense differentiation) would suggest that over time different word types should be frequent, but the correlation between frequency estimates over time seems to contradict this. While I don't think a surprising result should justify rejection, I think more care is warranted in interpreting these results than shown in the discussion.", "questions_to_authors": "at page 2 you mention that none of the assumptions _immediately_ relates to semantic long term evolution. What do you mean by immediately? I agree they model short-term interactions, but it's hard for me to think of a scenario where long-term change does not depend on short-term interactions. Could you add a footnote outlining one such scenario that would make the non-trivial link more explicit?\n\nat page 5 you mention that early subcorpora from the coha are relatively small: what is relatively? would your analysis change if you include those decades as well?\n\npage 7, top: you mention corpus of historical american english but abbreviate it as coca, which is which? from context I guess you use the coca here, but not sure. \n\nYou interpret a correlation of 0.25 as reasonably strong: I agree that it's nothing worrying in the context of this work, considering the degree of noise involved in quantifying such complex phenomena, but that correlation is hardly strong: could you clarify what leads you to dub it as such?\n\npage 8, top: what is t? the previous formula includes T, but not t. Maybe I'm missing something obvious, but I'm missing it nonetheless.", "paper_topic_and_main_contributions": "The paper studies under what conditions a branching point in semantic space leading to stable polysemy is expected to happen, considering three factors shown to affect long-term semantic change, i.e., frequency, discriminability, and non-conformist usage of lexical items. Through the use of population dynamics models, the authors present a theoretical and empirical analysis of the proposed model, highlighting how the presence of a branching point relates to low frequency, non-conformist usage and high discriminability, i.e., words are likelier to acquire a novel stable sense if they are used rarely, if users have non-conformist biases (thus prefer to use words in novel ways), and if usages of a same lexical item have higher discriminability. Frequency, discriminability, and polysemy on the evolutionary scale are measured in different ways to ensure patterns are robust. The empirical analysis relies on a curated set of a few thousand words with extensive sense annotations, as well as on several secondary data sources including historical and synchronic corpora (COHA and COCA), and lexica (cocnreteness and frequency ratings). \n\nThe main contribution is certainly in the adoption of models of population dynamics used in biology and economics in the context of semantic change, with an outstanding mathematical rigor and the combination of a theoretical analysis with an empirical analysis.\n\nOverall I liked the paper: there clearly is a lot of work to do in quantifying all variables that enter such complex population dynamics, but works such as this hold promise in giving the community tools to bring this work forward in principled ways and I think this paper should make it into the main conference.\n\n----------------------------------------------------------\n\nI thank the authors for their answer: I haven't eventually hanged my scores as I don't think the paper qualifies as transformative. That said, I do find it interesting and methodologically sound.", "excitement": 4, "reproducibility": 4, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"Typos_Grammar_Style_and_Presentation_Improvements": "Overall clearly written, in spite of how dense the mathematical treatment is, kudos! I signalled potential typos in the questions to the authors because their solution isn't obvious to me."}, "extra_text": {}}]

Author rebuttal:

Meta-review: The reviewers agree on the fact that this paper provides a valuable contribution to investigate the diachronic phenomenon of lexical polysemy, by providing a clearly defined theoretical and formal approach to gain a better understanding of language structure and use.
The main concern is related to the relevance of this formal approach for the nlp community. The methodology presentation is dense and would necessitate further details, in particular concerning the interpretation of results.
Decision: Accept-Main