# Contextual modulation of language comprehension in a dynamic neural model of
lexical meaning

Michael C. Stern<EMAIL_ADDRESS>Maria M. Piñango

###### Abstract

We propose and computationally implement a dynamic neural model of lexical
meaning, and experimentally test its behavioral predictions. We demonstrate
the architecture and behavior of the model using as a test case the English
lexical item have, focusing on its polysemous use. In the model, have maps to
a semantic space defined by two continuous conceptual dimensions,
connectedness and control asymmetry, previously proposed to parameterize the
conceptual system for language. The mapping is modeled as coupling between a
neural node representing the lexical item and neural fields representing the
conceptual dimensions. While lexical knowledge is modeled as a stable coupling
pattern, real-time lexical meaning retrieval is modeled as the motion of
neural activation patterns between metastable states corresponding to semantic
interpretations or readings. Model simulations capture two previously reported
empirical observations: (1) contextual modulation of lexical semantic
interpretation, and (2) individual variation in the magnitude of this
modulation. Simulations also generate a novel prediction that the by-trial
relationship between sentence reading time and acceptability should be
contextually modulated. An experiment combining self-paced reading and
acceptability judgments replicates previous results and confirms the new model
prediction. Altogether, results support a novel perspective on lexical
polysemy: that the many related meanings of a word are metastable neural
activation states that arise from the nonlinear dynamics of neural populations
governing interpretation on continuous semantic dimensions.

###### keywords:

lexical semantics , dynamic field theory , language comprehension

††journal: Cognition

[inst1]organization=Linguistics Department, Yale University,addressline=370
Temple St., city=New Haven, state=Connecticut, postcode=06511, country=USA

We propose a model of lexical meaning in the framework of Dynamic Field Theory
(DFT)

Model simulations capture known sentence comprehension effects and generate a
novel prediction

Sentence reading experiment replicates previous results and confirms new model
prediction

We argue that polysemy arises from metastability in neural dynamics on
continuous dimensions

###### Contents

  1. 1 Introduction
    1. 1.1 English ‘have’
    2. 1.2 Continuous conceptual space for lexical meaning
    3. 1.3 Further empirical evidence for continuous semantic dimensions
    4. 1.4 Dynamic Field Theory (DFT)
    5. 1.5 This paper
  2. 2 Dynamic neural model of lexical meaning
    1. 2.1 Model structure
    2. 2.2 Model simulations
  3. 3 Experiment design
    1. 3.1 Participants
    2. 3.2 Materials
    3. 3.3 Procedure
    4. 3.4 Data processing
  4. 4 Experiment results
    1. 4.1 Acceptability
    2. 4.2 Relationship between acceptability and reading time
    3. 4.3 Discussion
  5. 5 General discussion & conclusion
    1. 5.1 Summary & discussion
    2. 5.2 Novel predictions of our approach
    3. 5.3 Other perspectives
    4. 5.4 Conclusion
  6. 6 Data availability
  7. 7 Funding sources

##  1 Introduction

In language comprehension, linguistic forms evoke interpretations of meaning.
A basic unit of linguistic form is the lexical item, the systematic
relationship between phonetic/phonological, morphological, syntactic, and
semantic information (Anderson, 1992; Jackendoff, 1975). It is a well-known
observation that the specific interpretation or reading evoked by a lexical
item can vary depending on context. Polysemy refers to the situation whereby a
lexical item offers more than one interpretation yet those possibilities are
conceptually related. For example, the lexical item book can be described as
polysemous since its possible interpretations include (at least) both a
physical object (e.g., heavy book) and a collection of information represented
by an object (e.g., enjoyable book) (e.g., Brugman, 1988; Deane, 1988; Lakoff,
1990; Pustejovsky, 1995; Vicente, 2018).111Polysemy contrasts with homophony,
the situation where the possible interpretations appear semantically
unrelated, e.g., river bank vs. savings bank. Here we investigate the
conceptual basis of the constrained semantic variability observed in lexical
polysemy. To this end, we examine a possible source of this variability,
propose a neuro-computational implementation, and investigate the behavioral
consequences during sentence comprehension. Under our proposal, the many-to-
one relation between meaning and form which is salient in cases of lexical
polysemy can be seen as the norm rather than the exception, with differences
primarily in the magnitude of variability and the relatedness of the possible
interpretations.

###  1.1 English ‘have’

Our test case is the English lexical item have. have is typically interpreted
as a relation of possession between the referents of its arguments, as in 1.1
where the possession is alienable, or as in 1.1 where the possession is
inalienable.

. The linguistics professor has a motorcycle. (alienable possession)

. The oak tree has a healthy trunk. (inalienable possession)

When subjects are presented with less frequent argument combinations, as in
1.1 below, two types of responses are reported: (a) the inanimate subject “the
oak tree” leads to an inalienable possession interpretation, but this
conflicts with the fact that the object “the motorcycle” does not plausibly
enter into a part-whole relation with “the oak tree”, leading to a decrease in
acceptability; (b) the referent of the subject is anthropomorphized, e.g.,
“the person dressed as a tree…”, in order to maintain an alienable possession
interpretation (Zhang et al., 2018; Zhang, 2021). These facts are consistent
with a bias for have to evoke a possession interpretation.

. #The oak tree has a motorcycle.222“#” signifies that the sentence, while
grammatical, is judged less felicitous without additional context.

But the polysemy reportoire of have is larger than these two readings. have
can also evoke an interpretation of coincidental location. This would render
1.1 above with an interpretation that the motorcycle is in coincidental
spatial proximity to (e.g., next to, under, below, above) the oak tree, a
situation that we will refer to as adjacency (e.g., Myler, 2016; Zhang et al.,
2022). The tendency for have to evoke a possession reading is very strong, but
not indefeasible. One standard way to bring out an adjacency reading from have
is to add a prepositional phrase which makes explicit the spatial relation, as
in 1.1. Not surprisingly, presence of the modifier “next to it” improves
acceptability ratings relative to sentences like 1.1 (Zhang et al., 2018,
2022).

. The oak tree has a motorcycle next to it.

This said, presence of an explicit modifier is not the only way to make an
adjacency reading salient. A bias for an adjacency interpretation can also be
induced by the preceding context. Specifically, when a preceding sentence
evokes an adjacency interpretation, as in 1.1, then sentences like 1.1 are
more likely to trigger an adjacency interpretation as well as receive higher
acceptability ratings (Zhang et al., 2018, 2022), as seen in 1.1.

. The pine tree has a car next to it and the oak tree has a motorcycle.

This linguistic and behavioral pattern suggests a unified polysemy-based
analysis of English have involving readings raging from a purely coincidental
spatial relation to an alienable possession relation to an inalienable
possession relation. Crucially, these readings are not disconnected. The
distinction between adjacency, alienable possession, and inalienable
possession is a matter of degree, not category, not only between these three
reading types but also within them. In the case of coincidentality in spatial
location, for example, the situation conveyed by “the tree has a motorcycle”
is more coincidental than “the tree has a bench”, and that, in turn, is more
coincidental than “the tree has a swing”, or “the tree has a nest”. So, with
each situation we move towards less coincidentality and, interestingly,
towards greater asymmetry between arguments such that the first argument is
more and more perceived as possessing the second.

Similar gradability is observable within the alienable and inalienable
possession spaces. For alienable possession, “the woman has a car” can refer
to a variety of related situations distinguishable by degree of ownership: the
woman has a car because she stole it, because she borrowed it, rented it,
bought it. Only in the last instance would she “own” the car, yet in all
instances the relation between the woman and the car—one of asymmetry in
control—renders it one of possession. Finally, for the inalienable possession
space, the possibilities range from the peripheral “the woman has hair” to the
more inalienable “the woman has a liver”, to the completely inalienable “the
woman has a body”. Notably, while there is no coincidentality in these
examples, making it more like the alienable possession space, the control
relation between arguments—e.g., woman to her hair, woman to her liver, woman
to her body—has become less and less asymmetrical, similar to the relation in
the coincidental location space (Koch, 2012; Piñango, 2023; Zhang, 2021).

We conclude then that the lexical meaning of have, while constrained, is
variable along continuous dimensions. As a result, such meaning is best
characterized as a space within which specific readings can obtain. This
conclusion in turn raises the question of what the properties of such a
continuous space are that give rise to the constrained variability in meaning
that have exhibits. We address this question below.

###  1.2 Continuous conceptual space for lexical meaning

It has been proposed that the readings of have are supported by a conceptual
space organized in terms of two continuous cognitive dimensions or metrics:
control asymmetry and connectedness (Gärdenfors and Warglien, 2012; Piñango,
2019, 2023; Zhang, 2021). Control asymmetry measures the degree to which two
individuals in a situation differ in how much one controls the other. Control
asymmetry underpins perception of causality and causal chains. In doing so, it
gives rise to intuitions about intentionality and agency (e.g., Carey, 2009;
Croft, 2012; Talmy, 1988). It has also been shown to constrain language
development (e.g., Klein and Perdue, 1992). An evaluation of high control
asymmetry between two participants means that one of the participants can be
construed as a controller in the situation, that is, an intentional agent, and
not the other way around. A low control asymmetry evaluation means that
neither of the participants is construable as controller. In the case of have,
ultimate evaluation of control asymmetry depends on the context, including the
properties of the participants.

Connectedness measures the degree to which two individuals in a situation are
functionally or structurally related to one another. It is from connectedness
that intuitions emerge about coherence in the world, e.g., object
individuation (e.g., Carey, 2009; Gopnik et al., 2004; Krøjgaard, 2004).
Relations of connectedness are built along independently motivated conceptual
dimensions—spatial, temporal, informational, or functional (Piñango and Deo,
2016). In the case of have, ultimate evaluation of connectedness again depends
on the context and the perceived properties of the argument referents.

In Figure 1, three possible interpretations of have are plotted in the space
spanned by the two dimensions of connectedness (horizontal axis) and control
asymmetry (vertical axis). A coincidental adjacency interpretation, as in 1.1,
corresponds to low connectedness and low control asymmetry, and an alienable
possession interpretation, as in 1.1, corresponds to higher connectedness and
higher control asymmetry. An inalienable possession interpretation, as in 1.2,
corresponds to high connectedness and low control asymmetry.

. The oak tree has a thick trunk.

Figure 1: Three interpretations of have plotted in continuous 2D semantic
space. Numbers correspond to example sentence labels in the text.

As seen in Figure 2, when more possible interpretations of have are plotted
(including, in addition to the examples given so far, at least containment,
control, and kinship), they tend to fall on an inverted “U” shape. This
pattern indicates dependencies between the two dimensions which constrain
object perception and its linguistic encoding. We return to this point in the
context of our model in Section 2.

Figure 2: Six interpretations of English have. Dotted line indicates
hypothesized constraints on the relationship between the two semantic
dimensions. Adapted from Piñango (2019).

###  1.3 Further empirical evidence for continuous semantic dimensions

In addition to the robust observation of gradability between readings of have,
empirical support for a model of lexical meaning based on interpretable,
continuous dimensions comes from two other sources: (a) trajectories of
meaning change over time, and (b) real-time sentence comprehension effects.
Regarding (a), over an approximately 200-year period, the postposition kade in
the Indo-Aryan language Marathi has shifted gradually from primarily an
adjacency reading, to primarily an alienable possession reading, to primarily
an inalienable possession reading (Deo, 2015; Zhang, 2021). This trajectory
essentially traces the inverted “U” shape in Figure 2 from left to right. This
supports the notion that the potential readings of have are organized along
these continuous dimensions, rather than forming a countable set of discrete
meanings.

Regarding (b), evidence comes from acceptability judgments, self-paced
reading, and electroencephalography (EEG) experiments investigating the
availability of the coincidental adjacency reading associated with have as a
result of preceding context. Zhang et al. (2018) administered an acceptability
judgment task with target sentences consisting of have and two inanimate
arguments, as in 1.1. Each target sentence was preceded by a context sentence,
also consisting of have and two inanimate arguments. The crucial manipulation
was the meaning of the context sentence: adjacency, as in 1.1, or inalienable
possession, as in 1.3.

. The pine tree has big branches.

When preceded by a context sentence designed to evoke an adjacency
interpretation, the target sentence received higher acceptability ratings,
relative to when the same sentence was preceded by a sentence with a
possession meaning. This improvement in acceptability was attributed to a
gradient shift in interpretation towards adjacency due to the influence of the
context sentence.

Using a similar stimulus set as in the acceptability judgment task, Zhang et
al. (2018) observed decreased reading times for target sentences preceded by
an adjacency context sentence, relative to when they were preceded by a
possession context sentence. Moreover, EEG recordings indicated an N400 event-
related potential (ERP) in the possession condition relative to the adjacency
condition (Zhang et al., 2018). These results are consistent with a decreased
neurocognitive processing load in the adjacency condition, due to contextual
facilitation of an adjacency interpretation of the target sentence.

Finally, the magnitude of contextual modulation of have interpretation
correlates at an individual level with an independent measure of context
sensitivity, i.e., the Autism-Spectrum Quotient (AQ: Baron-Cohen et al.,
2001). Individuals with higher AQ scores (decreased context sensitivity)
exhibit a decreased difference in acceptability between conditions (Zhang et
al., 2022). The influence of context on interpretation is a gradient rather
than categorical phenomenon. Some of the variation in the magnitude of
contextual influence can be explained by the AQ.

Taken together, observations from historical change, acceptability judgments,
self-paced reading, EEG, and individual variation all point to gradience in
the cognitive representation of lexical meaning. Such gradience is captured by
a parameterized conceptual space such as the one schematized in Figures 1 and
2. The question that arises now is what are the neurocognitive properties of
such a system. To investigate this question we turn to Dynamic Field Theory
(DFT: Schöner et al., 2016), a formal framework for understanding the neural
activation dynamics underlying continuous cognitive dimensions.

###  1.4 Dynamic Field Theory (DFT)

In this subsection, we give a brief overview of DFT; a more detailed
description of the relevant mathematics is given in Section 2. In DFT,
features relevant for cognition are modeled as continuous parameters governed
by the activity of populations of neurons. The activity of a neural population
over time is described using a differential equation defining a dynamic neural
field (DNF: Amari, 1977). DNFs are characterized by point attractor dynamics.
This means that, at any given time, the activation pattern in a DNF is
attracted to a particular state, i.e., the point attractor state. The location
of the point attractor can change over time according to a variety of factors,
e.g., inputs to the DNF from sensory surfaces or other DNFs. Usually, when a
DNF is not receiving any input, the point attractor corresponds to an inactive
or resting state. When a DNF begins to be influenced by input, the point
attractor might shift to an active state. In particular, the dynamics of
lateral interaction within DNFs allow the formation of “peaks” of activation.
Depending on the cognitive dimension being represented by the DNF, an
activation peak might correspond to a movement goal, a percept, or another
kind of cognitive event. Since change within DNFs is characterized by point
attractor dynamics, but the location of the point attractor is itself ever-
changing, DNFs can be described as metastable (e.g., Kelso, 2012).
Metastability, invoking the interplay between stability and flexibility, is an
important property of cognition (Kelso, 1995). Stability offers resistance to
the ubiquitous influence of noise, and flexibility allows rapid change under
changing cognitive and environmental conditions. In the context of lexical
meaning, metastability offers a way to reconcile intuitions of discreteness
with evidence for underlying continuity.

DFT originally developed in the context of motor control research, especially
in the domains of eye movements (Kopecz and Schöner, 1995) and arm movements
(Erlhagen and Schöner, 2002). It has been increasingly applied in other
cognitive domains, including, recently, speech and language. DFT models of
speech and language have, so far, focused on the neurocognitive representation
of phonetic dimensions, e.g., voice onset time (VOT), and the location and
degree of constrictions formed by the tongue. Thus, activation peaks
correspond to articulatory movement goals. These models have offered novel
explanations for a variety of empirical phenomena: effects of auditory
perception on verbal response times (Roon and Gafos, 2016), effects of lexical
competitors on speech articulation in errors (Stern et al., 2022) and non-
errors (Stern and Shaw, 2023a, b), long-term phonological change (Gafos and
Kirov, 2009; Shaw and Tang, 2023), and individual differences in phonological
representations (Harper, 2021).

###  1.5 This paper

In this study, we extend neural field dynamics to dimensions of semantic
interpretation. While the relevant cognitive dimensions are specific to the
meaning system and therefore differ from those of previous DFT models of
speech, the basic dynamics of neural activity are the same. The model we
propose implements a mapping between the lexical item have and the continuous
semantic space schematized in Figures 1 and 2. Instead of articulatory
movement goals, peaks of neural activation correspond to semantic
interpretations. One contribution of the paper is to offer a neurocognitive
process explanation of the results described above: contextual modulation of
the timecourse and outcome of lexical interpretation, and individual variation
in the magnitude of this modulation. More generally, we offer an explanation
for the intuition that meaning is experienced as discrete (e.g., adjacency or
possession), despite evidence for a continuous substrate. Such apparent
discreteness, we propose, arises from metastability in a continuous space
defined by neurocognitive variables. In addition to capturing existing
results, simulations from the model also generate a novel empirical
prediction, which we test with an experiment combining self-paced reading and
acceptability judgments. We intend our model to be general, using the English
lexical item have as a test case or proof of concept. We propose that, while
individual lexical items vary in the relevant semantic dimensions, as well as
in the details of their coupling to those dimensions, the basic architecture
and mechanisms of our model do not vary.

The remainder of the paper is structured as follows. Section 2 describes the
structure of the model and the results of the simulations. Section 3 describes
the design of the experiment, and Section 4 reports the experimental results.
Section 5 discusses theoretical implications of the study and new predictions
that remain to be tested.

##  2 Dynamic neural model of lexical meaning

###  2.1 Model structure

The model consists of two dynamic neural fields (DNFs) and one dynamic node.
One DNF governs interpretation on the semantic dimension of control asymmetry
(CA), and the other DNF governs interpretation on the dimension of
connectedness (conn). The node corresponds to the lexical item have.
Activation of the node follows simple linear dynamics, given in Eq. 1.

$\tau\dot{u}(t)=-u(t)+s_{\text{ext}}(t)+q\xi(t)$ (1)

The rate of change of activation $\dot{u}(t)$ is negatively related to current
activation $u(t)$, defining a dynamical system with a point attractor at
$s_{ext}(t)+q\xi(t)$. $s_{\text{ext}}(t)$ represents external input to the
node, e.g. from perception or intention, and $\xi(t)$ represents normally
distributed noise weighted by a parameter $q$. Thus, when there is external
input $s_{ext}(t)$ to the node, the node’s activation is attracted to
$s_{ext}(t)$. When there is no input, activation is attracted to 0. $\tau$ is
a time constant, with higher values corresponding to slower rates of
evolution. In the simulations reported below, $\tau$ is set to $5$, and $q$ is
set to $0.1$. We set the magnitude of external input $s_{\text{ext}}$
depending on the condition being simulated.

Activation in each of the two DNFs unfolds according to Eq. 2.

$\begin{split}\tau\dot{u}(x,t)=-u(x,t)+h+s_{\text{ext}}(x,t)+s_{\text{node}}(x,t)+s_{\text{DNF}}(x,t)\\\
+\int k(x-x^{\prime})g(u(x^{\prime},t))dx^{\prime}+q\xi(x,t)\end{split}$ (2)

Activation $u$ is defined for each neuron $x$ representing the relevant
semantic dimension at each moment in time $t$. The range of $x$ is set to 100,
such that each neuron in the field is maximally sensitive (“tuned”) to a
particular percentage of the maximum conceivable value of that dimension. For
instance, when the neuron $x=80$ in the conn DNF is active, this corresponds
to an interpretation of “$80\%$ of maximum conceivable connectedness”.
Activation in the DNF has a point attractor at
$h+s_{\text{ext}}(x,t)+s_{\text{node}}(x,t)+s_{\text{DNF}}(x,t)+\int
k(x-x^{\prime})g(u(x^{\prime},t))dx^{\prime}+q\xi(x,t)$. The resting level $h$
is assumed to be below zero for all neurons, by convention at $-5$. We set the
time constant $\tau$ for the DNFs to $20$. Each field input
$s_{\text{ext}}(x,t)$, $s_{\text{node}}(x,t)$, and $s_{\text{DNF}}(x,t)$ is
represented as a separate Gaussian distribution of the form

$s(x,t)=a\exp\left[-\frac{(x-p)^{2}}{2w^{2}}\right]$ (3)

where $a$ controls the amplitude of the input, $p$ controls the position of
the input in the field, and $w$ controls the width of the input distribution.
In the simulations reported below, we set the amplitude $a_{\text{ext}}$ of
external input depending on the condition being simulated.
$s_{\text{node}}(x,t)$ represents input from the have node, whose amplitude is
defined straightforwardly as a linear function of the activation of the node:
$a_{\text{node}}(t)=u(node,t)$. This is a simplification relative to most DFT
models, where the amplitude of input from a node to a field would be a more
complex (sigmoidal) function of node activation. Our motivation for
eliminating the sigmoidal gating function on node-to-field input comes from
work on lexical neighborhood effects on articulation, where non-selected
lexical items (nodes) exert some influence on phonetic planning (DNFs) (Stern
and Shaw, 2023b). This issue is largely orthogonal to the present study
because there is only one node in the model. We chose to use the same node-
field coupling dynamics as in Stern and Shaw (2023b) for the sake of
simplicity and consistency. The same results could likely be achieved with a
relatively shallow or “soft” sigmoidal gating function.

The have node is coupled to the conn DNF with a wide distribution
($w_{\text{have}}$ = 40) positioned at the center of the field
($p_{\text{have}}$ = 50), as seen in Figure 3. When the have node becomes
active, it sends input to the entire conn field, consistent with an analysis
of polysemy for the lexical semantics of have. However, the center of the conn
field is favored, consistent with the fact that, all else equal, have tends to
evoke an interpretation of alienable possession (intermediate connectedness).

Figure 3: Distribution of input from the have node to the conn DNF.

$s_{\text{DNF}}(x,t)$ represents input from each DNF to the other. Via this
mechanism, patterns of activation in one DNF evoke corresponding patterns of
activation in the other DNF. This mechanism implements the “inverted U”
pattern described in Section 1 (Figure 2). In particular, as seen in Figure 4,
activation consistent with high control asymmetry evokes activation consistent
with intermediate connectedness (and vice versa; note the double-sided
arrows), and activation consistent with low control asymmetry evokes
activation consistent with both low connectedness and high connectedness (and
vice versa).

Figure 4: DNF-DNF coupling distribution parameters.

The amplitude $a_{\text{DNF}}$ of each input from one DNF to the other is
given by

$a_{DNF}=\frac{{\max(u(\text{sender}))-\max(u(\text{receiver}))}}{{\max(u(\text{sender}))-h}}\cdot\sum_{i}^{F_{\text{sender}}}\frac{c_{DNF}\cdot(u(x_{i})-h)}{1+(\frac{x_{i}-p_{\text{sender}}}{w_{\text{sender}}})^{4}}$
(4)

The term on the right,
$\sum_{i}^{F_{\text{sender}}}\frac{c_{DNF}\cdot(u(x_{i})-h)}{1+(\frac{x_{i}-p_{\text{sender}}}{w_{\text{sender}}})^{4}}$,
defines the basic magnitude of $a_{\text{DNF}}$. The magnitude of input from
each neuron $x_{i}$ in the field which is sending input (of size
$F_{\text{sender}}$) to the field receiving input is determined by its
activation above resting level $h$, weighted by a parameter $c_{\text{DNF}}$,
set to 0.3 in our simulations. This magnitude is further weighted by
$1+(\frac{x_{i}-p_{\text{sender}}}{w_{\text{sender}}})^{4}$, a nonlinear
(quartic) function of the distance from $x_{i}$ to the center of the sending
distribution $p_{\text{sender}}$, divided by the width of the sending
distribution $w_{\text{sender}}$. Neurons within one $w_{\text{sender}}$ of
$p_{\text{sender}}$ contribute substantially to $a_{\text{DNF}}$, while
neurons exceeding one $w_{\text{sender}}$ from $p_{\text{sender}}$ contribute
exponentially less. This value is summed for all neurons within the sending
field, and then weighted by the term on the left,
$\frac{{\max(u(\text{sender}))-\max(u(\text{receiver}))}}{{\max(u(\text{sender}))-h}}$.
When the maximum activation within the sending distribution (ranging from
$p_{\text{sender}}-w_{\text{sender}}$ to
$p_{\text{sender}}+w_{\text{sender}}$) is much greater than the maximum
activation in the receiving distribution, this term approaches 1, so
$a_{\text{DNF}}\approx\sum_{i}^{F_{\text{sender}}}\frac{c_{DNF}\cdot(u(x_{i})-h)}{1+(\frac{x_{i}-p_{\text{sender}}}{w_{\text{sender}}})^{4}}$.
However, as the maximum activation in the receiving distribution approaches
(or exceeds) the maximum activation in the sending distribution, the weighting
term approaches 0, reducing or eliminating $s_{\text{DNF}}(x,t)$. In this way,
the sending field cannot increase activation in the receiving field beyond its
own maximum activation, preventing an infinite positive feedback loop. The
centers $p$ and widths $w$ of each distribution are given in Table 1.

distribution |  $p$ |  $w$
---|---|---
low CA | $30$ | $20$
high CA | $70$ | $20$
low conn | $25$ | $12$
mid conn | $50$ | $12$
high conn | $75$ | $12$
Table 1: DNF coupling distributions.

Within-field lateral interaction between neurons is defined by an interaction
kernel $k(x-x^{\prime})$:

$\begin{split}k(x-x^{\prime})=\frac{c_{exc}}{\sqrt{2\pi\sigma_{exc}}}\exp\left[-\frac{(x-x^{\prime})^{2}}{2\sigma_{exc}^{2}}\right]\\\
-\frac{c_{inh}}{\sqrt{2\pi\sigma_{inh}}}\exp\left[-\frac{(x-x^{\prime})^{2}}{2\sigma_{inh}^{2}}\right]-c_{glob}\end{split}$
(5)

Each neuron $x^{\prime}$ which exceeds an activation threshold contributes
activation to other neurons $x$ as a function of their distance within the
field $(x-x^{\prime})$. As seen in Figure 5, interaction is excitatory
(weighted by $c_{exc}$, set here to $30$) for nearby neurons (defined by
$\sigma_{exc}$, set here to $5$) and inhibitory (weighted by $c_{inh}$, set
here to $5$) for more distant neurons (defined by $\sigma_{inh}$, set here to
$12.5$). $c_{glob}$, set here to 2, contributes global inhibition from each
above-threshold neuron.

Figure 5: Lateral interaction kernel $k(x-x^{\prime})$.

Lateral excitation helps to stabilize activation peaks (which correspond to
semantic interpretations), and lateral inhibition prevents runaway expansion
of activation peaks. Crucially, we set the parameters of the interaction
kernel such that only a single peak can form at a time in a given field for
the range of input amplitudes under consideration in our simulations, defining
selection dynamics.

As seen in Eq. 6 and Figure 6, the activation threshold for interaction is
given by a sigmoidal function $g(u)$, where $\beta$ (set here to $4$) controls
the steepness of the threshold:

$g(u)=\frac{1}{{1+\exp(-\beta u)}}$ (6)

Figure 6: Sigmoidal function $g(u)$ gating lateral interaction.

By convention, the threshold is set to $u=0$ so that lateral interaction kicks
in only when activation approaches $0$. Finally, noise in field activation is
simulated by adding normally distributed random values $\xi(x,t)$ weighted by
$q$, set here to $1$.

###  2.2 Model simulations

In this section, we use the model to simulate the interpretation of sentences
conveying adjacency meanings of have in two contexts: (1) following an
adjacency interpretation of have, and (2) following a possession
interpretation of have. Each simulation consists of three phases, summarized
in Table 2. In phase 1, the model receives external inputs (all with amplitude
$a=6$) which drive interpretation of the context sentence. In the adjacency
context, these inputs correspond to low CA and low conn; the have node also
receives input. In the possession context, external inputs also excite the
have node and the low side of the CA field, but the conn field receives input
corresponding to high connectedness, i.e., inalienable possession. Phase 1 is
the only phase which differs between conditions. In phase 2, all inputs are
removed. This corresponds to the time between interpreting the context
sentence and interpreting the target sentence. In phase 3, the model receives
external inputs corresponding to the adjacency have target sentence. These
inputs are identical in both conditions: have and low CA. Phases 1 and 3 each
run for 90 timesteps, which we found to be enough time for an activation peak
to stabilize in both DNFs. Phase 2 runs for 20 timesteps, which we found to be
enough time for both activation peaks to fall below the interaction threshold
($u=0$), but not enough time for the fields to return fully to the resting
level. Each simulation runs for a total of 200 timesteps.

|  Phase 1: context |  Phase 2: no input |  Phase 3: target
---|---|---|---
adjacency context |  low CA low conn have |  - |  low CA have
possession context |  low CA high conn have |  - |  low CA have
Table 2: Summary of external inputs $s_{\text{ext}}$ to each model component
in each phase of each simulation.

Examples of simulated interpretation in each context are displayed in Figure
7. In phase 1 (up to timestep 90) the have node becomes active, and begins to
send input to the conn field. The CA field quickly forms a stabilized peak
corresponding to an interpretation of low control asymmetry in both
conditions. Due to field coupling, this CA peak sends input to the conn field
on both the low and high ends. In the adjacency context, an activation peak
corresponding to low conn stabilizes and suppresses the rest of the field via
lateral inhibition. In the possession context, the winning activation peak is
on the high side of the field. During phase 2 (from timesteps 91–110), all
activation decreases towards resting level. Activation of the have node
returns almost back to its resting level. In the fields, activation falls
below the interaction threshold ($u=0$), but does not return fully to the
resting level. At timestep 111 (the beginning of phase 3), field activation is
still highly non-uniform, reflecting residual activation from phase 1. In the
CA field, another peak on the low side of the field forms in both conditions.
In the conn field, the location of the peak differs by condition, despite the
fact that the phase 3 inputs are identical between conditions. In the
adjacency context, phase 3 (target) processing stabilizes on another
interpretation of low conn; in the possession context, the stabilized peak
corresponds to an interpretation of high conn. In this way, the evolution of
activation is shaped by the preceding state of the system.

Figure 7: Activation history of the have node (left), the CA field (center),
and the conn field (right) in the adjacency context (top) and the possession
context (bottom) for a single simulation.

The examples in Figure 7 were selected in order to demonstrate the effect of
preceding context (phase 1 evolution) on target sentence interpretation (phase
3 evolution). However, not every simulated run of the model exhibits the same
effect. The presence of noise in the model introduces a stochastic influence
on the location of field stabilization in each simulation. In order to examine
the robustness of the contextual modulation effect, we simulated 1000
instances of interpretation in each of the two conditions. As seen in Figure
8, there is a bimodal distribution of interpretations in both contexts. That
is, for each context, an interpretation of either adjacency or possession for
the target sentence was possible. However, the likelihood of each
interpretation was influenced by context. In the adjacency context, low conn
(adjacency) interpretations were more likely; in the possession context, high
conn (possession) interpretations were more likely. Thus, while context does
not completely determine the course of field evolution, it exerts a strong
enough influence to be observable over many simulations.

Figure 8: Distribution of activation peak location in the conn field at the
end of each of 1000 simulations in each condition.

How do we relate these simulated results to the observed acceptability results
described in Section 1? Field stabilization at the low end of the conn field
corresponds to an adjacency interpretation, which is consistent with the two
inanimate arguments of have in the target sentence. Thus, a low conn peak
should correlate with a higher acceptability rating. On the other hand, a high
conn peak, corresponding to a possession interpretation, is inconsistent with
the two nouns in the target sentence, which cannot easily be construed to be
in a possession relationship. Thus, a high conn peak should correlate with a
lower acceptability rating. In order to transform the field stabilization
results into simulated acceptability results, we therefore reverse the value
of the location of field stabilization using the following equation

$\text{rating}=\frac{{100-conn}}{{100}}$ (7)

where $conn$ ranges from $0$ to $100$. As seen in Figure 9, simulated
acceptability was higher in the adjacency context relative to the possession
context, consistent with existing results.

Figure 9: Mean simulated acceptability by context.

Existing empirical results have also demonstrated that individual variation in
the magnitude of the by-context difference in acceptability is predicted by AQ
scores, such that individuals with higher AQ scores show a reduced influence
of context. We model individual variation in AQ by varying the parameter
$c_{\text{DNF}}$, which controls the magnitude of field coupling. Stronger
field coupling is consistent with a greater degree of system-level
expectations. In other words, given some interpretation on one semantic
dimension (e.g., control asymmetry (CA)), individuals can vary in the degree
to which they expect a corresponding interpretation on a related semantic
dimension (e.g., connectedness (conn)). We posit that individuals with higher
AQ scores are more influenced by system-level expectations, i.e. stronger
field coupling. With stronger system-level expectations, the processing system
is more rigid, and less influenced by real-time signals. This is consistent
with existing findings relating AQ scores to linguistic behavior. For
instance, individuals with higher AQ scores show greater compensation for
coarticulation in speech perception (Yu, 2010). In addition, higher AQ
individuals are less sensitive to phonetic duration when assigning judgments
of prosodic prominence (Bishop, 2016). Both sets of results suggest that
higher AQ individuals rely more on system-level expectations (e.g., expected
cooccurrence of phonetic signals), and less on the real-time signal itself
(e.g., the phonetic duration of a perceived word).

In order to apply this hypothesis to the case of contextual influence on the
interpretation of have, we varied $c_{\text{DNF}}$ from 0.3 to 0.7 in steps of
0.1, and at each level, we ran 1000 simulations in each condition. As seen in
Figure 10, higher values of $c_{\text{DNF}}$ corresponded with a reduction in
the difference in acceptability between conditions. In other words, stronger
field coupling reduced the magnitude of the contextual modulation effect. This
is because input from the low CA distribution equally favors the low conn and
high conn distributions. When this input is stronger, the lingering asymmetry
between these distributions from phase 1 is reduced more quickly, reducing the
influence of context on interpretation in phase 3.

Figure 10: Mean acceptability by condition at each level of $c_{\text{DNF}}$.

By modeling the timecourse of individual instances of semantic interpretation,
we can examine the relationship between interpretation content (the location
of field stabilization) and interpretation time (the timestep of field
stabilization) for individual simulations. As seen in Figure 11, this
relationship was modulated by context. In the adjacency context, a negative
correlation was observed: faster response times corresponded with higher
acceptability ratings. This is because the adjacency context primed a more
acceptable interpretation: when the field stabilized at a lower conn value
(higher acceptability), this stabilization was facilitated by the context. In
the possession context, a positive correlation was observed: faster response
times corresponded with lower acceptability ratings. This is because the
interpretation primed by the possession context was ultimately a less
acceptable one.

Figure 11: Relationship between acceptability and response time for each
simulation in each context.

To date, studies of contextual facilitation of have interpretation have not
simultaneously collected data regarding acceptability and processing time.
Below we report an experiment combining acceptability judgments and self-paced
reading. The purpose of the experiment is twofold: (a) to replicate previous
results regarding contextual facilitation of adjacency readings of have, as
well as individual variation in the magnitude of this effect indexed by the
AQ, and (b) to test the new model prediction represented in Figure 11.

##  3 Experiment design

###  3.1 Participants

56 adults participated in the experiment (ages 20-30; 32 women, 21 men, 3
nonbinary). All participants self-reported that they were native monolingual
speakers of American English, and that they had no history of speech,
language, hearing, or reading impairment. Participants were recruited through
Prolific (www.prolific.com). Before beginning the experiment, participants
provided informed consent under Yale University IRB #2000033871.

###  3.2 Materials

Each experimental stimulus consisted of a pair of sentences (a context
sentence followed by a target sentence) conjoined by and. Every target
sentence was designed to convey an adjacency interpretation of have, as in
3.2.

. …the oak tree has a skateboard that is red.

It is difficult to construe a possession interpretation of 3.2 because oak
trees do not typically possess skateboards (whether alienably or inalienably).
Every target sentence had the form “the [noun1] has a [noun2] that is [adj]”.
[noun2] in the target sentence is the critical word at which an interpretation
of have can be construed, since after reading [noun2], the participant has
read have and both of its arguments. The relative clause “that is [adj]” was
included as a spillover region. There were ten target sentences, each of which
was preceded by two different context sentences, for a total of 20
experimental stimuli. Each context sentence conveyed either an adjacency
reading or an inalienable possession reading of have, as in Table 3.

adjacency |  possession
---|---
The maple tree has a plastic box behind it and… |  The maple tree has a branch that is thick and…
Table 3: Example context sentence from each condition, corresponding to target
sentence 3.2.

Every context sentence had the structure “the [noun1] has a [noun2]
[modifier]”. [modifier] was either a prepositional phrase (in the adjacency
condition) or a “that is [adj]” phrase (in the possession condition). [noun1]
was identical between the two conditions in each set, and always contrasted
saliently with [noun1] in the target sentence in order to increase overall
felicitousness. In both conditions, [noun2] in the context was semantically
unrelated to [noun2] in the target sentence. Moreover, the first phoneme in
[noun2] in the context was always different from the first phoneme of [noun2]
in the target sentence, in order to minimize confounds from phonological
priming. All nouns were inanimate in order to maximize the availability of
adjacency interpretations. 60 filler stimuli were also included. 20 of the
fillers were of the same form as the experimental stimuli, but with contexts
that used verbs other than have to convey an adjacency reading (10 stimuli) or
a possession reading (10 stimuli). 40 of the fillers were completely unrelated
to the experimental stimuli: 20 conveyed interpretations of circumstantial
metonymy (e.g., “the grilled cheese at Table 6 ordered another coffee:), and
20 conveyed non-metonymous counterparts (e.g., “the customer at Table 6
ordered another coffee”). This yielded a total of 80 stimuli (20 experimental
+ 60 fillers).

In order to examine effects of individual variation in communicative context
sensitivity, participants completed the Autism-Spectrum Quotient (AQ: Baron-
Cohen et al., 2001). The AQ consists of 50 statements (e.g., “I prefer to do
things the same way over and over again”). The participant responds to each
statement by selecting one of four options: “definitely disagree”, “slightly
disagree”, “slightly agree”, “definitely agree”.

###  3.3 Procedure

Participants were instructed to complete the experiment in a quiet room where
they would be free from distractions for up to an hour. To begin each trial,
participants clicked on a button at the top of the screen with the words
“Click here to begin the next trial”. Then, the first word of the stimulus
appeared in the center of the screen. Participants pressed the spacebar to
advance to the next word. Participants were instructed to read as quickly as
possible while making sure to comprehend what they were reading. After
participants advanced past the last word, they were prompted by the following
instruction to give an acceptability rating of the entire stimulus: “How
likely would you be to say this sentence, or hear this sentence from another
native speaker of English?”. Participants gave their response on a seven-point
Likert scale (labeled “very unnatural” on the left end and “very natural” on
the right) by clicking on the corresponding button at the bottom of the
screen.

The experiment began with four practice trials unrelated to the experimental
stimuli. Then, each stimulus was presented twice, for a total of 160 trials
per subject. Each of the two blocks was pseudo-randomized such that no two
consecutive trials were from the same condition or the same stimulus set. The
presentation order of the two blocks was counter-balanced between
participants. After completing the combined self-paced reading and
acceptability judgment task, participants completed the AQ. The entire
procedure was conducted in the same session in Gorilla (Anwyl-Irvine et al.,
2020). The session lasted approximately 30-40 minutes.

###  3.4 Data processing

For the analysis of acceptability ratings, trials with acceptability response
times greater than 2.5 standard deviations from the participant’s mean were
removed. This led to the exclusion of 194 trials (2.20%). Before plotting the
rating data, raw ratings were z-scored by participant in order to abstract
away from idiosyncratic rating styles (e.g., staying towards the ends or
towards the center of the scale). In statistical models, this was accomplished
via random effects by participant. For the analysis of word reading times,
reading times less than 120 ms or greater than 2000 ms were removed (210
trials, 2.39%). For one participant, 38% of their trials were removed
according to these criteria. This participant’s data was subsequently
completely excluded from analysis, leaving a total of 2098 experimental trials
from 55 participants for analysis.

Reading times were log-transformed in order to approximate a normal
distribution. In order to assess the effects of control variables on reading
time, a linear mixed effects model was fit to the log-transformed RT (logRT)
of all words with fixed effects of word length (in characters), trial number,
and the preceding word’s logRT (all scaled and centered), a random intercept
by participant, and random slopes for all predictors by participant. The model
results are displayed in Table 4. All three control variables were found to
significantly affect logRT: words took longer to read when they had more
characters or when the preceding word took longer to read. Words were read
faster when the word came later in the experiment. Thus, rather than analyzing
raw logRT, we analyze the residuals of logRT after being regressed, by
participant, on the three control predictors described above. In other words,
we analyze the variance not predicted by the three control predictors.

|  Estimate |  Std. Error |  df |  t value |  p value
---|---|---|---|---|---
(Intercept) | $5.60$ | $0.03$ | $53.87$ | $198.29$ | $<.001$
char_length | $0.01$ | $0.00$ | $54.07$ | $4.23$ | $<.001$
trial_num | $-0.11$ | $0.01$ | $53.93$ | $-15.66$ | $<.001$
prec_logRT | $0.13$ | $0.01$ | $53.92$ | $19.66$ | $<.001$
Table 4: Effects of control predictors on logRT.

Each AQ response was initially coded on a four-step Likert scale where
“definitely disagree” = 1 and “definitely agree” = 4. For half of the
questions on the AQ, agreement signifies greater autistic traits and
disagreement signifies reduced autistic traits; this is reversed for the other
half of questions. For questions where disagreement signified greater autistic
traits, we reversed the numerical response so that higher values always
corresponded to greater autistic traits. Thus, individual AQ scores could
range from 50 (very low autistic traits) to 200 (very high autistic traits).

##  4 Experiment results

###  4.1 Acceptability

In order to assess the effect of context on acceptability, we fit nested
linear mixed effects models to acceptability ratings using the lme4 package
(Bates et al., 2015) in R (R Core Team, 2021). All models included random
intercepts by item and by participant, and random slopes for context by item
and by participant. Model comparison revealed that a control fixed factor for
trial number (scaled and centered) significantly improved model fit over a
baseline model that only included random effects ($\chi^{2}(1)=14.67$,
$p<.001$). Additionally including the experimental fixed factor of context
(treatment coded; reference level = possession) significantly improved model
fit over the control model ($\chi^{2}(1)=5.27$, $p<.05$). The results of the
full model are displayed in Table 5. Trial number significantly decreased
acceptability ratings, such that ratings generally decreased over the course
of the experiment. Regarding the experimental factor of interest, ratings were
significantly higher in the adjacency context relative to the possession
context.

|  Estimate |  Std. Error |  df |  t value |  p value
---|---|---|---|---|---
(Intercept) | $3.23$ | $0.25$ | $28.77$ | $12.96$ | $<.001$
trial number | $-0.11$ | $0.03$ | $1628.44$ | $-3.88$ | $<0.001$
context=adjacency | $0.28$ | $0.12$ | $29.07$ | $2.36$ | $<.05$
Table 5: Linear mixed effects model of acceptability ratings.

Figure 12 displays mean z-scored (by-participant) acceptability ratings in
each context. Both means are below 0, suggesting that the experimental stimuli
were generally less acceptable than the filler stimuli, consistent with the
general markedness of adjacency interpretations of have. However, consistent
with the results of the regression model, ratings were higher in the adjacency
context relative to the possession context.

Figure 12: Mean z-scored (by participant) acceptability ratings by context.

Recall from Section 2 that in the model, context affected interpretation not
by shifting the overall distribution of acceptability, but by increasing the
likelihood of a distinct, higher-acceptability interpretation. We compare this
simulated behavior to the measured behavior by examining the distribution of
ratings in each context. Figure 13 demonstrates that, consistent with the
simulations, the increase in mean acceptability in the adjacency context
relative to the possession context was not accomplished via on overall shift
in the distribution of ratings. For instance, the number of intermediate
ratings 3 and 4 was largely unaffected by context. Rather, the increase in
mean acceptability occurred because of a decrease in low ratings 1 and 2, and
an increase in high ratings 5 and 6.

Figure 13: Distribution of acceptability ratings by context.

In order to assess whether individual variation in the magnitude of contextual
facilitation is predicted by AQ scores, we plot the by-participant random
slopes for the effect of context against AQ score in Figure 14. A Spearman
test confirms a negative correlation ($\rho=-.36$, $p<.01$): subjects with
higher AQ scores showed a smaller effect of context, i.e. reduced contextual
facilitation of adjacency have sentences.

Figure 14: Relationship between by-participant context effect and AQ score.

###  4.2 Relationship between acceptability and reading time

Next, we turn to the by-trial relationship between acceptability ratings and
reading times. Recall that the model simulations predicted this relationship
to be modified by context: a negative correlation in the adjacency context,
and a positive correlation in the possession context. To test this prediction,
we fit nested linear mixed effects models to the summed residualized reading
times of the critical word [noun2] and each of the words in the spillover
region “that is [adj]”. All models included random intercepts by item and by
participant. Random slopes were not included because they led to model
convergence issues and were also not of theoretical interest in this case.

Adding a fixed factor of context did not lead to a significant improvement in
fit over a baseline model with only random effects ($\chi^{2}(1)=0.33$,
$p=.57$). However, adding a fixed factor for acceptability rating (z-scored by
subject) did lead to a significant improvement in fit over the baseline model
($\chi^{2}(1)=5.64$, $p<.05$). Adding a fixed factor for context back in did
not lead to an improvement in fit over the model with only a fixed factor for
acceptability ($\chi^{2}(1)=0.64$, $p=.42$). Importantly, however, adding an
interaction term did lead to a significant improvement in fit over the model
with only fixed factors for main effects ($\chi^{2}(1)=0.48$, $p<.05$). We
report the results of the full model with both main effects and their
interaction in Table 6. We observed a significant negative interaction between
context and acceptability, such that the relationship between acceptability
and reading time was more negative in the adjacency context relative to the
possession context. This result, also observable in Figure 15, is consistent
with the model prediction described in Section 2.2.

|  Estimate |  Std. Error |  df |  t value |  p value
---|---|---|---|---|---
(Intercept) | $-0.01$ | $-0.03$ | $52.65$ | $-0.39$ | $.70$
context=adjacency | $-0.02$ | $0.03$ | $2061$ | $-0.591$ | $.55$
acceptability | $-0.01$ | $0.02$ | $1822$ | $-0.38$ | $.70$
context:acceptability | $-0.07$ | $0.03$ | $2089$ | $-2.14$ | $<.05$
Table 6: Linear mixed effects model of residualized reading time for the
critical region. Figure 15: Mean residualized reading times of the critical
region (y-axis) by normalized acceptability rating (x-axis) and context
(color).

###  4.3 Discussion

The acceptability results confirm previously reported results regarding
contextual facilitation of adjacency have interpretations. The acceptability
of adjacency have sentences was improved following a context sentence that
also conveyed an adjacency have interpretation, relative to a context sentence
that conveyed a possession have interpretation. Moreover, individual variation
in the magnitude of this improvement was predicted by AQ scores: individuals
with higher AQ scores (lower context-sensitivity) showed reduced contextual
facilitation. Finally, consistent with the novel prediction of the model
simulations, the by-trial relationship between reading time and acceptability
evidenced context modulation. The relationship was more negative in the
adjacency context relative to the possession context.

##  5 General discussion & conclusion

###  5.1 Summary & discussion

We have argued for a dynamic neural model of lexical meaning and demonstrated
its behavior using the English lexical item have as a test case. The cognitive
basis of the model is a continuous meaning space with two parameters: control
asymmetry and connectedness. Interpretations of “possession” and “adjacency”
associated with have result from the neural dynamics governing interpretation
along those dimensions. The apparent discreteness of the different
interpretations is epiphenomenal, resulting from the property of metastability
in the neural dynamics.333The concept of metastability has previously been
invoked in cognitive science most frequently to explain phenomena in visual
perception, observed from both behaviorial (e.g., Chaudhuri and Glaser, 1991)
and brain measures (e.g., Sterzer et al., 2009). Metastability has also been
invoked to explain semantic ambiguity in language comprehension (Wildgen,
1995). Our model represents a mathematically explicit demonstration of the
role of metastability in language comprehension.

In the model, lexical meaning is a coupling pattern between a neural node
representing the lexical item and dynamic neural fields (DNFs) governing
interpretation on continuous semantic dimensions. Interpretation occurs in
time as activation of the lexical node causes peaks of activation in the
semantic DNFs. The locations of the peaks in feature space correspond to the
content of the interpretation. Dependencies between semantic dimensions,
schematized in Figures 1 and 2, are modeled as coupling patterns between DNFs.

Simulations from the model captured known empirical effects. In particular,
the interpretation evoked by English have was influenced by a preceding
interpretation. An adjacency interpretation was more likely following another
adjacency interpretation, and a possession interpretation was more likely
following another possession interpretation. This occurred in the model
because activation states persist in time, continuing to bias interpretation
until they return to a resting state.444The model parameter $\tau$, which
controls the rate of field evolution, modulates the temporal extent of
contextual bias on interpretation. Model simulations also exhibited
covariation between the magnitude of contextual modulation and the strength of
coupling between DNFs. Stronger coupling makes DNFs more resistant to the
effects of context. In other words, there is a stronger influence of long-term
knowledge, relative to immediate context, on lexical interpretation. Motivated
by other observations regarding individual variation in speech behavior
(described in Section 2.2), we related DNF coupling strength to the Autism-
Spectrum Quotient (AQ).

Finally, model simulations generated a novel prediction: an interaction
between context, acceptability, and response time. Specifically, the
prediction was that in an adjacency context, more acceptable (adjacency)
interpretations would be reached more quickly, while in a possession context,
more acceptable interpretations would be reached more slowly. This prediction
was empirically confirmed by the results of a novel experiment combining self-
paced reading and acceptability judgments. Results showed an interaction
between the effects of context and acceptability on response time on a trial
by trial basis, such that the relationship between acceptability and response
time was more negative in the adjacency context relative to the possession
context. That model simulations were able to generate this empirical
prediction demonstrates an important advantage of the DFT framework. In DFT,
both time and cognitive features are modeled as continuous dimensions. This
allows the generation of precise quantitative predictions regarding the
relationship between the timecourse and outcome of cognitive processing.555In
the domain of phonetics, for example, the spatial target of an articulatory
movement can be related to the time it takes to generate that target (Roon and
Gafos, 2016; Stern and Shaw, 2023b). As demonstrated in this study, when DNFs
represent semantic dimensions, we can relate the content of a semantic
interpretation to the time it takes to arrive at that interpretation. This
allows us to move beyond the assumption that less acceptable sentences should
always take longer to process, and thus that acceptability and response time
should always be negatively correlated.

###  5.2 Novel predictions of our approach

Our proposal that individual variation in the strength of coupling between
DNFs is indexed by the AQ generates testable predictions, including in domains
unrelated to linguistic meaning. For example, in an experimental task that
requires learning associations between object color (one DNF) and object shape
(another DNF), individuals with higher AQ scores are predicted to show greater
surprisal effects (e.g., slowed response times) when encountering an object
that violates the learned associations. Modeling learned dependencies between
dimensions as DNF coupling may also shed light on other issues in linguistics.
For example, phonological inventories (possible sounds in a language) and
phonotactic constraints (possible sound sequences in a language) may be
explained as the result of coupling between DNFs representing phonetic
dimensions. Under this view, DNF coupling patterns are an important component
of language-specific knowledge, and thus an important dimension of variation
between speakers of different languages. Among speakers of the same language,
processes conditioned by phonological knowledge, such as accent and perceptual
illusions (Davidson and Shaw, 2012; Dupoux et al., 1999; Hallé and Best, 2007;
Kabak and Idsardi, 2007), are predicted to covary with AQ scores.

###  5.3 Other perspectives

Before concluding, we briefly discuss the relationship of our proposal to
other perspectives on lexical meaning. The proposal that lexical items map to
continuous semantic spaces contrasts with models of lexical meaning based on
discrete concept representations (e.g., Dell, 1986; Levelt et al., 1999;
Roelofs, 1997; Stella et al., 2024). In these models, lexical meaning is
formalized as a set of weighted connections between an activation node
representing the lexical (e.g., CAT) and activation nodes representing
discrete concept representations (e.g., ALIVE, FURRY, etc.). These models
capture the intuition of the discreteness of semantic interpretations (e.g.,
adjacency or possession), but do not explain the evidence for a continuous
substrate described in Section 1.3. In Section 2, we explained how our model
fills that gap by showing how it reconciles intuitions of discreteness with
evidence for continuity.

Our proposal also contrasts with distributed representations of lexical
meaning, e.g., distributed parallel processing networks (e.g., Kawamoto, 1993;
Rumelhart et al., 1986), or vectors describing cooccurrence patterns in
written language corpora (e.g., Baayen et al., 2019; Landauer and Dumais,
1997; Mikolov et al., 2013). These models capture important facts related to
the semantic similarity of lexical items, e.g., priming effects on reaction
times (Kawamoto, 1993). But in contrast to our current effort, their focus is
not on understanding the dimensions themselves on which lexical meanings vary.
As a result, their models consist of a very large number of dimensions, each
of which is not interpretable on its own. For example, in a vector-based
model, the dimensionality of a word’s semantic representation is equal to the
number of words in the training corpus. In a parallel distributed processing
model, the dimensionality equals the number of connections between processing
units. Unlike the model we proposed here, each dimension of description, on
its own, is not intended to be meaningful with respect to cognition.

By contrast, in our model, interpretations are modeled as peaks of activation
in DNFs representing cognitively viable semantic dimensions. This model thus
allows us to understand the relatedness of the various interpretations of a
polysemous lexical item as proximity in the semantically parameterized space
represented by DNFs. It further allows us to understand the difference between
polysemy and homophony as a difference in the proximity of possible activation
peaks in the space defined by the semantic DNFs to which the lexical node is
coupled. Possible activation peaks are more proximal in the case of polysemy
and more distal in the case of homophony. This difference arises from
differences in the coupling patterns between lexical nodes and semantic DNFs.
This kind of solution demonstrates an advantage of a low-dimensional
“localist” framework like DFT.666This perspective also has the potential to
shed light on observed differences in the timecourse of processing polysemous
and homophonous words. Different interpretations of homophonous words tend to
inhibit each other, leading to slowed response times, while different
interpretations of polysemous words tend to prime each other, leading to
faster response times (Frisson, 2015; Klepousniotou and Baum, 2007;
Klepousniotou et al., 2012; MacGregor et al., 2015; Rodd et al., 2002). These
facts may be explained as a result of the basic dynamics of lateral
interaction within DNFs. As described in Section 2, neurons which are proximal
in a DNF tend to excite each other, while those which are more distal tend to
inhibit each other. These are the dynamics which allow the formation of
activation peaks. Neural recordings consistent with these dynamics have been
observed in rhesus monkey motor cortex (Georgopoulos et al., 1986) and cat
visual cortex (Jancke et al., 1999). The difference between polyseme and
homophone processing can be seen as an effect of metric feature distance on
target-distractor interaction, analogous to effects observed in the domains of
eye saccades (Kopecz and Schöner, 1995), manual reaching movements (Erlhagen
and Schöner, 2002), and speech articulation (Tilsen, 2009).

###  5.4 Conclusion

Using a single theoretical framework (DFT) and mathematics of description
(differential equations) allows explicit integration across the cognitive and
sensory-motor domains. Previous DFT modeling work has linked neural
representations of conceptual structure (Jackendoff, 2002) with visual
perception (Grieben and Schöner, 2022) and visual search behavior (Sabinasz et
al., 2023). Explicit coupling between abstract cognitive processes and
sensation/movement has been termed “grounding” of cognition (e.g., Sabinasz et
al., 2023; Sabinasz and Schöner, 2023). As described in Section 1.4, existing
DFT models of speech and language have focused on the sensory-motor domain,
with DNFs representing phonetic dimensions of articulatory movement and
auditory perception. In this paper we have extended DFT to linguistic meaning
through the lens of lexical polysemy, a cognitive domain that appears
relatively distinct from sensation and behavior. Our use of the same
theoretical framework and mathematics as these previous models paves the way
for explicitly coupling the cognitive and sensory-motor aspects of language.
This would represent a significant step towards a complete neurocognitive
model of language from meaning to form: a grounded model of linguistic
cognition.

##  6 Data availability

Data (experimental and simulated) and scripts for analysis and simulation are
available on OSF at https://osf.io/3bue9/

##  7 Funding sources

This research did not receive any specific grant from funding agencies in the
public, commercial, or not-for-profit sectors.

## References

  * Amari (1977) Amari, S.i., 1977.  Dynamics of pattern formation in lateral-inhibition type neural fields.  Biological Cybernetics 27, 77–87.  doi:10.1007/BF00337259.
  * Anderson (1992) Anderson, S.R., 1992.  A-Morphous Morphology.  Cambridge Studies in Linguistics, Cambridge University Press, Cambridge.  doi:10.1017/CBO9780511586262.
  * Anwyl-Irvine et al. (2020) Anwyl-Irvine, A.L., Massonnié, J., Flitton, A., Kirkham, N., Evershed, J.K., 2020.  Gorilla in our midst: An online behavioral experiment builder.  Behavior Research Methods 52, 388–407.  doi:10.3758/s13428-019-01237-x.
  * Baayen et al. (2019) Baayen, R.H., Chuang, Y.Y., Shafaei-Bajestan, E., Blevins, J.P., 2019.  The Discriminative Lexicon: A Unified Computational Model for the Lexicon and Lexical Processing in Comprehension and Production Grounded Not in (De)Composition but in Linear Discriminative Learning.  Complexity 2019, e4895891.  doi:10.1155/2019/4895891.
  * Baron-Cohen et al. (2001) Baron-Cohen, S., Wheelwright, S., Skinner, R., Martin, J., Clubley, E., 2001.  The Autism-Spectrum Quotient (AQ): Evidence from Asperger syndrome/high-functioning autism, males and females, scientists and mathematicians.  Journal of autism and developmental disorders 31, 5–17.  doi:10.1023/a:1005653411471.
  * Bates et al. (2015) Bates, D., Mächler, M., Bolker, B., Walker, S., 2015.  Fitting Linear Mixed-Effects Models Using lme4.  Journal of Statistical Software 67.  doi:10.18637/jss.v067.i01.
  * Bishop (2016) Bishop, J., 2016.  Individual differences in top-down and bottom-up prominence perception, pp. 668–672.  doi:10.21437/speechprosody.2016-137.
  * Brugman (1988) Brugman, C.M., 1988.  The Story of Over: Polysemy, Semantics, and the Structure of the Lexicon.  Garland.
  * Carey (2009) Carey, S., 2009.  The origin of concepts.  The origin of concepts, Oxford University Press, New York, NY, US.
  * Chaudhuri and Glaser (1991) Chaudhuri, A., Glaser, D.A., 1991.  Metastable motion anisotropy.  Visual Neuroscience 7, 397–407.  doi:10.1017/S0952523800009706.
  * Croft (2012) Croft, W., 2012.  Verbs: Aspect and Causal Structure.  Oxford University Press.
  * Davidson and Shaw (2012) Davidson, L., Shaw, J.A., 2012.  Sources of illusion in consonant cluster perception.  Journal of Phonetics 40, 234–248.  doi:10.1016/j.wocn.2011.11.005.
  * Deane (1988) Deane, P.D., 1988.  Polysemy and cognition.  Lingua 75, 325–361.  doi:10.1016/0024-3841(88)90009-5.
  * Dell (1986) Dell, G.S., 1986.  A Spreading-Activation Theory of Retrieval in Sentence Production.  Psychological Review 93, 283–321.  doi:10.1037/0033-295X.93.3.283.
  * Deo (2015) Deo, A., 2015.  Diachronic Semantics.  Annual Review of Linguistics 1, 179–197.  doi:10.1146/annurev-linguist-030514-125100. _eprint: https://doi.org/10.1146/annurev-linguist-030514-125100.
  * Dupoux et al. (1999) Dupoux, E., Kakehi, K., Hirose, Y., Pallier, C., Mehler, J., 1999.  Epenthetic vowels in Japanese: A perceptual illusion?  Journal of Experimental Psychology: Human Perception and Performance 25, 1568–1578.  doi:10.1037/0096-1523.25.6.1568.
  * Erlhagen and Schöner (2002) Erlhagen, W., Schöner, G., 2002.  Dynamic field theory of movement preparation.  Psychological Review 109, 545–572.  doi:10.1037/0033-295X.109.3.545.
  * Frisson (2015) Frisson, S., 2015.  About bound and scary books: The processing of book polysemies.  Lingua 157, 17–35.  doi:10.1016/j.lingua.2014.07.017.
  * Gafos and Kirov (2009) Gafos, A.I., Kirov, C., 2009.  A dynamical model of change in phonological representations: The case of lenition.  Approaches to Phonological Complexity , 219–240doi:10.1515/9783110223958.219.
  * Georgopoulos et al. (1986) Georgopoulos, A.P., Schwartz, A.B., Kettner, R.E., 1986.  Neuronal population coding of movement direction.  Science 233, 1416–1419.
  * Gopnik et al. (2004) Gopnik, A., Glymour, C., Sobel, D.M., Schulz, L.E., Kushnir, T., Danks, D., 2004.  A theory of causal learning in children: causal maps and Bayes nets.  Psychological Review 111, 3–32.  doi:10.1037/0033-295X.111.1.3.
  * Grieben and Schöner (2022) Grieben, R., Schöner, G., 2022.  Bridging DFT and DNNs: A neural dynamic process model of scene representation, guided visual search and scene grammar in natural scenes.  Proceedings of the Annual Meeting of the Cognitive Science Society , 44.
  * Gärdenfors and Warglien (2012) Gärdenfors, P., Warglien, M., 2012.  Using Conceptual Spaces to Model Actions and Events.  Journal of Semantics 29, 487–519.  doi:10.1093/jos/ffs007.
  * Hallé and Best (2007) Hallé, P.A., Best, C.T., 2007.  Dental-to-velar perceptual assimilation: A cross-linguistic study of the perception of dental stop+/1/ clusters.  The Journal of the Acoustical Society of America 121, 2899–2914.
  * Harper (2021) Harper, S., 2021.  Individual Differences in Phonetic Variability and Phonological Representation.  PhD thesis. University of Southern California.
  * Jackendoff (1975) Jackendoff, R., 1975.  Morphological and Semantic Regularities in the Lexicon.  Language 51, 639–671.  doi:10.2307/412891.
  * Jackendoff (2002) Jackendoff, R., 2002.  Foundations of Language: Brain, Meaning, Grammar, Evolution.  Oxford University Press UK.
  * Jancke et al. (1999) Jancke, D., Erlhagen, W., Dinse, H.R., Akhavan, A.C., Giese, M., Steinhage, A., Schöner, G., 1999.  Parametric population representation of retinal location: Neuronal interaction dynamics in cat primary visual cortex.  Journal of Neuroscience 19, 9016–9028.  doi:10.1523/jneurosci.19-20-09016.1999.
  * Kabak and Idsardi (2007) Kabak, B., Idsardi, W.J., 2007.  Perceptual distortions in the adaptation of English consonant clusters: syllable structure or consonantal contact constraints?  Language and Speech 50, 23–52.  doi:10.1177/00238309070500010201.
  * Kawamoto (1993) Kawamoto, A.H., 1993.  Nonlinear dynamics in the resolution of lexical ambiguity: A parallel distributed processing account.  Journal of Memory and Language 32, 474–516.  doi:10.1006/jmla.1993.1026.
  * Kelso (1995) Kelso, J.A.S., 1995.  Dynamic Patterns: The Self-Organization of Brain and Behavior.  MIT Press, Cambridge.
  * Kelso (2012) Kelso, J.A.S., 2012.  Multistability and metastability: understanding dynamic coordination in the brain.  Philosophical Transactions of the Royal Society B: Biological Sciences 367, 906–918.  doi:10.1098/rstb.2011.0351.
  * Klein and Perdue (1992) Klein, W., Perdue, C., 1992.  Utterance Structure: Developing grammars again. volume 5 of Studies in Bilingualism.  John Benjamins Publishing Company, Amsterdam.  doi:10.1075/sibil.5.
  * Klepousniotou and Baum (2007) Klepousniotou, E., Baum, S.R., 2007.  Disambiguating the ambiguity advantage effect in word recognition: An advantage for polysemous but not homonymous words.  Journal of Neurolinguistics 20, 1–24.  doi:10.1016/j.jneuroling.2006.02.001.
  * Klepousniotou et al. (2012) Klepousniotou, E., Pike, G.B., Steinhauer, K., Gracco, V., 2012.  Not all ambiguous words are created equal: an EEG investigation of homonymy and polysemy.  Brain and Language 123, 11–21.  doi:10.1016/j.bandl.2012.06.007.
  * Koch (2012) Koch, P., 2012.  Location, existence, and possession: A constructional-typological exploration.  Linguistics 50.  doi:10.1515/ling-2012-0018.
  * Kopecz and Schöner (1995) Kopecz, K., Schöner, G., 1995.  Saccadic motor planning by integrating visual information and pre-information on neural dynamic fields.  Biological Cybernetics 73, 49–60.  doi:10.1007/BF00199055.
  * Krøjgaard (2004) Krøjgaard, P., 2004.  A review of object individuation in infancy.  British Journal of Developmental Psychology 22, 159–183.  doi:10.1348/026151004323044555.
  * Lakoff (1990) Lakoff, G., 1990.  Women, Fire, and Dangerous Things: What Categories Reveal about the Mind.  University of Chicago Press, Chicago, IL.
  * Landauer and Dumais (1997) Landauer, T.K., Dumais, S.T., 1997.  A solution to Plato’s problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge.  Psychological Review 104, 211–240.  doi:10.1037/0033-295X.104.2.211.
  * Levelt et al. (1999) Levelt, W.J., Roelofs, A., Meyer, A.S., 1999.  A theory of lexical access in speech production.  Behavioral and Brain Sciences 22, 1–75.  doi:10.1017/S0140525X99001776.
  * MacGregor et al. (2015) MacGregor, L.J., Bouwsema, J., Klepousniotou, E., 2015.  Sustained meaning activation for polysemous but not homonymous words: evidence from EEG.  Neuropsychologia 68, 126–138.  doi:10.1016/j.neuropsychologia.2015.01.008.
  * Mikolov et al. (2013) Mikolov, T., Sutskever, I., Chen, K., Corrado, G.S., Dean, J., 2013.  Distributed Representations of Words and Phrases and their Compositionality, in: Advances in Neural Information Processing Systems, Curran Associates, Inc.
  * Myler (2016) Myler, N., 2016.  Building and Interpreting Possession Sentences.  The MIT Press.
  * Piñango (2019) Piñango, M.M., 2019.  Concept composition during language processing: Two case studies and a model, in: The Routledge Handbook of Chinese Applied Linguistics. Routledge, London, pp. 624–644.
  * Piñango (2023) Piñango, M.M., 2023.  Solving the elusiveness of word meanings: two arguments for a continuous meaning space for language.  Frontiers in Artificial Intelligence 6.  doi:10.3389/frai.2023.1025293. publisher: Frontiers.
  * Piñango and Deo (2016) Piñango, M.M., Deo, A., 2016.  Reanalyzing the Complement Coercion Effect through a Generalized Lexical Semantics for Aspectual Verbs.  Journal of Semantics 33, 359–408.  doi:10.1093/jos/ffv003.
  * Pustejovsky (1995) Pustejovsky, J., 1995.  The generative lexicon.  The MIT Press, Cambridge, MA, US.
  * R Core Team (2021) R Core Team, 2021.  R: A language and environment for statistical computing.
  * Rodd et al. (2002) Rodd, J., Gaskell, G., Marslen-Wilson, W., 2002.  Making Sense of Semantic Ambiguity: Semantic Competition in Lexical Access.  Journal of Memory and Language 46, 245–266.  doi:10.1006/jmla.2001.2810.
  * Roelofs (1997) Roelofs, A., 1997.  The WEAVER model of word-form encoding in speech production.  Cognition 64, 249–284.  doi:10.1016/S0010-0277(97)00027-9.
  * Roon and Gafos (2016) Roon, K.D., Gafos, A.I., 2016.  Perceiving while producing: Modeling the dynamics of phonological planning.  Journal of Memory and Language 89, 222–243.  doi:10.1016/j.jml.2016.01.005.
  * Rumelhart et al. (1986) Rumelhart, D.E., McClelland, J.L., AU, 1986.  Parallel Distributed Processing: Explorations in the Microstructure of Cognition: Foundations.  The MIT Press.
  * Sabinasz et al. (2023) Sabinasz, D., Richter, M., Schöner, G., 2023.  Neural dynamic foundations of a theory of higher cognition: the case of grounding nested phrases.  Cognitive Neurodynamics , 1–23doi:10.1007/s11571-023-10007-7.
  * Sabinasz and Schöner (2023) Sabinasz, D., Schöner, G., 2023.  A Neural Dynamic Model Perceptually Grounds Nested Noun Phrases.  Topics in Cognitive Science 15, 274–289.  doi:10.1111/tops.12630.
  * Schöner et al. (2016) Schöner, G., Spencer, J., Group, D.R., 2016.  Dynamic Thinking: A Primer on Dynamic Field Theory.  Oxford University Press, Oxford.
  * Shaw and Tang (2023) Shaw, J.A., Tang, K., 2023.  A dynamic neural field model of leaky prosody: proof of concept, in: Proceedings of the 2022 Annual Meeting on Phonology (AMP).  doi:https://doi.org/10.3765/amp.v10i0.5442.
  * Stella et al. (2024) Stella, M., Citraro, S., Rossetti, G., Marinazzo, D., Kenett, Y., Vitevitch, M., 2024.  Cognitive modelling of concepts in the mental lexicon with multilayer networks: Insights, advancements, and future challenges.  Psychonomic Bulletin & Review doi:10.3758/s13423-024-02473-9.
  * Stern et al. (2022) Stern, M.C., Chaturvedi, M., Shaw, J.A., 2022.  A dynamic neural field model of phonetic trace effects in speech errors.  Proceedings of the Annual Meeting of the Cognitive Science Society, 44 .
  * Stern and Shaw (2023a) Stern, M.C., Shaw, J.A., 2023a.  Neural inhibition during speech planning contributes to contrastive hyperarticulation.  Journal of Memory and Language 132, 104443.  doi:10.1016/j.jml.2023.104443.
  * Stern and Shaw (2023b) Stern, M.C., Shaw, J.A., 2023b.  Not all phonological neighbors affect production equivalently: predictions from a neural dynamic model, in: Proceedings of the 20th International Congress of Phonetic Sciences (ICPhS), pp. 4002–4006.
  * Sterzer et al. (2009) Sterzer, P., Kleinschmidt, A., Rees, G., 2009.  The neural bases of multistable perception.  Trends in Cognitive Sciences 13, 310–318.  doi:10.1016/j.tics.2009.04.006.
  * Talmy (1988) Talmy, L., 1988.  Force Dynamics in Language and Cognition.  Cognitive Science 12, 49–100.
  * Tilsen (2009) Tilsen, S., 2009.  Subphonemic and cross-phonemic priming in vowel shadowing: Evidence for the involvement of exemplars in production.  Journal of Phonetics 37, 276–296.  doi:10.1016/j.wocn.2009.03.004.
  * Vicente (2018) Vicente, A., 2018.  Polysemy and word meaning: an account of lexical meaning for different kinds of content words.  Philosophical Studies 175, 947–968.  doi:10.1007/s11098-017-0900-y.
  * Wildgen (1995) Wildgen, W., 1995.  Ambiguity in Linguistic Meaning in Relation to Perceptual Multistability, in: Kruse, P., Stadler, M. (Eds.), Ambiguity in Mind and Nature. Springer, Berlin, Heidelberg. Springer Series in Synergetics, pp. 221–240.
  * Yu (2010) Yu, A.C.L., 2010.  Perceptual Compensation Is Correlated with Individuals’ “Autistic” Traits: Implications for Models of Sound Change.  PLOS ONE 5, e11950.  doi:10.1371/journal.pone.0011950.
  * Zhang (2021) Zhang, M., 2021.  Linguistic Variation from Cognitive Variability: The Case of English Have.  Ph.D. thesis. Yale University.
  * Zhang et al. (2018) Zhang, M., Piñango, M.M., Deo, A., 2018.  Real-time roots of meaning change: Electrophysiology reveals the contextual-modulation processing basis of synchronic variation in the location-possession domain, in: Kalish, C., Rau, M., Zhu, J., Rogers, T.T. (Eds.), Proceedings of the 40th Annual Conference of the Cognitive Science Society. Austin, TX, pp. 2783–2788.
  * Zhang et al. (2022) Zhang, M., Piñango, M.M., Deo, A., 2022.  Word-Meaning Variation in English Have-Sentences: the Impact of Cognitive Vs. Social Factors on Individuals’ Linguistic Context-Sensitivity.  Language 98, 123–156.  doi:10.1353/lan.2021.0088.