# Finding Structure in Silence: The Role of Pauses in Aligning Speaker
Expectations

Maja Linke1 1Max Planck Institute for Human Cognitive and Brain Sciences,
Leipzig, Germany
2Linguistics Department, University of Tübingen, Tübingen, Germany  Michael
Ramscar2 1Max Planck Institute for Human Cognitive and Brain Sciences,
Leipzig, Germany
2Linguistics Department, University of Tübingen, Tübingen, Germany

###### Abstract

The intelligibility of speech relies on the ability of interlocutors to
dynamically align their expectations about the rates at which informative
changes in signals occur. Exactly how this is achieved remains an open
question. We propose that speaker alignment is supported by the statistical
structure of spoken signals and show how pauses offer a time-invariant
template for structuring speech sequences. Consistent with this, we show that
pause distributions in conversational English and Korean provide a memoryless
information source. We describe how this can facilitate both the initial
structuring and maintenance of predictability in spoken signals over time, and
show how the properties of this signal change predictably with speaker
experience. These results indicate that pauses provide a structuring signal
that interacts with the morphological and rhythmical structure of languages,
allowing speakers at all stages of lifespan development to distinguish signal
from noise and maintain mutual predictability in time.

###### keywords:

signal/noise discrimination; memorylessness; information structure; speaker
alignment; distributed learning

##  1 The problem of alignment in speech

Understanding how speakers align their expectations about the occurrence of
acoustic events in speech signals is central to explaining the human capacity
for vocal communication. However, the challenges this involves are easily
obscured by intuitions informed by reading and writing. In contrast to reading
and writing, which are self-paced and explicitly taught, speech is highly
dependent on timing and is usually learned implicitly through exposure to
continuous signals. Meanwhile, although the orderly and discrete way in which
letters, words, and phrases appear in texts can misleadingly imply that speech
is based on similar, corresponding alphabets of spoken gestures and
inventories of discrete forms, spontaneous speech signals are produced by
dynamic kinematic processes that guarantee a considerable amount of noise and
deviation in the way speech sounds and sequences are produced, such that many
of the ’acoustic segments’ listeners ’extract’ from speech signals are not
actually present in the physical stimulus (Port and Leary,, 2005; Ernestus et
al.,, 2002). The differences between the measurable attributes of physical
speech signals and their appearance to receivers pose a deep puzzle: while it
is common, and at some level perhaps necessary, to talk about articulation in
speech production (Goldman-Eisler,, 1961; Miller et al.,, 1984) and
segmentation in speech comprehension (Liberman et al.,, 1967; Cutler and
Clifton,, 1999), the array of findings showing that that much of what
listeners ’segment’ was never ’articulated’ in the first place, while much of
what is actually articulated is never segmented (Warren,, 1970; Samuel,,
2020), raise a question that has yet to be resolved: how do speakers bring
order to — and make sense of — the apparent chaos?

In what follows, we approach this question as a probabilistic puzzle rooted in
information theory, seeking to resolve an apparent contradiction between the
formal definition of information, and the specific kind of discrete, periodic
structure it requires, on one hand (see Shannon,, 1948, p. 17ff), and the
apparent absence of this structure in human communicative signals on the other
(see Port and Leary,, 2005; Ramscar,, 2019; Linke and Ramscar,, 2020, for
discussion). Applying the notion of information to speech is consistent with
current models that treat spoken communication as a probabilistic process that
relies on structured regularities in speech signals (e.g. Bell et al.,, 2003;
Aylett and Turk,, 2004; Bell et al.,, 2009; Tily et al.,, 2009; Wedel et al.,,
2013; Seyfarth,, 2014; Seyfarth et al.,, 2016; Wedel et al.,, 2018; Hall et
al.,, 2018; Priva and Jaeger,, 2018), such that speech perception is viewed as
a probabilistic process in which hearers attempt to infer the most likely
intended message from a noisy acoustic signal (Clayards et al.,, 2008;
Mitterer and McQueen,, 2009; Kleinschmidt and Jaeger,, 2015).

However, this probabilistic conception of communication serves to highlight a
critical difference between speech codes (and natural languages) and other
information-theoretic codes, namely that the former have to be learned. This
is a problem because of the highly skewed nature of lexical distributions
(which, when aggregated, approach power laws) (Estoup,, 1916; Zipf,, 1949):
the long-tailed nature of these distributions results in low-frequency words
being irregularly distributed across samples, and guarantee that any
individual speaker will only ever experience an incomplete sample of code
(Ramscar et al.,, 2014; Ramscar,, 2019). This, in turn, guarantees that each
speaker’s individual experience of codes – and hence their internal models of
them – will inevitably be unique, such that any individual’s experience will
necessarily differ from any group average.

The variability in individual speakers’ models of expectations raises a
problem for the whole idea of statistical regularities in speech signals.
Formally, what makes a signal a signal in information theory is that it
comprises a set of structured probabilistic events that are defined by a
shared code. Anything else is noise. If speech signals are signals in the same
sense, then this raises the question of how speakers ever manage to learn the
shared set of probabilities that structures them. In other words, how do
speakers ever manage to learn to align their individual expectations about the
structure of spoken signals, since this would appear to be necessary to make
statistical regularities in the temporal and acoustic properties of the signal
predictable and informative in the first place?

###  1.1 How do language users organize their expectations?

Part of the answer to this question lies in findings showing that speech
signals that are easily understood in context often become unintelligible when
they are presented in isolation (Pollack and Pickett,, 1963; Bard and
Anderson,, 1983; Ernestus et al.,, 2002), which suggests that speech codes
make considerable use of context. However, these findings also raise another
question: what, exactly, is context? One recent, successful approach to
answering this question has been to define contexts in terms of word
collocations in text, using this information to operationalize the ‘semantic
similarities’ between words as similarities between the collocational contexts
in which they occur (Harris,, 1954; Lund and Burgess,, 1996; Landauer and
Dumais,, 1997; Sahlgren,, 2008; McDonald and Ramscar,, 2001; Gleitman,, 2002).
Similarly, studies of the empirical structure of word frequency distributions
further support the idea that communicative context, in a broader sense, is
set by systematic patterns of co-variation between informative events, such as
for example speech phrases, words, syllables, and sounds. Analyses of
linguistic distributions at multiple levels of description (speech segments,
words, and syntactic phrases) show that learnable distributional regularities
organize speech sequences in clusters of informative contrasts that provide
sites of predictable variation, the information (Ramscar,, 2019; Ramscar,
2021b, ; Linke and Ramscar,, 2020).

These results suggest that lexical regularities are a source of information
for increasing the predictability of signal sequences, indicating that lexical
and grammatical forms might support the alignment process (Blevins et al.,,
2016; Ramscar et al.,, 2018). However, this suggestion simply serves to
underline the problem outlined above: not only does the production and
recognition of words rely on context, but in fact, it is often the case that
many of the ’acoustic segments’ presupposed by the acoustic model (dictionary
form, that models a word produced in isolation) are not actually present in
the speech signal, purplebut rather can only be inferred in context (Port and
Leary,, 2005; Ernestus et al.,, 2002). Moreover, this ’context’ is not merely
defined by the presence or absence of articulated parts of the signal, but
also by the timing of their articulation (Dilley and Pitt,, 2010; Morrill et
al.,, 2014; Baese-Berk et al.,, 2019; Lamekina and Meyer,, 2022). Given that
the identification of individual aspects of speech signals such as ’lexical
regularities’ relies on the alignment of speaker expectations, it follows that
these regularities themselves can only be noticed when learners have managed
to extract some structure from signals in the first place. This then raises
further questions: is there a consistent, time-invariant source of information
to support the alignment process? That is, if learners are to be able to
initially structure their expectations about speech codes to extract/infer
information from signals, and if these systematic patterns of expectation are
to be maintained across speakers regardless of their individual experience, it
follows that some objective source of information must be available in order
to facilitate this. What is it?

One possible source of information that would clearly seem to sidestep these
problems is silence, or more specifically, pauses: the regular manifestations
of silence in the speech signal. It has long been suggested that coordination
between speakers in turn-taking is achieved by a process known as production
rate entrainment (which involves the alignment of the rates at which auditory
events are transmitted and processed). Variations in pause duration have been
argued to play a crucial role in this process (Wilson and Wilson,, 2005).
Further, at least at the level of conversational turns, silent intervals
across languages converge on remarkably constant averages (Stivers et al.,,
2009; Weilhammer and Rabold,, 2003), which indicates that any variability in
silent interval duration is relatively invariant in time.

In what follows, we examine whether these apparent structural regularities
extend beyond turn-taking. Is temporal variation in speech pauses systematic,
and can it play a role in aligning the expectations of speakers and listeners
at the level of speech production and recognition as well?

Several empirical characteristics of speech pauses indicate that they could
play an important role in the alignment process. First, silence – or more
specifically the absence of articulated signal – is something that is clearly
and ’objectively’ present in the speech signal. Second, sensitivity to silence
does not seem to rely on experience. Instead, this perceptual contrast appears
to emerge prenatally and seems to structure other, more primitive forms of
vocalization (Mampe et al.,, 2009; Wermke et al.,, 2021) and serve as a first
cue to speech segmentation (Männel and Friederici,, 2009; Seidl and Cristià,,
2008; Holzgrefe-Lang et al.,, 2018). This is in contrast to sensitivity to
other more complex prosodic patterns and speech sounds, which vary across
languages and require more time and experience to learn. Temporal variation in
the articulated and the silent parts of the signal also appears to follow
distinct patterns across the lifespan. Experience leads to more individual
variability in articulation rates, whereas individual variabilities in pause
production decrease. In particular, as age and experience increase, the
average temporal resolution of the vocal signal (speech rate) increases and
becomes more variable between individual speakers and speech contexts (Quené,,
2005; Jacewicz et al.,, 2010; Hazan and Pettinato,, 2014; Tucker et al.,,
2021). By contrast, the duration and variability of speech pauses in
conversation is surprisingly stable across the lifespan (Redford,, 2013;
Neuberger,, 2013; Bóna,, 2011; Bona,, 2014; Hazan and Pettinato,, 2014).

The absence of effects of experience on pause durations might seem surprising,
however, these findings begin to make sense when considered against the
backdrop of the mechanisms involved in their processing. In particular, the
differential contribution of domain-general and domain-specific mechanisms
involved in speech perception and speech production suggests that speech
production and speech perception will develop differently over time (and this
actually seems to be the case, see Campbell et al.,, 2016; Campbell and
Tyler,, 2018). In the brain, the discrimination of ”general acoustic events”
(including non-events) appears to rely on specialized auditory mechanisms
which are subject to lifelong adaptation (Yan,, 2003), whereas the sequential
coordination of the motor processes involved in articulation (and thus
articulated durations) involves more general timing circuits that subserve a
variety of other capacities that involve orientation in space and time (Marien
et al.,, 2001; Ackermann et al.,, 2007). Depending on prior experience, some
of these latter processes appear to be ’fixed’ such that they function
independently of the requirements of the specific cognitive task (Krakauer et
al.,, 2006; Wong et al.,, 2017). Simultaneously, it seems that in both speech
perception and production, articulatory events and the variances in their
execution are highly context-specific, such that the uncertainties of the
contexts and the variances in the way articulations are performed within them
constitute a critical part of speaker expectation (Tremblay et al.,, 2008;
Maslowski et al.,, 2019). In other words, both the execution of these highly
automatized motor behaviors and their perception tend not to generalize across
modalities/contexts. It follows as a consequence of these considerations that
the constraints on timing that articulation imposes must in turn place
boundaries on the variability of the rates at which the informative changes in
speech can be produced. Accordingly, given the systematic limitations on
people’s ability to reliably judge noticeable differences with respect to
segment duration (Friberg and Sundberg,, 1995; Quené,, 2007), it seems that
when it comes to perception, the way in which the speech signal is interpreted
across hearers must be similarly bounded. All of the above points to a likely
source of misalignment in speaker/hearers: the diverging experience-driven
changes in the temporal distribution of informative auditory events within the
limits imposed by the converging temporal resolution of articulations.

Speech directed at children and preverbal infants is more informative in its
temporal structure and contains less information in its spectral variation
than speech directed at adults (Fernald,, 1989; Bard and Anderson,, 1983).
Notably, the extent to which distinct dimensions of prosodic variation (i.e.,
pauses, pitch, and phrase final lengthening) inform infants’ perception and
segmentation appears to vary with infants’ age and native language (Männel and
Friederici,, 2009, 2011; Sundara and Scutellaro,, 2011; Männel et al.,, 2013;
Skoruppa et al.,, 2013; Sundara et al.,, 2015). With experience infants’
attention gradually shifts away from prosody toward more complex structural
regularities in speech signals. However, pauses seem to remain a critical cue
to structure throughout childhood and across the adult lifespan (Mueller et
al.,, 2008; Peña et al.,, 2002; Männel and Friederici,, 2016). Whereas pause
durations and the syntactic structures in which they occur do not seem to
change substantially across adulthood, the way older speakers realize words
does appear to become increasingly context- and speaker-specific (Lieberman et
al.,, 1989). Critically, older speakers’ vowel realization, both in terms of
duration and the relationship between duration and formant dispersion, becomes
more variable in connected speech (Munson et al.,, 2011; Fletcher et al.,,
2015; Gahl and Baayen,, 2019). Notably, these effects do not transfer to
experiments where words are produced in isolation (see Watson and Munson,,
2007). This is important because vowels account for the largest part of the
variability in word and syllable durations in English, and these developments
seem to suggest that the temporal resolution of conversational speech signals
at the word and syllable levels change continuously across the lifespan.
Conversely, higher-level regularities such as syntactic phrasing and phrase-
level segmentation remain relatively stable.

This general idea – that learning inevitably changes individual models of the
world – is further supported by studies of memory performance in healthy older
speakers (Ramscar et al., 2013b, ; Ramscar et al.,, 2017). The processes
revealed in these studies seem to guarantee that aspects of the signal that
are informative in early communicative experience (e.g., timing, prosody,
phrase) will become increasingly uninformative (i.e., stable) as experience
grows, and sensitivity to the information provided by fine-grained
articulatory variation increases. These differences lie at the heart of the
problem of alignment in speech. The idea that speech signals are informative
is largely uncontroversial. However, formal measures of information ultimately
rely on the existence of objective ’events’, predictable changes in the
temporal and acoustic properties of the signal that are used consistently by
all speakers. As we have outlined above, the rates at which information is
extracted from the signal will change with speaker experience. Taken together,
the considerations above point to an obvious problem when it comes to speech
information: because what counts as an informative speech event will vary with
experience, most articulated parts of speech signals do not seem compatible
with any formal notion of information.

These problems appear to stand in opposition to the idea that the information
provided by phonemes, morphemes, or words can play a central role in speaker
alignment. Instead, they suggest that speakers must first achieve alignment in
relation to some objective rate at which events occur in speech, in order for
them to adapt their expectations and hence be able to extract the informative
events (and the systematic relations between them) from the signal (Edeline
and Weinberger,, 1993; Morrill et al.,, 2014; Finn and Hudson Kam,, 2015; Xie
et al.,, 2017). Given that articulations vary both physically and temporally,
and that human vocal communication (and learning) rely on speakers’ ability to
anticipate these events in time (Patel,, 2006, 2021), it seems that an aspect
of the signal that is stable in at least one of these dimensions is required
for these processes to occur. Which brings us back to pauses: can they provide
this stable source of information in the speech signal?

As we noted above, a basic prerequisite of an alignment signal is that the
information it provides must be invariant across speakers and available to
learners of all levels of experience. Formally, in a community of speakers
whose shared experience of a class of events differs, alignment will only be
possible if the rate at which the events from this class reoccur is somehow
independent of the degree to which speakers have sampled those events (i.e.,
if the results of sampling are somehow independent of experience). Yet all and
any of the articulated parts of the speech signal appear to be anything but
invariant. Accordingly, it follows that if pauses, which by definition are not
articulated, actually do serve as an alignment signal, then we should expect
them to be distributed in signals in such a way that the information
communicated by them will be independent of speaker experience (within some
minimum bound of experience (Shannon,, 1948)). Critically, given that the
properties of distributions are determined by both how we define their
constituents (what is measured) and their boundaries (how the observation
space is limited) it is important that we be clear about what we mean by
’speech pauses’ before we proceed with our analysis.

##  2 What are pauses and what do they do?

Not every silence associated with speaking is a pause. Moreover, it is clear
that even the events we might theoretically term ”pauses” do not form a single
coherent class. Previous work has shown that the durations of silent intervals
in speech follow a log-normal distribution, which in turn appears to be the
product of aggregating (at least) two distinct components: gaps, silent
intervals between speaker turns, and pauses, silent intervals within speaker’s
turns (cf. Heldner and Edlund,, 2010). With regards pauses, studies of speech
corpora show that pause distributions are bimodal or trimodal (Demol et al.,,
2006), with analyses suggesting that they cluster at around 150 ms, 500 ms,
and 1500 ms (Campione and Véronis,, 2002), providing empirical support for the
traditional classification of pauses into short ($<200$ ms), medium ($<1000$
ms) and long (up to $3000$ ms in spontaneous speech). However, while the
nature of the processes that give rise to these classes is poorly understood,
what is important for current purposes is that it is possible to make a
functional case for this classification.

There is evidence that pauses affect the ease with which speech utterances are
processed. Importantly, pauses of different duration affect sentence
processing differently: while pauses below a threshold of around 200 ms are
not explicitly detectable (Walker and Trimboli,, 1982), these very short
pauses do appear to improve speech recognition. By contrast, the absence of
silent intervals or unusually long pauses make sentences harder to comprehend
(Fors,, 2015). More generally, however, while it is clear that they provide
crucial information about the relations between events in speech processing,
pauses have also been subject of considerable study in relation to learning
and error processing in the brain. As highlighted above, feedback adaptation –
an important aspect of articulation – involves multiple neural systems whose
individual contributions are modulated by the durations of intervals between
events (Teki et al.,, 2011; Diedrichsen et al.,, 2005; Lewis and Miall,, 2003;
Buhusi and Meck,, 2005; Coull et al.,, 2011), which in turn affects the
quality of the learning outcomes (Foerde and Shohamy,, 2011; Baese-Berk and
Samuel,, 2022).

In auditory learning experiments, which like speech perception, involve
dynamic reorganization of temporal (when) and auditory (what) expectations
through exposure to structured sequences, the specific ranges of interval
durations also appear to influence what gets learned. Different delay
durations appear to serve as cues to discrimination over the two different
sources of information in tone sequences: tone frequency and tone duration.
Talking clearly involves more than discriminating between tones of different
durations, and speakers seem to be less sensitive to changes in interval
duration of speech sequences than tone sequences (and presumably more
sensitive to changes in spectral quantities) (Grondin et al.,, 2011). However,
the mechanisms involved in temporal discrimination of both speech and tone
sequences appear to be surprisingly similar, and adaptation to the temporal
dynamics of auditory sequences appears critical to speech segmentation and, by
consequence, speech intelligibility. Given these parallels, it is notable for
current purposes that results from auditory discrimination tasks indicate that
inter-event intervals (pauses) shorter than 250 ms and longer than 750 ms only
inform temporal discrimination. By contrast, intervals between 250 and 750 ms
aid in the discrimination of frequencies as well (Buonomano et al.,, 2009).
This qualitative divide in the information provided by shorter and longer
pauses is also evident in the differences in people’s sensitivity to small
time perturbations in intervals (both within and between tone sequences). In
particular, just noticeable differences in durations of intervals shorter than
240 ms are independent of the actual durations themselves, whereasjust
noticeable differences in intervals longer than 240 ms are a function of the
durations to be distinguished (Friberg and Sundberg,, 1995; Repp and Su,,
2013).

In relation to speech, the results summarized above indicate that differences
in the way pauses from different duration ranges are experienced may affect
the way subsequent changes in the signal are detected. Consistent with this,
it has been shown that the articulation rate of the earlier parts of
utterances co-determines which words and speech segments listeners extract
from the speech signal, such that shifting these rates can change what
listeners actually hear/extract (Dilley and Pitt,, 2010; Morrill et al.,,
2014; Baese-Berk et al.,, 2019). These effects of speech tempo on speech
perception are likely a function of the way variance in the signal influences
the way listeners experience the durations of consecutive sounds in sequences.
Studies have shown that subjective tone durations stretch or shrink in
relation to the durations of the preceding tones in a sequence (Nakajima et
al.,, 1992). Durations of subsequent tones are overestimated if the tones
immediately preceding them are considerably longer, whereas tones that follow
markedly shorter precedents are experienced as being shorter, with a
consequence of this effect being that speakers can experience consecutive
sound intervals whose durations are objectively different as being the same
(Hoopen et al.,, 2006). However, the introduction of silent intervals between
tones leads to a weakening or an inversion of this effect (Sasaki et al.,,
2010), a finding that also transfers from the isochronous sequences used in
experimental contexts to speech, where pause insertions have been shown to
increase the intelligibility of time-compressed speech (Ghitza,, 2011).

Our hypothesis is that alignment is achieved through the establishment of
shared expectations about the rate at which informative events will occur,
because, by definition, this is a fundamental requirement for speech events to
be ”informative”. Accordingly, we suggest that the intelligibility of speech
after linear time-compression (Ghitza,, 2011) results from a misalignment
between the rate at which informative events are expected and the rate at
which events actually occur. From this perspective, the reason why pause
insertions increase intelligibility is that they serve to counteract erroneous
information in the unnaturally compressed preceding part of the signal. This
makes the relations between events in the signal more consistent with the
temporal expectations speakers will have ordinarily acquired. In other words,
the analysis presented above indicates that pauses – which are most frequently
found at the boundaries of the syntactic and prosodic phrases that tend to
prompt speech rate transitions (Grosjean et al.,, 1979; Miller et al.,, 1984)
– may serve to help speakers reset and reorganize their expectations, making
changes in the signal informative via systematic alterations to segmentation
rate (or phase).

##  3 A theoretical account of the contribution of pauses to speech alignment

Our hypothesis is that pauses facilitate speaker alignment by making the rate
at which informative events happen in the signal predictable and informative.
Two simple, unambiguous predictions can be derived from it: first, if pauses
serve as an alignment signal, then the distribution(s) of pauses in speech
ought to be independent of speaker experience, such that they are identically
distributed across speakers. Second, even when speaker expectations are
aligned, variations in the rate at which informative events occur will need to
be synchronized, and this will be reflected in the way pause distributions
vary in time.

###  3.1 Formalizing a testable hypothesis

We next turn to determining the appropriate levels of analysis to apply to
these predictions. First, how do we formalize and quantify both convergence
and synchronization in the speech signal? We can summarize the requirements of
alignment as follows:

  1. 1.

the distribution of pauses ought to be structured so that speakers can extract
information from the signal based on a relatively short exposure in time.

  2. 2.

the information speakers extract from the signal should be independent of both
the individual speakers’ experience and fluctuations in pause durations and
articulation rates throughout the interviews in the corpus.

In other words, local variation in pause duration when collapsed across
speakers in time ought to be statistically independent of the history of the
communicative process, regardless of the timeframe used to operationalize
history. If the distribution of pauses has this property, then, in theory, at
any point in the communicative process, speakers’ expectations about this
aspect of the signal can be considered to be akin to a ’blank slate’. This
critical property for alignment – that the distribution of some aspect of the
time-varying signal be memoryless – has been shown to apply to discrete
communicative events at various levels of description – i.e. lexical,
sublexical, and phrasal – when they are considered in the communicative
contexts in which they are used in text and speech (Ramscar,, 2019; Linke and
Ramscar,, 2020). That is, empirically, communicative events approximate
geometric distributions at both higher and lower levels of analysis. This
applies to linguistic events that are more discrete (e.g. words and phrases),
and the more variant sublexical events they provide context for in speech.
This finding is important because the geometric is the only discrete
distribution that is memoryless.

Memorylessness describes a formal property of certain distributions of events
where differences in knowledge about the events that have occurred prior to a
certain point in time confer no advantage. This is because in these
distributions, the variance in the rates at which events occur guarantees that
knowledge about any events that have already occurred is uninformative in
relation to predicting future events. Because the mean of the distribution is
always equal to its variance, the variance is bounded by the mean, while the
mean is bounded by the distribution of variance. The principle can be
formalized in terms of a learning mechanism that seeks to minimize the
variable error in the observations with respect to a stable average (cf.
Peters and Adamou,, 2022). When a distribution of events is memoryless, it
follows that despite any local fluctuations, global event probabilities (or
magnitude, in pause duration) are unaffected by knowledge of the history of
the process. It thus follows theoretically, that once individuals have
experienced a reasonable sample of such a distribution, their models of it
will be largely independent of their idiosyncratic experiences. In other
words, memoryless distributions ought to provide signals that allow for rapid
adaptation of speaker expectations about the rate at which information will
arrive.

It follows accordingly that if the distribution of speech pauses is
memoryless, then it ought to approximate an exponential distribution (the
exponential is the only memoryless distribution for continuous variables).
Formally, the exponential is the probability distribution of the time
intervals between events in a process in which events occur continuously and
independently at a constant average rate. This means that once that speakers
have learned to interpret them, local patterns of variation in signals will
also have an experience-independent distributional structure. Thus, for
present purposes the speech signal can be seen to provide two distinct sources
of information: speech pauses which simply vary in duration; and articulated
parts of signals that both vary in duration and frequency and which have their
own relational structure in sequences. The latter structure reflects the
function of speech signals: that they are used to communicate, a process that
critically relies on mutual predictability.

####  3.1.1 Formalizing context: defining a baseline to measure misalignment
in time

The degree to which signals are predictable will be influenced by the amount
of information available prior to a given point: their context. This raises a
problem when we consider the communicative constraints speech codes must
satisfy, namely that the experiences of the users of a code will vary greatly,
both in what they have sampled and how often. This suggests that across
speakers, individual ability to segment the signal and then use this to model
context will vary. Moreover, these apparently separate processes will
interact, such that as a result of this interaction both what a ’segment’ is –
and in particular, the amount of information required for its presence to be
inferred – and the amount of information that ’segment’ in turn contributes to
contexts will both change with experience.

It follows that because articulations vary both with context and individuals’
experience over time, they cannot themselves provide a baseline for our
theoretical analysis of pause distributions. Rather, to test our hypothesis we
require a signal dimension that develops linearly over time. One source of
such information is sequence position. Sequence – or utterance – length is
determined by variation in structural regularities at various levels,
including word order, word morphology, and argument patterns. The rates at
which regularities at these first two levels – which roughly correspond to
syllable and short word boundaries – are produced appear to be relatively
invariant both in terms of development of individual speakers and different
languages (Poeppel and Assaneo,, 2020; Luo and Poeppel,, 2007). By contrast,
sequence-level patterns of development at any timescale are characterized by
distributional changes that involve an increase both in the length of
sequences and the frequency of shorter sequences. Accordingly, we will use
sequence position and its pattern of development with experience as a baseline
in our analysis. We will examine the relationship between this baseline and
our hypothesized time invariant source of information provided by pauses and
analyze the predicted changes this leads to with increasing speaker
experience.

####  3.1.2 The hypothesis: predictable divergence between distinct signal
dimensions over time

If pauses provide information about the rate at which other informative events
occur in signals, and if experience changes the rate at which events occur
(and hence even their nature), it follows that the relationship between pauses
and shared rates (i.e., word and syllable boundaries) ought to change at those
points that are most affected by experience.

Lifelong experience is typically accompanied by some form of specialization.
Adulthood typically involves the pursuit of different vocational paths and
different interests. These inevitably increase both context-specific knowledge
and vocabulary (Ramscar et al.,, 2014), which ought to be reflected in the
production of signals that are increasingly context-specific, that we expect
in turn to interact with sequence position. This prediction can be explained
as follows: we have described above how communication of context-specific
knowledge relies on – and hence will develop through – a transmission process
that requires the maintenance of mutual predictability. We have suggested that
this is achieved by the systematic adaptation of phrase structure and sequence
length, a process that, at the utterance level, serves to reduce communicative
uncertainty across structured sequences. Accordingly, it follows that if
segmentation rate increases are a function of the relative predictability of
the structured sequence, experience ought to lead to an increase in
segmentation rate and a decrease in segmentation rate variability in later
sequence positions.

A further implication of the interaction between experience, sequence
position, and segmentation rate is that because context-specific signals are
irregularly distributed themselves, experience will also lead to increases in
the variability of local segmentation rates – bursts of activity – as opposed
to global increases that would spread out uniformly across older speakers’
signals. Notably, the correlation between information rates and signal
sparsity appears to be an instance of a more general phenomenon. Bursty
patterns of activity are a characteristic of complex event dynamics, such as
for example traffic and internet activity (Karsai et al.,, 2018), and the way
words occur in language use (Katz,, 1996; Altmann et al.,, 2009). Which brings
us back to the analogy between intervals between general classes of events and
speech pauses. While gaps between events are a well-known quantity in the
analysis of complex event dynamics, to our knowledge intervals between events
have not previously been considered a source of information in relation to
distributions of automatized complex cognitive behaviors. Yet, given that it
has been shown that fluctuations in inter-event times are a better predictor
of irregular bursts of activity characteristic to complex behaviors in humans
than the event distributions themselves (Goh and Barabási,, 2008), there is
reason to suppose that they might also provide information about the processes
that give rise to these behaviors.

As reviewed in section 2, pauses from different ranges of duration modulate
the extent to which exposure to acoustic signals leads to temporal adaptation,
and whether this exposure also results in adaptation to sensory prediction
error. These two signal dimensions - timing and the information provided by
the frequency spectrum - contribute to distinct aspects of behavior: first,
uncertainty management, which involves coordination of expectations in time;
second, permanent adaptation in patterns of execution (e.g., the way speech
signals are produced in context). Both of these mechanisms involve learning
and take time to develop. The extent to which speakers’ ability to utilize
them efficiently changes with experience is determined by the structure of the
speech samples they are exposed to, and the order in which distinct aspects of
the signal become predictable and thus informative. At phrase level, for
example, it is less likely that adult speakers will encounter novel verb
argument structures. By contrast, the number of nouns they encounter within
these structures will increase steadily across the lifespan (Ramscar et al.,,
2014). As a consequence, the information provided by verb argument structures
will decrease in relation to the increasing number of context-specific nouns
conditioned on them. More generally, experience will lead to an increasing
asymmetry between variability (and uncertainty) in some aspects of the signal
(e.g., context-specific articulations) in relation to the relative
invariability of the communicative contexts they are conditioned on (Ramscar,
2021b, ). Simultaneously, more experienced speakers will acquire increasing
certainty about those aspects of the signal/environment that are relatively
invariant in time – e.g., how to structure sequences for successful
uncertainty management and efficient message transmission.

These theoretic assumptions allow us to formalize two key questions we shall
now address: First, are speech pauses distributed so as to allow speaker
alignment in the way we suggest? Second, are the interactions between pause
duration, timing, and speaker experience consistent with our predictions? If
speech sequences are structured for incremental uncertainty reduction, the
average information rate should increase with the relative sequence position
(order). This means that information in speech ought not to be uniformly
distributed in sequences (as indeed is the case (Genzel and Charniak,, 2002,
2003)). We suggested above that this asymmetry in the temporal distribution of
information in speech sequences will increase with speaker experience,
increasing the differences between the rates at which individual speakers
segment the signal. We hypothesize that speech pauses serve to offset these
differences and help speakers organize their expectations about the rate at
which information arrives in time. These considerations yield three concrete
predictions that we will test in the analysis that follows:

  1. 1.

That the aggregated samples of pause durations will converge on the
exponential distribution.

  2. 2.

That experience will optimize speech production by local adaptation of signal
variability, which will lead to an increase in information density
(’segmentation rate’) in the utterance final positions of longer utterances.
That, in final positions of longer utterances, the uncertainty reduction by
the previous part of the utterance allows information to be transmitted at
higher rates, and a decrease in segmentation rate in the utterance initial
positions and short utterances, where the uncertainty is high and information
rates are low. This in turn will lead to an increase in signal sparsity and
increasingly bursty patterns of activity in pause production.

  3. 3.

That this tendency ought to be reflected in a systematic divergence from the
mean pause duration with phrase length and the proximity of the phrase
boundaries in speech produced by older speakers – i.e., we should expect more
extreme values at the boundaries of both very short and very long phrases.

###  3.2 Corpus Data

We analyzed pauses from the Buckeye Corpus of Conversational English (Pitt et
al.,, 2005) and the Korean Corpus of Spontaneous Speech (Yun et al.,, 2015).
The corpora each contain phonetically transcribed speech from informal
interviews with 40 speakers balanced by age and gender. The young cohort in
the English corpus consists of speakers below the age of 30, the older
speakers are aged 40 and upwards, with more age variance in the older speaker
group. The Korean speakers are aged 15 to 47 years, with a median of 29.

All phrases produced by the interviewees were manually transcribed and word
and phone boundaries were annotated with an automated speech aligner.
Subsequently, the aligner annotations were manually corrected by trained
annotators. Periods of silence that occurred between word boundaries were
tagged as pauses. Absences of articulation accompanied by audible breathing or
other sound were tagged separately. Short periods of silence that occurred
between word boundaries were labeled as silent phones, stop closures, or
assigned to surrounding phones (Kiesling et al.,, 2006). For the purposes of
the analyses reported here, we focus exclusively on silent pauses between
words.

The Buckeye corpus contains $26952$ and the Korean corpus $21571$ pauses.
98.7% of the pauses in the English sample and 99.75 % in the Korean sample are
shorter than 3000 ms. To facilitate the analysis of pause duration in relation
to utterance position, each pause was assigned to the utterance position of
the word it preceded.

We examined the interaction of pause distribution, segmentation rate
variability, and experience, using two parameters: utterance position and age
cohort. Compared to the Korean sample, the English sample provides a larger
span of speaker ages and concomitantly speaker experience. This enables us to
analyze speech data that allows for a strong test of this hypothesis. Previous
findings have shown that response differences between age cohorts can be
explained by the systematic changes of co-variation patterns in the samples
speakers are exposed to and learn from across the lifespan and that the onset
of these ’aging effects’ is measurable in speakers’ performance relatively
early (in their twenties, see Figure 4, panel D) (Ramscar et al., 2013b, ).
Therefore, despite the differences in the age range, we can reasonably expect
to find measurable differences in the performance of the ’older’ group of
speakers (speakers above the age of 30) in the Korean sample.

##  4 Results

For the pauses extracted from the English and the Korean corpus we estimate
the rate parameter $\lambda$, and model the exponential distribution using
maximum likelihood estimation (for details, see Supplementary Materials).

Figure 1 shows the model and empirical distribution with best fits to the
target range of durations (0-3000 ms). The empirical distribution of speech
pauses in both English and Korean approximates the exponential, showing some
divergence in the high-frequency range that hosts the shortest pauses
($<100ms$) and in the tail of the distribution, where the random sample model
fit predicts a larger range of values (extremely rare pauses longer than 3000
ms). The model distributions fitted to the selected range of values, such that
the simulation approximates the best fit within the range (instead of the best
fit to the number of events imposed by the corpus size), and the empirical
distribution shows a close fit to the exponential model and the truncated
random sample of exponentially distributed values.

To test for the distance between the model and empirical distribution we
performed a two-sample Kolmogorov-Smirnov test. The test shows a relatively
small, but significant difference between the empirical distribution and the
truncated model, in both languages ($D_{ks}=0.09,p<0$). It seems worth noting
here that the test is very sensitive to small differences between
distributions and also shows a significant difference between the truncated
exponential and the exponential model ($D_{ks}=0.01,p<0$). The distance
between the empirical distribution and the model reflects the misalignment in
the high-frequency part of the distribution that holds the shortest pauses.
This is unsurprising given that unvoiced stops and silent vowels (whose
durations vary in the range of 20-100 ms) were excluded from the analysis.
(Detailed test statistics and discussion of alternative distributional
hypotheses are provided in the supplementary materials.)

Figure 1: Left panel (A): probability density function of pause distribution
for pauses shorter than 3000 ms (bottom row) and a random sample from an
exponential distribution (top row) of identical size and rate parameter. The
shaded area shows the truncated exponential model, limited in the analyzed
range of values $(0,3000)$. The sample means (red dot) and model mean
(transparent red dot) center at the theoretical mean (red line). Right panel:
the distribution of sample means in samples ($n=50$) drawn from the
distributions shown on the left. Means from random samples (B) converge on a
normal distribution that centers at the theoretical mean. Means from samples
of consecutive events (C) show the same behavior for model distributions,
while means from consecutive samples drawn from the empirical data are both
more dispersed and left-skewed, indicating local biases in the distribution of
pause durations.

Consistent with previous findings (Linke and Ramscar,, 2020), individual
speakers’ samples seem to deviate randomly, with samples approximating the
gamma distribution with varying scale parameters. The aggregate approaches the
exponential distribution (which is a special case of gamma). This means that
despite a multitude of sources that concomitantly feed into individual
variation (i.e. individual experience, syntactic structure, and various other
factors that shape interactions and rates at which acoustic events are
extracted from signals) the aggregate distribution maintains a structure that
can allow speakers to converge on a stable mean expectation. To examine the
effects this individual variation has on the local distribution of variance,
we run a sampling simulation. In order to investigate whether speech pauses
exhibit bursty patterns of activity, we draw 1000 random samples of 50
’pauses’ from each distribution and samples of 50 consecutive ’pauses’,
comparing the distribution of mean duration in relation to the theoretical
mean $1/\lambda$. The right panel shows the distribution of averages from
random samples (top) and sequences (bottom) for Korean (right column) and
English (left column). Sample averages from random samples and samples of
consecutive events from the model distribution converge on a Gaussian
distribution that centers at the theoretical mean. We observe more variance in
the means of sequential samples. Samples of consecutive events drawn from the
empirical distribution, show a strong left skew and more dispersion,
suggesting that extreme values in pause durations are not distributed
uniformly in speech sequences.

These results suggest that pause distributions possess two desirable
properties: one, a time-invariant global distribution that can provide
developing speakers with a consistent source of information in the otherwise
noisy signal they are exposed to; two, systematic local fluctuations in
average pause duration that can allow adult speakers at different levels of
experience to rapidly adapt to changes in local segmentation rates given
relatively short signal samples. All of which raises a critical question: are
local fluctuations in mean pause durations systematic in relation to changes
in the distribution of information (and uncertainty) in signals?

| RANDOM |  |  |  |
---|---|---|---|---|---
ENGLISH | Mean | Median | SD | SE | IOD1111 | CV2222(%)
model | 407.63 | 407.35 | 60.26 | 1.91 | 8.91 | 14.78
empirical | 409.96 | 405.86 | 59.85 | 1.89 | 8.74 | 14.60
KOREAN |  |  |  |  |  |
model | 468.13 | 463.06 | 67.96 | 2.15 | 9.87 | 14.51
empirical | 464.14 | 461.25 | 51.89 | 1.64 | 5.80 | 11.18
| CONSECUTIVE |  |  |  |
ENGLISH | Mean | Median | SD | SE | IOD | CV(%)
model | 412.40 | 409.51 | 54.77 | 1.73 | 7.27 | 13.28
empirical | 412.12 | 390.90 | 126.83 | 4.01 | 39.03 | 30.78
KOREAN |  |  |  |  |  |
model | 466.75 | 464.31 | 61.56 | 1.95 | 8.12 | 13.19
empirical | 468.23 | 447.11 | 130.32 | 4.12 | 36.27 | 27.83
1Index of Dispersion, 2Coefficient of Variance (%)
Table 1: Distribution of pause duration from samples of conversational English
and Korean. Mean durations in random samples drawn from the empirical
distribution of Korean pauses are less dispersed than the model mean
distribution. As shown in Figure 1 of the results section of our article,
samples of consecutive pauses from the empirical distribution are more
dispersed than consecutive samples from the model distribution. This indicates
that pauses from different ranges of duration are not uniformly distributed in
time, and instead appear in local bursts.

#### How does pause duration interact with the event rate? What is the event
rate?

Formally, the exponential is a distribution of waiting times between events
generated by a Poisson process. The $\lambda$ parameter defines the rate at
which these ’events’ occur: the average number of ’events’ within a fixed time
interval. We discussed earlier how in language, the informative changes in
signal dimensions that can constitute informative ’event’ boundaries shift
more or less systematically with speaker experience. As a consequence, the
rates at which the respective ’events’ occur ought to shift more or less
systematically too. It follows therefore that rate estimates only ever
approximate the convergence rate, and do not represent fixed, objective
estimates of the rate at which individuals will extract informative changes
from the signal.

With respect to the pause distributions, which as we have shown in both Korean
and English approximate the exponential distribution, the rate parameters
($\lambda_{ko}=0.0022$, $\lambda_{en}=0.0024$) indicate that within a fixed
frame of $1000$ ms, Korean speakers ought to converge on a ’minimal agreement’
that informative changes in the signal can be ’expected’ to occur every $464$
ms ($1/\lambda$) on average and that, given that pause likelihood decreases
exponentially with pause duration, the probability of subsequent acoustic
events occurring increases exponentially with pause duration. In other words,
if pauses are information and information processing is probabilistic, an
exponential decrease in probability as a function of pause duration indicates
that there are large differences in the way small perturbations in pauses from
different ranges of duration interact with probability.

In this model, the probability of an informative change (articulation)
increases considerably as pause duration increases from 100 ms to 150 ms,
while hearing more silence is almost equally unexpected between 750 to 800 ms.
This in turn provides an interesting probabilistic perspective on the possible
role of pause duration in the dynamics of uncertainty management, and the
response to informative changes in articulations. It suggests that all
articulations following longer pauses are uninformative because they are over-
expected, while the informativeness of articulations following short pauses
will vary with the expectations built up by the previous part of the
articulated signal. If we apply the same reasoning to pauses from the middle
range, then the information provided by subsequent articulations ought to be a
compromise function of both pause probability and the articulated prior. With
respect to pauses in speech, and the way they manage expectations (i.e., the
information rate), an over-expected stretch of speech signal immediately
following a long pause can be conceptualized as follows:

  * [1269 ms PAUSE] that a president would do something …

In this example, the pause duration leads to an expectation of the way that
will be signaled. In order to be intelligible in isolation, that would
ordinarily be signaled using multiple, discriminable acoustic segments dh ae
t. However, in the context of the long pause that precedes it, the measurable
acoustic-phonetic information it contains can deviate from the isolated signal
as long as the information it contributes does not violate speakers’
expectations about what can follow. That is, at points where articulated
signals are over-expected, the only thing that will violate expectations is
the absence of articulation – hearing any articulation is more probable than
hearing more silence. Simultaneously, speakers’ expectations about the way a
signal following a pause will unfold in time (where word and syllable
boundaries occur) appear to be relatively fixed. This means that whatever is
articulated instead of dh ae t – even if it is a mere burst of noise – must
occur within the expected time interval in order to maintain the
intelligibility of those parts of the signal that follow it (see Doelling et
al.,, 2014).

At the other end of the pause spectrum, the fine-grained acoustic detail that
follows the bulk of short pauses ought to become increasingly informative and
diversified in signals in which they occur. Because short pauses provide
little useful information on their own, listeners ought to get better at
noticing whether any violation of prior expectation actually occurred in the
acoustic signal and respond with fine-grain temporal adaptation. From this
perspective, the articulated signals that are learned and remembered are
systematic independent of speaker experience, because they are shaped by the
pause distribution and vary consistently with pause duration.

Accordingly, it follows that if the exponential model applies to speech pause
distributions in the way we suggest, then segmentation rates ought to become
increasingly diversified with experience. To investigate this question we
analyze experience-related change in utterance structure and the distribution
of pauses.

###  4.1 The interaction between sequence length, pause duration, and
experience

We analyze the frequency distribution of utterance positions and pause
durations. Prior analyses have shown that the distribution of words across
utterance position, and word length in phonemes in speech data follows the
geometric distribution. This indicates that segmentation rates that
approximate word and phoneme boundaries in spontaneously produced signals vary
consistently in time. The correlation between log-transformed frequency and
frequency rank in these distributions reflects their fit to the geometric
distribution.

The analyses presented in Figure 2 show that frequency of utterance positions
closely approximate a geometric distribution in both languages and cohorts
($R^{2}_{en}>0.994$, $R^{2}_{ko}>0.997$). While Korean utterances are on
average shorter ($M=4.017$, $SD=3.302$, $n=57661$) than English utterances
($M=5.710$, $SD=5.357$, $n=50841$), older speakers of both languages produce
longer utterances more often (Mann-Whitney, Korean:
$M_{o}=4.37,M_{y}=3.74,U=0.47,p<.0032$, English:
$M_{o}=6.13,M_{y}=5.50,U=0.28,p<.0763$). The medians are significantly
different in older speakers of English (Mood, Korean:
$Mdn_{o}=4.14,Mdn_{y}=3.64,Z=-1.13,p-.2573$, English:
$Mdn_{o}=6.20,Mdn_{y}=5.65,Z=2.43,p<.015$), indicating divergence in scale and
more individual variability in utterance length in older speakers of English.
Note that we are not interested in individual variation in the analyses
reported here, rather the analysis explicitly targets aggregate behavior. The
results show that the older speakers maintain the optimal distribution despite
the increase in variability across individuals. (All descriptive statistics
and results of statistical tests are provided in the supplementary materials.)

As discussed above, spontaneous behavior can be expected to vary across
individuals, and with experience, the variance in the articulated parts of
signals can be expected to increase. Accordingly, we examined whether the
variance in individual behavior does in fact systematically increase in the
aggregate (despite the many sources of variation that shape individual
behavior in seemingly unsystematic ways). As expected, the distributions
maintain their shape (they stay geometric) and as a result, the slope of the
older speakers’ distribution decreases. The changes in slope indicate a
decrease in the information provided by the relationships between words, i.e.,
their relative probabilities in context. Typically, decreases in performance
variability over a finite set of outcomes like this are taken as a mark of
learning, and the decrease in noise to signal ratio associated with it (cf.
Shmuelof and Krakauer,, 2014; Tucha and Lange,, 2004; Herman et al.,, 2009).

This course of development is consistent with the idea that changes in the
signals produced by older speakers reflect the patterns of learning that can
be expected to accompany increased experience rather than any ’pathological’
decline in performance (cf. Ramscar et al.,, 2014; Campbell et al.,, 2016).
The decrease in structural uncertainty (i.e., the amount of variance in the
conditional probabilities among adjacent words) in older speakers facilitates
a redistribution of functional load: the uncertainty at word transitions
decreases, freeing up resources to allow learning of fine-grained, context-
specific patterns of articulation (cf. Poulisse et al.,, 2020).

Figure 2: Left panel: Frequency distributions of utterance position (left) and
binned speech pause duration (right, bin size 50 ms) for younger (blue) and
older (red) speakers. Lines show model fits to geometric (linear after half
log transformation). Both the pause distribution and the utterance position
distribution show close fits to geometric with and $R^{2}>0.99$respectively.
Note that the lines that represent the geometric model distribution are hard
to distinguish because the distribution and the model fits are nearly
identical. In the left column, the younger and the older cohorts’ distribution
and their respective fits overlap completely. Right panel: point-wise
correlations of pause duration (left) ranked by frequency show some minimal
misalignment in the rank distribution. As can be seen in the rightmost column,
the ranked distributions of utterance positions are identical. Older speakers
produce longer utterances on average while maintaining the shape of the
distribution and the relationship between utterance length and utterance
probability. This correlation is unusual, when same analyses are performed on
text, the correlation between ranked values from any two samples in a mixed
corpus tend to be weaker.

However, whereas we observe a marked effect of experience on the articulated
part of signals, it does not appear to affect pause distributions. The
frequency distributions of pauses (with pause duration binned at 10, 20, or 50
ms) in both age groups closely approximate the geometric ($R^{2}_{en}>0.984$,
$R^{2}_{ko}>0.993$) and both distributions have identical slopes.
Simultaneously, the mean pause duration decreases in the older cohorts. The
differences in the means are not significant (Mann-Whitney, Korean:
$M_{o}=439.28,M_{y}=454.96,U=0.1,p=.5291$, English:
$M_{o}=400.88,M_{y}=408.21,U=0.0698,p=.6588$), and neither are the differences
in the medians (Mood, Korean: $Mdn_{o}=419,Mdn_{y}=441,Z=-0.95,p=.3398$,
English: $Mdn_{o}=381,Mdn_{y}=413,Z=-0.12,p=.9081$). In English, we observe
more variability across older speakers and a decrease in variance in the
aggregate. (See Supplementary materials for a full summary of descriptive
statistics.) A closer inspection of differences in the probability density
(Figure 3) reveals that older speakers of both languages produce more pauses
from the middle range of durations (250-750 ms). In other words, older
speakers of both languages produce fewer pauses that markedly diverge from the
mean duration. This suggests that in pause production, experience leads to a
gradual convergence on the mean.

Figure 3: Left panel: Difference in probability density of utterance position
(right panel) and pause duration (left panel) in speech samples produced by
older speakers of English (top row) and Korean (bottom row). The red line
marks the sample mean, the gray area highlights pauses from the middle range
of durations (250-750 ms) and the standard deviation from the mean in the
probability of utterance position. As can be seen, plots reveal a shift
towards the mean (convergence) in pauses shorter than 1000 ms, indicating that
longer than average pauses become shorter and shorter than average pauses
become longer in older speakers, decreasing the individual variance in pause
duration. By contrast, for utterance position experience shifts the average
towards the right showing an increase in variability (i.e, while pauses
converge, utterances appear to diverge). The effect is more protracted across
utterance positions in English speakers, which is consistent with the longer
average utterance length in English. Right panel: Pairwise pause variability
(nPVI) as a function of pause duration and speaker age. The top panel shows
the relationship between pause duration and pairwise variability, which is
identically u-shaped in both languages, reaching its minimum at the mean pause
duration. The bottom right panel shows the differences between cohorts (areas,
where the difference is significantly larger than 0, are highlighted in red),
which show opposite patterns in Korean and English.

To summarize these findings, experience appears to result in a redistribution
of uncertainty across utterance positions as it increases. The differences
between the distributions indicate that experience-related changes in the
distribution of uncertainty in the articulated parts of signals increase
linearly with utterance position. The fact that the distribution of pause
durations does not change with experience indicates that the relationship
between pause duration, utterance length, and uncertainty will change
systematically over time. The slopes in the distribution of utterance
positions decrease, indicating a decrease in differences in the distribution
of uncertainty across utterances. This implies that if pause durations reflect
uncertainty, the relative differences between consecutive pauses should also
decrease with utterance length. This also suggests that alignment in
communication relies on two distinct notions of convergence in probability.
Both alignment and stochastic convergence rest on the idea that a stream of
random or unpredictable events or quantities (noise) can settle into a
predictable behavior over time. A predictable behavior can be characterized
by:

  1. 1.

a decrease in contrasts between consecutive values (the observed events or
quantities eventually become indistinguishable)

  2. 2.

a stable probability distribution, where the contrast between consecutive
values is maintained, but the change is kept predictable (which can be
achieved by learning to ignore unpredictable variation)

We propose that communication between speakers at different levels of
experience relies on both of these different notions of convergence and that
the degree to which speakers utilize one or the other changes across the
lifespan. So far, we have described these distinct aspects of alignment as
structural or systemic (pertaining to relationships between informative
events) and contrastive (pertaining to discriminable changes in the
informative events themselves). Consistent with this theoretical analysis,
these results suggest that experience acts as a ’sink’ in that it decreases
the variability of higher-level structural or relational information,
eventually making highly predictable events indistinguishable.

To further examine this, we next analyzed the effect of experience on the
relationships between consecutive pauses and their interaction with pause
duration. Changes in the relationships between consecutive pauses indicate
uncertainty changes and the rate at which the signal is segmented. Larger
differences ought to indicate larger changes in segmentation rates of
consecutive articulation. That is the deviation from the ’event’ or
segmentation rate in the articulated stretch of signal that separates two
pauses ought to be reflected in the durational contrast, such that convergence
in rate, or an increasingly uniform distribution of information, mediated by
the convergence in sequential order, would result in a decrease in durational
contrast between consecutive pauses.

###  4.2 Changes in durational contrast between consecutive pauses

To quantify these changes in durational contrasts, we calculate the normalized
pairwise variability index (nPVI) of adjacent pauses (pairs of pauses
separated by an articulation). This metric quantifies the average durational
contrast between consecutive events in acoustic sequences (e.g., notes in a
melody or vowels in speech utterances). It was originally developed to
distinguish timing patterns in languages that differ in prosodic structure
(Ling et al.,, 2000; Grabe and Low,, 2008) and captures the relative
variability of segment durations in relation to the event onsets of
isochronous sequences. The nPVI for a pause occurring at position k and k+1 in
a sample of m silent pauses of duration d is calculated as

$\sum_{k=1}^{m-1}\frac{|d_{k}-d_{k+1}|}{(d_{k}+d_{k+1})/2}/(m-1)$

The metric allows us to estimate differences in the duration of adjacent
pauses independent of local fluctuations in the articulation rate. The nPVI
ought to reveal changes in the temporal relationships independent of the pause
durations themselves. i.e., if pauses do inform timing, relative changes in
duration provide information about changes in the segmentation rates of
articulated signals that separate two consecutive pauses, independent of
context-related variability of segmentation rates.

We observe a decrease in the average nPVI in older speakers of both languages
(Mann-Whitney, Korean: $M_{o}=.336,M_{y}=.345,U=.154,p=.327$, English:
$M_{o}=.425,M_{y}=.430,U=1.462,p=.713$), which could indicate a decrease in
rate variability in the articulated parts of the signal that constitute the
transitions between consecutive pauses. Moreover, there is less variability in
temporal contrast between adjacent pauses in Korean (Mann-Whitney:
$M_{ko}=.341,M_{en}=.427,U=1.462,p<0$), a trend similar to those previously
observed in vowel durations (Grabe and Low,, 2008).

We model the relationship between pause duration and the nPVI as a non-linear
two-way interaction with experience (Figure 3, left panel) in a generalized
additive model using the R library mgcv. Generalized additive models allow us
to examine non-linear interactions between multiple predictor variables while
accounting for the highly skewed distribution. We fit a Gamma model with a log
link function. The model is specified as follows:

$nPVI\sim s(PauseDuration,by=cohort,k=5)$

We find a u-shaped effect of pause duration on durational contrast in English
(older: $edf=3.977$, $F=187.6$, $p<0$, younger: $edf=3.976$, $F=245.9$, $p<0$)
and Korean (older: $edf=3.978$, $F=207.8$, $p<0$, younger: $edf=3.976$,
$F=176.0$, $p<0$). To test for differences between the cohorts, we examine the
difference curve between the smooths of the two factor levels (older and
younger speakers). The relationship between pause duration and durational
contrast to adjacent pauses does not differ significantly between the cohorts
in pauses from the middle range of durations, whereas cohort differences in
pauses shorter than 250 ms and longer than 750 ms are significant (Figure 3,
the bottom left panel shows the difference between the smooths of the two
cohorts, the factor levels ’older’ and ’younger’, parts of confidence
intervals that do not include 0 are highlighted in red). In pauses produced by
older Korean speakers, there is an increase in durational contrast between
shorter pauses and their neighbors, and a decrease in longer pauses. By
contrast, older speakers of English decrease the durational contrast between
longer pauses and successors and increase it in shorter pauses.

To test whether the differences in the duration of pauses produced by older
speakers is correlated to the increasing sparsity in the distribution of
information in the way we suggest, we next model the probability and duration
of pauses produced by younger and older speakers as a function of utterance
length and utterance position.

Figure 4: Mean pause duration as a function of utterance length for older(red)
and younger (blue) speakers of English (a, top left) and Korean (b, top
right). In the Korean sample, pauses occur at phrase initial boundaries only,
pauses in the English sample are distributed across the utterance - the
distribution of utterance position of words preceded by pauses is geometric.
Pause probability decreases with utterance position in both younger and older
speakers, but pause probability appears to shift towards the later positions
in older speakers (panel c): In English, experience increases the average
duration of pauses preceding non-final words in shorter sequences and
decreases the average pause duration in longer sequences. In Korean, the
cohorts diverge in pause durations preceding longer utterances only but
generally appear to model a similar behavior, which becomes less noisy with
experience – older speakers produce shorter pauses, and there is less variance
in duration. Panel d shows the model expectation: effect of experience-related
changes in English speakers’ sensitivity to the frequency of co-occurrence
relationship (system sensitivity) and cue frequency (local sensitivity) on
performance on the paired associate learning task by age group.

###  4.3 Does experience change the relationship between pause and utterance
length?

In the English sample, pauses are distributed across utterances and the
distributions of utterance positions preceded by pauses are geometric; they do
not differ from the overall distribution in both cohorts. In Korean, silent
pauses are found at the utterance initial boundary only. This is consistent
with the differences in the prosodic structure of Korean, which tends towards
isochronous syllable timing (Tark,, 2012; Moon-Hwan,, 2004), and English,
which is stress-timed and highly variable in syllable timing.

We fit a generalized additive model of pause duration as a smooth function of
utterance length for each cohort, adding a factor term for the utterance final
boundary (a categorial predictor to distinguish between final and non-final
positions of utterances). We use a Gamma model with a log link function to
account for the highly skewed distribution. The model is specified as follows:

$PauseDuration\sim s(UtteranceLength,by=cohort)+UtteranceFinal$

The model estimate of the average duration of pauses in non-final positions is
411 ms in English and 444 ms in Korean. Only older speakers of English seem to
deviate from the average pause duration in non-final positions of longer
utterances. In the model, the average pause duration in older speakers of
English decreases linearly with utterance length (English, older:
$edf=1,F=6.5620,p=.0104$, younger: $edf=1,F=0.031,p=.8610$, Korean: older:
$edf=1,F=1.028,p=.311$, younger: $edf=1,F=0.429,p=.513$).

The Korean data does not support our hypothesis that experience ought to
increase the burstiness of the pause distribution in older speakers. On one
hand, this could be an effect of the relatively large differences in the age
range of the English and Korean cohorts. On the other, as mentioned above, the
temporal structure of Korean speech sequences differs fundamentally from the
temporal structure of English. Alternation in syllable duration is an
important functional feature of the sequential structure in English: the
variability in stress patterns is a source of information. Korean, by
contrast, is markedly less variable in vowel (and syllable) duration and
appears to approach an isochronous temporal structure similar to mora-timing
in Japanese (Tark,, 2012; Moon-Hwan,, 2004). This suggests that the functional
load on alignment in timing might be substantially reduced and more evenly
distributed across other functional features of the signal in Korean. To
explore whether the differences in the cohort effects reflect a general
difference in the distribution of pauses and durational contrasts in English
and Korean, we conducted a final set of sampling simulations to address this
question.

###  4.4 Contrasting age-cohort differences in pause variability and pause
duration in consecutive and random samples

To examine the distribution of sample averages we obtained means from blocks
of consecutive pause durations and normalized durational contrasts (nPVI) from
older and younger speakers’ speech. We simultaneously extracted means from
blocks of randomly ordered pauses to serve as a baseline. Figure 5 shows the
distributions of mean pause duration and mean nPVI for blocks of 20 pauses.
Pause duration averages from random samples approximate a Gaussian
distribution that centers around the theoretical mean in Korean and English.
The mean nPVI in random samples is higher than the mean nPVI in consecutive
pauses in English ($M_{ran}=0.4362,M_{cons}=0.4267,U=0.2564,p<0.01$). The
difference between the model nPVI and the empirical nPVI indicates that the
order in which pauses from different ranges of duration occur decreases the
average distance between adjacent pauses in English, but not in Korean
($M_{ran}=0.3595,M_{cons}=0.3572,U=0.0815,p=.15$).

In the cohort comparison, the distribution of nPVI averages from samples of
consecutive pauses indicates local reductions of durational contrast in older
speakers of English ($M_{o}=0.417,M_{y}=0.435,U=0.1958,p<.001$) and Korean
($M_{o}=0.34,M_{y}=0.378,U=0.2564,p<.001$). There is a significant difference
between the random and the empirical distribution of pairwise variability in
English ($M_{ran}=0.436,M_{cons}=0.427,U=0.147,p<.01$). We find no such
difference in Korean ($M_{ran}=0.359,M_{cons}=0.357,U=0.081,p=.15$). This
’clumpiness’ in the relationship between consecutive pauses in English
suggests that the order in which temporal events unfold is more informative in
English than in Korean. This is consistent with findings that reveal
differences in the extent to which language users exhibit preferences in
perceptual grouping of rhythmical sequences. English speakers are sensitive to
the relationships between durations of consecutive events, whereas speakers of
the more rhythmically consistent Japanese do not exhibit strong grouping
preferences (Iversen et al.,, 2008). In other words, temporal fluctuations of
consecutive intervals constitute signals in English. This does not appear to
be the case in Korean (or Japanese).

Figure 5: Distribution of mean nPVI (left panel) and mean pause duration
(right panel) in blocks of consecutive (top row) or randomly sampled events
(bottom row) for older (red) and younger (blue) speakers. The dashed red line
marks the sample mean. Mean values from random samples converge on a normal
distribution that centers on the sample mean. Means from samples of
consecutive pauses suggest differences between the cohorts and the languages.
In Korean, there is more dispersion in younger than in older speakers’
consecutive samples, which could indicate that local and global patterns of
pause distribution get more similar (less sparse/bursty) across the lifespan.
By contrast, the distribution of averages from the English sample turns
increasingly bimodal with speaker age and interview time in consecutive
samples, indicating an increase in local bursts of shorter pauses in older
speakers and longer pauses in younger speakers that also increases throughout
the interview (shaded areas show the distribution of samples from later
blocks). The divergent patterns between the languages suggest that alignment
is achieved through local optimization (bursts of activity) in English and
globally (through an increasingly uniform distribution) in Korean.

The distribution of pause durations from consecutive samples also reveals
differences between the languages. In English, distributions of averages are
bimodal (suggesting local bursts of activity) and show diverging patterns in
older and younger speakers: bursts of shorter than average pauses in older
speakers and longer than average pauses in younger speakers. This tendency
increases in the later interview blocks, suggesting that the effect is
cumulative and develops at multiple timescales (utterance, interview time, and
speaker experience). In Korean, we find the opposite effect: older speakers’
averages are markedly less dispersed and show more convergence across local
samples, which can mean that the variability in pause duration decreases
globally in Korean. Younger Korean speakers’ samples appear to be far more
variable in average duration and look more similar to older English speakers’
distribution. The dispersion in consecutive samples we see in Figure 1 and
table 1 appear to reflect bursty patterns produced by older speakers of
English and younger speakers of Korean. We interpret these sample differences
as divergent effects of lifelong experience on the distribution of pauses in
spontaneous Korean and English. In English, differences between older and
younger speakers increase at those points where experience-driven changes are
greatest, at the boundaries of longer phrases. The results of the analyses
indicate that patterns of pause production systematically interact with local
changes in information rates, providing support for our hypothesis. In Korean,
contrary to our prediction, experience appears to lead to a global decrease in
the temporal variability of pause durations. Given the many uncertainties that
follow from the differences between the languages and the speech samples at
our disposal (the corpora are similar in many ways, yet not strictly
parallel), however, these findings cannot serve as strong evidence of
functional interactions between pause and information rate. Instead, they can
serve to inform future research.

##  5 Summary and Discussion

In this article, we examined the hypothesis that speech pauses play a crucial
role in the systematic temporal structuring of speech signals and the
maintenance of mutual predictability in time. We presented a theoretical
rationale for the hypothesis and evidence to support it. We suggest that
pauses provide information about fluctuations in articulation rates and that
predictable interactions between pause duration and information rate
facilitate alignment between speakers at different levels of experience. We
approach the problem of alignment as a task of learning models that maintain
mutual predictability of signals transmitted across multiple timescales. These
models are learned from exposure to a noisy signal and structured by
generations of speakers. We argue that a time-invariant source of information
is necessary to counter the inevitable misalignment of expectations (i.e.,
differences in experience) that this complex distributed learning entails. We
highlight how the distribution of information in human vocal signals
contributes to learnability and efficient transmission across the lifespan.

We proposed memorylessness as a key prerequisite for successful alignment and
efficient transmission and our finding that pause distributions from both
speech sources, Korean and English, closely approximate the exponential
distribution thus appears to fulfill this requirement. We hypothesized that to
enable alignment in the way suggested, the exponential source ought to exhibit
the following three properties:

  1. 1.

a global distribution that provides developing speakers with a consistent
source of information in the noisy signal they are exposed to

  2. 2.

a time-invariant source of information to ensure that all speakers will
acquire and maintain sufficiently similar models of expectations independent
of the points in time they enter the speaker community

  3. 3.

systematic local fluctuations in the temporal relationships between pauses to
allow adult speakers at different levels of experience to rapidly adapt to
local changes in segmentation rates

Our results indicate that pauses meet all three requirements. Their empirical
distributions increase the sampling efficiency in random samples, and their
global distribution is characterized by local fluctuations, which lead to a
skew in the distribution of sample averages from sequences of consecutive
pauses. To investigate whether these local fluctuations are systematically
correlated to variation in the distribution of information, we analyzed the
distribution of pauses across sequences of different lengths, comparing speech
samples of younger and older adults.

We found that experience increases the average utterance length in
conversational speech and that this change leads to a systematic
redistribution of information across utterance positions. We suggested that
this redistribution of information reflects a decrease in uncertainty about
structural regularities that set the utterance context and increase the
efficiency of message transmission. The result is a difference in the
distribution of information between the cohorts that increases linearly as a
function of utterance position. The distribution of pauses, by contrast, does
not change significantly with experience. The only change we observe in the
distribution of pauses is a gradual reduction in the frequency of pauses that
diverge notably from the mean pause duration indicating a global reduction of
temporal contrast in pauses from the middle range of durations (250 - 750 ms)
and a regression to the mean. Notably, we observe almost identical patterns of
change in the cumulative distributions of English and Korean. Further, these
effects are consistent with the predictions of the theoretical model derived
from the quantitative structure of languages and learning theory.

Our results show that the misalignment in the distribution of information
across utterances in relation to the relatively stationary distribution of
pauses leads to a predictable decrease in the average pause duration in longer
utterances produced by older speakers. This finding indicates a shift in the
relationship between pause duration and the utterance position that is
systematic – it scales linearly with utterance position – and is thus
consistent with the suggestion that the relationship between pause duration
and the changes in time intervals at which informative changes in the signal
are observed are predictable.

Importantly, we find different patterns of age-related changes in the spread
of Korean and English pause distributions. We hypothesized that the rates at
which speakers segment the signal across sequences would become more variable
with experience, increasing the signal sparsity (burstiness) over time. The
effect is evident in the English sample, but not in the Korean sample.
Contrary to our hypothesis, older speakers of Korean appear to minimize
durational contrasts globally. By contrast, English speakers appear to
minimize durational contrasts locally as predicted. Retrospectively, given
that our hypothesis was that pause durations provide an alignment signal
through consistent interaction with segmentation rate, the divergence in the
patterns of lifelong development between the two languages need not be
surprising. Our hypothesis was informed by evidence of the cumulative effect
of experience on the performance of English speakers, consistent with the
vocabulary development specific to the relatively impoverished information
structure of English morpho-syntax (Ramscar et al.,, 2014). However, Korean
and English differ significantly in the extent to which patterns of lexical
productivity are implicit (characterized by regularities such as a rich
morphology) or explicit (characterized by less productive, explicitly
lexicalized forms) (Ramscar, 2021a, ). Korean relies heavily on a rich
morphological structure to maintain systematic variation in the distribution
of word forms. English morphology, by contrast, is far less informative such
that far more meanings are realized in explicitly lexicalized, often
idiosyncratic forms. From a learning perspective, this has a differential
impact on lifelong development of vocabularies and the distribution of
functional load across speech sequences (contexts) in Korean and English.

One possible explanation of the effect is as follows: Language learning relies
on regularities, such as for example, relative invariance in the patterns of
inflection (Ramscar et al., 2013a, ). Unattested forms, e.g., regular plurals,
can often be easily inferred from the general pattern of inflection (squid-
squids, octopus-octopuses, wug-wugs, niz-nizzes), providing language learners
with an important source of predictable variance. By contrast, irregular forms
can only be learned explicitly (see Ramscar, 2021a, , for review). By
implication, the fact that the relatively impoverished morphological structure
of English relies more on word forms that cannot be derived implicitly leads
to a redistribution of functional load to those aspects of the signal that
support the learning of explicit forms. Conversely, in Korean the functional
load ought to be distributed across a variety of morphological cues
(particles, endings and functional prefixes).

We have argued that the learning of explicit word forms and the alignment of
speaker expectations in a communicative system characterized by non-linearity
are facilitated by context. Because context is set both by the highly variable
aspects of communicative codes such as regular patterns of co-occurrence
between words, phrases, and segments (Ramscar,, 2019; Linke and Ramscar,,
2020), but also the less variable aspects of speech signals such as prosodic
stress patterns and the variability in duration (McQueen and Dilley,, 2020),
the differences in the lexical productivity of word forms we have described
can result in very different predictions when it comes to the dynamics of
lifelong learning. It is thus not entirely surprising that the experience-
related changes in the patterns of pause distribution lead to increasingly
uniform signal distributions in Korean and increasingly sparse signal
distributions in English. We suggest that these differences in pause
distributions could reflect differences in the dynamics of lifelong learning
that interact with the linguistic structure set by the morpho-syntax and
prosody/timing. These considerations highlight the necessity of extending
these analyses to other languages that are placed along what seems to be a
gradient scale of structural organization in human communicative codes.

## Data Accessibility

The Buckeye and the Seoul corpus are freely accessible corpora for non-
commercial uses. Extracted data used in this analysis and the analysis code
associated with the current submission are available at
https://doi.org/10.5061/dryad.n5tb2rbxr. Any updates will also be published in
the Dryad Digital Repository.

## Disclosure of interest

The authors report no conflict of interest.

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