4.1 General overview

Naïve discriminative learning (NDL) is a computational modeling framework that is grounded in simple but powerful principles of discrimination learning (Ramscar & Yarlett Reference Ramscar and Yarlett2007, Ramscar et al. Reference Ramscar, Yarlett, Dye, Denny and Thorpe2010, Baayen et al. Reference Baayen, Milin, Filipović Durdević, Hendrix and Marelli2011, Rescorla Reference Rescorla1988). The general cognitive mechanisms assumed in this theory have been shown to be able to model a number of important effects observed in animal learning and human learning, e.g. the blocking effect (Kamin Reference Kamin, Campbell and Church1969) and the feature-label ordering effect (Ramscar et al. Reference Ramscar, Yarlett, Dye, Denny and Thorpe2010). NDL has recently been extended to language learning and language usage, and several studies have shown that it can successfully model different morphological phenomena and their effects onto human behavior, e.g. reaction times in experiments investigating morphological processing (e.g. Baayen et al. Reference Baayen, Milin, Filipović Durdević, Hendrix and Marelli2011, Blevins, Ackerman & Malouf Reference Blevins, Ackerman, Malouf, Harley and Siddiqi2016; see Plag Reference Plag2018: Section 2.7.7 for an introduction).

Discriminative learning theory rests on the central assumption that learning results from exposure to informative relations among events in the environment. Humans (and other organisms) use these relations, or ‘associations’, to build cognitive representations of their environments. Crucially, these associations (and the resulting representations) are constantly updated on the basis of new experiences. Formally speaking, the associations are built between features (henceforth cues) and classes or categories (henceforth outcomes) that co-occur in events in which the learner is predicting the outcomes from the cues. The association between cues and outcomes is computed mathematically using the so-called Rescorla–Wagner equations (Rescorla & Wagner Reference Rescorla, Wagner, Black and Prokasy1972, Wagner & Rescorla Reference Wagner, Rescorla, Boakes and Halliday1972, Rescorla Reference Rescorla1988; see Appendix A for a technical description). The equations work in such a way that the association strength or ‘weight’ of an association between a cue and an outcome increases every time that this cue and outcome co-occur. Importantly, this association weight decreases whenever the cue occurs without the outcome being present in a learning event. During learning, weights are continuously recalibrated. At any stage of learning, the association weight between a cue and an outcome can be conceptualized as the support which that specific cue can provide for that specific outcome given the other cues and outcomes which had been encountered during the learning history.

Let us look at an example of how our understanding of the world is constantly modulated by the matches and mismatches between our past experiences and what we actually observe. Our example is a phenomenon known as ‘anti-priming’ found by Marsolek (Reference Marsolek2008). He presented speakers with sequences of two pictures and asked these speakers to say the name of the second picture. The critical manipulation was implemented in the first picture, which could be either similar, to some extent, to the target picture (e.g. grand piano, followed by table), or unrelated (e.g. orange, followed by table). In contrast to typical priming findings, Marsolek observed that speakers responded more quickly for unrelated pairs compared to related pairs. This ‘anti-priming’ – caused by prior presentation of a related picture – follows straightforwardly from the learning rule of Rescorla & Wagner (Reference Rescorla, Wagner, Black and Prokasy1972). The weights of visual features (i.e. the cues) that are shared by grand piano and table, such as having legs and a large flat surface, are strengthened for grand piano but weakened for table when the picture of the grand piano is presented. Slower response times in this case of anti-priming are a direct consequence of critical features losing strength to table compared to cases in which a visually unrelated prime, such as an orange, had been presented.

Taking a morphological example, the association of the phonological string /aɪz/ with a causative meaning (‘make’) in English would be strengthened each time a listener encounters the word modernize and weakened each time the listener hears the words size or eyes. The association strengths resulting from such experiences influence language processing in both production and comprehension.

Technically, the mathematical engine of NDL, i.e. the Rescorla–Wagner equations, is an optimized computational implementation of an error-driven discrimination learning. This engine can be viewed as implementing ‘incremental regression’ (for a nearly identical algorithm from physics, see Widrow & Hoff (Reference Widrow and Hoff1960) and for a Bayesian optimized algorithm, Kalman (Reference Kalman1960)). NDL was first applied to large corpus data and used to study chronometric measures of lexical processing by Baayen et al. (Reference Baayen, Milin, Filipović Durdević, Hendrix and Marelli2011). An extension of the learning algorithm is reported in Sering, Milin & Baayen (Reference Sering, Milin and Baayen2018b). Implementations are available both for R (Shaoul et al. Reference Shaoul, Schilling, Bitschnau, Arppe, Hendrix and Baayen2014) and Python (Sering et al. Reference Sering, Weitz, Kuenstle and Schneider2018a).

Once a network has been trained, it provides different measures that represent different aspects of the association strength between cues and outcomes. These measures may subsequently be used as predictors of human responses (e.g. response times in lexical decision experiments). In the present study, we will use three NDL measures to predict the acoustic duration of S in regression analyses.

Other approaches to learning are available, for instance, the Bayesian model presented in Kleinschmidt & Jaeger (Reference Kleinschmidt and Jaeger2015). Where NDL comes into its own, compared to models based on probability theory, is when there are thousands or tens of thousands of different features (cues) that have to be learned to discriminate equally large numbers of classes (outcomes). Cues compete for outcomes in often unforeseeable ways reminiscent of chaotic systems, which is why it is a truly daunting challenge to capture the dynamics of such systems with probabilities defined over hand-crafted hierarchies of units (i.e. with probabilistic statistics). Errors at lower levels of the hierarchy tend to propagate to higher levels and render the performance of such models less than optimal. This is why in computational linguistics, there is a strong movement in the direction of end-to-end models which bypass the engineering by hand of intermediate representations using neural networks. NDL adopts this end-to-end approach. In contrast to approaches in machine learning, however, NDL does not use any hidden layers. Rather, it makes use of the simplest possible network architecture, with just one input layer and one output layer.

NDL thus offers a simple method for assessing the consequences of discrimination learning that has hardly any free parameters (namely, only a learning rate, typically set to 0.001, and the maximum amount of learning $\unicode[STIX]{x1D706}$, set to 1.0). Consequently, once the representations for the input and output layers of the network have been defined and the learning rate and $\unicode[STIX]{x1D706}$ have been set, its performance is determined completely by the corpus on which it is trained.

NDL also differs from standard applications of neural networks in machine learning in that it uses very large numbers of input and output features. We therefore refer to the NDL networks as ‘wide learning’ networks. The weights of these networks are updated incrementally by applying the learning rule of Rescorla and Wagner to the so-called learning events. Learning events are defined as moments in learning time at which a set of cues and a set of outcomes are evaluated jointly. Association weights between cues and outcomes are strengthened for those outcomes that were correctly predicted and weakened for all other outcomes. For technical details, see Milin et al. (Reference Milin, Feldman, Ramscar, Hendrix and Baayen2017b) and Sering et al. (Reference Sering, Milin and Baayen2018b), and for a simple introductory implementation, see Plag (Reference Plag2018: Section 7.4.4).

This approach to simulate language learning has proved useful for, e.g. modeling child language acquisition (Ramscar et al. Reference Ramscar, Yarlett, Dye, Denny and Thorpe2010, Reference Ramscar, Dye, Popick and O’Donnell-McCarthy2011, Ramscar, Dye & Klein Reference Ramscar, Dye and Klein2013a, Ramscar et al. Reference Ramscar, Dye and McCauley2013b), for disentangling linguistic maturation from cognitive decline over the lifespan (Ramscar et al. Reference Ramscar, Hendrix, Shaoul, Milin and Baayen2014, Reference Ramscar, Sun, Hendrix and Baayen2017), for predicting reaction times in the visual lexical decision task (Baayen et al. Reference Baayen, Milin, Filipović Durdević, Hendrix and Marelli2011, Milin et al. Reference Milin, Feldman, Ramscar, Hendrix and Baayen2017b) and self-paced reading (Milin, Divjak & Baayen Reference Milin, Divjak and Baayen2017a), as well as for auditory comprehension (Baayen et al. Reference Baayen, Shaoul, Willits and Ramscar2016b, Arnold et al. Reference Arnold, Tomaschek, Lopez, Sering and Baayen2017). The computational model developed by Arnold et al. (Reference Arnold, Tomaschek, Lopez, Sering and Baayen2017) is based on a wide learning network that has features derived automatically from the speech signal as input. This model outperformed off-the-shelf deep learning models on single-word recognition and shows hardly any degradation in performance when presented with speech in noise (see also Shafaei Bajestan & Baayen Reference Shafaei Bajestan and Baayen2018).

By adopting an end-to-end approach with wide learning, naïve discriminative learning approaches morphology, the study of words’ forms and meanings, from a very different perspective than the standard post-Bloomfieldian hierarchical calculus based on phonemes, morphemes, and words. The relation between form and meaning is addressed directly, without intervening layers of representations. In what follows, we will make use of wide learning networks primarily as a convenient tool from machine learning. In Section 6, we will briefly return to the question of the implications of successful end-to-end learning for morphological theory.

4.2 From NDL to phonetic durations

The present study follows up on Tucker et al. (Reference Tucker, Sims and Baayen2019), who used NDL measures to predict the durations of stem vowels of regular and irregular verbs in English in the Buckeye corpus. Their NDL wide learning network had diphones as cues, and as outcomes both content lexemes (or more specifically, pointers to the meanings of content words) and morphological functions (such as plural or the clitic has). In what follows, we refer to these pointers to meanings/functions as lexomes (see Milin et al. Reference Milin, Feldman, Ramscar, Hendrix and Baayen2017b for a detailed discussion). Tucker et al. observed that the prediction accuracy of statistical model fits to vowel duration improved substantially when classical predictors such as frequency of occurrence and neighborhood density were replaced by predictors grounded in naïve discriminative learning.

Following their lead, we implemented a network that has morphological function lexomes as outcomes, but restricted them to those that are implicated with English word-final S: clitic, genitive plural, genitive singular, plural noun, singular noun, third person verb, verb, verb participle, past-tense verb, and other (such as adverbs). The number of morphological functions is larger than that examined in the original Plag et al. (Reference Plag, Homann and Kunter2017) study, as we also include S that is word-final in past-tense or past-participle forms as a result of reduction (e.g. in pass for passed). Voicing of S was based on the phonetic transcription provided by the Buckeye corpus.

The findings by Tucker et al. (Reference Tucker, Sims and Baayen2019) indicate that speakers have to balance opposing forces during articulation, one that seeks to lengthen parts of the signal in the presence of strong bottom-up support and one that seeks to shorten them in case of high uncertainty. To parameterize these forces, we derived three different measures from the NDL wide learning network which are used as predictors of S duration: the S lexomes’ activations, their priors, and their activation diversities. Table 4 provides an example of a simple NDL network where the diphone cues for the word form ‘dogs’ are associated with, among others, the lexome of the morphological function plural. We will discuss each measure in turn.

Table 4 The table illustrates a cue-to-outcome network with a set of cues ${\mathcal{C}}$ with $k$ cues $c$ and a set of lexome outcomes ${\mathcal{O}}$ with $n$ outcomes $o$. We illustrate the calculation of NDL  measures for the lexome of the morphological function plural as an outcome, located in the second column, and its associated cue set ${\mathcal{C}}_{\unicode[STIX]{x1D6FA}}=\mathtt{ld~dO~Og~gz~zb}$, located in rows 3–7. Each $i\mathit{th}$ cue $c$ is associated with each $j\mathit{th}$ outcome $o$ by a weight $w_{i,j}$, representing their connection strength, where $i=1,2,\ldots ,k$ and $j=1,2,\ldots ,n$. Summed weights for ${\mathcal{C}}_{\unicode[STIX]{x1D6FA}}$ afferent to $o_{j}$ give the $j\mathit{th}$ activation $a$. The cues in $c_{1}$, $c_{2}$ represent any kind of cues that might occur in the first and second row.

A lexome’s activation represents the bottom-up support for that lexome, given the cues in the input. The activation for a given lexome is obtained simply by the summation of the weights on the connections from those cues that are instantiated in the input to that outcome (equivalent to the weights marked in red in Table 4). Hence, activation represents a measure of the cumulative evidence in the input.

A lexome’s prior is a measure of an outcome’s baseline activation, calculated by the sum of all absolute weights pertinent to the lexome outcome (equivalent to the weights in the column marked in light gray in Table 4).Footnote ^[5] The prior can be understood as a measure of network entrenchment. It is an NDL measure that is independent of a particular input to the network; rather it captures a priori availability which results from learning and typically corresponds to frequency of occurrence.

Finally, a lexome’s activation diversity is a measure of the extent to which the input makes contact with the lexicon. Activation diversity is the sum of the absolute activations pertinent from a cue set to all lexome outcomes (equivalent to the activations located in the bottom row highlighted in dark gray in Table 4). One can think of this measure as quantifying the extent to which the cues in the input perturb the state of the lexicon. If the cues were to support only the targeted outcome, leaving all other outcomes completely unaffected, then the perturbation of the lexicon would be relatively small. However, in reality, learning is seldom this crisp and clear-cut, and the states of outcomes other than the targeted ones are almost always affected as well. In summary, the more the lexicon as a whole is perturbed, the greater the uncertainty about the targeted lexomes will be.

Tucker et al. (Reference Tucker, Sims and Baayen2019) observed that vowel duration decreased with activation diversity. When uncertainty about the targeted outcome increases, acoustic durations decrease (for further examples of shortening under uncertainty, see also Kuperman et al. (Reference Kuperman, Pluymaekers, Ernestus and Baayen2007) and Cohen (Reference Cohen2014a)). Arnold et al. (Reference Arnold, Tomaschek, Lopez, Sering and Baayen2017) performed an auditory experiment in which subjects had to indicate whether they could identify the words presented to them. These words were randomly selected from the GECO corpus (Schweitzer & Lewandowski Reference Schweitzer and Lewandowski2013). Arnold et al. observed that words with low activation diversity (i.e. with short vectors that hardly penetrate lexical space) were quickly rejected, whereas words with large activation diversity (i.e. with long vectors that reach deep into lexical space) were more likely to be identified, but at the cost of longer response times.

Tucker et al. (Reference Tucker, Sims and Baayen2019) also observed that prediction accuracy decreases when instead of using the diphones in the transcription of what speakers actually said, the diphones in the dictionary forms are used. We therefore worked with diphones derived from the actual speech. However, we considered a broader range of features as cues.

Several studies that made use of discriminative learning actually worked with two networks, one network predicting lexomes from form cues, resulting in form-to-lexome networks, and the other predicting lexome outcomes from lexome cues, creating lexome-to-lexome networks (Baayen et al. Reference Baayen, Shaoul, Willits and Ramscar2016b, Milin et al. Reference Milin, Divjak and Baayen2017a, Reference Milin, Feldman, Ramscar, Hendrix and Baayenb, Baayen, Milin & Ramscar Reference Baayen, Milin and Ramscar2016a). Lexome-to-lexome networks stand in the tradition of distributional semantics (Landauer & Dumais Reference Landauer and Dumais1997, Lund & Burgess Reference Lund and Burgess1996a, Shaoul & Westbury Reference Shaoul and Westbury2010a, Mikolov et al. Reference Mikolov, Sutskever, Chen, Corrado, Dean, Burges, Bottou, Welling, Ghahramani and Weinberger2013). The row vectors of the weight matrix of lexome-to-lexome networks of NDL specify, for each lexome, the association strengths of that lexome with the full set of lexomes. These association strengths can be interpreted as gauging collocational strengths. In the present study, we do not work with a separate lexome-to-lexome network. Rather, we used a joint network that contains both lexomes and their diphones as cues and morphological functions as outcomes.Footnote ^[6]

4.3 Cue-to-outcome structure

Let us now turn to the actual modeling procedures that we employed and the evaluation of these models that led us to focus on inflectional lexomes as outcomes.

As a general strategy, we wanted to explore various constellations of cues and outcomes. We also considered the possibility that S duration might be co-determined by the lexomes in a word’s immediate context. Therefore, just as in models for distributional semantics, such as those presented by Lund & Burgess (Reference Lund and Burgess1996b), Shaoul & Westbury (Reference Shaoul and Westbury2010b), and Mikolov et al. (Reference Mikolov, Sutskever, Chen, Corrado, Dean, Burges, Bottou, Welling, Ghahramani and Weinberger2013), we placed an n-word window around a given target word and restricted cues and outcomes to features within this window. By varying the window size between zero and maximally two to the left or the right of the target word, and the specific features selected for cues and outcomes, we obtained a total of 38 NDL networks.

We created diphone cues on the basis of an entire phrase. This procedure created transition cues between words. A sequence such as ‘dogs bark’ gives the diphone cues dO Og gz zb bA Ar rk with zb as the transition cue.

Table 5 illustrates several different choices for cues and outcomes, given the phrase the small dogs bark at the cat, where dogs is the pivotal word carrying S. Examples 1, 2, and 5 illustrate models in which lexomes are outcomes and examples 3 and 4 have diphones as outcomes. Example 1 has only diphones as cues, and this model is a standard form-to-lexome network following the approach originally taken by Baayen et al. (Reference Baayen, Milin, Filipović Durdević, Hendrix and Marelli2011) and Tucker et al. (Reference Tucker, Sims and Baayen2019). Example 2 has lexomes as cues and outcomes; this is a standard lexome-to-lexome network (see Baayen et al. Reference Baayen, Milin and Ramscar2016a, Milin et al. Reference Milin, Feldman, Ramscar, Hendrix and Baayen2017b for applications of such networks for modeling reaction times). Model 3 seeks to predict diphones from lexomes. Model 4 complements the lexome cues with diphone cues. Model 5 also combines lexomes and diphones as cues, but these are used to predict lexomic outcomes. Importantly, these lexomes include the inflectional lexomes that are realized with S in English. The pertinent lexome in the present example is the one for plural number (plural). Note that model 5 allows us to test the hypothesis that the support for plural is obtained not only from a word’s diphones but also from its collocates.

Table 5 Possible cue–outcome configurations for the phrase the small dogs bark at the cat using a five-word window centered on dogs.

Models were trained by moving a given word window across the whole of the Buckeye corpus.Footnote ^[7] The window was moved across the corpus such that each word token was in the center of the window once. Consequently, a given S word will have occurred in each of the positions in the window. Each window provided a learning event at which prediction accuracy was evaluated and connection weights were recalibrated.

A wide variety of selections of cues and outcomes was investigated with the aim of obtaining insight into which combinations of cues and outcomes, under a discriminative learning regime, best predict S duration. Models with lexomes as outcomes, specifically those for the morphological functions of the S (clitic, genitive plural, genitive singular, plural noun, singular noun, third person verb, verb, verb participle, past-tense verb, and other) address the possibility that it is the learnability of the inflectional lexomes that drives the acoustic duration of S. Models that take diphones as outcomes address the hypothesis that it is the learnability of diphones (i.e. of context-sensitive phones) that is at issue.

In classical models of speech production, e.g. the weaver model of Levelt et al. (Reference Levelt, Roelofs and Meyer1999) and the model of Dell (Reference Dell1986), the flow of processing goes from conceptualization to articulation. Against this background, models in which lexomes are predicted instead of being predictors are unexpected. Nevertheless, there are three reasons why it makes sense to include such models in our survey.

First, for a survey, it is important to consider a wide range of possible combinations, including ones that are at first sight counter-intuitive. This is essential for allowing data to inform theory.

The second reason is technical in nature: NDL makes the simplifying assumption that each outcome can be modeled independently from all other outcomes. It is this assumption that motivates why NDL is referred to as naïve discriminative learning. For discriminative learning to take place, multiple cues are required for a given outcome so that over learning time it can become clear, due to cue competition, which cues are informative and which are uninformative. Informative cues obtain larger association strengths and uninformative cues obtain association strengths close to zero. If the learnability of inflectional lexomes is what drives S duration, then the NDL network must include inflectional lexomes as outcomes. If we were to take these inflectional lexomes as cues and use them to predict a diphone such as gz as outcome, the network would only learn the relative frequencies with which the inflectional lexomes are paired with gz in the corpus (cf. Ramscar et al. Reference Ramscar, Yarlett, Dye, Denny and Thorpe2010).

Third, any production system must have some form of feedback control so that the sensory consequences of speaking can be evaluated properly. Without such feedback, which comprises sensory feedback from the articulators as well as proprioceptive feedback from hearing one’s own speech, learning cannot take place (see Hickok Reference Hickok2014 for a detailed discussion). For the error-driven learning to be at all possible, distinct articulatory and acoustic targets must be set up before articulation, against which the feedback from the articulatory and auditory systems can be compared. In what follows, the diphone outcomes are a crude approximation of the speaker’s acoustic targets, and the connections from the diphones to the lexomes are part of the speech control loop. For a computational model providing a more detailed proposal for resonance between the production and comprehension systems, see Baayen et al. (Reference Baayen, Chuang, Shafaei-Bajestan and Blevins2019).

4.4 NDL measures as predictors

Having trained the 38 networks, we then analyzed their performance using random forests (as implemented in the party package for R), focusing on the variable importance of the NDL measures derived from these networks. The optimal network that emerged from this analysis is the one with a five-word window and the structure of example 5 in Table 5. Critical lexomes, i.e. morphological functions, were predicted from all lexomes and their diphones within a five-word window centered on the target word. Given the literature on conditional probabilities for upcoming (or preceding) information, such as the probability of the current word, given the next word (Jurafsky et al. Reference Jurafsky, Bell, Girand and Gussenhoven2000, Pluymaekers et al. Reference Pluymaekers, Ernestus and Baayen2005b, Tremblay et al. Reference Tremblay, Derwing, Libben and Westbury2011, Bell et al. Reference Bell, Brenier, Gregory, Girand and Jurafsky2009), we included in our survey of cue and outcome structures windows of size three, with the target word in either first or second position. The corresponding networks lacked precision compared to the above network trained on learning events of five words.Footnote ^[8] The latter network is also sensitive to co-occurrence of the target word with the preceding and upcoming word, but it is sensitive as well to co-occurrence with words further back and further ahead in time.

In the light of the literature on boundary strength and its consequences for lexical processing (Seidenberg Reference Seidenberg and Coltheart1987, Weingarten, Weingarten & Will Reference Weingarten, Nottbusch, Will, Pechmann and Habel2004, Hay Reference Hay2002, Reference Hay2003, Hay & Baayen Reference Hay, Baayen, Booij and Van Marle2002, Baayen et al. Reference Baayen, Shaoul, Willits and Ramscar2016b, Reference Baayen, Chuang, Shafaei-Bajestan and Blevins2019), we considered separately the activation and activation diversity calculated for the diphone straddling the boundary between stem and S, and the activation and activation diversity calculated from all other remaining cues (lexomes and diphones). This resulted in a total of five NDL measures as predictors of S duration:

1. 1. PriorMorph: the prior for weights from a cue set to a word’s inflectional lexome.

2. 2. ActFromBoundaryDiphone: the activation of an inflectional lexome by the boundary diphone.

3. 3. ActFromRemainingCues: the activation of an inflectional lexome by all other (lexome and diphone) cues.

4. 4. ActDivFromBoundaryDiphone: the activation diversity calculated over the vector of activations over all inflectional lexomes of S, given the boundary diphone as cue.

5. 5. ActDivFromRemainingCues: the activation diversity, again calculated over the vector of activations of all inflectional lexomes, but now using the remaining cues in the learning event.

There are nine values that PriorMorph can assume, one value for each of the nine inflectional lexomes that we distinguished (clitic, genitive plural, genitive singular, plural noun, singular noun, third person verb, verb, verb participle, past-tense verb, and other). The boundary diphone will usually differ from word to word depending on the stem-final consonant and the specific realization of the S. For any specific boundary diphone, there are again nine possible values of ActFromBoundaryDiphone and ActDivFromBoundaryDiphone, one for each inflectional lexome. For a given target word, e.g. dogs, we consider the activation and activation diversity, given [gz] as cue, for the corresponding inflectional outcome, here noun plural. The values of ActFromRemainingCues and ActDivFromRemainingCues depend on the words that happen to be in the moving window, and hence their values vary from token to token. In this way, each target word was associated with five measures for its inflectional lexome.

Although the prior, activation, and activation diversity measures have been found to be useful across many studies, there is considerable uncertainty about how they might predict the duration of English S.

With respect to PriorMorph, the general strong correlation of NDL priors with word frequency would suggest, given the many studies reporting durational shortening for increasing frequency (see, e.g. Zipf Reference Zipf1929, Jurafsky et al. Reference Jurafsky, Bell, Gregory, Raymond, Bybee and Hopper2001a, Bell et al. Reference Bell, Jurafsky, Fosler-Lussier, Girand, Gregory and Gildea2003, Gahl Reference Gahl2008), that a greater PriorMorph correlates with shorter S. However, recent findings emerging from production studies using electromagnetic articulography suggest that a higher prior (or frequency of occurrence) might predict increased rather than decreased S duration: Tomaschek et al. (Reference Tomaschek, Tucker, Baayen and Fasiolo2018c) observed that, other things being equal, greater frequency enables speakers to execute articulatory gestures with more finesse, in parallel to the general finding that motor skills improve with practice. It is also possible that PriorMorph will not be predictive at all, as Tucker et al. (Reference Tucker, Sims and Baayen2019) did not observe an effect of the prior for stem vowel duration.

For the activation measures (ActFromBoundaryDiphone and ActFromRemainingCues), our expectation is that a greater activation will afford durational lengthening. Arnold et al. (Reference Arnold, Tomaschek, Lopez, Sering and Baayen2017) observed, using an auditory word identification task, that a greater activation corresponded to higher recognition scores. Since a higher signal to noise ratio is expected to give rise to improved recognition rates, the prediction follows for English S that when the activation is higher, there must be more signal compared to noise, and this higher signal to noise ratio is, for a fricative such as S, likely to be realized by lengthening. This is indeed what Tucker et al. (Reference Tucker, Sims and Baayen2019) observed for vowel duration in regular verbs: as activation increased, the duration of the stem vowel increased likewise.

Turning to the activation diversity measure, here Tucker et al. (Reference Tucker, Sims and Baayen2019) observed a strong effect, with larger activation diversity predicting shorter duration. This result fits well with the finding of Arnold et al. (Reference Arnold, Tomaschek, Lopez, Sering and Baayen2017) that in auditory word identification, words with a low activation diversity elicited fast negative responses, whereas words with higher activation diversity had higher recognition scores that came with longer decision times. In fact, the activation diversity measure can be understood as a measure of lexicality: a low lexicality is an index of noise, whereas a high lexicality indicates that the speech signal is making contact with possibly many different words. The other side of the same coin is that discriminating the target lexome in a densely populated subspace of the lexicon takes more time. For speech production, Tucker et al. (Reference Tucker, Sims and Baayen2019) argued that when lexicality is high, the system is in a state of greater uncertainty as many lexomes are co-activated with the targeted outcome. Importantly, if some part of the signal, e.g. English S, contributes to greater uncertainty, it is disadvantageous for both the listener and the speaker to extend its duration. All that extending its duration accomplishes is that uncertainty is maintained for a longer period of time. It makes more sense to reduce the duration of those parts of the signal that do not contribute to discriminating the targeted outcome from its competitors. These considerations led us to expect a negative correlation between activation diversity and S duration.