An experimental and computational study of an Estonian single-subject word naming experiment

1 Introduction

Classical printed dictionaries of languages such as English and Estonian present the vocabulary of a language by means of a list alphabetically ordered by lexeme. The user first has to look up this lexeme. Once located, the dictionary provides further information on inflectional variants, pronunciation, and a description of its meaning and senses. The classical dictionary has a long history of inspiring theories of speakers' knowledge of the words and expressions of their language, a body of knowledge often referred to as their “mental lexicon.” In comprehension, the first stage of lexical processing is taken to be a process of “lexical access,” resulting in the identification of the entry of the lexeme on the basis of its form. Once this entry in the mental lexicon has been identified, lexical access is completed, and information about pronunciation and semantics becomes available.

The process of lexical access has been conceptualized in different ways. Moving away from an alphabetical ordering of form entries, Forster (1976) proposed a mental dictionary with entries ordered by decreasing frequency, in order to capture the pervasive effect of frequency of occurrence (Kliegl et al., 2004; Brysbaert et al., 2011). Alternatively, the interactive activation model of McClelland and Rumelhart (1981) does not impose an ordering on the entries (word units), but assigns words a resting activation level reflecting their frequency of use. In order to deal with morphologically complex words within these frameworks, decomposition of complex words into their constituents was introduced as this would reduce memory load and speed up processing. Taft and Forster (1976)'s affix stripping model was inspired by hash coding as described in Knuth (1973), although it is questionable whether a processing model exposed to actual word tokens would benefit from the stripping procedure (Schreuder and Baayen, 1994). A substantial body of literature has argued for obligatory morphological decomposition (e.g., Rastle et al., 2004; Taft, 2004; Rastle and Davis, 2008; Smolka et al., 2014). However, Marelli et al. (2014) and Amenta et al. (2015) have shown that many experimental effects believed to support obligatory decomposition in reading are confounded with measures of orthography-to-semantics and phonology-to-semantics consistency (see also Baayen and Smolka, 2020; Chuang et al., 2022). Using survival analysis, Schmidtke et al. (2017) were able to show that whole-word frequency effects arise early, often before constituent frequency effects. Lõo et al. (2022) suggested that phenomena previously attributed to morphological decomposition may actually emerge already early on from an interplay between formal and semantic effects. Furthermore, the lexicon as a static repository of lexical knowledge has been criticized by Libben (2022), who argued for a “flexicon,” conceptualized as a dynamic and interconnected system of symbolic units that is continuously updated with experience.

A very different approach to lexical processing had already been developed 20 years earlier (Seidenberg and McClelland, 1989; Seidenberg and Plaut, 2014; Harm and Seidenberg, 1999, 2004), using deep learning networks. However, after the inconclusive end to the connectionist debate (see McClelland and Patterson, 2002b,a; Pinker and Ullman, 2002a,b), many researchers interested in the mental lexicon felt that connectionist models were just not up to the task, and that even computational modeling in general is a fruitless enterprise. Discussions of experimental results within the conceptual framework of the interactive activation model flourished, and continue to flourish.

For the present study, which uses word naming to probe lexical processing in Estonian, the computational models for word naming that have been put forward are particularly relevant, such as the connectionist model of Seidenberg and McClelland (1989), the DRC model of Coltheart et al. (2001), the CDP model of Perry et al. (2007, 2010) and Ziegler et al. (2020) and the NDR_*a* model of Hendrix et al. (2019). The earliest of these models did not take words' meanings into account, the network architecture comprised letter units, phoneme units, and a hidden layer. The DRC, CDP, and NDR_*a* models all agree that meaning may be a factor in reading aloud, but the role of meaning is not explored or, in the case of the NDR_*a* model, meaning is represented by symbolic units that are place-holders for, or pointers to (Milin et al., 2017), words' “real meanings” (conceptualized as embeddings). The connectionist model of Seidenberg and McClelland and the NDR_*a* model make use of networks that are trained, the former using backpropagation (Williams and Hinton, 1986) and the latter using the Rescorla-Wagner learning rule (Rescorla and Wagner, 1972). In contrast, the lexical route of both the DRC and the CDP model builds on the interactive activation model of McClelland and Rumelhart (1981).

In the present study, we address two issues that these computational models have not addressed. The first is the potential role of word meaning. High-dimensional semantic representations from distributional semantics (Landauer and Dumais, 1997; Mikolov et al., 2013b) offer new ways of addressing the potential role of meaning in reading. The second issue is that models have been developed mainly for English, and for relatively short words of maximally two syllables (Hendrix et al., 2019; Perry et al., 2010). However, in a highly inflecting language such as Estonian, longer words are common, such as käsureal “on the command line,” parkimiskell “parking clock,” kooselus “in cohabitation,” and kehaosad “body parts.”

In the present study, we therefore do not make use of the interactive activation model, but instead make use of a computational framework that goes back to the insights of the connectionists: the Discriminative Lexicon Model (DLM, Baayen et al., 2019; Heitmeier et al., 2026). This modeling framework, implemented in the JudiLing package for julia (Luo et al., 2024), embeds words' forms in a high-dimensional form space, and makes use of distributional semantics (Harris, 1954; Firth, 1968; Landauer and Dumais, 1997) to embed words' meanings in a second high-dimensional space. Central to this approach to the mental lexicon are the comprehension mappings from the form space to the semantic space, and the production mappings from the semantic space to the form space. Linear mappings are often of excellent quality, but deep mappings can also be set up. The advantage of a linear mapping is interpretability. For instance, when using letter 3-grams to embed words in form space, a linear mapping will associate each 3-gram with its own embedding. The 3-grams that overlap with a given affix are correlated with the centroid of the embeddings of the words sharing that affix, i.e., with its prototypical meaning in semantic space (Baayen et al., 2025). Deep mappings, on the other hand, may offer improved precision. The DLM has been shown to be able to “understand” and “produce” complex words across a wide range of typologically different languages, including Finnish (closely related to Estonian, Nikolaev et al., 2025), and also provides a series of measures that are predictive for reaction times in the visual lexical decision task (Heitmeier et al., 2023b), spoken word duration (Gahl and Baayen, 2024), and Mandarin pitch contours (Chuang et al., 2026; Lu et al., 2026).

In what follows, we report a word naming experiment that also registered eye-movements. The word naming task requires participants to identify the word shown, and to subsequently pronounce it. Previous models investigated non-lexical and lexical routes, with lexical routes either bypassing actual word meaning, or using abstract nodes to represent word meaning. In the present study, we do not model the non-lexical route, even though such a route is part of the general Discriminative Learning Model framework (see Baayen et al., 2019), and explore, following up on Hendrix et al. (2019), how much can already be achieved with a model for the lexical route that makes use of state-of-the-art semantic representations for words' meanings, instead of symbolic place-holders for those meanings.

Importantly, the DLM is a model for subliminal, highly automatized lexical processing, capturing aspects of what Hulstijn (2024) and Huettig and Hulstijn (2025) refer to as basic language cognition. BLC is the cognitive system that underlies normal day to day spontaneous conversational language use. Except for people with severe cognitive impairments, basic language proficiency is mastered by everyone, irrespective of their intelligence or their working memory capacity. Huettig and Hulstijn (2025) contrast BLC with the cognition of the “enhanced literate mind” (ELM). The cognitive skills that underlie ELM are acquired thanks to extensive training in literacy, and are not mastered, or only partially mastered, by the non-negligible part of the population that has some form of dyslexia. In what follows, we make the assumption that for skilled readers, part of their ELM has been automatized, and has become similar to the automatized skills of BLC. The modeling with the DLM addresses these automatized skills at the intersection of BLC and ELM. Because we do not model the non-lexical route in this paper (for reasons we will explain below), nor any of the many meta-linguistic skills that are part of ELM, our modeling is unavoidably incomplete.

For the naming experiment that we carried out, we registered first and total fixation duration, the number of fixations, pronunciation latencies, as well as pronunciation durations. We address five main questions.

• First, are DLM-based measures predictive for the early stages of reading as captured by eye-movement measures, or are they predictive only for later stages of lexical processing? The same question can be asked for word frequency, neighborhood density, and inflectional paradigm size as predictors for fixation durations and fixation counts.
• Second, do measures derived from a deep DLM network outperform measures from a linear DLM network? Seidenberg and McClelland (1989) proposed a three-layer network for the non-lexical route, here, we ask whether a hidden layer is necessary for the lexical route.
• Third, does computational modeling with the DLM advance our understanding of the comprehension and production stages of the lexical route?
• Fourth, how much progress can be made without considering a non-lexical route, and working with only a lexical route? Since semantic predictors appear to be less predictive in the word naming task as compared to the lexical decision task (Balota et al., 2004; Baayen et al., 2006, 2007; Yap et al., 2012), it is not self-evident that a model that generates predictions that are unavoidably informed by word embeddings will actually be successfully.
• Fifth, are measures derived from the DLM high-quality predictors that are competitive with classical measures such as word frequency and inflectional paradigm size?

The remainder of this study is structured as follows. We first provide some background motivating the use of the word naming task and a single-subject mega-study design. We then introduce further details about the discriminative lexicon model (DLM). This is followed by statistical analyses, where for each response variable, we compare generalized additive mixed models (Wood, 2017) for a statistical baseline model with standard predictors and the corresponding DLM model. Our conclusions are presented in the general discussion section.

2 Task, predictors, and experimental design

2.1 Task

For probing lexical processing, the lexical decision task as well as eye-movement registration have been widely used (see, e.g., Whaley, 1978; Balota et al., 1999; Rayner and Duffy, 1986; Bertram and Hyönä, 2003). The lexical decision task has been an excellent tool for gauging many aspects of lexical processing, but it is a task with a word-nonword discrimination component (Balota and Chumbley, 1984; Grainger and Jacobs, 1996) that is not part of daily language use. The word naming task, because it does not have a decision component, is arguably closer to normal language use.

In the present study, we utilize the word naming task to examine how words presented on a screen are read out loud. We combined this task with eye-movement registration to clarify whether lexical measures are predictive for the earliest stages of information processing during reading, as the word naming task not only has its pros, but also its cons. The naming task combines comprehension (reading) and production (pronouncing the word). This makes it more difficult to assess what the task actually captures. Tracking the eyes during reading might provide information specifically about the initial comprehension processes involved in the task.

Several studies have reported that semantic predictors are less predictive in the word naming task as compared to the lexical decision task (Balota et al., 2004; Yap et al., 2012; Baayen et al., 2006, 2007). It is possible that the naming task is carried out primarily by means of converting an orthographic representation into a phonological representation (Coltheart et al., 2001), and if production then proceeds purely on the basis of this phonological representation, then little or no effects of meaning are expected. As meaning plays a central role in the normal comprehension and production processes as formalized in the DLM, the naming task is especially suited for testing the predictions of this model against experimental data. If meaning is indeed not accessed in the word naming task, then the meaning-based predictions of the DLM cannot be expected to have any explanatory value for the response variables in this task.

2.2 Predictors

Classical predictors for word naming latencies include word frequency, word length, and neighborhood density (Coltheart et al., 1977; Yarkoni et al., 2008). Within interactive activation frameworks, word frequency determines resting activation levels, word length determines the amount of bottom-up input, and neighborhood density gauges the amount of between-word lexical competition. Orthographic depth has also been reported to predict naming latencies (Balota et al., 2006).

Lõo et al. (2018b) conducted a multi-participant study of word naming with inflected nouns in Estonian, the language under investigation in the present study. They found that nouns with higher word frequency, larger orthographic neighborhoods, larger inflectional paradigms, and larger morphological families were processed with shorter naming latencies and produced with shorter acoustic durations.

More recently, it has also become clear that the phonetic detail of speech production is co-determined by semantics. Plag et al. (2017) observed that the duration of syllable-final [s] in English is co-determined by the semantics realized by this exponent (singular on verbs, plural on nouns, genitive singular or plural, etc (see also Lõo et al., 2023 for similar findings for syllable-final [s] in Estonian). Gahl and Baayen (2024) showed that the spoken word duration of English heterographic homophones is in part predictable from their semantics, using distributional semantics and the DLM model. Chuang et al. (2026) and Lu et al. (2026) document that the phonetic detail of how the tones of Mandarin Chinese word tokens in a corpus of spontaneous conversations are realized co-varies systematically with the corresponding contextualized embeddings. Clearly, word embeddings have opened up new ways of assessing systematicities in semantic space, and systematicities between form and meaning, that are outside of the scope of standard symbolic approaches to semantics (see also Mandera et al., 2017; Westbury and Wurm, 2022; Amenta et al., 2017, 2015).

Interestingly, investigations of inflectional and derivational semantics using embeddings have shown that the “meanings” of classical symbolic features such as tense, number, and case are far more intricate than was previously assumed. Baayen and Moscoso del Prado Martín (2005) showed that in English, irregular verbs and regular verbs are positioned differently in the semantic space. Shafaei-Bajestan et al. (2022, 2024) documented for English that the shift in semantic space from a singular noun to its corresponding plural noun varies systematically with semantic class (e.g., fruits, vehicles, and animals). For Russian (Chuang et al., 2023) and Finnish (Nikolaev et al., 2023), the shift in semantic space from a singular noun to its plural varies consistently by case.

For the modeling of word naming in Estonian, this body of work on embeddings is relevant because words' meanings can now be represented with much more finesse than was possible with abstract semantic symbols. For instance, just as in Finnish (Nikolaev et al., 2023), Estonian plural shift vectors cluster by case, as shown in Figure 1. In order to do justice to the semantic intricacies of inflected words, it is essential to work with empirical embeddings (see also Chuang et al., 2026). Nikolaev et al. (2025) argue for Finnish nominal inflection that it is the isomorphies between the form and semantic spaces that makes it possible for DLM mappings to be productive (see also Orzechowska and Baayen, 2025, for Polish).

Importantly, given the evidence that the relation between form and meaning is much tighter than was previously thought, i.e., less arbitrary and therefore more predictable, the lexical route in word naming may be more effective than has been assumed thus far. The DLM provides the means for assessing the possible role of semantic embeddings in lexical processing. In other words, the DLM modeling in the present study can, within the context of dual route models of reading aloud, be seen as a new way of modeling the lexical route.

An issue with lexical predictors that is only addressed in part in the present study is that the lexicon is not static, but is updated continuously at both small and large time-scales. For the continuous updating of lexical knowledge within large lexical decision experiments (see Heitmeier et al., 2023b, 2026), and for continuing vocabulary development over the lifetime (see Keuleers et al., 2015); for the mental lexicon as a mental “flexicon” (see Libben, 2022). In this study, we work with predictors (both classical and DLM-derived) that are static in the sense that they do not take into account that the participant's mental lexicon was likely changing over time as the long naming experiment proceeded (cf. Heitmeier et al., 2023b). However, we will address the question of whether in the course of the experiment, the effects of predictors change. Such changes would be indicative of changing task strategies, a changing mental lexicon, or both.

2.3 Single-subject design

A problem with many earlier studies of lexical processing is that they make use of underpowered experimental designs with repeated measures for subjects and items (Westfall et al., 2014). Studies with a large number of words and a large number of participants overcome these problems (Balota et al., 2007; Ferrand et al., 2010; Keuleers et al., 2012; Tucker et al., 2019; Lõo et al., 2026). Collecting data for such mega-studies is relatively expensive and time consuming, however. One solution is to run an experiment with a large number of words, but a single participant. Such a study design allows us to also use thousands of items with a relatively low acquisition cost. Although sampling a single speaker is a cost-effective methodological choice, it might be argued that this procedure cannot meaningfully address the question of lexical processing in speakers of a given language, in our case, Estonian. To address this concern, consider the following.

First, standard experiments probe the knowledge of a sample of speakers of a language, but is this knowledge in any way representative of “the language”? Possibly, socially accepted normative Estonian (as documented in standard dictionaries and grammars) could be viewed as the emergent cumulation of the knowledge that individual speakers of Estonian have of their language. However, it is unlikely that any single speaker has full mastery of the cumulative knowledge that is represented in large corpora and dictionaries. In other words, it is far from straightforward to determine what a speaker of “the Estonian language” would be, as it is unclear what exactly the “Estonian language” might be.

A corpus could be seen as a practical approximation of the social norm of the “Estonian language,” albeit limited by accessibility of texts and rendered static by its own collection process. But the knowledge captured by large corpora is far more extensive than that of any single speaker. Whereas most high-frequency words are known and used by all speakers, knowledge of low-frequency words is much more fragmentary, and depends on speaker's individual expertise, hobbies, and interests. As a consequence, corpora overestimate both the number of words that individual speakers know, and the frequencies of the less common words in the usage of individual speakers. This is an important caveat for the present modeling study, in which we make use of corpus-derived frequencies and type counts (when estimating orthographic neighborhood density) to probe the mental lexicon of an individual speaker of Estonian. It should be kept in mind that the size of inflectional paradigms was also calculated from a corpus, and is an estimate of community usage, and as a consequence unavoidably overestimating the paradigm sizes that characterize the active use of paradigms for our participant.

Complementing corpora, dictionaries constitute yet another window on the social norm. Modern dictionaries are corpus-based, but still mostly human-curated, discrete, smaller in volume than corpora, and even more static. Instead of representing an omniscient external observer, dictionaries are compiled by humans with their inherently limited knowledge, albeit equipped with tools and access to information well above the average speaker. For this experiment, dictionaries were used to derive a measure of entropy, which we quantified as the uncertainty associated with the possible pronunciations of a given written word form. The resulting measure reflects a social norm that may diverge from the knowledge of the speaker that participated in our experiment.

Second, although single-subject study designs are still quite rare in psycholinguistic research (for examples, see Pham, 2014; Sun, 2018), they have a long history in applied sciences, such as applied education, psychology, and linguistics (see, e.g., McReynolds and Thompson, 1986; Beeson and Robey, 2006; Horner et al., 2005). Single-subject mega-studies offer the advantage of eliminating participant as a source of random noise. This simplifies statistical evaluation and makes it possible to investigate substantial numbers of different words. Compared to experiments conducted with smaller numbers of words, but larger numbers of subjects sampled from the same population, the power to detect effects of word properties increases (Pham, 2014). Of course, if the interest is in the variation between speakers, designs with multiple speakers are preferable. Gardner et al. (1987) showed that engineers were faster to respond to specialist words from engineering compared to specialist words from nursing, and that the reverse held for nurses. As shown by Heitmeier et al. (2023b), in the British Lexicon project (Keuleers et al., 2012), the effect of neighborhood density shows enormous between-subject variability, with facilitation for some, inhibition for others, and for yet others, no effect at all. This variability exists even for a selected group of WEIRD (Henrich et al., 2010) participants sampled from university students and staff in London, and thus likely underestimates substantially the variability in the lexical processing in the highly diverse population of speakers of English. Kuperman and Van Dyke (2013) sampled young readers (16–24 years) from a local community with at most high-school level of education. Within this interesting but again restricted sample, they observed clear differences in frequency effects of words and stems for more and less proficient readers. However, for charting the differences in lexical processing between speakers across all regions and socio-economic strata, large-scale studies are required, possibly using crowd-sourcing (Keuleers et al., 2015).

The present study does not aim to provide a characterization of how in general speakers of “Estonian” process words. We expect that fairly similar results can be obtained for other highly educated native speakers of Estonian, and that the present results will generalize much less well to speakers with much less reading experience. As the focus of the present study is on cognitive computational modeling, and as data on differences in lexical usage between individual speakers (Johns, 2021) from different areas, age groups, and socio-economic backgrounds are not available, whereas having data for a large number of words is important, collecting these data from a single speaker is sufficient.

2.4 Statistical approach

For assessing the predictive and explanatory potential of the DLM for the response variables (first fixation duration, total fixation duration, number of fixations, word duration, and naming latency), for each response variable we compared two regression models. One model was fitted with well-established classical predictors such as frequency, length, neighborhood density, and inflectional paradigm size. Since this model provides our evaluation baseline, we refer to it as our baseline model. The second model (henceforth the DLM model) was fitted with DLM-based predictors replacing the lexical predictors (frequency, neighborhood density, and inflectional paradigm size). For each of the response variables, a question of particular interest is how good the fit of the DLM model is compared to that of the baseline model. There are several reasons for expecting that the DLM model will not outperform the statistical baseline. For instance, the DLM model is trained on only part of the immense vocabulary of Estonian, it does not have access to information about the order of learning, nor to information about the dispersion of words' token frequencies across different registers and social strata. Furthermore, our computational experiments with the DLM model only address the lexical route of the naming process, and does not take into account the role of training in literacy. Given the many limitations of the model, the question therefore is how close the model can get to the baseline model.

Importantly, classical measures such as frequency, neighborhood density, and inflectional paradigm size, are not tied to any computationally implemented model scaling up to realistic data for richly inflecting languages such as Estonian. One can take a word's frequency as indicative of a word's resting activation level, but this metaphor is part of the interactive activation model which, as clarified above, is computationally intractable.

Furthermore, it is unclear to what extent frequency is a variable that is theoretically precise. Frequency is tightly correlated with many other variables, such as contextual diversity (Adelman et al., 2006; Johns, 2021; Johns and Jones, 2022), word length, collocational preferences, semantic richness, and morphological family size, and once all these confounding variables are partialled out, very little explanatory value is left for frequency as a pure count measure (Baayen, 2011). Although word frequency and related variables such as inflectional paradigm size are powerful predictors, they currently lack theoretical and algorithmic precision.

3 The discriminative lexicon model

We use the DLM to gauge the extent to which meaning is involved in the two stages of the lexical route: understand a word's meaning, and pronouncing the word given its meaning. Here, we make the assumption that in the naming task, the meanings of words are engaged.

As already mentioned previously, the DLM conceptualizes lexical comprehension as a mapping from a word's form to its meaning, and production as a mapping from meaning to form. Forms and meanings are represented as high-dimensional vectors. Convenient (but crude) form vectors that we will make use of are binary vectors indicating the presence and absence of overlapping letter n-grams in a word's orthographic form. Semantic vectors are generally taken from word embedding spaces such as word2vec (Mikolov et al., 2013a), fastText (Grave et al., 2018), or GloVe (Pennington et al., 2014). The form and semantic vectors are collected into two matrices: the (modality-specific) C matrix containing all form vectors and the (modality-free) S matrix containing all semantic vectors (example matrices can be seen in Figure 2). For modeling the transformation between meaning and form, various methods have been explored, and are implemented in the JudiLing package (Luo et al., 2024), for a comprehensive introduction, see Heitmeier et al. (2026). First, in “Linear Discriminative Learning” (LDL), two linear transformations are computed: F, a transformation from the form to the meaning matrix modeling comprehension, and G, a transformation from the meaning to the form matrix modeling production:

S=CF

C=SG

Since for larger matrices C and S the transformations are only approximate, we write:

S^=CF

C^=SG

Instead of applying a linear transformation, the mapping between S and C can also be modeled with non-linear, deep learning networks (Deep Discriminative Learning, DDL, Heitmeier et al., 2025), in which case we replace the linear F and G matrices with two non-linear functions f and g representing the deep-learning networks together with two sets of trainable parameters Θ_*f* and Θ_*g*:

S^=f(C,Θf)

C^=g(S,Θg)

3.1 Model implementation

For computing F (or G) as well as for obtaining Θ_*f* or (Θ_*g*), methods are available which generally follow one of three scenarios for lexical learning (see, Heitmeier et al., 2023a, for detailed discussion):

• Learning of a mapping independent of frequency of use and order of acquisition.
• Learning of a mapping, taking frequency into account, but disregarding order of acquisition.
• Learning of a mapping, taking both frequency of occurrence and order of learning into account.

For the present study, we obtained the best results with two frequency-informed models, both following scenario 2, one using linear mappings (FIL), and one using incremental deep learning (FIDDL). These models do not take into account the order in which words were learned, as order information is not available to us.¹

Frequency-informed learning (FIL) implements frequency-weighted multivariate multiple regression. For technical details, the reader is referred to Heitmeier et al. (2023a) and Heitmeier et al. (2026). Multivariate multiple regression mappings (henceforth standard linear mappings) without frequency weights have been used in a wide range of modeling studies addressing lexical processing in, for example, Estonian, Korean, Mandarin, Kinyarwanda, Latin, and English (Chuang et al., 2020, 2022; van de Vijver and Uwambayinema, 2022; Baayen et al., 2018, 2019). Whereas standard linear mappings provide type-based learning, FIL implements usage-based learning. The frequencies that FIL used for weighting were the frequencies provided by the Estonian National Corpus (Koppel et al., 2023).² The number of parameters of the FIL model (the weights on the connections in its mapping from form to meaning) is 4,981 distinct letter trigrams × 300 fastText dimensions = 1,494,300.

We also implemented a model with deep discriminative learning, using a training regime referred to with the acronym FIDDL (frequency-informed deep discriminative learning). As a first step, a list of all tokens was obtained by expanding the type frequency list of the words in the experiment reported below. These frequencies were obtained from the Estonian National Corpus 2023 (ENC23) (Koppel et al., 2023). The total number of tokens of the (19,314) word types in our dataset is too large for modeling (79,792,744). We therefore scaled down the original frequencies by a factor 1,000, and rounded upwards, resulting in a type list with 19,314 words and a total of 289,580 tokens. From this list, we created a random sequence of the 289,580 tokens, with each type represented by its corresponding amount of tokens.

The FIDDL model was trained on this list of tokens with the mean squared error (MSE) loss, a single hidden layer with 1,000 units, the Adam optimizer with learning rate 0.001, and batchsize 512. The number of parameters for the FIDDL model was (4, 981 × 1, 000) + (1, 000 × 300) = 5.28 million.

Both the FIL and FIDDL models were trained with 300-dimensional fastText vectors (Grave et al., 2018) to represent words' meanings, and with vectors specifying words' letter trigrams to represent their forms.

We note here that because the DLM is a learning model, it does not need “counters in the head” that keep track of how frequently words have been encountered (such as resting activation levels directly calculated from word frequency counts). Theories that work with such counters adopt a form of naive realism as they assume that it is possible to have veridical observations of words (that can then be counted). However, it has been pointed out repeatedly that the human mind cannot perceive the world as such, and that our perceptions are filtered through the specifics of human perceptual system and human culture (see, e.g., Kant et al., 1999; Merleau-Ponty et al., 2013; Husserl, 1913; and more recently Hoffman, 2019). Learning-driven models make it possible to take these insights into account, and obviate the need for counters in the head.

3.2 Comprehension accuracy and DLM measures

Type-based accuracies were 17.4% for FIL and 78.4% for FIDDL. In a type-based evaluation, FIL struggles with low-frequency words. However, its accuracy evaluated in terms of percentage of tokens recognized correctly is substantially higher, at 74.4%. Token-wise evaluation of FIDDL is at 97.0%.

For each of these two models, we calculated a measure, Target Correlation, that specifies for a given word what the Pearson correlation is of that word's predicted embedding and its gold-standard fastText embedding. The better and more precise a word's meaning has been learned, the shorter naming latencies are expected to be. Given the very different accuracies of the two models, a question of particular interest is to see which model provides the Target Correlation measure that best predicts human performance.

We also calculated a DLM measure for the part of the lexical route that maps meanings onto forms. This measure, henceforth Semantic Support for Form, is the sum of the activations that a word's 3-grams receive from its corresponding semantic embedding. Formally, the semantic support measure for word i is defined as ciTc^i, where ^*T* denotes the transpose. Gahl and Baayen (2024) reported that this measure is a strong predictor of the spoken word durations of English heterographic homophones such as thyme and time. Furthermore, Saito et al. (2024) provides evidence from articulography that the greater the amount of support that an n-gram receives is, the more it is hyper-articulated. We therefore calculated the amount of semantic support for the words in our experiment, using frequency-informed learning with a linear network (FIL).³ The resulting measure is not correlated with Word Length (r = −0.03, it is weakly correlated with Contextual Independence (r = 0.21), but more clearly correlated with FIL-based Target Correlation (r = 0.56).

4 Experiment

4.1 Participant

There was a single participant for the experiment, a 45-year-old healthy right-handed male Estonian native speaker with corrected-to-normal vision, a doctorate degree, and high socio-economic status (the second author of the paper). The participant took part in the experiment voluntarily, and did not gain financially from participation.

4.2 Materials

The materials were 30,000 Estonian words with a wide range of lexical distributional properties. These words were taken from the Estonian National Corpus 2013.⁴ Based on the corpus, a word frequency list was created. This frequency list was divided into 30 frequency bands, and from each frequency band 1,000 words were randomly selected. This list was randomized and divided into 30 experimental lists. Each experimental list contained 1,000 words.

4.3 Procedure

The participant was instructed to read aloud the words on the computer screen as naturally as possible. He was seated in front of a computer screen with a distance of 60 cm. The participant rested his forehead on the Eyelink 1,000 head rest. The chin rest was removed to allow speaking.

The experiment was programmed and presented using the ExperimentBuilder software by SR Research. The screen size was 27 inches and the screen resolution was 1,024 × 768 pixels.

Before the experimental task, the eye-tracking system was calibrated for spatial accuracy below 0.5. Each trial started with a drift correction on the left, followed by a blank screen for 500 ms after which the target word appeared on the screen. The stimuli were presented in the black Courier New Bold font (font size 48) on a white background for 2,000 ms, followed by a blank screen for 750 ms. One session was divided into 20 blocks. Each block contained 50 items, and there was the possibility of taking a break after each block. A single session lasted approximately 90 min. The 30 experimental lists were run on different days, but approximately at the same time of day (starting around 10 am). Data collection was carried out over a period of half a year.

During debriefing after the experiment, the participant reported experiencing the stimuli as a constant stream of transitions between unrelated meanings and domains. The participant reported finding unexpected semantic connections that furthered creative interpretation and meditation. This feedback shows that the participant was not engaging in semantics-free orthography-to-phonology conversion, but was experiencing the meanings of the stimuli.

4.4 Analysis with GAMs

For statistical evaluation, we used generalized additive mixed effects models (GAMMs, Hastie and Tibshirani, 1990; Wood, 2017; R-package mgcv, version 1.8). GAMMs allow the testing of nonlinear relationships between the dependent and the predictor variables. The analyses we present are the result of exploratory data analyses. We set α = 0.0001, and only report predictors with p < α. Only the simplest, well-supported models are reported.

4.5 Preprocessing

Before the analysis, the audio and eye-tracking data was checked and pre-processed. The audio data for the first three lists were removed due to technical issues with the recording setup. One list was accidentally recorded twice, so we only included the first recording.

Word durations and production latencies were automatically calculated from the recording using a Matlab script. 478 words were identified as misspoken in this process and removed. This left us with audio information for 25,523 words.

Eye gaze data information was obtained using fixation reports from Eyelink Dataviewer. Eye-tracking data was not recorded for two full lists and an additional 1,049 trials across the remaining lists were removed due to audio recording errors. This left us with 23,473 word responses that had both eye-tracking and word production information. Finally, all responses with acoustic durations greater than 1.5 seconds were considered outliers (2.5 standard deviation of the mean). This left us with the final data set that contains word duration, production latency, and eye fixation information for 19,314 words.⁵

4.6 Response variables

We investigated three eye-tracking measures as response variables to capture early and late effects during the visual scan of the presented word: First fixation duration (the duration of the initial fixation in milliseconds), Total fixation duration (the total reading time on the word), and Number of fixations (how many fixations a word received).

Furthermore, we looked at two production measures: Naming latency (the time taken to start articulating the word from the time it appeared on the screen), and Acoustic duration (the time of the articulation). Production latencies were logarithmically transformed. Without this transformation, the model residuals depart substantially from normality.

4.7 Predictors

For each of the words in our dataset, we considered the following predictors.

Word Frequency is the token frequency of the stimulus word. Previous research (Lõo et al., 2018a,b) has shown that in Estonian, more frequent nouns are read and named faster than less frequent words, as has been observed in many other languages (Whaley, 1978; Balota et al., 1999). Since stimuli in word naming were presented in isolation, without any contextual information to aid in disambiguation of possible homonyms, word frequencies are cumulated for homographs. Word frequency counts are based on the ENC23, which comprises 3.8 billion tokens. Word frequency counts were log-transformed in order to avoid adverse effects of higher-frequency outliers for regression modeling.

Inflectional Paradigm Size is the number of forms observed for a certain lemma from the Balanced Corpus of Estonian, which comprises of 15 million tokens.⁶ For example, for the lemma senat “senate,” the paradigm size was four: senat “nominative singular,” senati “genitive singular,” senatile “allative singular,” senatis “inessive singular.” The distribution of paradigm sizes was highly skewed. This skew was mostly eliminated by a square root transformation. Previously, inflectional paradigm size effects in Estonian have been reported in visual lexical decision task (Lõo et al., 2018a) and text reading (Lõo et al., 2024a), as well as in word production task (Lõo et al., 2018b) and in spontaneous speech (Lõo et al., 2023).

Orthographic Neighborhood Density (Coltheart, 1978) is the number of orthographic neighbors, calculated with the R-package vwr from the Balanced Corpus of Estonian using the dictionary form of the word. The orthographic neighborhood counts were logarithmically transformed in order to reduce the strong rightward skew in their distribution.

Although neighborhood density has been widely studied (Landauer and Streeter, 1973; Balota et al., 2007), there is no general consensus on its effects on lexical processing. For English lexical decision, Heitmeier et al. (2023b) observed, for the British lexicon project (Keuleers et al., 2012), that the effect of neighborhood density varied substantially between individual participants, facilitatory for some, inhibitory for others, with no robust main effect.

For Estonian, no neighborhood effect was found in visual lexical decision (Lõo et al., 2018a). In word naming, however, both facilitatory and inhibitory effects have been reported (Lõo et al., 2018b): larger neighborhoods predicted longer naming latencies in a smaller experiment with 200 items, but shorter latencies in a larger experiment with 2,800 items.

We also considered an Entropy measure for the possible pronunciations of a written word form. For example, in the word form kassi “cat, gen/part,” the [s] is pronounced long for the genitive, and overlong for the partitive. As most of the words had unambiguous pronunciations, we decided to make use of a simpler variable set to 0 when a single pronunciation of the form was possible, and 1 when multiple pronunciations were possible. The count of pronunciations was based on the Combined Dictionary of Estonian (Langemets et al., 2024; Tavast et al., 2020).

Word Length is the number of characters of the stimulus word. Longer words are expected to take longer to read and produce.

POS is the part of speech of the stimulus word. Function words tend to be pronounced with shorter acoustic duration and read faster than content words, and verbs are pronounced with shorter duration and read faster than nouns (e.g., Gahl et al., 2012; Dilts, 2013; Lõo et al., 2024b; Rayner, 1998; Furtner et al., 2009).

Manner of articulation of the first segment in the word, with levels approximant, fricative, nasal, plosive, trill, and vowel. This factorial predictor was included to control for artifacts of the voice key, the sensitivity of which varies by manner of articulation.

Target Correlation is a measure that provides the Pearson correlation between the semantic vector predicted by the DLM model and its corresponding gold standard target vector. If the target correlation for a word is higher, this implies that the DLM model has been more successful in learning the association between that word's form and its meaning. In other words, the higher the target correlation, the more accurate the mapping from form to meaning is. Previous work found that Target Correlation is predictive for reaction times in lexical decision experiments, particularly when calculated from FIL or FIDDL models (e.g., Heitmeier et al., 2023a, 2025).

Contextual Independence was first proposed by Gahl and Baayen (2024) as a tool for assessing the extent to which a word can be understood independently of the context in which it occurs. Whereas in normal language use, words appear in the context of other words, with meanings that are co-determined by these contexts, in the lexical decision and word naming tasks, words are presented in isolation. Participants must make decisions about these words without the help of words in the context. From a learning perspective, we can consider the target word itself and the other words with which it co-occurs as cues that predict each other. Gahl and Baayen (2024) therefore used the Rescorla-Wagner learning rule (Rescorla and Wagner, 1972) to predict the words in an utterance from the words in that utterance. Denoting the number of different words by n, with infinite learning, the n × n matrix *W* predicting words from each other will converge to the identity matrix, i.e., a mapping from words to words in which any word w will predict itself with weight 1, and any other word with weight 0. However, with much more restricted learning experience, words will predict themselves less well, and will depend on the words they co-occur with to be fully supported. The contextual independence for word w is its weight (equivalently its connection strength) to itself, i.e., its diagonal value in *W*. Gahl and Baayen (2024) calculated contextual independence on the basis of the British National Corpus (Burnard, 1995), and found it to predict visual lexical decision latencies as well, and perhaps better, than the frequencies in this corpus. This led us to also calculate contextual independence for Estonian. The algorithm was trained on the lemmatized ENC23 corpus⁷ with a learning rate λ = 0.001. Just like word frequency distributions, the distribution of contextual independence has a long right tail. The rightward skew was substantially reduced by means of a logarithmic transformation.

Conceptually, the two learning-based predictors decompose the standard frequency effect into two components. The first component, represented by Target Correlation, approximates the effect of usage on the learning of what words mean given their forms. The learning process itself is co-determined by word similarity (thus implicitly capturing neighborhood effects), the systematic correspondences between form and meaning due to morphology (thus implicitly capturing inflectional paradigm size effects), and word frequency. The second component, represented by Contextual Independence, approximates (more crudely than we would like) the consequences of the fact that words are not islands in a frequency list, but are used in utterances together with other words. In the naming task, words occur in isolation, but this does not imply that the experience gained with words in context is inert. The contextual independence measure seeks to assess the extent to which in normal usage words depend on the words in their context. The more collocationally restricted a word is, the more it will depend on its collocates, and the lower its contextual independence will be. This measure attempts to probe the consequences of having encountered a word in many contexts for the special case that this word is presented in isolation. The contextual independence measure is calculated from a lemmatized corpus to make calculations tractable, and therefore provides only a crude approximation of the contextual independence of inflected forms.

Semantic Support for Form estimates the support that a word's form receives from its meaning, as explained above in Section 3.2.

Finally, we included two predictors for capturing how the participant proceeded in the course of the (very long) experiment. List marks the order of the stimulus lists, ranging from 1–30. Trial marks the order of the stimulus within a given list, ranging from 1–1,000.

4.8 Results for comprehension

The lexical route, in the present conceptualization of the naming task, has two stages, a comprehension stage in which the meaning of an orthographic string is predicted, and a subsequent stage in which this meaning is articulated. In this section, we consider GAM models for the first phase of the word naming process. We consider each of the five response variables in turn. A summary of the model is provided in Table 1.

Table 1. Summary of the quantile GAM fitted to the First Fixation Duration.

4.8.1 First fixation duration

The first fixation duration was modeled with a quantile gam (Fasiolo et al., 2020a), as the distribution of the first fixation durations was highly non-normal and could not be corrected to normality. Non-linear effects for median first fixation duration were present for the two time scales (Trial and List) and for Word Length. The effect of these predictors is presented in Figure 3. First fixations were the longest for words with approximately five letters. For longer words, first fixation durations may be shorter, as a subsequent fixation to a later point in the word is more likely to occur. For very long words, the median was also high, but confidence intervals are wide. None of the other measures were predictive for first fixation durations, suggesting that the initial fixation duration gauges visual scanning only. There was no serious collinearity of the predictors: κ = 9.8 (following Belsley et al., 1980).

4.8.2 Total fixation duration

Total fixation duration was modeled with a scaled-t GAM, using the scat directive of the bam function of the mgcv package (Wood, 2017). In addition to non-linear effects of Trial and List, an effect of Word Length was present, such that longer words elicited longer total fixation durations (all p ≪ 0.0001), as expected. This effect, however, leveled off for the longer words, as shown in the upper right panel of Figure 4. The contour plot for the interaction of Word Length by List is visualized in the lower left panel of Figure 4. The effect of Word Length changed as the experiment proceeded. Later in the experiment, the participant tended to fixate less long on long words, whereas early in the experiment, the long words elicited somewhat longer total fixation durations.

Furthermore, for Word Frequency a modest nonlinear effect was observed, with the expected decrease in total fixation duration for more frequent words. For the most frequent words, this trend leveled off. The AIC of this model was 271,583.5. The collinearity index for the predictors was κ = 22.9, indicating moderate collinearity. Concurvity for the smooths of Word Frequency and Word Length are substantial, indicating that their smooths can be predicted to a considerable extent from the other smooths in the model (for a discussion of concurvity, see Gahl and Baayen, 2026). Given that Word Frequency and Word Length are not independent (r = −0.35), it is unsurprising that the regression model cannot fully tease their effects apart.

Word Frequency can be replaced by FIL-based Target Correlation in interaction with Contextual Independence, with an equivalent AIC (271,584.7).⁸ The contour plot for this tensor product interaction is shown in the lower left panel of Figure 4. For lower values of Contextual Independence, the effect of Target Correlation is U-shaped. For larger values of Contextual Independence, the effect of Target Correlation disappears. For smaller and larger values of Target Correlation, a greater Contextual Independence predicts shorter total fixation durations.

The concurvity of the interaction of Target Correlation and Contextual Independence with the other predictors is 0.21, which compares favorably with the concurvity of Word Frequency with the other predictors (0.45). The model with learning-based measures therefore provides a very similar goodness of fit with less confounded, and hence better interpretable, predictors. A summary of the model is provided in Table 2.

Table 2. Summary of a scaled t(3,199.917) GAM fitted to the Total Fixation Duration, with baseline predictors (AIC: 271,583.5).

4.8.3 Number of fixations

The number of fixations, analyzed with a Poisson GAM, varied non-linearly with Trial, List, and Word Length, as shown in Figure 5 (all p ≪ 0.0001). A summary of the model is provided in Table 3.

Table 3. Summary of a poisson GAM fitted to the total number of fixations (AIC: 70,005.9).

The effects of List and of Trial within List show how attention changed at shorter and longer time scales. As expected, the number of fixations increased with Word Length. The effect of Word Length and List interacted. In the course of the experiment, the overall trend of List indicates that as the experiment proceeded, more fixations were executed. The interaction of Word Length and List indicates that early in the experiment (low values of list), the effect of Word Length was stronger, and that later in the experiment (high values of list), its effect was weaker. Apparently, in the course of the experiment, short words became progressively more difficult. However, according to our preset α = 0.0001, it is doubtful that this interaction would replicate.

In addition to these predictors, a linear effect was observed for Word Frequency, such that a greater frequency of occurrence afforded fewer fixations. However, as for the interaction of Word Length and List, this effect is unlikely to be robust, given that we set α = 0.0001 for the present exploratory analyses. We also note here that the variable importance of Word Frequency is the smallest of all predictors, and is even less than the variable importance of Trial. Finally, we observed that DLM measures were not supported for the total number of fixations.

The collinearity for the four predictors in this model is 22.9, which is higher than desirable, but the concurvities for the smooths are fairly small, indicating that the partial effects capture distinct parts of the variance.

In summary, for the total number of fixations, we did not find solid support for any lexical predictors other than Word Length.

4.8.4 Naming latencies

Two generalized additive models were fitted to the log-transformed naming latencies, a baseline model and a DLM model. Both models included an AR(1) process for the errors (ρ = 0.2) and used the scat directive to adjust t-distributed residuals to normality. Both models also included as control variables Manner of articulation, Trial, List, and Word Length.

A robust and parsimoneous baseline model included the classical predictors: part of speech (POS, a factor with 13 levels), the interpretational entropy of the word (Ent, binary), frequency of occurrence (Log Frequency) and the (square-root transformed) number of inflected variants attested for a word's lemma (Paradigm Size). Table 4 provides the summary for this model, and Figure 6 presents plots for the nonlinear effects. The upper left panel of this figure shows that in the course of a session, naming latencies first decreased and then increased again. In the course of the sequence of sub-experiments, naming latencies generally decreased, but in an undulating way (second panel). The magnitude of these undulations varied somewhat by Trial (third panel). The upper right panel shows that naming latencies decreased linearly with Word Frequency. The bottom center panel indicates that the lower values of Paradigm Size predict longer naming latencies. Shorter RTs for words with larger inflectional Paradigm Size have been reported in earlier studies in Estonian (Lõo et al., 2018a,b). The second lower panel clarifies that both very short and longer words elicited longer reaction times, with an optimum around lengths 5–6. The final panel on the bottom row presents the interaction of Word Length by List. For early lists, longer words elicited somewhat longer naming latencies, but by the end of the experiment, this effect reversed such that longer words were named slightly more quickly.

Table 4. Summary of a Gaussian GAM fitted to the log-transformed Naming Latencies with baseline predictors.

The reference level for Manner is “approximant,” and for Entropy, non-zero entropy. Concurvity scores are given for the smooth terms. AIC: –35,076.69. ΔAIC: the increase in AIC when a predictor, and all its interaction terms, are removed from the model specification.

Using the increase in AIC when a predictor and all its interaction terms are withheld from the model specification as a measure of variable importance, List and Manner emerge as the strongest predictors, followed by Word Length and Trial. POS and Entropy have the lowest variable importance.

The condition number for the predictors of the baseline model is high, 25.7. Unsurprisingly, there are some high concurvity scores (see Table 4), notably for some of the predictors of primary theoretical interest, ranging from 0.49 for word frequency to 0.72 for inflectional Paradigm Size. This makes it difficult to assess the individual contributions of these predictors. For Word Frequency, for instance, almost 50% of its effect is predictable from the other predictors in the model.

The DLM model replaced the paradigm size, frequency, part of speech, and entropy measures with Target Correlation and Contextual Independence. Of the two DLM models, the Target Correlation of the FIDDL model outperformed the corresponding measure from the FIL model (AICs: –35,041 and –34,995 respectively), therefore Figure 7 and Table 5 report the GAM with FIDDL-based Target Correlation.

Table 5. Summary of a GAM fitted to log Naming Latencies with DLM predictors: Target Correlation calculated from a FIDDL model, and Contextual Independence.

AIC: –35,041. Concurvity scores are given for the smooth terms. ΔAIC: the increase in AIC when a predictor, and all its interaction terms, are removed from the model specification.

Figure 7 presents the partial effects of the smooth terms, and Table 5 presents the model summary. A comparison of Figures 6, 7 clarifies that the effects of Trial and List are estimated to be very similar by the two models. The same holds for the effect of Word Length.

The lower right panel of Figure 7 presents the interaction of Target Correlation and Contextual Independence. Naming latencies generally decreased with increasing Target Correlation, but this effect becomes weaker for larger values of contextual independence. For target correlations in the interval [0.2, 0.8], naming latencies decrease as Contextual Independence increases, for the remaining highest values of target correlation, the effect of Contextual Independence reverses with a small effect size.

The condition number for the DLM model is κ = 23.6, similar in magnitude to that of the baseline model. Although concurvity is high for Word Length, it is low for the tensor product smooth of Target Correlation and Contextual Independence. Therefore, the contribution of the DLM predictors is not strongly confounded with other predictors.

The classical model has a lower AIC (–35,077) than the FIDDL model (–35,041), and is clearly the better model. However, to put this in perspective, a model with only control variables (Trial, List, Manner, Word Length) already achieves an AIC equal to –34,864.22. The baseline model improves on this by 212 AIC units, and the DLM model by 176 AIC units. In other words, the DLM model provides an improvement of about 83% of the improvement offered by the baseline model.

4.8.5 Spoken word duration

We also analyzed the spoken word durations, again comparing a baseline GAM with a DLM GAM. Both GAMs set the family directive to scat, thus using a scaled t-distribution for the residuals. Figure 8 and Table 6 report on the baseline GAM. A small effect of Trial is visible, although this may not replicate (p > α = 0.0001). Unsurprisingly, its variable importance is small (Δ AIC = 18). An undulating effect of List is well-supported. Word Length was a strong predictor with a linear effect. Unsurprisingly, word length in seconds increased with word length measured in letters.

Table 6. Model summary of a scaled t(5.274,0.074) baseline GAM fitted to Spoken Word Duration (AIC: –38,281).

Turning to the predictors of theoretical interest, as expected, spoken word durations decreased with Word Frequency, but less so for higher frequencies. The Orthographic Neighborhood Density had a small, almost linear effect for values below 2.5. For larger values, no effect was present. Its variable importance is tiny (Δ AIC = 8). For the (square-root transformed) Paradigm Size, a U-shaped effect emerged. For the highest values, no effect was present.

The condition number κ for the predictors is 27.4, indicating severe collinearity. As can be seen in Table 6, there is medium concurvity as well, with highest values for POS and Word Length. Given the ubiquitous correlations between neighborhood counts, word length, word frequency, and paradigm size, these concurvity scores are unsurprising. Importantly, they clarify that in this model, it is not possible to clearly disentangle from each other the effects of these predictors.

The DLM GAM is summarized in Table 7. A model based on FIL (AIC –38,200) outperformed the model based on FIDDL (–38,049). We therefore report the model with FIL-based predictors.

Table 7. Summary of the scaled t(5.129,0.073) DLM GAM fit to Spoken Word Duration with FIL-based Target Correlation and Contextual Independence as predictors (AIC: –38,200).

Effects of control variables (Trial, List, and Word Length) are extremely similar to those in the model with baseline predictors, and hence are not shown. As observed for the total fixation durations and naming latencies, an interaction of Target Correlation by Contextual Independence is present. The tensor product smooth for these predictors is visualized in Figure 9. Overall, greater target correlations predict shorter word durations. For intermediate valued target correlations, a greater Contextual Independence predicts shorter durations, but this effect reverses for the largest values of Target Correlation. The effect of Contextual Independence is modest, but well supported: removal of this predictor from the model specification results in an increase of 70 AIC units.

It is noteworthy for the DLM model that there is little collinearity (κ = 13.8). Furthermore, all concurvity scores are small. The effects of Contextual Independence and Target Correlation do not show signs of being confounded with Word Length. Thus, although the model with baseline predictors provides the better fit (AIC –38,281) compared to the DLM model (AIC –38,200), it offers a clearer window on the word durations. Note, however, that a model with only control variables (Trial, List, Manner, Word Length) already achieves an AIC equal to –37,833.9. The baseline model improves on this by 447 AIC units, and the DLM model by 366 AIC units. Compared to the control model, the DLM model therefore provides an improvement of some 82% of the improvement offered by the baseline model.

4.9 The production phase: semantic support for form

Thus far, we have considered one DLM measure that is straightforwardly interpretable as a measure gauging the comprehension part of the naming task: Target Correlation. But the naming task requires not only comprehension, but also production. For assessing the role of learning in word production, there is a DLM measure that holds some promise: Semantic Support for Form.

It turns out that Semantic Support for Form is also predictive for the spoken word durations of the words in our experiment. Its effect emerges most clearly in a three-way interaction with Target Correlation and Contextual Independence, which we modeled with a tensor product smooth. Replacing the two-way interaction reported above in Table 7 with this three-way interaction leads to a decrease in AIC from –38,199.9 to –38,289.1, a decrease of no less than 89 AIC units. A summary of this model is provided in Table 8. Interestingly, this model outperforms the corresponding baseline model (AIC –38,281.07) by some 8 AIC units.

Table 8. Summary of the GAM fitted to Spoken Word Duration with a three-way tensor product smooth for Contextual Independence, Target Correlation, and Semantic Support for Form, using FIL for the latter two measures.

The model was fitted with the family directive set to scat.

The three-way interaction is visualized in Figure 10. Darker shades of gray denote shorter durations. In this interaction plot, panels are organized by deciles of Semantic Support, with the first decile in the lower left, and the last decile in the upper right. Longer durations (whiter colors) are found for the higher values of Semantic Support. This dovetails well with the findings of Gahl and Baayen (2024), who also observed a positive correlation of semantic support and spoken word duration. There is no evidence of an effect of Target Correlation and Contextual Independence for the early deciles of Semantic Support. But from the 5th decile onward, the two-way interaction emerges, such that a greater Target Correlation predicts shorter durations, and a greater Contextual Independence predicts longer durations. In general, the main trends in the top panels align with the effects in the GAM with only a two-way interaction (cf. Figure 9).

The Semantic Support for Form measure also has some explanatory value for the naming latencies.⁹ Table 9 presents the model summary. The AIC of this model is –35,047.6, which improves on the AIC of the previous model (35,040.9) for the naming latencies by some 6 AIC units. (However, the baseline model is superior in terms of AIC: –35,077.) Figure 11 provides the interaction plot for the three-way interaction. Panels are again organized by the deciles of Semantic Support for Form, from the first decile in the lower left to the last decile in the upper right. Overall, as Semantic Support for Form increases, naming latency decreases (the panels in the top row are darker). Furthermore, an interaction of Target Correlation and Contextual Independence, similar to the interaction presented above in Figure 7 for the simpler model, is present for the lower deciles of Semantic Support for Form, and gradually diminishes for increasing deciles, with hardly any effect for the highest three deciles.

Table 9. Summary of a GAM fitted to Naming latency with a three-way interaction for Target Correlation (based on FILL), Contextual Independence, and Semantic Support for Form (based on FIL).

The model was fitted with the family directive set to scat, and with the autocorrelation parameter ρ set to 0.2.

A comparison of the interaction plot for spoken word duration and that for naming latency reveals that the effects of Target Correlation and Contextual Independence are in complementary distribution across the deciles of Semantic Support for Form. For instance, whereas the two-way interaction of Target Correlation by Contextual Independence is absent for the first decile of Semantic Support for Form in the model for spoken word duration, it is most strongly present in the same decile in the model for naming latency. This pattern of complementarity is all the more remarkable because there is only a small correlation between naming latency and spoken word duration (r = 0.05, t_{(19, 312)} = 7.36, p < 0.0001).

To come to some understanding of what this pattern of results means, it is useful to think of Semantic Support for Form as an indicator of how well the meaning-to-form part of the lexical route in the naming task performs. Low values indicate this route is not useful and basically out of commission. High values, by contrast, indicate that this route is highly effective. In what follows, we focus on the two extremes, represented by the first and last deciles of Semantic Support for Form.

For low Semantic Support for Form, the production part of the lexical route is not functional. In other words, this part of the lexical route is blocked. In this case, naming latencies are long, and the measures reflecting comprehension, TargetCorrelation and Contextual Independence, are visible for the naming latencies, with higher values predicting shorter latencies, indicative of facilitated understanding of words' meanings. But these two measures do not predict spoken word duration, presumably because the participant is forced to resort to the non-lexical route, using grapheme-to-phoneme spell-out for articulation (see, Baayen et al., 2019 for discussion of a non-lexical, direct, route in the context of the discriminative lexicon framework).

At the other extreme, for high Semantic Support for Form, the production part of the lexical route is functioning at its best. Now, naming latencies are very short, and words are articulated clearly and confidently, with long spoken word durations. Effects of the comprehension variables (Target Correlation and Contextual Independence) are absent for the naming latencies, possibly a floor effect. At the same time, these very same measures are highly predictive for the spoken word durations. Higher values of Target Correlation predict shorter durations, possibly due to fast comprehension of words' meanings overflowing into pronunciation. Higher values of Contextual Independence predict longer spoken word durations, possibly due to less dependence on co-articulation with neighboring words in context.

In between these two extremes, we see how the cognitive system of our speaker is adapting to the different conditions under which it has to operate to perform the naming task.

5 General discussion

The data that we collected in this study provide clear answers to our four main research questions.

Our first research question asks whether DLM measures are predictive for eye-movements. Table 10 provides an overview of the main predictors and whether they contribute to the models for the five response variables: First Fixation Duration, Number of Fixations, Total Fixation Duration, Naming Latency, and Spoken Word Duration. Whereas Trial, List, and Word Length were invariably predictive, the DLM measures were not predictive for first fixation durations nor for the total number of fixations. The same holds for Word Frequency, Neighborhood Density, and Inflectional Paradigm Size. It is only the total fixation duration response variable that reflects, to some extent, Word Frequency, Target Correlation, and Contextual Independence. This pattern of results leads to the conclusion that in our naming experiment, visual scanning and visual information uptake was not influenced by lexical knowledge. This may be due to the high reading proficiency of our participant, or to the structure of the Estonian language. Given that there are many studies documenting lexical effects in the eye-tracking record for other languages (Kuperman et al., 2008, 2024; Miwa et al., 2014), this non-result surprised us.

Table 10. Overview of supported effects of predictors by response variable.

Our second research question asks whether measures derived from a deep DLM network outperform measures from a linear DLM network. Table 11 presents the AIC scores for the FIL and FIDDL models for the three temporal response variables in the models for the comprehension part of the lexical route.¹⁰ The deep network (FIDDL) outperforms the linear network (FIL) for the naming latencies, but FIL is performing better for the total fixation duration (albeit by a small margin) and for Duration.

Table 11. Overview of model fit, using AIC, for the two DLM models, for the three temporal response variables (total fixation duration, response latency, and spoken word duration.

This result is of theoretical interest because the deep mapping (FIDDL) provides the superior performance with respect to accuracy, which was 17.4% for FIL and 78.4% for FIDDL. Apparently, prediction accuracy in the machine learning sense is not necessarily a reliable guide to how well a model performs when predicting human lexical processing.

Our third research question asks whether computational modeling with the DLM might advance our understanding of the comprehension and production stages of the lexical route. We addressed this question with the Target Correlation measure, which is a measure derived from the comprehension mapping, and with the Semantic Support for Form measure, which is a measure derived from the production mapping. Low values of Semantic Support for Form indicate that it is impossible to calculate with precision a word's form from its meaning. We observed that words with greater Semantic Support for Form had shorter naming latencies and longer spoken word durations. A three-way interaction of this measure with Target Correlation and Contextual Independence was present, for both the naming latencies and the spoken word durations. The joint effect of the latter two measures varied across the deciles of Semantic Support for Form in opposite ways for the naming latencies and the spoken word durations. For spoken word durations, their effect was most prominent for the highest deciles (i.e., for words realized with long durations), diminishing steadily for the lower deciles, and vanishing for the lowest deciles. For the naming latencies, their effect was most prominent for the lowest deciles, and gradually decreased for increasing deciles, with no effect for the highest deciles (the words with the shortest naming latencies).

When Semantic Support for Form has low values, generating a word's form from its meaning in a sufficiently precise way is not possible. In this case, the second half of the lexical route is out of commission. Naming latencies are long. In these long latencies, the benefits of Target Correlation and Contextual Independence for the comprehension half of the lexical route are clearly visible. At the same time, for low Semantic Support for Form, word durations are the shortest, and these short durations do not bear the mark of Target Correlation and Contextual Independence.

It is conceivable that since the Target Correlation and Contextual Independence measures are visible only in longer naming latencies and longer spoken word durations, we are in effect observing floor and ceiling effects. However, a quantile GAM (Fasiolo et al., 2020b) fitted to the second decile of the spoken word durations robustly supported the three-way interaction. This argues against the possibility that the pattern of results is trivial and not of theoretical interest.

We therefore regard the observed pattern of results as informative, and propose that it indicates that for the lowest values of Semantic Support for Form, the speaker was falling back on the non-lexical route, with his articulation being based on a direct mapping from the written form to the corresponding sounds. Under this interpretation, falling back on the non-lexical route then comes with the cost of long naming latencies and short, possibly under-articulated, spoken words.

Our fourth research question asks how much can be achieved with a computational model that does not implement the non-lexical route, and that focuses on the lexical route only. The implementation of the lexical route with the DLM assumes that for naming a word, an experienced reader will articulate that word starting from its perceived meaning. The obligatory involvement of meaning in the DLM is of specific interest as the word naming task has often been observed to be less sensitive to word meaning (see, e.g., Balota et al., 2004; Baayen et al., 2006, 2007; Yap et al., 2012). Our analyses suggest that the DLM model for the lexical route has considerable explanatory power. The Target Correlation, Contextual Independence, and Semantic Support for Form measures are well-supported as predictors which, as noticed above, shed new light on the two stages of the lexical route and the consequences of an underperforming production stage.

Our fifth research question directs attention to the explanatory value of DLM-based predictors in comparison to the explanatory value of classical predictors such as word frequency and inflectional paradigm size. What we found is that for the comprehension stage of the lexical route, the DLM models are not as accurate as the statistical baseline model. In terms of AIC, the DLM models capture about 82% of the reduction in AIC that the baseline lexical predictors afford compared to a control model with only trial, list, and word length as predictors. However, once the meaning-to-form stage of the lexical route is taken into account by means of the Semantic Support for Form measure, the DLM model for spoken word duration outperforms the baseline model by a small but non-negligible margin.

That a simple computational model cannot approximate with precision all aspects of the rich knowledge of a highly educated speaker of Estonian, as evidenced across five different response measures for the naming task, is unsurprising. What does require explanation is why observational measures such as Word Frequency or Inflectional Paradigm Size perform so well specifically for the naming latencies and total fixation durations, even though these measures have no clear algorithmic foundation. The DLM attempts to provide such an algorithmic foundation. There are many possible reasons for why, although the DLM gets quite far, it does not get far enough for the naming latencies and the total fixation durations.

• The non-lexical route for word naming is not modeled. Unfortunately, modeling the non-lexical route is difficult to model for Estonian, because the mapping between orthography and phonemic transcription is not entirely straightforward: the language distinguishes three segment lengths (short, long, and overlong), but long and overlong segment length are not represented consistently in the orthography, likewise palatalization is written inconsistently. We therefore leave implementation of a computational model for the direct route of Estonian to future research.
• The DLM models are trained on only the words presented in the experiment, but the participant has a much broader experience with the vocabulary of his language.
• The consequences of explicit training in reading are not considered. There are cases where fast subliminal automated processes break down. For instance, some Estonian orthographic words can be pronounced in two ways. The participant was aware of these cases, and was making conscious decisions. The cognitive skills of the “Enhanced Literate Mind” (Huettig and Hulstijn, 2025; Hulstijn, 2024) come into play here, but these are outside the scope of the DLM.
• Another consideration is that the form and meaning embeddings that we used are far from perfect. The form embeddings are crude, and fastText embeddings may not adequately represent the dominant senses that a highly educated speaker would think of first. A further concern is that fastText is trained on a text base that is much larger than what the participant in our experiment can ever have experienced.
• There also may be a lack of precision in the FIDDL model due to thinning the empirical frequencies, as a consequence of which differences between the lower frequencies are not well visible to the model.

Although there are many ways in which the computational modeling of the present data can be improved, our results provide a clear proof of concept that considerable headway can be made for providing an algorithmically precise explanation of the effects of classical variables such as frequency, neighborhood density, and paradigm size in the lexical naming route.¹¹

Across all five response variables, we observed that trial and list contributed without exception to each of the five models, indicating that the effects of experimental time, at both short time scales (trial within session) and long time scales (session) are pervasive. These longitudinal changes are likely due to fluctuations in attention, learning, and fatigue (see also Baayen et al., 2017; Pham and Baayen, 2015; Heitmeier et al., 2023b). Interestingly, the effect of word length changed somewhat as the experiment progressed, as indicated by the interaction of word length by list, which was present for the total fixation durations and the naming latencies, and possibly also for the number of fixations. This interaction of frequency by length is likely due to the over-representation of longer words in the experiment. In normal language use, shorter words are used most often. In the experiment, however, high-frequency words are presented only once, and large numbers of longer lower frequency words are encountered at a rate that is atypical for normal language use. The participant is adjusting to this atypical distribution of frequencies. Later in the experiment, longer words required fewer fixations, less long fixations, and response latencies became somewhat shorter. In other words, in the course of the experiment, the participant became more skilled at reading out loud longer Estonian words. This may be due to a changing task strategy, to lexical learning in the course of the experiment, or both. This finding provides a clear counterexample to the claim of Thul et al. (2021) that in experiments, longitudinal effects of experimental time do not interact with predictors of theoretical interest. Baayen et al. (2022) provided a counterexample from the British Lexicon Project (Keuleers et al., 2012). Here, we have shown that word length, a predictor of clear theoretical interest with a pervasive effect across all response variables, has an effect that changes in the course of the experiment. Furthermore, the interaction of word length by session is also of theoretical interest, as it shows that in a mega-experiment, participants can learn to adjust to the atypical distribution of words presented to them.

A problem for many of the baseline GAM models is substantial collinearity of predictors and concurvity of smooths. For instance, in the case of the naming latencies, the concurvities range from 0.49 (for frequency) to 0.63 (for length), making it impossible to tell with precision what the contribution of frequency is, independently from word length, and vice versa. Problems of concurvity are much reduced when word frequency, inflectional paradigm size, and neighborhood density are replaced by the tensor product interaction of the DLM predictors. Their joint contribution is much less confounded with word length than is the case for measures such as word frequency and neighborhood density, and thus improved interpretational clarity is obtained.

The DLM measures that we have considered in this study decompose the standard word frequency effect into three distinct components. Target Correlation takes into account how frequency of use shapes the learning of the mapping between word form and meaning. Semantic Support for Form takes into account how frequency of use modulates the mapping from meaning to form. Contextual Independence assesses the knowledge of how words are used in utterances. The Contextual Independence measure is extremely crude, and is explored in the present study because it has some potential, but we hope that improved implementations for the underlying idea will be forthcoming. The three DLM measures highlight different aspects of the consequences of words' frequencies of use for lexical learning. For the spoken word durations, these measures provided provided a window on the mental lexicon of our participant that improved on that provided by the classical measures of our baseline GAM.

We are not aware of any computational implementation of an interactive activation model—the model that provides the interpretational metaphors for the majority of current studies on lexical processing—that can handle languages with rich and complex morphologies such as Estonian, although the PONG model of Snell (2024) may prove us wrong. The problem as we see it is that the vast numbers of different word forms in languages such as found in Estonian would, in interactive activation models, require exponential amounts of between-word inhibitory connections, rendering them cognitively, biologically, and computationally unattractive. We hasten to add that we do not ascribe biological reality to the simple artificial neural networks that we have implemented. The strength of the DLM is that it offers tools for assessing in a mathematically precise way, the consequences of usage for how accurately speakers can learn the vocabulary of their language, and how learning accuracy affects lexical processing. This learning does not require symbolic form and meaning representations. To the contrary, error-driven, predictive, discriminative learning is possible, and can thrive, thanks to systematic correspondences between the form space C and the semantic space S. The mappings between C to S that we used to approximate comprehension and production in the lexical route of the naming task can be successful only thanks to the systematic statistical correspondences that exist between the form and meaning spaces (see Nikolaev et al., 2025, for discussion of the nominal morphology of a related language, Finnish). It is noteworthy that even though the vast majority of words that were named are morphologically complex, nevertheless no special measures [such as obligatory morphographic decomposition, as posited by Rastle et al. (2004)] were required to get the model to work for complex words. Nor was it necessary to implement separate whole-word representations for all complex words, as proposed by Giraudo and Grainger (2003). In the age of deep learning and large language models, DLM models may look extremely simplistic, but they can be surprisingly powerful.

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Footnotes

Edited by: Matthew W. Crocker, Saarland University, Germany

Reviewed by: Caitlyn Antal, University of Cambridge, United Kingdom

Alaa Alzahrani, King Saud University, Saudi Arabia

Footnotes

Order-sensitive incremental learning with linear mappings implementing the Widrow-Hoff learning rule has been used to model second and third language acquisition (Chuang et al., 2021) as well as trial-to-trial learning in the British Lexicon Project (Heitmeier et al., 2023b; Keuleers et al., 2012).

https://doi.org/10.15155/3-00-0000-0000-0000-08C04M

Deep mappings can learn this mapping perfectly, and for these mappings, the semantic support for form becomes equivalent to word length, rendering the measure superfluous.

https:doi.org/10.15155/1-00-0000-0000-0000-00158L

The dataset and analyses are available on OSF at https://doi.org/10.17605/OSF.IO/8TVKG.

https://www.cl.ut.ee/korpused/grammatikakorpus/

https://doi.org/10.15155/3-00-0000-0000-0000-08565L

The corresponding AICs for FIDDL was 271,589.4.

The three-way interaction did not improve model fit for the total fixation durations, although the difference in AIC was small, about 2 AIC units in favor of the simpler model, a difference which we judged not to be large enough to support a complex three-way interaction.

We do not consider the effect of Semantic Support for Form here, as it is necessarily calculated with FIL, and hence stands in the way of interpretable comparisons across FIL and FIDDL.

We note here that with respect to the deep learning model, we have not explored the space of hyper-parameters for deep learning models, and have simply used the default settings suggested by Heitmeier et al. (2025). In this way, we have protected ourselves against a fishing expedition for hyper-parameters that might optimize predictivity for the naming data.