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Multiplex lexical networks reveal patterns in early word acquisition in children

Massimo Stella, Nicole M. Beckage, Markus Brede

arXiv:1609.03207v2physics.soc-phcond-mat.dis-nncs.CLcs.LG

TL;DR

The paper asks whether single-layer or multiplex lexical-network structure can explain toddlers’ normative word-acquisition trajectories. It models four types of word relationships and finds that multiplex structure predicts early learning better, while association becomes most predictive later.

Abstract

from arXiv · show

Network models of language have provided a way of linking cognitive processes to the structure and connectivity of language. However, one shortcoming of current approaches is focusing on only one type of linguistic relationship at a time, missing the complex multi-relational nature of language. In this work, we overcome this limitation by modelling the mental lexicon of English-speaking toddlers as a multiplex lexical network, i.e. a multi-layered network where N=529 words/nodes are connected according to four types of relationships: (i) free associations, (ii) feature sharing, (iii) co-occurrence, and (iv) phonological similarity. We provide analysis of the topology of the resulting multiplex and then proceed to evaluate single layers as well as the full multiplex structure on their ability to predict empirically observed age of acquisition data of English speaking toddlers. We find that the emerging multiplex network topology is an important proxy of the cognitive processes of acquisition, capable of capturing emergent lexicon structure. In fact, we show that the multiplex topology is fundamentally more powerful than individual layers in predicting the ordering with which words are acquired. Furthermore, multiplex analysis allows for a quantification of distinct phases of lexical acquisition in early learners: while initially all the multiplex layers contribute to word learning, after about month 23 free associations take the lead in driving word acquisition.

Multiplex network construction and analysis

The authors build a four-layer multiplex lexical network from independent measures of toddlers’ word relationships. Its layers encode distinct topological information, and together connect words that are disconnected within individual layers.

Multiplex network construction and analysis

  • The network combines free associations, feature sharing, child-directed-speech co-occurrence, and phonological similarity from four independent measures.Figure 1a–b visualizes 24 of the 529 words, with edge colours distinguishing relationship types.Source: Multiplex network construction and… · p. 2, Figure 1 · p. 3
  • The multiplex is connected even though all but the association layer are fragmented, with largest components spanning 24.2%–62.4% of the 529 words.A path through the multiplex may use different relationship types.Source: Multiplex network construction and… · p. 2
  • The phonological layer has a smaller mean degree; all layers except co-occurrence show higher clustering, non-zero assortativity, and slightly longer paths than configuration models.The authors describe these patterns as suggesting core-periphery structure; co-occurrence and association have heavier-tailed degree distributions than synonym and phonological layers.Source: Multiplex network construction and… · p. 2
  • The four-layer representation is irreducible: aggregating layers would lose topological information because each encodes different information.Figure 1e presents the reducibility analysis.Source: Multiplex network construction and… · pp. 2–3, Figure 1 · p. 3
  • Feature and co-occurrence degrees are negatively correlated (Kendall Tau κ ≈−0.16, p < 0.0001), while co-occurrence and phonological degrees are positively correlated (κ ≈0.27, p < 0.0001).The authors suggest the negative association may reflect semantic differentiation and the positive association supports an interaction between phonological similarity and co-occurrence.Source: Multiplex network construction and… · p. 3
  • Links overlap among the feature, co-occurrence, and association layers, but otherwise do not overlap significantly more than expected under configuration models.Figure 1d reports edge overlap relative to configuration-model expectations.Source: Multiplex network construction and… · p. 3, Figure 1 · p. 3

Multiplex Orderings: Results and Discussion

The study ranks words by network structure and word-specific features against normative toddler acquisition orderings. Predictive features shift with age: multiplex closeness leads early, while association-layer degree becomes strongest later, though late-stage comparisons are less certain.

Multiplex Orderings: Results and Discussion

  • Words were ordered by network measures and compared with word frequency and length using overlap with normative age-of-acquisition orderings derived from parent reports.The analysis assumes earlier acquisition for words more central in the language environment; the authors describe the model as descriptive.Source: Multiplex Orderings: Results and… · pp. 3–4
  • The authors distinguish VELS at months 19–20, ELS at 20–23, and LLS at 23–28; closeness leads in ELS, while association degree and frequency match or slightly outperform other features in LLS.In VELS, results for the first 40 words were below the stated 2.5% significance threshold.Source: Multiplex Orderings: Results and… · p. 4
  • No ordering outperforms all others throughout acquisition, motivating analysis of how layer influence changes over the lexicon’s development.The authors interpret the shifts as consistent with children first learning initial words and later generalizing based on network connectivity.Source: Multiplex Orderings: Results and… · pp. 4–5
  • Association-layer degree was the best-performing single-layer ordering, reaching up to 100% more predictive power than random guessing.The authors conjecture that associations perform well because they relate strongly to semantic memory.Source: Multiplex Orderings: Results and… · p. 4
  • Up to 160% more words than random guessing were predicted by multiplex closeness in early learning, which consistently outperformed single-layer orderings at that stage.Multiplex closeness also predicted up to 25% more than association-layer degree; late-stage statistical significance deteriorated markedly.Source: Multiplex Orderings: Results and… · pp. 4–5

Optimisation of layer influences

The authors optimize layer weights for degree and closeness, then examine how layer influence and predictive performance vary across learning stages. Early learning favors global multiplex structure, whereas association influence dominates later stages; phonology contributes little in the original network.

Optimisation of layer influences

  • Optimized linear combinations of layer-specific degree or closeness maximize normalized word gains, with weights interpreted as layer influence.The analysis uses Monte Carlo robustness checks on subsets containing 80% of original word trajectories.Source: Optimisation of layer influences · p. 5
  • Optimized multiplex improvements depend strongly on layer structure and overlap, since randomized multiplexes produce far smaller word gains.In ELS, even optimized degree combinations yield smaller gains than unweighted multiplex closeness, while optimized closeness performs better than unweighted closeness.Source: Optimisation of layer influences · pp. 5–6
  • The phonological layer has negligible optimized weight, approximately 10^-3, and its degree- and closeness-based orderings perform poorly.Adding extended adult phonology leaves semantic-layer influences consistent, while phonology matters more for neighbourhood degree than closeness and approaches zero later.Source: Optimisation of layer influences · p. 5
  • In VELS, all layers contribute equally to optimized closeness, but later association influence rises to 80%; optimized closeness also supports the importance of global multiplex structure in early learning.For degree, association and feature norms contribute most in VELS; associations dominate ELS, and co-occurrence becomes very small in LLS.Source: Optimisation of layer influences · pp. 5–6
  • Optimal influence orderings outperform association degree and multiplex closeness when predicting VELS words, but perform worse at later stages; sampling gives p = 0.01.Optimal influences through the middle of ELS and in LLS yield word gains up to 25% higher than VELS optimal gains.Source: Optimisation of layer influences · pp. 5–6

CONCLUSIONS AND FUTURE WORK

The multiplex lexical network captures more linguistic information than single-layer analyses and its predictive features change across three stages of acquisition. The conclusions are bounded by a projected, relatively small, normative English vocabulary and point to individual-child and cross-language validation as future work.

CONCLUSIONS AND FUTURE WORK

  • The MLN represents semantic, phonological, and syntactic contexts, capturing more linguistic information than separate single-layer analyses.The authors describe it as a projection of an individual child’s full mental lexicon, not the complete lexicon itself.Source: CONCLUSIONS AND FUTURE WORK · pp. 6–8
  • The analysis distinguishes very early learning, when all but phonology contribute substantially, a transition in early learning, and late learning dominated by associations.The authors suggest that associations may better proxy superordinate words; assessing taxonomic organization as a mediator is left for future work.Source: CONCLUSIONS AND FUTURE WORK · p. 6
  • Multiplex closeness outperforms combinations of local network features early, while free associations dominate late acquisition; the best overall predictions use weighted multiplex single-layer closeness.The authors propose that free associations may better detect superordinate words, while early closeness may reflect shorter relational distances in semantic and syntactic space.Source: CONCLUSIONS AND FUTURE WORK · pp. 6–7
  • The findings describe normative acquisition, which may differ from an individual child’s word-learning order despite probabilistic sampling from norms averaged across roughly 1,000 reports.The authors identify longitudinal data from individual children as a direction for testing the universality of learning strategies in VELS and ELS.Source: CONCLUSIONS AND FUTURE WORK · pp. 7–8
  • The model uses a relatively small vocabulary, and the study focuses on English; the authors propose extending vocabulary and testing other languages.They also identify context-dependent information and individual children’s learning trajectories as future directions.Source: CONCLUSIONS AND FUTURE WORK · p. 8
  • The original phonological layer has marginal influence, but an extended adult phonological network identifies nouns as early candidates and predicts acquisition significantly.The authors relate the original layer’s poor performance to a mismatch: early learned words are noun-rich, whereas its degree and closeness orderings identify mainly non-nouns, especially verbs.Source: CONCLUSIONS AND FUTURE WORK · p. 8

Age of acquisition dataset

The age-of-acquisition dataset uses MacArthur-Bates CDI norms to construct probabilistic word-learning orderings. It treats a word as known once at least 50% of children in a month reportedly produce it.

Age of acquisition dataset

  • Orderings are sampled from MacArthur-Bates CDI norms, which average more than 1,000 vocabulary reports for children aged 16–30 months.The norms give the percentage of children at each age who reportedly produce and understand each word.Source: Age of acquisition dataset · p. 8
  • A word is treated as known once 50% of children in a given month reportedly produce it.Within each month, learned words are sampled in sequence with probabilities proportional to production rates above that threshold, removing each selected word before the next draw.Source: Age of acquisition dataset · p. 8
  • Sampling begins at month 16 and continues until every word has been placed in an order.Higher production rates probabilistically indicate earlier learning; the passage gives “mommy” and “ball” versus “chair” as an example.Source: Age of acquisition dataset · p. 8

Construction of the multiplex network

The multiplex lexical network combines four kinds of word relationships in a 529-word vocabulary. Its words are drawn from the intersection of the CDI data and words connected on at least one layer.

Construction of the multiplex network

  • The network has 529 words, representing the intersection of CDI data and words connected on at least one layer.The four layers are free association, shared semantic features, child-directed speech co-occurrence, and phonological similarity.Source: Construction of the multiplex network · pp. 8–9
  • A free-association link runs from a cue word to its associate, and the association layer is treated as undirected.The feature layer links words sharing at least one semantic feature; edge weights in layers (i)–(iii) are ignored.Source: Construction of the multiplex network · p. 8
  • Co-occurrence links require more than 45 occurrences, while phonological links require IPA edit distance one.The co-occurrence threshold was chosen approximately to match the link density of the other semantic layers.Source: Construction of the multiplex network · p. 8

Cognitive interpretation of network metrics

The paper uses network measures to characterize word importance and potential routes through the mental lexicon. These measures have different interpretations, and the authors remain agnostic about why some words may be more important.

Cognitive interpretation of network metrics

  • Degree counts a word’s links, while multidegree sums its degrees across all layers.Degree on the phonological layer corresponds to the size of a word’s phonological neighborhood.Source: Cognitive interpretation of network… · p. 9
  • Higher degree in semantic networks has been associated with lower age-of-acquisition norms.The authors suggest degree can summarize a word’s increased importance, while remaining agnostic about its cause.Source: Cognitive interpretation of network… · p. 9
  • Closeness relates to how quickly information spreads from a word to others.Prior work found that words closer on semantic topologies tend to be processed together in shorter time.Source: Cognitive interpretation of network… · p. 9
  • Betweenness captures how often a word falls on shortest paths between pairs of words.It represents centrality under hypothetical navigation through the mental lexicon.Source: Cognitive interpretation of network… · p. 9
  • PageRank estimates the likelihood of reaching a word by random walk, and multiplex closeness, betweenness, and PageRank allow jumps across layers.High PageRank words in semantic networks have been found easier to retrieve in fluency tasks.Source: Cognitive interpretation of network… · p. 9

Overlap measures and word ranking

Predicted acquisition trajectories rank words by scores, while empirical trajectories are sampled from CDI age-of-acquisition norms. Predictive performance is evaluated by overlap with empirical learning order, adjusted against random fluctuations.

Overlap measures and word ranking

  • Predicted trajectories rank words from highest to lowest score, averaging over all resolutions of tied scores.The empirical trajectory ensemble is sampled from production probabilities in the age-of-acquisition norms.Source: Overlap measures and word ranking · p. 9
  • At time t, overlap counts words shared by predicted and empirical trajectories up to t, averaged over empirical orderings.The empirical orderings are derived from CDI norms.Source: Overlap measures and word ranking · p. 9
  • Word gain subtracts expected random overlap from trajectory overlap, and vocabulary-normalized gain divides word gain by t.The gain Z-score expresses deviation from random guessing in standard deviations.Source: Overlap measures and word ranking · p. 9

Calculating optimal combinations of layers

The method combines single-layer word scores using coefficients that represent each layer’s influence. Those coefficients are optimized for vocabulary-normalized word gain, either across the full period or in specific learning phases.

Calculating optimal combinations of layers

  • A multiplex word score is a convex combination of the word’s scores from individual layers.The coefficients α, β, and γ represent layer influence in the combined score.Source: Calculating optimal combinations of… · p. 9
  • Optimization selects layer influences to maximize vocabulary-normalized word gain over the full period or specific learning phases.The score is evaluated after randomly leaving out 20% of words, then performance is evaluated on all words.Source: Calculating optimal combinations of… · p. 9
  • The optimization uses differential evolution and averages results across 50 held-out-word configurations and 30 normative acquisition orderings.The 20% holdout was chosen to avoid removing too many words in very early learning stages.Source: Calculating optimal combinations of… · p. 9

ADDITIONAL INFORMATION

The authors declare no competing financial interests, acknowledge EPSRC support for M.S., and acknowledge use of muxViz software.

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