Momentum in Language Change

A Model of Self-Actuating S-shaped Curves

in Language Dynamics and Change
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Like other socially transmitted traits, human languages undergo cultural evolution. While humans can replicate linguistic conventions to a high degree of fidelity, sometimes established conventions get replaced by new variants, with the gradual replacement following the trajectory of an s-shaped curve. Although previous modelling work suggests that only a bias favoring the replication of new linguistic variants can reliably reproduce the dynamics observed in language change, the source of this bias is still debated. In this paper we compare previous accounts with a momentum-based selection account of language change, a replicator-neutral model where the popularity of a variant is modulated by its momentum, i.e. its change in frequency of use in the recent past. We present results from a multi-agent model that are characteristic of language change, in particular by exhibiting spontaneously generated s-shaped transitions that do not require externally triggered actuation. We discuss several empirical questions raised by our model, pertaining to both momentum-based selection as well as other biases and pressures which have been suggested to influence language change.

Momentum in Language Change

A Model of Self-Actuating S-shaped Curves

in Language Dynamics and Change

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    Figure 1

    Competition between two syntactic patterns of yes/no questions, as observed in a corpus of Middle English writing (Ellegård, 1953). The established question syntax (e.g., “Went he?”) was gradually replaced by its modern variant (e.g., “Did he go?”) along an s-shaped trajectory.

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    Figure 2

    Exponentially weighted moving averages (EWMAs) of the same input data but with different smoothing factors, as well as their corresponding momentum terms. (a.i) Four EWMAs with smoothing factors article image

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    (from top to bottom) are initialized at article image

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    and repeatedly updated using the same constant input data series article image

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    . (a.ii) Same as (a.i), but with the input data series article image

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    switching from all article image

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    s to all article image

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    s after 60 data points. (b) Corresponding momentum terms article image

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    derived from the trajectories above, by taking each EWMA and subtracting the value of the EWMA with the lowest smoothing factor from above (article image

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    ). Line styles correspond to those in (a).

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    Figure 3

    Momentum-based selection dynamics of a single agent’s variable usage rate in a deterministic production-perception loop, with learning rates article image

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    and momentum bias article image

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    . At every time step, the agent updates their own usage rate (solid black line) by aligning to their own average momentum-biased production with a sample resolution of article image

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    (indicated by the dashed black line). This stable loop is perturbed by administering fabricated input data suggesting 100 % usage of the incoming variant at the time points marked by asterisks, demonstrating the two regimes of momentum-based selection. (a) Stability: a single fabricated data point after 100 interactions causes a sudden increase in the agent’s usage rate (solid black line) as well as the momentum term (dot-dashed grey line, right axis), but the feedback loop stabilizes again. (b) Directed transitions: adding another fabricated data point after 200 interactions raises the momentum term high enough to trigger self-reinforcing runaway change, giving rise to an s-shaped transition.

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    Figure 4

    Successful transitions generated by simulation runs in conditions with and without momentum-based selection. The graphs show the development of the average proportion of use of the incoming variant across the population (black line, left axis) from the point where it crosses the 5 % mark until it reaches 95 %, alongside the average momentum term during that period (grey line, right axis). Transitions are aligned at the point where the trajectory first crosses the 50 % mark of incoming variant usage. (a) 20 trajectories randomly drawn from the 21,909 successful transitions generated by momentum-based selection with momentum bias article image

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    , population sizes article image

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    and various settings of article image

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    . (b) all 28 transitions generated in 17,280 simulation runs with article image

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    , equivalent to neutral evolution, with various settings of article image

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    and population sizes article image

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    . Note the different time scales. The momentum term, ineffective when article image

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    , is shown for reference.

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    Figure 5

    Transitions generated by two simulation runs using identical parameter settings (article image

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    ). The graphs show the development of the average proportion of use of the incoming variant across the population (black line, left axis) as well as the average momentum term influencing the agents’ perception (grey line, right axis). Shaded intervals indicate the range (minimum and maximum values) attested in the population. (a) A successful, s-shaped transition typical of momentum-based selection: an initially noisy momentum value rises high enough to trigger self-reinforcement of the momentum bias (at around 450 interactions) until it saturates and tails off again. (b) Example of a rare, interrupted transition: despite the onset of a directed shift, the wide range of momentum biases across the population destabilizes the feedback loop, causing the average momentum to break down and invert, returning the usage frequency of the incoming variant back towards its initial low level.

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