Fast but Not Furious. When Sped Up Bit Rate of Information Drives Rule Induction

Abstract

The language abilities of young and adult learners range from memorizing specific items to finding statistical regularities between them (item-bound generalization) and generalizing rules to novel instances (category-based generalization). Both external factors, such as input variability, and internal factors, such as cognitive limitations, have been shown to drive these abilities. However, the exact dynamics between these factors and circumstances under which rule induction emerges remain largely underspecified. Here, we extend our information-theoretic model (Radulescu et al., 2019), based on Shannon's noisy-channel coding theory, which adds into the "formula" for rule induction the crucial dimension of time: the rate of encoding information by a time-sensitive mechanism. The goal of this study is to test the channel capacity-based hypothesis of our model: if the input entropy per second is higher than the maximum rate of information transmission (bits/second), which is determined by the channel capacity, the encoding method moves gradually from item-bound generalization to a more efficient category-based generalization, so as to avoid exceeding the channel capacity. We ran two artificial grammar experiments with adults, in which we sped up the bit rate of information transmission, crucially not by an arbitrary amount but by a factor calculated using the channel capacity formula on previous data. We found that increased bit rate of information transmission in a repetition-based XXY grammar drove the tendency of learners toward category-based generalization, as predicted by our model. Conversely, we found that increased bit rate of information transmission in complex non-adjacent dependency aXb grammar impeded the item-bound generalization of the specific a_b frames, and led to poorer learning, at least judging by our accuracy assessment method. This finding could show that, since increasing the bit rate of information precipitates a change from item-bound to category-based generalization, it impedes the item-bound generalization of the specific a_b frames, and that it facilitates category-based generalization both for the intervening Xs and possibly for a/b categories. Thus, sped up bit rate does not mean that an unrestrainedly increasing bit rate drives rule induction in any context, or grammar. Rather, it is the specific dynamics between the input entropy and the maximum rate of information transmission.

Keywords: bit rate; category formation; channel capacity (information rate); entropy; generalization (psychology); rule induction.

FIGURE 1

Mean rate of correct acceptance for Familiar-syllable XXY and New-syllable XXY strings in both conditions: Fast Rate and Slow Rate. Error bars show standard error of the mean.

FIGURE 2

Mean rate of correct rejection for Familiar-syllable X1X2Y and New-syllable X1X2Y strings in both conditions: Fast Rate and Slow Rate. Error bars show standard error of the mean.

FIGURE 3

On the X-axis the four types of test items: Familiar-Syllable XXY, New-syllable XXY, Familiar-syllable X1X2Y, New-syllable X1X2Y. On the Y-axis the mean rate of correct answers: correct acceptance for XXY strings (with familiar or new syllables) and correct rejections of X1X2Y (with familiar or new syllables).

FIGURE 4

Histogram of proportion of correct responses per participant in Slow Rate Condition.

FIGURE 5

Histogram of proportion of correct responses per participant in Fast Rate Condition.

FIGURE 6

Boxplots of proportions of acceptance of language-specific aXb strings in Slow Rate Condition as compared to Fast Rate Condition.

FIGURE 7

Boxplots of proportions of acceptance of language-deviant aXb strings in Slow Rate Condition as compared to Fast Rate Condition.