Languages with more speakers tend to be harder to (machine-)learn.

Computational language models (LMs), most notably exemplified by the widespread success of OpenAI's ChatGPT chatbot, show impressive performance on a wide range of linguistic tasks, thus providing cognitive science and linguistics with a computational working model to empirically study different aspects of human language. Here, we use LMs to test the hypothesis that languages with more speakers tend to be easier to learn. In two experiments, we train several LMs-ranging from very simple n-gram models to state-of-the-art deep neural networks-on written cross-linguistic corpus data covering 1293 different languages and statistically estimate learning difficulty. Using a variety of quantitative methods and machine learning techniques to account for phylogenetic relatedness and geographical proximity of languages, we show that there is robust evidence for a relationship between learning difficulty and speaker population size. However, contrary to expectations derived from previous research, our results suggest that languages with more speakers tend to be harder to learn.

A large quantitative analysis of written language challenges the idea that all languages are equally complex.

One of the fundamental questions about human language is whether all languages are equally complex. Here, we approach this question from an information-theoretic perspective. We present a large scale quantitative cross-linguistic analysis of written language by training a language model on more than 6500 different documents as represented in 41 multilingual text collections consisting of ~ 3.5 billion words or ~ 9.0 billion characters and covering 2069 different languages that are spoken as a native language by more than 90% of the world population. We statistically infer the entropy of each language model as an index of what we call average prediction complexity. We compare complexity rankings across corpora and show that a language that tends to be more complex than another language in one corpus also tends to be more complex in another corpus. In addition, we show that speaker population size predicts entropy. We argue that both results constitute evidence against the equi-complexity hypothesis from an information-theoretic perspective.

Testing the Relationship between Word Length, Frequency, and Predictability Based on the German Reference Corpus.

In a recent article, Meylan and Griffiths (Meylan & Griffiths, 2021, henceforth, M&G) focus their attention on the significant methodological challenges that can arise when using large-scale linguistic corpora. To this end, M&G revisit a well-known result of Piantadosi, Tily, and Gibson (2011, henceforth, PT&G) who argue that average information content is a better predictor of word length than word frequency. We applaud M&G who conducted a very important study that should be read by any researcher interested in working with large-scale corpora. The fact that M&G mostly failed to find clear evidence in favor of PT&G's main finding motivated us to test PT&G's idea on a subset of the largest archive of German language texts designed for linguistic research, the German Reference Corpus consisting of ∼43 billion words. We only find very little support for the primary data point reported by PT&G.

A non-parametric significance test to compare corpora.

Classical null hypothesis significance tests are not appropriate in corpus linguistics, because the randomness assumption underlying these testing procedures is not fulfilled. Nevertheless, there are numerous scenarios where it would be beneficial to have some kind of test in order to judge the relevance of a result (e.g. a difference between two corpora) by answering the question whether the attribute of interest is pronounced enough to warrant the conclusion that it is substantial and not due to chance. In this paper, I outline such a test.

Language structure is influenced by the number of speakers but seemingly not by the proportion of non-native speakers.

Large-scale empirical evidence indicates a fascinating statistical relationship between the estimated number of language users and its linguistic and statistical structure. In this context, the linguistic niche hypothesis argues that this relationship reflects a negative selection against morphological paradigms that are hard to learn for adults, because languages with a large number of speakers are assumed to be typically spoken and learned by greater proportions of adults. In this paper, this conjecture is tested empirically for more than 2000 languages. The results question the idea of the impact of non-native speakers on the grammatical and statistical structure of languages, as it is demonstrated that the relative proportion of non-native speakers does not significantly correlate with either morphological or information-theoretic complexity. While it thus seems that large numbers of adult learners/speakers do not affect the (grammatical or statistical) structure of a language, the results suggest that there is indeed a relationship between the number of speakers and (especially) information-theoretic complexity, i.e. entropy rates. A potential explanation for the observed relationship is discussed.

Studying Lexical Dynamics and Language Change via Generalized Entropies: The Problem of Sample Size.

Recently, it was demonstrated that generalized entropies of order α offer novel and important opportunities to quantify the similarity of symbol sequences where α is a free parameter. Varying this parameter makes it possible to magnify differences between different texts at specific scales of the corresponding word frequency spectrum. For the analysis of the statistical properties of natural languages, this is especially interesting, because textual data are characterized by Zipf's law, i.e., there are very few word types that occur very often (e.g., function words expressing grammatical relationships) and many word types with a very low frequency (e.g., content words carrying most of the meaning of a sentence). Here, this approach is systematically and empirically studied by analyzing the lexical dynamics of the German weekly news magazine Der Spiegel (consisting of approximately 365,000 articles and 237,000,000 words that were published between 1947 and 2017). We show that, analogous to most other measures in quantitative linguistics, similarity measures based on generalized entropies depend heavily on the sample size (i.e., text length). We argue that this makes it difficult to quantify lexical dynamics and language change and show that standard sampling approaches do not solve this problem. We discuss the consequences of the results for the statistical analysis of languages.

The statistical trade-off between word order and word structure - Large-scale evidence for the principle of least effort.

Languages employ different strategies to transmit structural and grammatical information. While, for example, grammatical dependency relationships in sentences are mainly conveyed by the ordering of the words for languages like Mandarin Chinese, or Vietnamese, the word ordering is much less restricted for languages such as Inupiatun or Quechua, as these languages (also) use the internal structure of words (e.g. inflectional morphology) to mark grammatical relationships in a sentence. Based on a quantitative analysis of more than 1,500 unique translations of different books of the Bible in almost 1,200 different languages that are spoken as a native language by approximately 6 billion people (more than 80% of the world population), we present large-scale evidence for a statistical trade-off between the amount of information conveyed by the ordering of words and the amount of information conveyed by internal word structure: languages that rely more strongly on word order information tend to rely less on word structure information and vice versa. Or put differently, if less information is carried within the word, more information has to be spread among words in order to communicate successfully. In addition, we find that-despite differences in the way information is expressed-there is also evidence for a trade-off between different books of the biblical canon that recurs with little variation across languages: the more informative the word order of the book, the less informative its word structure and vice versa. We argue that this might suggest that, on the one hand, languages encode information in very different (but efficient) ways. On the other hand, content-related and stylistic features are statistically encoded in very similar ways.

Population Size Predicts Lexical Diversity, but so Does the Mean Sea Level --Why It Is Important to Correctly Account for the Structure of Temporal Data.

In order to demonstrate why it is important to correctly account for the (serial dependent) structure of temporal data, we document an apparently spectacular relationship between population size and lexical diversity: for five out of seven investigated languages, there is a strong relationship between population size and lexical diversity of the primary language in this country. We show that this relationship is the result of a misspecified model that does not consider the temporal aspect of the data by presenting a similar but nonsensical relationship between the global annual mean sea level and lexical diversity. Given the fact that in the recent past, several studies were published that present surprising links between different economic, cultural, political and (socio-)demographical variables on the one hand and cultural or linguistic characteristics on the other hand, but seem to suffer from exactly this problem, we explain the cause of the misspecification and show that it has profound consequences. We demonstrate how simple transformation of the time series can often solve problems of this type and argue that the evaluation of the plausibility of a relationship is important in this context. We hope that our paper will help both researchers and reviewers to understand why it is important to use special models for the analysis of data with a natural temporal ordering.