The choice associated with words is a fundamental property of natural languages. It lies at the heart of quantitative linguistics, computational linguistics and language sciences more generally. Information theory gives us tools at hand to measure precisely the average amount of choice associated with words: the word entropy. Here, we use three parallel corpora, encompassing ca. 450 million words in 1916 texts and 1259 languages, to tackle some of the major conceptual and practical problems of word entropy estimation: dependence on text size, register, style and estimation method, as well as non-independence of words in co-text. We present two main findings: Firstly, word entropies display relatively narrow, unimodal distributions. There is no language in our sample with a unigram entropy of less than six bits/word. We argue that this is in line with information-theoretic models of communication. Languages are held in a narrow range by two fundamental pressures: word learnability and word expressivity, with a potential bias towards expressivity. Secondly, there is a strong linear relationship between unigram entropies and entropy rates. The entropy difference between words with and without co-textual information is narrowly distributed around ca. three bits/word. In other words, knowing the preceding text reduces the uncertainty of words by roughly the same amount across languages of the world.

Explaining the diversity of languages across the world is one of the central aims of typological, historical, and evolutionary linguistics. We consider the effect of language contact-the number of non-native speakers a language has-on the way languages change and evolve. By analysing hundreds of languages within and across language families, regions, and text types, we show that languages with greater levels of contact typically employ fewer word forms to encode the same information content (a property we refer to as lexical diversity). Based on three types of statistical analyses, we demonstrate that this variance can in part be explained by the impact of non-native speakers on information encoding strategies. Finally, we argue that languages are information encoding systems shaped by the varying needs of their speakers. Language evolution and change should be modeled as the co-evolution of multiple intertwined adaptive systems: On one hand, the structure of human societies and human learning capabilities, and on the other, the structure of language.

The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding – under an arbitrary coding scheme – and show that it predicts Zipf’s law of abbreviation, namely a tendency in natural languages for more frequent words to be shorter. We apply this result to investigate optimal coding also under so-called non-singular coding, a scheme where unique segmentation is not warranted but codes stand for a distinct number. Optimal non-singular coding predicts that the length of a word should grow approximately as the logarithm of its frequency rank, which is again consistent with Zipf’s law of abbreviation. Optimal non-singular coding in combination with the maximum entropy principle also predicts Zipf’s rank-frequency distribution. Furthermore, our findings on optimal non-singular coding challenge common beliefs about random typing. It turns out that random typing is in fact an optimal coding process, in stark contrast with the common assumption that it is detached from cost cutting considerations. Finally, we discuss the implications of optimal coding for the construction of a compact theory of Zipfian laws more generally as well as other linguistic laws.

In linguistics, there is little consensus on how to define, measure, and compare complexity across languages. We propose to take the diversity of viewpoints as a given, and to capture the complexity of a language by a vector of measurements, rather than a single value. We then assess the statistical support for two controversial hypotheses: the trade-off hypothesis and the equi-complexity hypothesis. We furnish meta-analyses of 28 complexity metrics applied to texts written in overall 80 typologically diverse languages. The trade-off hypothesis is partially supported, in the sense that around one third of the significant correlations between measures are negative. The equi-complexity hypothesis, on the other hand, is largely confirmed. While we find evidence for complexity differences in the domains of morphology and syntax, the overall complexity vectors of languages turn out virtually indistinguishable.

Byte-pair encoding (BPE) is widely used in NLP for performing subword tokenization. It uncovers redundant patterns for compressing the data, and hence alleviates the sparsity problem in downstream applications. Subwords discovered during the first merge operations tend to have the most substantial impact on the compression of texts. However, the structural underpinnings of this effect have not been analyzed cross-linguistically. We conduct in-depth analyses across 47 typologically diverse languages and three parallel corpora, and thereby show that the types of recurrent patterns that have the strongest impact on compression are an indicator of morphological typology. For languages with richer inflectional morphology there is a preference for highly productive subwords on the early merges, while for languages with less inflectional morphology, idiosyncratic subwords are more prominent. Both types of patterns contribute to efficient compression. Counter to the common perception that BPE subwords are not linguistically relevant, we find patterns across languages that resemble those described in traditional typology. We thus propose a novel way to characterize languages according to their BPE subword properties, inspired by the notion of morphological productivity in linguistics. This allows us to have language vectors that encode typological knowledge induced from raw text. Our approach is easily applicable to a wider range of languages and texts, as it does not require annotated data or any external linguistic knowledge. We discuss its potential contributions to quantitative typology and multilingual NLP.