The number of tokens it takes to encode parallel text in different languages is known to vary. These disparities are called token premiums. Having high token premiums leads to less throughput during training and increases costs at inference. In this paper, we show that even after controlling for dataset size, vocabulary size, and data content, monolingual tokenizers exhibit a wide range of token premiums across languages. To understand the cross-linguistic differences that cause these token premiums, we train a suite of approximately 7,000 comparable monolingual tokenizers for 97 languages, manipulating tokenization algorithm, vocabulary size, and dataset size. We measure token premiums and test for a relationship between factors such as data similarity (between tokenizer training and evaluation), vocabulary size, and pre-tokenization. We also investigate the role of language-specific features such as writing system and word length. We find that similarity between training and test data does not impact token premiums, but vocabulary size and pre-tokenization do. While simply increasing vocabulary size does not lead to reduced token premium effects, we can determine an ``optimal'' vocabulary size for each language to achieve significantly reduced token premium effects. We also train superword tokenizers which allow merges over whitespaces, and we find that they both reduce token premium effects and improve compression overall. Thus, intervening on the vocabulary size or the pre-tokenizer significantly reduces crosslingual token premium effects.

Language models perform differently across languages. It has been previously suggested that morphological typology may explain some of this variability (Cotterell et al., 2018). We replicate previous analyses and find additional new evidence for a performance gap between agglutinative and fusional languages, where fusional languages, such as English, tend to have better language modeling performance than morphologically more complex languages like Turkish. We then propose and test three possible causes for this performance gap: morphological alignment of tokenizers, tokenization quality, and disparities in dataset sizes and measurement. To test the morphological alignment hypothesis, we present MorphScore, a tokenizer evaluation metric, and supporting datasets for 22 languages. We find some evidence that tokenization quality explains the performance gap, but none for the role of morphological alignment. Instead we find that the performance gap is most reduced when training datasets are of equivalent size across language types, but only when scaled according to the so-called "byte-premium" -- the different encoding efficiencies of different languages and orthographies. These results suggest that no language is harder or easier for a language model to learn on the basis of its morphological typology. Differences in performance can be attributed to disparities in dataset size. These results bear on ongoing efforts to improve performance for low-performing and under-resourced languages.

How should text dataset sizes be compared across languages? Even for content-matched (parallel) corpora, UTF-8 encoded text can require a dramatically different number of bytes for different languages. In our work, we define the byte premium between two languages as the ratio of bytes used to encode content-matched text in those languages. We compute byte premiums for 1155 languages, and we use linear regressions to estimate byte premiums for other languages. We release a tool to obtain byte premiums for any two languages, enabling comparisons of dataset sizes across languages for more equitable multilingual model development and data practices.