Tokenization — the practice of converting strings of characters from an alphabet into sequences of tokens over a vocabulary — is a critical step in the NLP pipeline. The use of token representations is widely credited with increased model performance but is also the source of many undesirable behaviors, such as spurious ambiguity or inconsistency. Despite its recognized importance as a standard representation method in NLP, the theoretical underpinnings of tokenization are not yet fully understood. In particular, the impact of tokenization on language model estimation has been investigated primarily through empirical means. The present paper contributes to addressing this theoretical gap by proposing a unified formal framework for representing and analyzing tokenizer models. Based on the category of stochastic maps, this framework enables us to establish general conditions for a principled use of tokenizers and, most importantly, the necessary and sufficient conditions for a tokenizer model to preserve the consistency of statistical estimators. In addition, we discuss statistical and computational concerns crucial for designing and implementing tokenizer models, such as inconsistency, ambiguity, finiteness, and sequentiality. The framework and results advanced in this paper contribute to building robust theoretical foundations for representations in neural language modeling that can inform future theoretical and empirical research.

Modern language models represent probability distributions over character strings as distributions over (shorter) token strings derived via a deterministic tokenizer, such as byte-pair encoding. While this approach is highly effective at scaling up language models to large corpora, its current incarnations have a concerning property: the model assigns nonzero probability mass to an exponential number of noncanonical token encodings of each character string—these are token strings that decode to valid character strings but are impossible under the deterministic tokenizer (i.e., they will never be seen in any training corpus, no matter how large). This misallocation is both erroneous, as noncanonical strings never appear in training data, and wasteful, diverting probability mass away from plausible outputs. These are avoidable mistakes! In this work, we propose methods to enforce canonicality in token-level language models, ensuring that only canonical token strings are assigned positive probability. We present two approaches: (1) canonicality by conditioning, leveraging test-time inference strategies without additional training, and (2) canonicality by construction, a model parameterization that guarantees canonical outputs but requires training. We demonstrate that fixing canonicality mistakes improves the likelihood of held-out data for several models and corpora.

Modern language models are internally—and mathematically—distributions over token strings rather than character strings, posing numerous challenges for programmers building user applications on top of them. For example, if a prompt is specified as a character string, it must be tokenized before passing it to the token-level language model. Thus, the tokenizer and consequent processing are very sensitive to the specification of the prompt (e.g., whether the prompt ends with a space or not). This paper presents algorithms for converting token-level language models to character-level ones. We present both exact and approximate algorithms. In the empirical portion of the paper, we benchmark the practical runtime and approximation quality. Across four publicly available language models, we find that—even with a small computation budget—our method is able to accurately approximate the character-level distribution at reasonably fast speeds, and that a significant improvement in the language model’s compression rate (bits/byte) is achieved.

Language models are widely used in computational psycholinguistics to test theories that relate the negative log probability (the surprisal) of a region of interest (a substring of characters) under a language model to its cognitive cost experienced by readers, as operationalized, for example, by gaze duration on the region.However, the application of modern language models to psycholinguistic studies is complicated by the practice of using tokenization as an intermediate step in training a model.Doing so results in a language model over token strings rather than one over character strings.Vexingly, regions of interest are generally misaligned with these token strings.The paper argues that token-level language models should be (approximately) marginalized into character-level language models before they are used in psycholinguistic studies to compute the surprisal of a region of interest; then, the marginalized character-level language model can be used to compute the surprisal of an arbitrary character substring, which we term a focal area, that the experimenter may wish to use as a predictor.Our proposal of marginalizing a token-level model into a character-level one solves this misalignment issue independently of the tokenization scheme.Empirically, we discover various focal areas whose surprisal is a better psychometric predictor than the surprisal of the region of interest itself.

Vilém Zouhar, Clara Meister, Juan Gastaldi, Li Du, Mrinmaya Sachan, Ryan Cotterell. Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2023.