Tokenization and the Noiseless Channel

TL;DR

This paper investigates how subword tokenization efficiency, measured via information-theoretic metrics like Rényi entropy, correlates with downstream NLP model performance, especially in machine translation.

Contribution

It introduces an information-theoretic framework for understanding tokenizer effectiveness and demonstrates Rényi entropy as a strong predictor of translation quality.

Findings

Rényi entropy with α=2.5 correlates highly with BLEU scores.

Optimal Shannon entropy encoding can produce very long codes for rare tokens.

Efficiency metrics based on Rényi entropy outperform compressed length in predicting performance.

Abstract

Subword tokenization is a key part of many NLP pipelines. However, little is known about why some tokenizer and hyperparameter combinations lead to better downstream model performance than others. We propose that good tokenizers lead to \emph{efficient} channel usage, where the channel is the means by which some input is conveyed to the model and efficiency can be quantified in information-theoretic terms as the ratio of the Shannon entropy to the maximum possible entropy of the token distribution. Yet, an optimal encoding according to Shannon entropy assigns extremely long codes to low-frequency tokens and very short codes to high-frequency tokens. Defining efficiency in terms of R\'enyi entropy, on the other hand, penalizes distributions with either very high or very low-frequency tokens. In machine translation, we find that across multiple tokenizers, the R\'enyi entropy with $\alpha = 2.5$ has a very strong correlation with \textsc{Bleu}: $0.78$ in comparison to just $-0.32$ for compressed length.