Formalizing BPE Tokenization

TL;DR

This paper formalizes byte pair encoding tokenization used in NLP, analyzing the semantics of popular tokenizers and exploring incremental, memory-efficient tokenization methods.

Contribution

It provides a formal definition of BPE tokenization, compares SentencePiece and HuggingFace tokenizers, and introduces methods for incremental, memory-efficient tokenization.

Findings

Formal semantics of SentencePiece and HuggingFace tokenizers

Relationship between different tokenization rule constructions

Proposed incremental, constant-memory tokenization method

Abstract

In this paper, we formalize practical byte pair encoding tokenization as it is used in large language models and other NLP systems, in particular we formally define and investigate the semantics of the SentencePiece and HuggingFace tokenizers, in particular how they relate to each other, depending on how the tokenization rules are constructed. Beyond this we consider how tokenization can be performed in an incremental fashion, as well as doing it left-to-right using an amount of memory constant in the length of the string, enabling e.g. using a finite state string-to-string transducer.