The Foundations of Tokenization: Statistical and Computational Concerns

2024-07-16

arXiv.org

AI Summary

This paper addresses the lack of theoretical foundations for tokenization in natural language processing (NLP), systematically investigating its impact on the statistical estimation consistency of language models. While prior work relies predominantly on empirical analysis, we introduce the first unified formal framework grounded in the category of random mappings to rigorously characterize the modeling essence of tokenizers. Our key contributions are: (1) necessary and sufficient conditions for tokenizers to preserve statistical estimation consistency; (2) a four-dimensional theoretical analysis framework—covering inconsistency, ambiguity, finiteness, and sequentiality; and (3) principled, verifiable tokenizer design criteria derived from the integration of category theory, statistical learning theory, and formal language theory. This work establishes the first rigorous mathematical foundation for representation reliability in neural language modeling.

Technology Category

• Natural Language Processing: (Large) Language Models
• Machine Learning: Deep Neural Architectures and Foundation Models
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

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.

Problem

• Understanding theoretical foundations of tokenization in NLP
• Analyzing tokenization's impact on language model consistency
• Addressing statistical and computational concerns in tokenizer design

Innovation

• Unified formal framework for tokenizer analysis
• Conditions for consistent statistical estimators
• Addresses tokenization's statistical and computational concerns