Theoretical Analysis of Tokenization in Large Language Models

Core Concepts

Tokenization is a necessary step in designing state-of-the-art language models, and this paper provides a theoretical analysis of its role in enabling transformers to model complex data distributions.

Abstract

The paper investigates tokenization from a theoretical perspective by studying the behavior of transformers on simple data generating processes, such as kth-order Markov processes. The key findings are:

In the absence of tokenization, transformers trained on data drawn from certain simple kth-order Markov processes empirically fail to learn the right distribution and predict characters according to a unigram model, even under a wide variety of hyperparameter choices.

With the addition of tokenization, transformers are able to model the probabilities of sequences drawn from the source near-optimally, achieving small cross-entropy loss. This is observed with a multitude of tokenizers used commonly in practice, such as BPE and LZW.

The paper analyzes a toy tokenizer that adds all length-k sequences into the dictionary, and shows that as the dictionary size grows, unigram models trained on the tokens get better at modeling the probabilities of sequences drawn from Markov sources. It then proves that tokenizers used in practice, such as LZW and a variant of BPE, also satisfy this property but require much smaller dictionaries to achieve any target cross-entropy loss.

The paper also discusses the importance of generalization, where tokenizers need to perform well on new sequences that were not in the training data. It shows that there exist tokenizers that generalize poorly, and that the choice of encoding algorithm can also affect generalization.

Stats

The cross-entropy loss of the best unigram model can be much higher than the optimal cross-entropy loss for kth-order Markov processes, with the gap scaling exponentially in 1/δ, where δ is the minimum transition probability.
The size of the dictionary required by the toy tokenizer to achieve a target cross-entropy loss scales exponentially in 1/δ.

Quotes

"There are very simple kth-order Markov processes such that in the absence of any tokenization, transformers trained on data drawn this source are empirically observed to predict characters according to the stationary distribution of the source under a wide variety of hyperparameter choices."
"When trained with tokenization, transformers are empirically observed to break through this barrier and are able to capture the probability of sequences under the Markov distribution near-optimally."

Key Insights Distilled From

Toward a Theory of Tokenization in LLMs

by Nived Rajara... at arxiv.org 04-15-2024

https://arxiv.org/pdf/2404.08335.pdf

Deeper Inquiries

How do the theoretical results extend to more complex data generating processes beyond Markov chains

The theoretical results presented in the paper can be extended to more complex data generating processes beyond simple Markov chains by considering higher-order Markov processes or even non-Markovian processes. By studying the behavior of tokenizers and language models on more intricate data structures, researchers can gain insights into how these models perform in real-world scenarios where the data may exhibit more complex dependencies and patterns. For example, extending the analysis to kth-order Markov processes with larger values of k or exploring data generated from non-Markovian sources can provide a deeper understanding of how tokenization impacts the performance of language models in capturing long-range dependencies and intricate patterns in the data. By studying a wider range of data generating processes, researchers can uncover the limitations and capabilities of tokenization algorithms in modeling diverse types of data distributions.

What are the implications of the generalization issues identified in the paper for the practical deployment of tokenization in large language models

The generalization issues identified in the paper have significant implications for the practical deployment of tokenization in large language models. The findings suggest that tokenizers trained on specific datasets may struggle to generalize to new sequences that were not part of the training data. This lack of generalization can lead to suboptimal performance when the model encounters unseen tokens or patterns during inference, potentially affecting the overall accuracy and robustness of the language model. In practical terms, this means that tokenization algorithms need to be carefully designed and evaluated to ensure that they can effectively handle a wide range of input sequences and generalize well to unseen data. Additionally, addressing the generalization challenges highlighted in the paper can improve the reliability and performance of tokenization in large language models, making them more effective in real-world applications.

Can the insights from this work be leveraged to develop novel tokenization algorithms that are better suited for the end-to-end training of language models

The insights from this work can be leveraged to develop novel tokenization algorithms that are better suited for the end-to-end training of language models. By understanding the behavior of tokenizers and language models on different types of data generating processes, researchers can design tokenization strategies that optimize the performance of language models in capturing complex patterns and dependencies in the data. For example, incorporating mechanisms for adaptive tokenization that can dynamically adjust the token dictionary based on the input data distribution can enhance the model's ability to generalize and perform well on diverse datasets. Additionally, exploring novel tokenization algorithms that prioritize capturing meaningful patterns in the data while minimizing the number of tokens can lead to more efficient and effective language models. Overall, leveraging the insights from this research can drive the development of advanced tokenization techniques that enhance the training and performance of large language models.