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Counting Ability of Large Language Models and Impact of Tokenization (2410.19730v2)

Published 25 Oct 2024 in cs.CL and cs.AI

Abstract: Transformers, the backbone of modern LLMs, face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to constant-depth computation. This restriction places them in the complexity class TC$0$, making them theoretically incapable of solving tasks that demand increasingly deep reasoning as input length grows. Counting, a fundamental component of many reasoning tasks, also requires reasoning depth to grow linearly to be performed inductively. While previous studies have established the upper limits of counting ability in Transformer-based expert models (i.e., models specifically trained for counting tasks), these findings do not directly extend to general-purpose LLMs due to differences in reasoning mechanisms. Recent work has highlighted how Chain of Thought (CoT) reasoning can help alleviate some of the architectural limitations of Transformers in counting tasks. However, little attention has been paid to the role of tokenization in these models. Unlike expert models that often use character-level tokenization, LLMs typically rely on byte-level (BPE) tokenizers, which fundamentally alters the way reasoning is processed. Our work investigates the impact of tokenization on the counting abilities of LLMs, uncovering substantial performance variations based on input tokenization differences. We provide both theoretical and experimental analyses, offering insights into how tokenization choices can undermine models' theoretical computability, thereby inspiring the design of new tokenization methods to enhance reasoning in LLMs.

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Authors (3)
  1. Xiang Zhang (395 papers)
  2. Juntai Cao (4 papers)
  3. Chenyu You (66 papers)
Citations (1)

Summary

Overview of the Impact of Tokenization on Counting Ability in LLMs

The paper presented in the paper, "Counting Ability of LLMs and Impact of Tokenization," examines the limitations in counting tasks of Transformer-based LLMs and theorizes the influence of tokenization on these models' performance. The backdrop to the research is transformers' computational constraints, characterized by their association with the complexity class TC0^0. Such constraints prevent transformers from naturally achieving depth in reasoning, something critical for counting tasks where reasoning needs grow linearly with input length.

Counting Complexity and Model Architecture

Counting is fundamental to a variety of reasoning tasks, which requires a computational depth or a sequential computation complexity that increases with input size. Historically, this has been well-documented in computability theory and proven challenging for contemporary models such as Transformers—a limitation theoretically mitigated in recurrent architectures like RNNs and LSTMs, as they imitate finite counter machines' capabilities through recurrent dependencies.

Modern LLMs typically scale by increasing the number of parameters instead of modifying the architecture's inherent constraints. While the Chain of Thought (CoT) reasoning mechanism offers a mechanism to leverage sequential token outputs to approximate recursive reasoning, which is imperative for tasks like counting, the practical performance of these models falls short of theoretical expectations due to factors unexplored adequately, among them tokenization.

The Role and Impact of Tokenization

Tokenization significantly impacts an LLM’s performance in counting tasks due to the variance in how inputs are interpreted by the model. Unlike character-level tokenization familiar in specialized counting models, LLMs commonly employ byte-level (BPE) tokenizers, grouping multiple characters into a single token to enhance processing efficiency. This strategy, while computationally advantageous, obscures essential information, impairing arithmetic task performance where granularity is crucial.

The paper adopts a model-agnostic approach to explore how varying tokenization can undermine counting abilities, showcasing instances where tokenization choices lead to up to an 80% drop in accuracy. Such variations are critical since models like GPT-4 struggle with counting even small quantities of characters, underscoring a gap between theoretical computability and realized performance.

Experiments and Findings

Through methodical experiments using closed-source LLMs like GPT-4o mini, strings of varying tokenization formats were analyzed. These included pure letter sequences prone to BPE-based merging, and variations employing spaces, commas, and quotes as delimiters. The findings consistently pointed to enhanced performance when tokenization was conducted at finer granularity, separating items individually, and reducing reliance on token awareness—a pivotal insight demonstrating how intricacies of tokenization can disrupt model capabilities in reasoning tasks.

Additionally, a notable discovery was the model's improved sensitivity to less frequent tokens, attributed to potentially simpler, less densely packed token embeddings. Such patterns indicate practical implications on how future architectures might consider tokenization influences during design and training to alleviate current computational limitations.

Implications and Future Directions

This paper highlights the critical yet underappreciated role of tokenization in determining LLMs' performance on reasoning tasks that require counting. Recognizing that architectural constraints of transformers inherently limit counting capabilities, the paper spotlights tokenization as crucial leverage for performance optimization. These insights guide the development of novel tokenization strategies that could bridge theoretical and practical capabilities, allowing LLMs to handle a broader spectrum of reasoning tasks efficiently. Future research should explore bespoke tokenization methods tailored for reasoning tasks and continually assess these strategies as models evolve to handle more complex computations effectively.

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