Large language models (LLMs) have taken the world by storm, demonstrating an impressive ability to generate human-quality text, translate languages, and even write different kinds of creative content. But how well do these models *actually* generalize? A new research paper, "Unlocking Tokens as Data Points for Generalization Bounds on Larger Language Models," explores the theoretical underpinnings of LLM performance, providing intriguing insights into why these massive models don't just memorize their training data. Traditional methods for measuring generalization often fall short when applied to LLMs due to their sheer size and the complex, non-independent nature of text data. This research introduces a novel approach that focuses on individual *tokens* rather than entire documents, leveraging the power of martingales, a mathematical tool for analyzing sequences of dependent events. This token-level analysis allows researchers to tap into the vast amount of data used to train LLMs, resulting in far tighter generalization bounds than previously possible. Interestingly, the researchers found that these token-level bounds favor less restrictive compression techniques. They were able to achieve non-vacuous bounds for massive, real-world models like LLaMA2-70B, simply using post-training quantization—a technique that compresses the model's weights without altering its underlying structure. This is a significant step forward, as previous attempts at establishing non-vacuous bounds often relied on highly compressed models that generated nonsensical text. This work not only sheds light on the theoretical guarantees of LLMs, but it also reveals a surprising connection between the generalization abilities of different LLaMA model variants. The research suggests that chat-optimized LLMs, like LLaMA2-Chat, may exhibit looser generalization bounds than their base counterparts, potentially due to their specialized training on dialogue data. The team explored this further by investigating how LLMs handle different types of sequences. When trained on structured sequences derived from mathematical expressions, even compressed models retained their ability to capture the underlying patterns. Conversely, when trained on random sequences, the same models quickly lost their predictive power as compression increased. This points to a fascinating distinction between memorization and reasoning in LLMs. Overall, this research gives us a powerful new framework for understanding the generalization capabilities of LLMs. By unlocking the potential of token-level analysis, it opens exciting avenues for future research. This could lead to even tighter bounds and more practical insights into the limitations and strengths of these transformative AI models.