Large Language Models (LLMs) have made significant strides in natural language processing, and a precise understanding of the internal mechanisms driving their success is essential. In this work, we analyze the trajectories of token embeddings as they pass through transformer blocks, linearizing the system along these trajectories through their Jacobian matrices. By examining the relationships between these block Jacobians, we uncover the phenomenon of \textbf{transformer block coupling} in a multitude of LLMs, characterized by the coupling of their top singular vectors across tokens and depth. Our findings reveal that coupling \textit{positively correlates} with model performance, and that this relationship is stronger than with other hyperparameters such as parameter count, model depth, and embedding dimension. We further investigate how these properties emerge during training, observing a progressive development of coupling, increased linearity, and layer-wise exponential growth in token trajectories. Additionally, experiments with Vision Transformers (ViTs) corroborate the emergence of coupling and its relationship with generalization, reinforcing our findings in LLMs. Collectively, these insights offer a novel perspective on token interactions in transformers, opening new directions for studying their mechanisms as well as improving training and generalization.

翻译：大语言模型（LLMs）在自然语言处理领域取得了显著进展，精确理解驱动其成功的内在机制至关重要。本研究分析了词元嵌入在通过Transformer块时的轨迹，并通过其雅可比矩阵沿这些轨迹对系统进行线性化。通过考察这些块雅可比矩阵之间的关系，我们在多种LLMs中揭示了**Transformer块耦合**现象，其特征是跨词元和深度的顶部奇异向量发生耦合。我们的发现表明，耦合与模型性能呈**正相关**，且这种关联性强于与其他超参数（如参数量、模型深度和嵌入维度）的关系。我们进一步研究了这些特性在训练过程中如何形成，观察到耦合的渐进发展、线性度的增加以及词元轨迹的逐层指数增长。此外，在Vision Transformers（ViTs）上的实验证实了耦合的出现及其与泛化能力的关系，从而强化了我们在LLMs中的发现。总体而言，这些见解为理解Transformer中词元交互提供了新的视角，为研究其机制以及改进训练和泛化能力开辟了新的方向。