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 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 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 the emergence of these properties through training, observing the progressive development of coupling, as well as increased linearity and layer-wise exponential growth in the token trajectories. Additionally, experiments with ViTs further validate emergence of coupling and its correlation between coupling and generalization, complementing our findings in LLMs. Collectively, these insights provide a novel perspective on token interactions in transformers and open directions for studying and improving training and generalization.