The recent advancements in the field of machine learning have seen significant innovations in transformer architectures, particularly in addressing challenges related to length generalization, feature learning dynamics, and attention concentration. The integration of novel modules like State-Exchange Attention (SEA) has demonstrated substantial improvements in reducing rollout errors for dynamical systems, enhancing the model's ability to capture complex interactions between field variables. Additionally, advancements in arithmetic transformers have achieved notable length generalization, addressing the limitations of previous models in handling sequences of varying lengths and operand counts. Comparative studies on feature learning dynamics between attention mechanisms and convolutional layers have revealed that attention processes data more compactly and stably, contributing to more robust model performance. Furthermore, new approaches like Value Residual Learning have been introduced to alleviate attention concentration in deeper transformer layers, offering computational efficiency and improved representation learning. These developments collectively push the boundaries of transformer capabilities, making them more versatile and effective across a range of tasks.