The field of transformer research is moving towards improving efficiency and interpretability. Recent studies have focused on developing theoretical frameworks to understand the learning dynamics of transformer models, such as the Mixture-of-Transformers framework, which allows for the specialization of transformer blocks and improves training efficiency. Another direction is the development of energy-based frameworks to understand and modify attention mechanisms, which has led to the proposal of new attention structures inspired by classical optimization algorithms. Additionally, research has explored the emergence of induction heads in transformers, which are crucial for in-context learning, and has provided theoretical explanations for their origin. The use of physical information in loss functions has also been proposed, allowing for the development of physically grounded and architecture-agnostic loss functions. Notable papers include: Mixture-of-Transformers Learn Faster, which provides a unified theoretical explanation for transformer-level specialization and learning dynamics. On the Emergence of Induction Heads for In-Context Learning, which theoretically explains the origin of induction heads in transformers. Energy Loss Functions for Physical Systems, which proposes a framework to leverage physical information in loss functions for prediction and generative modeling tasks.