While the theta-lazy training regime offers significant advantages in terms of rapid convergence and potential for improved generalization, there are certain limitations and drawbacks that need to be considered. One potential limitation is the trade-off between speed of convergence and model complexity. In the theta-lazy regime, the emphasis on driving training loss to zero quickly may result in oversimplified models that lack the capacity to capture the full complexity of the underlying data distribution. This could lead to issues such as underfitting and reduced model expressiveness. To address this limitation, it is essential to strike a balance between fast convergence and model complexity, possibly by incorporating regularization techniques or adjusting the initialization schemes to encourage a more diverse representation of the data.