Deeper understanding of optimization dynamics

Develop a deeper theoretical understanding of the optimization dynamics for training single-head tied attention beyond the asymptotic characterization of minima provided in this work, clarifying the mechanisms that govern convergence and learning behavior.

Background

While the paper characterizes the asymptotics of the global minima and confirms empirical alignment with gradient-based training, it stops short of a full theory of the optimization process itself.

The authors explicitly identify the broader paper of optimization dynamics as an open challenge beyond their present analysis.