  Transformer training is notoriously difficult, requiring a careful design of
optimizers and use of various heuristics. We make progress towards
understanding the subtleties of training Transformers by carefully studying a
simple yet canonical linearized shallow Transformer model. Specifically, we
train linear Transformers to solve regression tasks, inspired by J.~von Oswald
et al.~(ICML 2023), and K.~Ahn et al.~(NeurIPS 2023). Most importantly, we
observe that our proposed linearized models can reproduce several prominent
aspects of Transformer training dynamics. Consequently, the results obtained in
this paper suggest that a simple linearized Transformer model could actually be
a valuable, realistic abstraction for understanding Transformer optimization.
