  The training and generalization dynamics of the Transformer's core mechanism,
namely the Attention mechanism, remain under-explored. Besides, existing
analyses primarily focus on single-head attention. Inspired by the demonstrated
benefits of overparameterization when training fully-connected networks, we
investigate the potential optimization and generalization advantages of using
multiple attention heads. Towards this goal, we derive convergence and
generalization guarantees for gradient-descent training of a single-layer
multi-head self-attention model, under a suitable realizability condition on
the data. We then establish primitive conditions on the initialization that
ensure realizability holds. Finally, we demonstrate that these conditions are
satisfied for a simple tokenized-mixture model. We expect the analysis can be
extended to various data-model and architecture variations.
