Title: Understanding Attention Mechanisms. Abstract: Attention mechanisms have advanced the state of the art in several machine learning tasks. Despite significant empirical gains, there is a lack of theoretical analyses on understanding their effectiveness. In this paper, we address this problem by studying the landscape of population and empirical loss functions of attention-based neural networks. Our results show that, under mild assumptions, every local minimum of a two-layer global attention model has low prediction error, and attention models require lower sample complexity than models not employing attention. We then extend our analyses to the popular self-attention model, proving that they deliver consistent predictions with a more expressive class of functions. Additionally, our theoretical results provide several guidelines for designing attention mechanisms. Our findings are validated with satisfactory experimental results on MNIST and IMDB reviews dataset.