Easy attention: A simple attention mechanism for temporal predictions with transformers

[EN] To improve the robustness of transformer neural networks used for temporal-dynamics prediction of chaotic systems, we propose a novel attention mechanism called easy attention, which we demonstrate in time-series reconstruction and prediction. While the standard self-attention only makes use of the inner product of queries and keys, it is demonstrated that the keys, queries, and softmax are not necessary for obtaining the attention score required to capture long-term dependencies in temporal sequences. Through the singular-value decomposition on the softmax attention score, we further observe that self-attention compresses the contributions from both queries and keys in the space spanned by the attention score. Therefore, our proposed easy-attention method directly treats the attention scores as learnable parameters. This approach produces excellent results when reconstructing and predicting the temporal dynamics of chaotic systems exhibiting more robustness and less complexity than self-attention or the widely used long short-term memory network. We show the improved performance of the easy-attention method in the Lorenz system, a turbulence shear flow, and a model of a nuclear reactor.