An ability to predict the popularity dynamics of individual items within a complex evolving system has important implications in a wide range of domains. Here we propose a deep learning attention mechanism to model the process through which individual items gain their popularity. We analyze the interpretability of the model with the four key phenomena confirmed independently in the previous studies of long-term popularity dynamics quantification, including the intrinsic quality, the aging effect, the recency effect and the Matthew effect. We analyze the effectiveness of introducing attention model in popularity dynamics prediction. Extensive experiments on a real-large citation data set demonstrate that the designed deep learning attention mechanism possesses remarkable power at predicting the long-term popularity dynamics. It consistently outperforms the existing methods, and achieves a significant performance improvement.