Modeling and predicting citation dynamics of individual papers is important due to its critical role in a wide range of decisions in science. While current modeling framework successfully captures citation dynamics of typical papers, there exists a non-negligible, and perhaps most interesting, fraction of atypical papers whose citation trajectories do not follow the normal rise-andfall pattern. Here, we systematically study and classify citation patterns of atypical papers, finding that they can be characterized by sleeping beauties, second acts, and a combination of both. We propose a second-act model that can accurately describe the citation dynamics of second-act papers. The model not only provides a mechanistic framework to understand citation patterns of atypical papers, separating factors that drive impact, but it also offers new capabilities to identify the time of exogenous events that influence citations.

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