Analyzing the temporal sequence of texts from sources such as social media, news, and parliamentary debates is a challenging problem as it exhibits time-varying scale-free properties and fine-grained timing irregularities. We propose a Hyperbolic Hawkes Attention Network (HYPHEN), which learns a data-driven hyperbolic space and models irregular powerlaw excitations using a hyperbolic Hawkes process. Through quantitative and exploratory experiments over financial NLP, suicide ideation detection, and political debate analysis we demonstrate HYPHEN’s practical applicability for modeling online text sequences in a geometry agnostic manner.