  A standard measure of the influence of a research paper is the number of
times it is cited. However, papers may be cited for many reasons, and citation
count offers limited information about the extent to which a paper affected the
content of subsequent publications. We therefore propose a novel method to
quantify linguistic influence in timestamped document collections. There are
two main steps: first, identify lexical and semantic changes using contextual
embeddings and word frequencies; second, aggregate information about these
changes into per-document influence scores by estimating a high-dimensional
Hawkes process with a low-rank parameter matrix. We show that this measure of
linguistic influence is predictive of $\textit{future}$ citations: the estimate
of linguistic influence from the two years after a paper's publication is
correlated with and predictive of its citation count in the following three
years. This is demonstrated using an online evaluation with incremental
temporal training/test splits, in comparison with a strong baseline that
includes predictors for initial citation counts, topics, and lexical features.
