  The behaviour of information cascades (such as retweets) has been modelled
extensively. While point process-based generative models have long been in use
for estimating cascade growths, deep learning has greatly enhanced diverse
feature integration. We observe two significant temporal signals in cascade
data that have not been emphasized or reported to our knowledge. First, the
popularity of the cascade root is known to influence cascade size strongly; but
the effect falls off rapidly with time. Second, there is a measurable positive
correlation between the novelty of the root content (with respect to a
streaming external corpus) and the relative size of the resulting cascade.
Responding to these observations, we propose GammaCas, a new cascade growth
model as a parametric function of time, which combines deep influence signals
from content (e.g., tweet text), network features (e.g., followers of the root
user), and exogenous event sources (e.g., online news). Specifically, our model
processes these signals through a customized recurrent network, whose states
then provide the parameters of the cascade rate function, which is integrated
over time to predict the cascade size. The network parameters are trained
end-to-end using observed cascades. GammaCas outperforms seven recent and
diverse baselines significantly on a large-scale dataset of retweet cascades
coupled with time-aligned online news -- it beats the best baseline with an
18.98% increase in terms of Kendall's $\tau$ correlation and $35.63$ reduction
in Mean Absolute Percentage Error. Extensive ablation and case studies unearth
interesting insights regarding retweet cascade dynamics.
