  Our goal is to $\textit{efficiently}$ discover a compact set of temporal
logic rules to explain irregular events of interest. We introduce a
neural-symbolic rule induction framework within the temporal point process
model. The negative log-likelihood is the loss that guides the learning, where
the explanatory logic rules and their weights are learned end-to-end in a
$\textit{differentiable}$ way. Specifically, predicates and logic rules are
represented as $\textit{vector embeddings}$, where the predicate embeddings are
fixed and the rule embeddings are trained via gradient descent to obtain the
most appropriate compositional representations of the predicate embeddings. To
make the rule learning process more efficient and flexible, we adopt a
$\textit{sequential covering algorithm}$, which progressively adds rules to the
model and removes the event sequences that have been explained until all event
sequences have been covered. All the found rules will be fed back to the models
for a final rule embedding and weight refinement. Our approach showcases
notable efficiency and accuracy across synthetic and real datasets, surpassing
state-of-the-art baselines by a wide margin in terms of efficiency.
