Informed Temporal Modeling via Logical Specification of Factorial LSTMs

Consider a world in which events occur that involve various entities. Learning how to predict future events from patterns of past events becomes more difficult as we consider more types of events. Many of the patterns detected in the dataset by an ordinary LSTM will be spurious since the number of potential pairwise correlations, for example, grows quadratically with the number of events. We propose a type of factorial LSTM architecture where different blocks of LSTM cells are responsible for capturing different aspects of the world state. We use Datalog rules to specify how to derive the LSTM structure from a database of facts about the entities in the world. This is analogous to how a probabilistic relational model (Getoor & Taskar, 2007) specifies a recipe for deriving a graphical model structure from a database. In both cases, the goal is to obtain useful inductive biases by encoding informed independence assumptions into the model. We specifically consider the neural Hawkes process, which uses an LSTM to modulate the rate of instantaneous events in continuous time. In both synthetic and real-world domains, we show that we obtain better generalization by using appropriate factorial designs specified by simple Datalog programs.