Transformer Embeddings of Irregularly Spaced Events and Their Participants

We propose an approach to modeling irregularly spaced sequences of discrete events. We begin with a continuous-time variant of the Transformer, which was originally formulated (Vaswani et al., 2017) for sequences without timestamps. We embed a possible event (or other boolean fact) at time $t$ by using attention over the events that occurred at times $< t$ (and the facts that were true when they occurred). We control this attention using pattern-matching logic rules that relate events and facts that share participants. These rules determine which previous events will be attended to, as well as how to transform the embeddings of the events and facts into the attentional queries, keys, and values. Other logic rules describe how to change the set of facts in response to events. Our approach closely follows Mei et al. (2020a), and adopts their Datalog Through Time formalism for logic rules. As in that work, a domain expert first writes a set of logic rules that establishes the set of possible events and other facts at each time $t$. Each possible event or other fact is embedded using a neural architecture that is derived from the rules that established it. Our only difference from Mei et al. (2020a) is that we derive a flatter, attention-based neural architecture whereas they used a more serial LSTM architecture. We find that our attention-based approach performs about equally well on the RoboCup dataset, where the logic rules play an important role in improving performance. We also compared these two methods with two previous attention-based methods (Zuo et al., 2020; Zhang et al., 2020a) on simpler synthetic and real domains without logic rules, and found our proposed approach to be at least as good, and sometimes better, than each of the other three methods.