  We introduce anticipation: a method for constructing a controllable
generative model of a temporal point process (the event process) conditioned
asynchronously on realizations of a second, correlated process (the control
process). We achieve this by interleaving sequences of events and controls,
such that controls appear following stopping times in the event sequence. This
work is motivated by problems arising in the control of symbolic music
generation. We focus on infilling control tasks, whereby the controls are a
subset of the events themselves, and conditional generation completes a
sequence of events given the fixed control events. We train anticipatory
infilling models using the large and diverse Lakh MIDI music dataset. These
models match the performance of autoregressive models for prompted music
generation, with the additional capability to perform infilling control tasks,
including accompaniment. Human evaluators report that an anticipatory model
produces accompaniments with similar musicality to even music composed by
humans over a 20-second clip.
