Expectancy-based rhythmic entrainment as continuous Bayesian inference

When presented with complex rhythmic auditory stimuli, humans are able to track underlying temporal structure (e.g., a “beat”), both covertly and with their movements. This capacity goes far beyond that of a simple entrained oscillator, drawing on contextual and enculturated timing expectations and adjusting rapidly to perturbations in event timing, phase, and tempo. Previous modeling work has described how entrainment to rhythms may be shaped by event timing expectations, but sheds little light on any underlying computational principles that could unify the phenomenon of expectation-based entrainment with other brain processes. Inspired by the predictive processing framework, we propose that the problem of rhythm tracking is naturally characterized as a problem of continuously estimating an underlying phase and tempo based on precise event times and their correspondence to timing expectations. We present two inference problems formalizing this insight: PIPPET (Phase Inference from Point Process Event Timing) and PATIPPET (Phase and Tempo Inference). Variational solutions to these inference problems resemble previous “Dynamic Attending” models of perceptual entrainment, but introduce new terms representing the dynamics of uncertainty and the influence of expectations in the absence of sensory events. These terms allow us to model multiple characteristics of covert and motor human rhythm tracking not addressed by other models, including sensitivity of error corrections to inter-event interval and perceived tempo changes induced by event omissions. We show that positing these novel influences in human entrainment yields a range of testable behavioral predictions. Guided by recent neurophysiological observations, we attempt to align the phase inference framework with a specific brain implementation. We also explore the potential of this normative framework to guide the interpretation of experimental data and serve as building blocks for even richer predictive processing and active inference models of timing.
Author summary In motor and perceptual tasks involving auditory rhythms, humans show a remarkable proficiency for recognizing an underlying “beat” structure and using it to precisely anticipate the timing of auditory events. Models have been built to describe the faculty of perceptual and motor “entrainment,” but they have done little to describe this process in a general language consistent with other perceptual and cognitive processes. Here, we treat entrainment as the formal problem of estimating the phase and tempo underlying a structured auditory rhythm in real time, based on a set of expectations for what phases of the rhythm are likely to be marked by auditory events. When this problem is solved mathematically, the solution reproduces some surprising nuances of human entrainment. It does so by introducing two new elements that have not been modeled before: uncertainty about phase and tempo, and a systematic biasing effect of strong expectations with the power to distort perceived passage of time. This model of entrainment is a plausible description of what may be happening in motor-associated regions of the brain during rhythm listening.