Expectancy-based rhythmic entrainment as continuous Bayesian inference

Abstract

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.

A silent disco: Differential effects of beat-based and pattern-based temporal expectations on persistent entrainment of low-frequency neural oscillations

“…Speculatively, this second peak may be indicative of expectations based on, not just the distribution of possible intervals, but also their transitional probabilities, which would predict a sound at 780 ms. Probabilistic models incorporating statistical regularities in inter-onset intervals at different levels have indeed been used to explain aspects of temporal processing (Cannon, 2021;Elliott, Wing, & Welchman, 2014;van der Weij, Pearce, & Honing, 2017). In future work, linking such models directly to neural markers of pattern-based expectations may provide more insight in the mechanisms underlying pattern-based expectations.…”

“…Probabilistic models incorporating statistical regularities in inter-onset intervals at different levels have indeed been used to explain aspects of temporal processing (Cannon, 2021;Elliott, Wing, & Welchman, 2014;van der Weij et al, 2017). In future work, linking such models directly to neural markers of pattern-based expectations may provide more insight in the mechanisms underlying pattern-based expectations.…”

“…We did observe lower ratings for the last probe positions after pattern-based than random sequences in Experiment 1. One speculative explanation for this is that while listeners are able to form expectations following temporal patterns, they only do so one interval at a time (e.g., they use each event as a cue for the next interval, but in the absence of an event, no next interval is predicted), and in a probabilistic way (Cannon, 2021;Damsma et al, 2021;van der Weij, Pearce, & Honing, 2017). In this case, it is possible that the expectation for an event at 780 ms would lead to an inverted U-shape in responses, similar to the inverted U around a beat, but with a wider distribution.…”

The sweet spot between predictability and surprise: musical groove in brain, body, and social interactions

“…Panels A and B of Figure 1 illustrate how beat- and meter-based temporal predictions can be conceptualized as probability distributions ( Large and Jones, 1999 ; Danielsen et al, 2019 ; Koelsch et al, 2019 ; Cannon, 2021 ), with their mean and spread reflecting the accuracy and certainty of these predictions, respectively. Prediction certainty determines the weight of the prediction error, that is, the degree to which it affects the metrical model.…”

Amodal population clock in the primate medial premotor system for rhythmic tapping

“…Cannons model (Cannon, 2021) combines a drift-diffusion process that quantifies the passage of time and an inhomogeneous point process that generates predicted events as a function of phase. The cyclical neural sequences with mixed time coding strategies could be the neural correlate for this drift-diffusion process.…”