Expectancy-based rhythmic entrainment as continuous Bayesian inference

Pitch biases sensorimotor synchronization to auditory rhythms

Current models of rhythm perception propose that humans track musical beats using the phase, period, and amplitude of sound patterns. However, a growing body of evidence suggests that pitch can also influence the perceived timing of auditory signals. In the present study, we conducted two experiments to investigate whether pitch affects the phase and period of sensorimotor synchronization. To do so, we asked participants to synchronize with a repeating tone, whose pitch on each trial was drawn from one of six different octaves (110-3520 Hz). In Experiment 1, we observed U-shaped patterns in both mean asynchrony and continuation tapping rates, with participants tapping latest and slowest when synchronizing to low and extremely high (above 2000 Hz) pitches, and tapping earliest and fastest to moderately high pitches. In Experiment 2, we found that extremely high pitches still produced slower timing than moderately high pitches when participants were exposed to an exclusively high-pitched context. Based on our results, we advocate for the incorporation of pitch into models of rhythm perception and discuss possible origins of these effects.

Inferring when to move

Most of our movement consists of sequences of discrete actions at regular intervals-including speech, walking, playing music, or even chewing. Despite this, few models of the motor system address how the brain determines the interval at which to trigger actions. This paper offers a theoretical analysis of the problem of timing movements. We consider a scenario in which we must align an alternating movement with a regular external (auditory) stimulus. We assume that our brains employ generative world models that include internal clocks of various speeds. These allow us to associate a temporally regular sensory input with an internal clock, and actions with parts of that clock cycle. We treat this as process of inferring which clock best explains sensory input. This offers a way in which temporally discrete choices might emerge from a continuous process. This is not straightforward, particularly if each of those choices unfolds during a time that has a (possibly unknown) duration. We develop a route for translation to neurology, in the context of Parkinson's disease-a disorder that characteristically slows down movements. The effects are often elicited in clinic by alternating movements. We find that it is possible to reproduce behavioural and electrophysiological features associated with parkinsonism by disrupting specific parameters-that determine the priors for inferences made by the brain. We observe three core features of Parkinson's disease: amplitude decrement, festination, and breakdown of repetitive movements. Our simulations provide a mechanistic interpretation of how pathology and therapeutics might influence behaviour and neural activity.

Measuring self-similarity in empirical signals to understand musical beat perception

Experiencing music often entails the perception of a periodic beat. Despite being a widespread phenomenon across cultures, the nature and neural underpinnings of beat perception remain largely unknown. In the last decade, there has been a growing interest in developing methods to probe these processes, particularly to measure the extent to which beat-related information is contained in behavioral and neural responses. Here, we propose a theoretical framework and practical implementation of an analytic approach to capture beat-related periodicity in empirical signals using frequency-tagging. We highlight its sensitivity in measuring the extent to which the periodicity of a perceived beat is represented in a range of continuous time-varying signals with minimal assumptions. We also discuss a limitation of this approach with respect to its specificity when restricted to measuring beat-related periodicity only from the magnitude spectrum of a signal and introduce a novel extension of the approach based on autocorrelation to overcome this issue. We test the new autocorrelation-based method using simulated signals and by re-analyzing previously published data and show how it can be used to process measurements of brain activity as captured with surface EEG in adults and infants in response to rhythmic inputs. Taken together, the theoretical framework and related methodological advances confirm and elaborate the frequency-tagging approach as a promising window into the processes underlying beat perception and, more generally, temporally coordinated behaviors.

Rats synchronize predictively to metronomes

Predictive auditory-motor synchronization, in which rhythmic movements anticipate rhythmic sounds, is at the core of the human capacity for music. Rodents show impressive capabilities in timing and motor tasks, but their ability to predictively coordinate sensation and action has not been demonstrated. Here, we reveal a clear capacity for predictive auditory-motor synchronization in rodent species using a modeling approach for the quantitative exploration of synchronization behaviors. We trained 8 rats to synchronize their licking to metronomes with tempi ranging from 0.5to 2 Hz and observed periodic lick patterns locked to metronome beats. We developed a flexible Markovian modeling framework to formally test how well different candidate strategies could explain the observed lick patterns. The best models required predictive control of licking that could not be explained by reactive strategies, indicating that predictive auditory-motor synchronization may be more widely shared across mammalian species than previously appreciated.

Dynamical mechanisms of how an RNN keeps a beat, uncovered with a low-dimensional reduced model

Despite music's omnipresence, the specific neural mechanisms responsible for perceiving and anticipating temporal patterns in music are unknown. To study potential mechanisms for keeping time in rhythmic contexts, we train a biologically constrained RNN, with excitatory (E) and inhibitory (I) units, on seven different stimulus tempos (2-8 Hz) on a synchronization and continuation task, a standard experimental paradigm. Our trained RNN generates a network oscillator that uses an input current (context parameter) to control oscillation frequency and replicates key features of neural dynamics observed in neural recordings of monkeys performing the same task. We develop a reduced three-variable rate model of the RNN and analyze its dynamic properties. By treating our understanding of the mathematical structure for oscillations in the reduced model as predictive, we confirm that the dynamical mechanisms are found also in the RNN. Our neurally plausible reduced model reveals an E-I circuit with two distinct inhibitory sub-populations, of which one is tightly synchronized with the excitatory units.

Neural dynamics of predictive timing and motor engagement in music listening

Why do humans spontaneously dance to music? To test the hypothesis that motor dynamics reflect predictive timing during music listening, we created melodies with varying degrees of rhythmic predictability (syncopation) and asked participants to rate their wanting-to-move (groove) experience. Degree of syncopation and groove ratings are quadratically correlated. Magnetoencephalography data showed that, while auditory regions track the rhythm of melodies, beat-related 2-hertz activity and neural dynamics at delta (1.4 hertz) and beta (20 to 30 hertz) rates in the dorsal auditory pathway code for the experience of groove. Critically, the left sensorimotor cortex coordinates these groove-related delta and beta activities. These findings align with the predictions of a neurodynamic model, suggesting that oscillatory motor engagement during music listening reflects predictive timing and is effected by interaction of neural dynamics along the dorsal auditory pathway.

Probing Beat Perception with Event-Related Potentials (ERPs) in Human Adults, Newborns, and Nonhuman Primates

The aim of this chapter is to give an overview of how the perception of rhythmic temporal regularity such as a regular beat in music can be studied in human adults, human newborns, and nonhuman primates using event-related brain potentials (ERPs). First, we discuss different aspects of temporal structure in general, and musical rhythm in particular, and we discuss the possible mechanisms underlying the perception of regularity (e.g., a beat) in rhythm. Additionally, we highlight the importance of dissociating beat perception from the perception of other types of structure in rhythm, such as predictable sequences of temporal intervals, ordinal structure, and rhythmic grouping. In the second section of the chapter, we start with a discussion of auditory ERPs elicited by infrequent and frequent sounds: ERP responses to regularity violations, such as mismatch negativity (MMN), N2b, and P3, as well as early sensory responses to sounds, such as P1 and N1, have been shown to be instrumental in probing beat perception. Subsequently, we discuss how beat perception can be probed by comparing ERP responses to sounds in regular and irregular sequences, and by comparing ERP responses to sounds in different metrical positions in a rhythm, such as on and off the beat or on strong and weak beats. Finally, we will discuss previous research that has used the aforementioned ERPs and paradigms to study beat perception in human adults, human newborns, and nonhuman primates. In doing so, we consider the possible pitfalls and prospects of the technique, as well as future perspectives.

Do we all synch alike? Brain-body-environment interactions in ASD

Autism Spectrum Disorder (ASD) is characterized by rigidity of routines and restricted interests, and atypical social communication and interaction. Recent evidence for altered synchronization of neuro-oscillatory brain activity with regularities in the environment and of altered peripheral nervous system function in ASD present promising novel directions for studying pathophysiology and its relationship to ASD clinical phenotype. Human cognition and action are significantly influenced by physiological rhythmic processes that are generated by both the central nervous system (CNS) and the autonomic nervous system (ANS). Normally, perception occurs in a dynamic context, where brain oscillations and autonomic signals synchronize with external events to optimally receive temporally predictable rhythmic information, leading to improved performance. The recent findings on the time-sensitive coupling between the brain and the periphery in effective perception and successful social interactions in typically developed highlight studying the interactions within the brain-body-environment triad as a critical direction in the study of ASD. Here we offer a novel perspective of autism as a case where the temporal dynamics of brain-body-environment coupling is impaired. We present evidence from the literature to support the idea that in autism the nervous system fails to operate in an adaptive manner to synchronize with temporally predictable events in the environment to optimize perception and behavior. This framework could potentially lead to novel biomarkers of hallmark deficits in ASD such as cognitive rigidity and altered social interaction.

Syncopation as Probabilistic Expectation: Conceptual, Computational, and Experimental Evidence

Definitions of syncopation share two characteristics: the presence of a meter or analogous hierarchical rhythmic structure and a displacement or contradiction of that structure. These attributes are translated in terms of a Bayesian theory of syncopation, where the syncopation of a rhythm is inferred based on a hierarchical structure that is, in turn, learned from the ongoing musical stimulus. Several experiments tested its simplest possible implementation, with equally weighted priors associated with different meters and independence of auditory events, which can be decomposed into two terms representing note density and deviation from a metric hierarchy. A computational simulation demonstrated that extant measures of syncopation fall into two distinct factors analogous to the terms in the simple Bayesian model. Next, a series of behavioral experiments found that perceived syncopation is significantly related to both terms, offering support for the general Bayesian construction of syncopation. However, we also found that the prior expectations associated with different metric structures are not equal across meters and that there is an interaction between density and hierarchical deviation, implying that auditory events are not independent from each other. Together, these findings provide evidence that syncopation is a manifestation of a form of temporal expectation that can be directly represented in Bayesian terms and offer a complementary, feature-driven approach to recent Bayesian models of temporal prediction.

Rhythmic temporal prediction enhances neural representations of movement intention for brain-computer interface

Objective.Detecting movement intention is a typical use of brain-computer interfaces (BCI). However, as an endogenous electroencephalography (EEG) feature, the neural representation of movement is insufficient for improving motor-based BCI. This study aimed to develop a new movement augmentation BCI encoding paradigm by incorporating the cognitive function of rhythmic temporal prediction, and test the feasibility of this new paradigm in optimizing detections of movement intention.Methods.A visual-motion synchronization task was designed with two movement intentions (left vs. right) and three rhythmic temporal prediction conditions (1000 ms vs. 1500 ms vs. no temporal prediction). Behavioural and EEG data of 24 healthy participants were recorded. Event-related potentials (ERPs), event-related spectral perturbation induced by left- and right-finger movements, the common spatial pattern (CSP) and support vector machine, Riemann tangent space algorithm and logistic regression were used and compared across the three temporal prediction conditions, aiming to test the impact of temporal prediction on movement detection.Results.Behavioural results showed significantly smaller deviation time for 1000 ms and 1500 ms conditions. ERP analyses revealed 1000 ms and 1500 ms conditions led to rhythmic oscillations with a time lag in contralateral and ipsilateral areas of movement. Compared with no temporal prediction, 1000 ms condition exhibited greater beta event-related desynchronization (ERD) lateralization in motor area (P< 0.001) and larger beta ERD in frontal area (P< 0.001). 1000 ms condition achieved an averaged left-right decoding accuracy of 89.71% using CSP and 97.30% using Riemann tangent space, both significantly higher than no temporal prediction. Moreover, movement and temporal information can be decoded simultaneously, achieving 88.51% four-classification accuracy.Significance.The results not only confirm the effectiveness of rhythmic temporal prediction in enhancing detection ability of motor-based BCI, but also highlight the dual encodings of movement and temporal information within a single BCI paradigm, which is promising to expand the range of intentions that can be decoded by the BCI.

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

The neural substrate for beat extraction and response entrainment to rhythms is not fully understood. Here we analyze the activity of medial premotor neurons in monkeys performing isochronous tapping guided by brief flashing stimuli or auditory tones. The population dynamics shared the following properties across modalities: the circular dynamics of the neural trajectories form a regenerating loop for every produced interval; the trajectories converge in similar state space at tapping times resetting the clock; and the tempo of the synchronized tapping is encoded in the trajectories by a combination of amplitude modulation and temporal scaling. Notably, the modality induces displacement in the neural trajectories in the auditory and visual subspaces without greatly altering the time-keeping mechanism. These results suggest that the interaction between the medial premotor cortex's amodal internal representation of pulse and a modality-specific external input generates a neural rhythmic clock whose dynamics govern rhythmic tapping execution across senses.

Probabilistic modelling of microtiming perception

Music performances are rich in systematic temporal irregularities called "microtiming", too fine-grained to be notated in a musical score but important for musical expression and communication. Several studies have examined listeners' preference for rhythms varying in microtiming, but few have addressed precisely how microtiming is perceived, especially in terms of cognitive mechanisms, making the empirical evidence difficult to interpret. Here we provide evidence that microtiming perception can be simulated as a process of probabilistic prediction. Participants performed an XAB discrimination test, in which an archetypal popular drum rhythm was presented with different microtiming. The results indicate that listeners could implicitly discriminate the mean and variance of stimulus microtiming. Furthermore, their responses were effectively simulated by a Bayesian model of entrainment, using a distance function derived from its dynamic posterior estimate over phase. Wide individual differences in participant sensitivity to microtiming were predicted by a model parameter likened to noisy timekeeping processes in the brain. Overall, this suggests that the cognitive mechanisms underlying perception of microtiming reflect a continuous inferential process, potentially driving qualitative judgements of rhythmic feel.

Dynamic models for musical rhythm perception and coordination

Rhythmicity permeates large parts of human experience. Humans generate various motor and brain rhythms spanning a range of frequencies. We also experience and synchronize to externally imposed rhythmicity, for example from music and song or from the 24-h light-dark cycles of the sun. In the context of music, humans have the ability to perceive, generate, and anticipate rhythmic structures, for example, "the beat." Experimental and behavioral studies offer clues about the biophysical and neural mechanisms that underlie our rhythmic abilities, and about different brain areas that are involved but many open questions remain. In this paper, we review several theoretical and computational approaches, each centered at different levels of description, that address specific aspects of musical rhythmic generation, perception, attention, perception-action coordination, and learning. We survey methods and results from applications of dynamical systems theory, neuro-mechanistic modeling, and Bayesian inference. Some frameworks rely on synchronization of intrinsic brain rhythms that span the relevant frequency range; some formulations involve real-time adaptation schemes for error-correction to align the phase and frequency of a dedicated circuit; others involve learning and dynamically adjusting expectations to make rhythm tracking predictions. Each of the approaches, while initially designed to answer specific questions, offers the possibility of being integrated into a larger framework that provides insights into our ability to perceive and generate rhythmic patterns.

Modeling enculturated bias in entrainment to rhythmic patterns

Long-term and culture-specific experience of music shapes rhythm perception, leading to enculturated expectations that make certain rhythms easier to track and more conducive to synchronized movement. However, the influence of enculturated bias on the moment-to-moment dynamics of rhythm tracking is not well understood. Recent modeling work has formulated entrainment to rhythms as a formal inference problem, where phase is continuously estimated based on precise event times and their correspondence to timing expectations: PIPPET (Phase Inference from Point Process Event Timing). Here we propose that the problem of optimally tracking a rhythm also requires an ongoing process of inferring which pattern of event timing expectations is most suitable to predict a stimulus rhythm. We formalize this insight as an extension of PIPPET called pPIPPET (PIPPET with pattern inference). The variational solution to this problem introduces terms representing the likelihood that a stimulus is based on a particular member of a set of event timing patterns, which we initialize according to culturally-learned prior expectations of a listener. We evaluate pPIPPET in three experiments. First, we demonstrate that pPIPPET can qualitatively reproduce enculturated bias observed in human tapping data for simple two-interval rhythms. Second, we simulate categorization of a continuous three-interval rhythm space by Western-trained musicians through derivation of a comprehensive set of priors for pPIPPET from metrical patterns in a sample of Western rhythms. Third, we simulate iterated reproduction of three-interval rhythms, and show that models configured with notated rhythms from different cultures exhibit both universal and enculturated biases as observed experimentally in listeners from those cultures. These results suggest the influence of enculturated timing expectations on human perceptual and motor entrainment can be understood as approximating optimal inference about the rhythmic stimulus, with respect to prototypical patterns in an empirical sample of rhythms that represent the music-cultural environment of the listener.

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

Groove-defined as the pleasurable urge to move to a rhythm-depends on a fine-tuned interplay between predictability arising from repetitive rhythmic patterns, and surprise arising from rhythmic deviations, for example in the form of syncopation. The perfect balance between predictability and surprise is commonly found in rhythmic patterns with a moderate level of rhythmic complexity and represents the sweet spot of the groove experience. In contrast, rhythms with low or high complexity are usually associated with a weaker experience of groove because they are too boring to be engaging or too complex to be interpreted, respectively. Consequently, the relationship between rhythmic complexity and groove experience can be described by an inverted U-shaped function. We interpret this inverted U shape in light of the theory of predictive processing and provide perspectives on how rhythmic complexity and groove can help us to understand the underlying neural mechanisms linking temporal predictions, movement, and reward. A better understanding of these mechanisms can guide future approaches to improve treatments for patients with motor impairments, such as Parkinson's disease, and to investigate prosocial aspects of interpersonal interactions that feature music, such as dancing. Finally, we present some open questions and ideas for future research.

Correction: Expectancy-based rhythmic entrainment as continuous Bayesian inference

[This corrects the article DOI: 10.1371/journal.pcbi.1009025.].