Computational models of interval timing

Mechanism of Duration Perception in Artificial Brains Suggests New Model of Attentional Entrainment

While cognitive theory has advanced several candidate frameworks to explain attentional entrainment, the neural basis for the temporal allocation of attention is unknown. Here we present a new model of attentional entrainment guided by empirical evidence obtained using a cohort of 50 artificial brains. These brains were evolved in silico to perform a duration judgment task similar to one where human subjects perform duration judgments in auditory oddball paradigms. We found that the artificial brains display psychometric characteristics remarkably similar to those of human listeners and exhibit similar patterns of distortions of perception when presented with out-of-rhythm oddballs. A detailed analysis of mechanisms behind the duration distortion suggests that attention peaks at the end of the tone, which is inconsistent with previous attentional entrainment models. Instead, the new model of entrainment emphasizes increased attention to those aspects of the stimulus that the brain expects to be highly informative.

Neurocomputational Models of Interval Timing: Seeing the Forest for the Trees

Extracting temporal regularities and relations from experience/observation is critical for organisms' adaptiveness (communication, foraging, predation, prediction) in their ecological niches. Therefore, it is not surprising that the internal clock that enables the perception of seconds-to-minutes-long intervals (interval timing) is evolutionarily well-preserved across many species of animals. This comparative claim is primarily supported by the fact that the timing behavior of many vertebrates exhibits common statistical signatures (e.g., on-average accuracy, scalar variability, positive skew). These ubiquitous statistical features of timing behaviors serve as empirical benchmarks for modelers in their efforts to unravel the processing dynamics of the internal clock (namely answering how internal clock "ticks"). In this chapter, we introduce prominent (neuro)computational approaches to modeling interval timing at a level that can be understood by general audience. These models include Treisman's pacemaker accumulator model, the information processing variant of scalar expectancy theory, the striatal beat frequency model, behavioral expectancy theory, the learning to time model, the time-adaptive opponent Poisson drift-diffusion model, time cell models, and neural trajectory models. Crucially, we discuss these models within an overarching conceptual framework that categorizes different models as threshold vs. clock-adaptive models and as dedicated clock/ramping vs. emergent time/population code models.

Dopamine precursor depletion affects performance and confidence judgements when events are timed from an explicit, but not an implicit onset

Dopamine affects processing of temporal information, but most previous work has tested its role in prospective tasks, where participants know in advance when the event to be timed starts. However, we are often exposed to events whose onset we do not know in advance. We can evaluate their duration after they have elapsed, but mechanisms underlying this ability are still elusive. Here we contrasted effects of acute phenylalanine and tyrosine depletion (APTD) on both forms of timing in healthy volunteers, in a within-subject, placebo-controlled design. Participants were presented with a disc moving around a circular path and asked to reproduce the duration of one full revolution and to judge their confidence in performance. The onset of the revolution was either known in advance (explicit onset) or revealed only at the end of the trial (implicit onset). We found that APTD shortened reproduced durations in the explicit onset task but had no effect on temporal performance in the implicit onset task. This dissociation is corroborated by effects of APTD on confidence judgements in the explicit task only. Our findings suggest that dopamine has a specific role in prospective encoding of temporal intervals, rather than the processing of temporal information in general.

Oscillation/Coincidence-Detection Models of Reward-Related Timing in Corticostriatal Circuits

The major tenets of beat-frequency/coincidence-detection models of reward-related timing are reviewed in light of recent behavioral and neurobiological findings. This includes the emphasis on a core timing network embedded in the motor system that is comprised of a corticothalamic-basal ganglia circuit. Therein, a central hub provides timing pulses (i.e., predictive signals) to the entire brain, including a set of distributed satellite regions in the cerebellum, cortex, amygdala, and hippocampus that are selectively engaged in timing in a manner that is more dependent upon the specific sensory, behavioral, and contextual requirements of the task. Oscillation/coincidence-detection models also emphasize the importance of a tuned ‘perception’ learning and memory system whereby target durations are detected by striatal networks of medium spiny neurons (MSNs) through the coincidental activation of different neural populations, typically utilizing patterns of oscillatory input from the cortex and thalamus or derivations thereof (e.g., population coding) as a time base. The measure of success of beat-frequency/coincidence-detection accounts, such as the Striatal Beat-Frequency model of reward-related timing (SBF), is their ability to accommodate new experimental findings while maintaining their original framework, thereby making testable experimental predictions concerning diagnosis and treatment of issues related to a variety of dopamine-dependent basal ganglia disorders, including Huntington’s and Parkinson’s disease.

The human cerebellum is essential for modulating perceptual sensitivity based on temporal expectations

A functional benefit of attention is to proactively enhance perceptual sensitivity in space and time. Although attentional orienting has traditionally been associated with cortico-thalamic networks, recent evidence has shown that individuals with cerebellar degeneration (CD) show a reduced reaction time benefit from cues that enable temporal anticipation. The present study examined whether the cerebellum contributes to the proactive attentional modulation in time of perceptual sensitivity. We tested CD participants on a non-speeded, challenging perceptual discrimination task, asking if they benefit from temporal cues. Strikingly, the CD group showed no duration-specific perceptual sensitivity benefit when cued by repeated but aperiodic presentation of the target interval. In contrast, they performed similar to controls when cued by a rhythmic stream. This dissociation further specifies the functional domain of the cerebellum and establishes its role in the attentional adjustment of perceptual sensitivity in time in addition to its well-documented role in motor timing.

The ecological significance of time sense in animals

Time is a fundamental dimension of all biological events and it is often assumed that animals have the capacity to track the duration of experienced events (known as interval timing). Animals can potentially use temporal information as a cue during foraging, communication, predator avoidance, or navigation. Interval timing has been traditionally investigated in controlled laboratory conditions but its ecological relevance in natural environments remains unclear. While animals may time events in artificial and highly controlled conditions, they may not necessarily use temporal information in natural environments where they have access to other cues that may have more relevance than temporal information. Herein we critically evaluate the ecological contexts where interval timing has been suggested to provide adaptive value for animals. We further discuss attributes of interval timing that are rarely considered in controlled laboratory studies. Finally, we encourage consideration of ecological relevance when designing future interval-timing studies and propose future directions for such experiments.

Towards Ecologically Valid Interval Timing

Research on interval timing has provided significant insight into how intervals are perceived and produced in well-controlled laboratory settings. However, for timing theories to explain real-world performance, it is imperative that they provide better quantitative predictions and be applicable to timing tasks that are relevant in ecologically valid settings.

Drift-diffusion explains response variability and capacity for tracking objects

Being able to track objects that surround us is key for planning actions in dynamic environments. However, rigorous cognitive models for tracking of one or more objects are currently lacking. In this study, we asked human subjects to judge the time to contact (TTC) a finish line for one or two objects that became invisible shortly after moving. We showed that the pattern of subject responses had an error variance best explained by an inverse Gaussian distribution and consistent with the output of a biased drift-diffusion model. Furthermore, we demonstrated that the pattern of errors made when tracking two objects showed a level of dependence that was consistent with subjects using a single decision variable for reporting the TTC for two objects. This finding reveals a serious limitation in the capacity for tracking multiple objects resulting in error propagation between objects. Apart from explaining our own data, our approach helps interpret previous findings such as asymmetric interference when tracking multiple objects.

Activity in perceptual classification networks as a basis for human subjective time perception

Despite being a fundamental dimension of experience, how the human brain generates the perception of time remains unknown. Here, we provide a novel explanation for how human time perception might be accomplished, based on non-temporal perceptual classification processes. To demonstrate this proposal, we build an artificial neural system centred on a feed-forward image classification network, functionally similar to human visual processing. In this system, input videos of natural scenes drive changes in network activation, and accumulation of salient changes in activation are used to estimate duration. Estimates produced by this system match human reports made about the same videos, replicating key qualitative biases, including differentiating between scenes of walking around a busy city or sitting in a cafe or office. Our approach provides a working model of duration perception from stimulus to estimation and presents a new direction for examining the foundations of this central aspect of human experience.

Predicting change: Approximate inference under explicit representation of temporal structure in changing environments

In our daily lives timing of our actions plays an essential role when we navigate the complex everyday environment. It is an open question though how the representations of the temporal structure of the world influence our behavior. Here we propose a probabilistic model with an explicit representation of state durations which may provide novel insights in how the brain predicts upcoming changes. We illustrate several properties of the behavioral model using a standard reversal learning design and compare its task performance to standard reinforcement learning models. Furthermore, using experimental data, we demonstrate how the model can be applied to identify participants' beliefs about the latent temporal task structure. We found that roughly one quarter of participants seem to have learned the latent temporal structure and used it to anticipate changes, whereas the remaining participants' behavior did not show signs of anticipatory responses, suggesting a lack of precise temporal expectations. We expect that the introduced behavioral model will allow, in future studies, for a systematic investigation of how participants learn the underlying temporal structure of task environments and how these representations shape behavior.

Neural correlates of time distortion in a preaction period

An intention to move distorts the perception of time. For example, a visual stimulus presented during the preparation of manual movements is perceived longer than actual. Although neural mechanisms underlying this action-induced time distortion have been unclear, here we propose a new model in which the distortion is caused by a sensory-motor interaction mediated by alpha rhythm. It is generally known that viewing a stimulus induces a reduction in amplitude of occipital 10-Hz wave ("alpha-blocking"). Preparing manual movements are also known to reduce alpha power in the motor cortex ("mu-suppression"). When human participants prepared movements while viewing a stimulus, we found that those two types of classical alpha suppression interacted in the third (time-processing) region in the brain, inducing a prominent decrease in alpha power in the supplementary motor cortex (SMA). Interestingly, this alpha suppression in the SMA occurred in an asymmetric manner (such that troughs of alpha rhythm was more strongly suppressed than peaks), which can produce a gradual increase (slow shift of baseline) in neural activity. Since the neural processing in the SMA encodes a subjective time length for a sensory event, the increased activity in this region (by the asymmetric alpha suppression) would cause an overestimation of elapsed time, resulting in the action-induced time distortion. Those results showed a unique role of alpha wave enabling communications across distant (visual, motor, and time-processing) regions in the brain and further suggested a new type of sensory-motor interaction based on neural desynchronization (rather than synchronization).

Sensorimotor Synchronization With Auditory and Visual Modalities: Behavioral and Neural Differences

It has long been known that the auditory system is better suited to guide temporally precise behaviors like sensorimotor synchronization (SMS) than the visual system. Although this phenomenon has been studied for many years, the underlying neural and computational mechanisms remain unclear. Growing consensus suggests the existence of multiple, interacting, context-dependent systems, and that reduced precision in visuo-motor timing might be due to the way experimental tasks have been conceived. Indeed, the appropriateness of the stimulus for a given task greatly influences timing performance. In this review, we examine timing differences for sensorimotor synchronization and error correction with auditory and visual sequences, to inspect the underlying neural mechanisms that contribute to modality differences in timing. The disparity between auditory and visual timing likely relates to differences in the processing specialization between auditory and visual modalities (temporal vs. spatial). We propose this difference could offer potential explanation for the differing temporal abilities between modalities. We also offer suggestions as to how these sensory systems interface with motor and timing systems.

Timing in the absence of a clock reset

Prominent models of time perception assume a reset of the timing mechanism with an explicit onset of the interval to be timed. Here we investigated the accuracy and precision of temporal estimations when the duration does not have such an explicit onset. Participants were tracking a disc moving on a circular path with varying speeds, and estimated the duration of one full revolution before the stimulus stopped. The onset of that revolution was either cued (explicit), or undetermined until the stimulus stopped (implicit). Reproduced duration was overestimated for short and underestimated for long durations, and variability of the estimates scaled with the duration in both temporal conditions. However, the bias was more pronounced in the implicit condition. In addition, if the stimulus path was partially occluded, duration of the occluded motion was correctly estimated. In a second experiment, we compared the precision in the explicit and implicit conditions by asking participants to discriminate the duration of one revolution before the stimulus stopped to that of a static stimulus presentation in a forced-choice task. Sensitivity of discrimination was worse in the implicit onset condition, but surprisingly, still comparable to the explicit condition. In summary, the estimates follow principles described in prospective timing paradigms, although not knowing beforehand when to start timing decreases sensitivity of temporal estimations. Since in naturalistic contexts, we often do not know in advance which durations might be relevant to estimate, the simple task presented here could become a valuable tool for testing models of temporal estimation.

Learning what to expect and when to expect it involves dissociable neural systems

Two experiments with Long-Evans rats examined the potential independence of learning about different features of food reward, namely, "what" reward is to be expected and "when" it will occur. This was examined by investigating the effects of selective reward devaluation upon responding in an instrumental peak timing task in Experiment 1 and by exploring the effects of pre-training lesions targeting the basolateral amygdala (BLA) upon the selective reward devaluation effect and interval timing in a Pavlovian peak timing task in Experiment 2. In both tasks, two stimuli, each 60 s long, signaled that qualitatively distinct rewards (different flavored food pellets) could occur after 20 s. Responding on non-rewarded probe trials displayed the characteristic peak timing function with mean responding gradually increasing and peaking at approximately 20 s before more gradually declining thereafter. One of the rewards was then independently paired repeatedly with LiCl injections in order to devalue it whereas the other reward was unpaired with these injections. In a final set of test sessions in which both stimuli were presented without rewards, it was observed that responding was selectively reduced in the presence of the stimulus signaling the devalued reward compared to the stimulus signaling the still valued reward. Moreover, the timing function was mostly unaltered by this devaluation manipulation. Experiment 2 showed that pre-training BLA lesions abolished this selective reward devaluation effect, but it had no impact on peak timing functions shown by the two stimuli. It appears from these data that learning about "what" and "when" features of reward may entail separate underlying neural systems.

Embodiment and the origin of interval timing: kinematic and electromyographic data

Recent evidence suggests that interval timing (the judgment of durations lasting from approximately 500 ms. to a few minutes) is closely coupled to the action control system. We used surface electromyography (EMG) and motion capture technology to explore the emergence of this coupling in 4-, 6-, and 8-month-olds. We engaged infants in an active and socially relevant arm-raising task with seven cycles and response period. In one condition, cycles were slow (every 4 s); in another, they were fast (every 2 s). In the slow condition, we found evidence of time-locked sub-threshold EMG activity even in the absence of any observed overt motor responses at all three ages. This study shows that EMGs can be a more sensitive measure of interval timing in early development than overt behavior.

A Brief History of “The Psychology of Time Perception”

Basic mechanisms of interval timing and associative learning are shared by many animal species, and develop quickly in early life, particularly across infancy, and childhood. Indeed, John Wearden in his book “The Psychology of Time Perception”, which is based on decades of his own research with colleagues, and which our commentary serves to primarily review, has been instrumental in implementing animal models and methods in children and adults, and has revealed important similarities (and differences) between human timing (and that of animals) when considered within the context of scalar timing theory. These seminal studies provide a firm foundation upon which the contemporary multifaceted field of timing and time perception has since advanced. The contents of the book are arguably one piece of a larger puzzle, and as Wearden cautions, “The reader is warned that my own contribution to the field has been exaggerated here, but if you are not interested in your own work, why would anyone else be?” Surely there will be many interested readers, however the book is noticeably lacking in it neurobiological perspective. The mind (however it is conceived) needs a brain (even if behaviorists tend to say “the brain behaves”, and most neuroscientists currently have a tenuous grasp on the neural mechanisms of temporal cognition), and to truly understand the psychology of time, brain and behavior must go hand in hand regardless of the twists, turns, and detours along the way.