Bayesian optimization of time perception

The impact of task measurements on sequential dependence: a comparison between temporal reproduction and discrimination tasks

Decisions about a current stimulus are influenced by previously encountered stimuli, leading to sequential bias. However, the specific processing levels at which serial dependence emerges remain unclear. Despite considerable evidence pointing to contributions from perceptual and post-perceptual processes, as well as response carryover effects impacting subsequent judgments, research into how different task measurements affect sequential dependencies is limited. To address this gap, the present study investigated the role of task type in shaping sequential effects in time perception, employing a random-dot kinematogram (RDK) in a post-cue paradigm. Participants had to remember both the duration and the direction of the RDK movement and perform the task based on a post-cue, which was equally likely to be direction or duration. To delineate the task type, we employed the temporal bisection task in Experiment 1 and the duration reproduction task in Experiment 2. Both experiments revealed a significant sequential bias: durations were perceived as longer following longer previous durations, and vice versa. Intriguingly, the sequential effect was enhanced in the reproduction task following the same reproduction task (Experiment 2), but did not show significant variation by the task type in the bisection task (Experiment 1). Moreover, comparable response carryover effects were observed across two experiments. We argue that the differential impacts of task types on sequential dependence lies in the involvement of memory reactivation process in the decision stage, while the post-decision response carryover effect may reflect the assimilation by subjective, rather than objective, durations, potentially linking to the sticky pacemaker rate and/or decisional inertia.

Opposing sequential biases in direction and time reproduction: Influences of task relevance and working memory

Our current perception and decision-making are shaped by recent experiences, a phenomenon known as serial dependence. While serial dependence is well-documented in visual perception and has been recently explored in time perception, their functional similarities across non-temporal and temporal domains remain elusive, particularly in relation to task relevance and working memory load. To address this, we designed a unified experimental paradigm using coherent motion stimuli to test both direction and time reproduction. The direction and time tasks were randomly mixed across trials. Additionally, we introduced pre-cue versus post-cue settings in separate experiments to manipulate working memory load during the encoding phase. We found attractive biases in time reproduction but repulsive biases in direction estimation. Notably, the temporal attraction was more pronounced when the preceding task was also time-related. In contrast, the direction repulsion remained unaffected by the nature of the preceding task. Additionally, both attractive and repulsive biases were enhanced by the post-cue compared to the pre-cue. Our findings suggest that opposing sequential effects in non-temporal and temporal domains may originate from different processing stages linked to sensory adaptation and post-perceptual processes involving working memory.

Temporal context modulates cross-modality time discrimination: Electrophysiological evidence for supramodal temporal representation

Although the peripheral nervous system lacks a dedicated receptor, the brain processes temporal information through different sensory channels. A critical question is whether temporal information from different sensory modalities at different times forms modality-specific representations or is integrated into a common representation in a supramodal manner. Behavioral studies on temporal memory mixing and the central tendency effect have provided evidence for supramodal temporal representations. We aimed to provide electrophysiological evidence for this proposal by employing a cross-modality time discrimination task combined with electroencephalogram (EEG) recordings. The task maintained a fixed auditory standard duration, whereas the visual comparison duration was randomly selected from the short and long ranges, creating two different audio-visual temporal contexts. The behavioral results showed that the point of subjective equality (PSE) in the short context was significantly lower than that in the long context. The EEG results revealed that the amplitude of the contingent negative variation (CNV) in the short context was significantly higher (more negative) than in the long context in the early stage, while it was lower (more positive) in the later stage. These results suggest that the audiovisual temporal context is integrated with the auditory standard duration to generate a subjective time criterion. Compared with the long context, the subjective time criterion in the short context was shorter, resulting in earlier decision-making and a preceding decrease in CNV. Our study provides electrophysiological evidence that temporal information from different modalities inputted into the brain at different times can form a supramodal temporal representation.

Influences of temporal and probabilistic expectation on subjective time of emotional stimulus

Subjective time perception can change based on a stimulus's valence and expectancy. Yet, it is unclear how these two factors might interact to shape our sense of how long something lasts. Here, we conducted two experiments examining the effects of temporal and probabilistic expectancy on the perceived duration of images with varying emotional valence. In Experiment 1, we varied the temporal predictive cue with varying stimulus-onset asynchronies (SOAs), while in Experiment 2, we manipulated the cue-emotion probabilistic associations. Our results revealed that stimuli appearing earlier than anticipated were perceived as shorter, whereas less infrequent stimuli seemed to last longer. In addition, negative images were perceived longer than neural ones. However, no significant interaction between expectancy and stimulus valence was observed. We interpret these using the internal clock model, suggesting that while emotional stimuli primarily affect the pacemaker's rhythm through arousal, expectation steers attention, influencing how we register time's passage.

Rapid calibration to dynamic temporal contexts

The prediction of future events and the preparation of appropriate behavioural reactions rely on an accurate perception of temporal regularities. In dynamic environments, temporal regularities are subject to slow and sudden changes, and adaptation to these changes is an important requirement for efficient behaviour. Bayesian models have proven a useful tool to understand the processing of temporal regularities in humans; yet an open question pertains to the degree of flexibility of the prior that is required for optimal modelling of behaviour. Here we directly compare dynamic models (with continuously changing prior expectations) and static models (a stable prior for each experimental session) with their ability to describe regression effects in interval timing. Our results show that dynamic Bayesian models are superior when describing the responses to slow, continuous environmental changes, whereas static models are more suitable to describe responses to sudden changes. In time perception research, these results will be informative for the choice of adequate computational models and enhance our understanding of the neuronal computations underlying human timing behaviour.

Blocked versus interleaved: How range contexts modulate time perception and its EEG signatures

Accurate time perception is a crucial element in a wide range of cognitive tasks, including decision-making, memory, and motor control. One commonly observed phenomenon is that when given a range of time intervals to consider, people's estimates often cluster around the midpoint of those intervals. Previous studies have suggested that the range of these intervals can also influence our judgments, but the neural mechanisms behind this "range effect" are not yet understood. We used both behavioral tests and electroencephalographic (EEG) measures to understand how the range of sample time intervals affects the accuracy of people's subsequent time estimates. Study participants were exposed to two different setups: In the "blocked-range" (BR) session, short and long intervals were presented in separate blocks, whereas in the "interleaved-range" (IR) session, intervals of various lengths were presented randomly. Our findings indicated that the BR context led to more accurate time estimates compared to the IR context. In terms of EEG data, the BR context resulted in quicker buildup of contingent negative variation (CNV), which also reached higher amplitude levels and dissolved more rapidly during the encoding stage. We also observed an enhanced amplitude in the offset P2 component of the EEG signal. Overall, our results suggest that the variability in time intervals, as defined by their range, influences the neural processes that underlie time estimation.

Emergent perceptual biases from state-space geometry in trained spiking recurrent neural networks

A stimulus held in working memory is perceived as contracted toward the average stimulus. This contraction bias has been extensively studied in psychophysics, but little is known about its origin from neural activity. By training recurrent networks of spiking neurons to discriminate temporal intervals, we explored the causes of this bias and how behavior relates to population firing activity. We found that the trained networks exhibited animal-like behavior. Various geometric features of neural trajectories in state space encoded warped representations of the durations of the first interval modulated by sensory history. Formulating a normative model, we showed that these representations conveyed a Bayesian estimate of the interval durations, thus relating activity and behavior. Importantly, our findings demonstrate that Bayesian computations already occur during the sensory phase of the first stimulus and persist throughout its maintenance in working memory, until the time of stimulus comparison.

A Bayesian observer model reveals a prior for natural daylights in hue perception

Incorporating statistical characteristics of stimuli in perceptual processing can be highly beneficial for reliable estimation from noisy sensory measurements but may generate perceptual bias. According to Bayesian inference, perceptual biases arise from the integration of internal priors with noisy sensory inputs. In this study, we used a Bayesian observer model to derive biases and priors in hue perception based on discrimination data for hue ensembles with varying levels of chromatic noise. Our results showed that discrimination thresholds for isoluminant stimuli with hue defined by azimuth angle in cone-opponent color space exhibited a bimodal pattern, with lowest thresholds near a non-cardinal blue-yellow axis that aligns closely with the variation of natural daylights. Perceptual biases showed zero crossings around this axis, indicating repulsion away from yellow and attraction towards blue. These biases could be explained by the Bayesian observer model through a non-uniform prior with a preference for blue. Our findings suggest that visual processing takes advantage of knowledge of the distribution of colors in natural environments for hue perception.

Order effects in stimulus discrimination challenge established models of comparative judgement: A meta-analytic review of the Type B effect

This paper provides a comprehensive review of the Type B effect (TBE), a phenomenon reflected in the observation that discrimination sensitivity varies with the order of stimuli in comparative judgment tasks, such as the two-alternative forced-choice (2AFC) paradigm. Specifically, when the difference threshold is lower (higher) with the constant standard preceding rather than following the variable comparison, one speaks of a negative (positive) TBE. Importantly, prominent psychophysical difference models such as signal detection theory (Green & Swets, 1966) cannot easily account for the TBE, and are hence challenged by it. The present meta-analysis provides substantial evidence for the TBE across various stimulus attributes, suggesting that the TBE is a general feature of discrimination experiments when standard and comparison are presented successively. Thus, inconsistent with psychophysical difference models, subjective differences between stimuli are not merely a function of their physical differences but rather also depend on their temporal order. From the literature, we identify four classes of potential candidate theories explaining the origin of the TBE, namely (1) differential weighting of the stimulus magnitudes at the two positions (e.g., Hellström, Psychological Research, 39, 345-388 1977), (2) internal reference formation (e.g., Dyjas, Bausenhart, & Ulrich, Attention, Perception, & Psychophysics, 74, 1819-1841 2012), (3) Bayesian updating (e.g., de Jong, Akyürek, & van Rijn, Psychonomic Bulletin and Review, 28, 1183-1190 2021), and (4) biased threshold estimation (García-Pérez & Alcalá-Quintana, Attention, Perception & Psychophysics, 72, 1155-1178 2010). As these models, to some extent, make differential predictions about the direction of the TBE, investigating the respective boundary conditions of positive and negative TBEs might be a valuable perspective for diagnostic future research.

The Effect of Emotion on Time Perception in Youth Athletes with Different Alerting Efficiencies

Purpose

Time perception plays a critical role in executing movements in various competitions. However, less research has been conducted on the alerting component of attention in the processing of time perception, and that the effects of emotion on the alerting network show inconsistent effects. This study is aimed to explore the factors that may influence time perception in youth athletes and these relationships.

Methods

A total of 225 participants were recruited to assess alerting efficiency using the Attention Network Test and were divided into high and low alerting efficiency groups based on the front and back 27% of the ranked alerting scores as a dividing metric, and subsequently participants completed Time replication task under different emotionally induced conditions.

Results

Alerting efficiency had a significant effect on time perception, with the high alerting efficiency subjects having higher time estimation accuracy [F (1106) = 6.32, p = 0.013, η2p = 0.10] and being more inclined to overestimate time perception [F (1106) = 12.64, p = 0.001, η2 p = 0.11]. An interaction was found between emotion and alerting efficiency on time replication ratio [F (2106) = 3.59, p = 0.031, η2p = 0.08], and further simple effects analyses found that the low alerting efficiency subjects tended to overestimate time in the anger state relative to the happy and neutral states [F (2106) = 5.93, p < 0.01, η2p = 0.10].

Conclusion

These findings suggest that high alerting efficiency in youth athletes is associated with greater time perception response advantage; The time perception of low alerting efficiency youth athletes was more likely to be affected by emotions. This study provides a reference for the training of time perception and specialized perceptual ability of youth athletes, enriches the index system of psychological selection of youth athletes.

Neural mechanisms of sequential dependence in time perception: the impact of prior task and memory processing

Our perception and decision-making are susceptible to prior context. Such sequential dependence has been extensively studied in the visual domain, but less is known about its impact on time perception. Moreover, there are ongoing debates about whether these sequential biases occur at the perceptual stage or during subsequent post-perceptual processing. Using functional magnetic resonance imaging, we investigated neural mechanisms underlying temporal sequential dependence and the role of action in time judgments across trials. Participants performed a timing task where they had to remember the duration of green coherent motion and were cued to either actively reproduce its duration or simply view it passively. We found that sequential biases in time perception were only evident when the preceding task involved active duration reproduction. Merely encoding a prior duration without reproduction failed to induce such biases. Neurally, we observed activation in networks associated with timing, such as striato-thalamo-cortical circuits, and performance monitoring networks, particularly when a "Response" trial was anticipated. Importantly, the hippocampus showed sensitivity to these sequential biases, and its activation negatively correlated with the individual's sequential bias following active reproduction trials. These findings highlight the significant role of memory networks in shaping time-related sequential biases at the post-perceptual stages.

An FPGA implementation of Bayesian inference with spiking neural networks

Spiking neural networks (SNNs), as brain-inspired neural network models based on spikes, have the advantage of processing information with low complexity and efficient energy consumption. Currently, there is a growing trend to design hardware accelerators for dedicated SNNs to overcome the limitation of running under the traditional von Neumann architecture. Probabilistic sampling is an effective modeling approach for implementing SNNs to simulate the brain to achieve Bayesian inference. However, sampling consumes considerable time. It is highly demanding for specific hardware implementation of SNN sampling models to accelerate inference operations. Hereby, we design a hardware accelerator based on FPGA to speed up the execution of SNN algorithms by parallelization. We use streaming pipelining and array partitioning operations to achieve model operation acceleration with the least possible resource consumption, and combine the Python productivity for Zynq (PYNQ) framework to implement the model migration to the FPGA while increasing the speed of model operations. We verify the functionality and performance of the hardware architecture on the Xilinx Zynq ZCU104. The experimental results show that the hardware accelerator of the SNN sampling model proposed can significantly improve the computing speed while ensuring the accuracy of inference. In addition, Bayesian inference for spiking neural networks through the PYNQ framework can fully optimize the high performance and low power consumption of FPGAs in embedded applications. Taken together, our proposed FPGA implementation of Bayesian inference with SNNs has great potential for a wide range of applications, it can be ideal for implementing complex probabilistic model inference in embedded systems.

Influences of temporal order in temporal reproduction

Despite the crucial role of complex temporal sequences, such as speech and music, in our everyday lives, our ability to acquire and reproduce these patterns is prone to various contextual biases. In this study, we examined how the temporal order of auditory sequences affects temporal reproduction. Participants were asked to reproduce accelerating, decelerating or random sequences, each consisting of four intervals, by tapping their fingers. Our results showed that the reproduction and the reproduction variability were influenced by the sequential structure and interval orders. The mean reproduced interval was assimilated by the first interval of the sequence, with the lowest mean for decelerating and the highest for accelerating sequences. Additionally, the central tendency bias was affected by the volatility and the last interval of the sequence, resulting in a stronger central tendency in the random and decelerating sequences than the accelerating sequence. Using Bayesian integration between the ensemble mean of the sequence and individual durations and considering the perceptual uncertainty associated with the sequential structure and position, we were able to accurately predict the behavioral results. The findings highlight the critical role of the temporal order of a sequence in temporal pattern reproduction, with the first interval exerting greater influence on mean reproduction and the volatility and the last interval contributing to the perceptual uncertainty of individual intervals and the central tendency bias.

Encoding, working memory, or decision: how feedback modulates time perception

The hypothesis that individuals can accurately represent temporal information within approximately 3 s is the premise of several theoretical models and empirical studies in the field of temporal processing. The significance of accurately representing time within 3 s and the universality of the overestimation contrast dramatically. To clarify whether this overestimation arises from an inability to accurately represent time or a response bias, we systematically examined whether feedback reduces overestimation at the 3 temporal processing stages of timing (encoding), working memory, and decisions proposed by the scalar timing model. Participants reproduced the time interval between 2 circles with or without feedback, while the electroencephalogram (EEG) was synchronously recorded. Behavioral results showed that feedback shortened reproduced times and significantly minimized overestimation. EEG results showed that feedback significantly decreased the amplitude of contingent negative variation (CNV) in the decision stage but did not modulate the CNV amplitude in the encoding stage or the P2-P3b amplitudes in the working memory stage. These results suggest that overestimation arises from response bias when individuals convert an accurate representation of time into behavior. Our study provides electrophysiological evidence to support the conception that short intervals under approximately 3 s can be accurately represented as "temporal gestalt."

Context-specific and context-invariant computations of interval timing

Introduction

An accurate sense of time is crucial in flexible sensorimotor control and other cognitive functions. However, it remains unknown how multiple timing computations in different contexts interact to shape our behavior.

Methods

We asked 41 healthy human subjects to perform timing tasks that differed in the sensorimotor domain (sensory timing vs. motor timing) and effector (hand vs. saccadic eye movement). To understand how these different behavioral contexts contribute to timing behavior, we applied a three-stage Bayesian model to behavioral data.

Results

Our results demonstrate that the Bayesian model for each effector could not describe bias in the other effector. Similarly, in each task the model-predicted data could not describe bias in the other task. These findings suggest that the measurement stage of interval timing is context-specific in the sensorimotor and effector domains. We also showed that temporal precision is context-invariant in the effector domain, unlike temporal accuracy.

Discussion

This combination of context-specific and context-invariant computations across sensorimotor and effector domains suggests overlapping and distributed computations as the underlying mechanism of timing in different contexts.

Differentiated, rather than shared, strategies for time-coordinated action in social and non-social domains in autistic individuals

Autism spectrum disorder (ASD) is a neurodevelopmental condition with a highly heterogeneous adult phenotype that includes social and non-social behavioral characteristics. The link between the characteristics assignable to the different domains remains unresolved. One possibility is that social and non-social behaviors in autism are modulated by a common underlying deficit. However, here we report evidence supporting an alternative concept that is individual-centered rather than deficit-centered. Individuals are assumed to have a distinctive style in the strategies they adopt to perform social and non-social tasks with these styles presumably being structured differently between autistic individuals and typically-developed (TD) individuals. We tested this hypothesis for the execution of time-coordinated (synchronized) actions. Participants performed (i) a social task that required synchronized gaze and pointing actions to interact with another person, and (ii) a non-social task that required finger-tapping actions synchronized to periodic stimuli at different time-scales and sensory modalities. In both tasks, synchronization behavior differed between ASD and TD groups. However, a principal component analysis of individual behaviors across tasks revealed associations between social and non-social features for the TD persons but such cross-domain associations were strikingly absent for autistic individuals. The highly differentiated strategies between domains in ASD are inconsistent with a general synchronization deficit and instead highlight the individualized developmental heterogeneity in the acquisition of domain-specific behaviors. We propose a cognitive model to help disentangle individual-centered from deficit-centered effects in other domains. Our findings reinforce the importance to identify individually differentiated phenotypes to personalize autism therapies.

Neural correlates of aftereffects induced by adaptations to single and average durations

Duration perception can be heavily distorted owing to repetitive exposure to a relatively long or short sensory event, often causing a duration aftereffect. Here, we used a novel procedure to show that adaptations to both single and average durations produced the duration aftereffect. Participants completed a duration reproduction task (Experiment 1) or a duration category rating task (Experiment 2) after long-term adaptations to a stimulus of medium duration and to stimuli of averagely medium duration. We found that adaptations to both single and average durations resulted in duration aftereffects. The simultaneously recorded functional magnetic resonance imaging (fMRI) data revealed that the reduction in neural activity due to long-term adaptation to single duration was observed in the right supramarginal gyrus (SMG) of the parietal lobe, while adaptation to average duration resulted in fMRI adaptations in the left postcentral gyrus (PCG) and middle cingulate gyrus (MCG). At the individual level, the magnitude of the behavioral aftereffect was positively correlated with the magnitude of fMRI adaptation in the right SMG after adaptation to single duration, while there were no significantly positive correlations between the behavioral aftereffect and fMRI adaptations in the left PCG and MCG. These results suggest that there are different neural mechanisms for aftereffects caused by adaptations to single and average durations.

Role of the subthalamic nucleus in perceiving and estimating the passage of time

Sense of time (temporal sense) is believed to be processed by various brain regions in a complex manner, among which the basal ganglia, including the striatum and subthalamic nucleus (STN), play central roles. However, the precise mechanism for processing sense of time has not been clarified. To examine the role of the STN in temporal processing of the sense of time by directly manipulating STN function by switching a deep brain stimulation (DBS) device On/Off in 28 patients with Parkinson's disease undergoing STN-DBS therapy. The test session was performed approximately 20 min after switching the DBS device from On to Off or from Off to On. Temporal sense processing was assessed in three different tasks (time reproduction, time production, and bisection). In the three temporal cognitive tasks, switching STN-DBS to Off caused shorter durations to be produced compared with the switching to the On condition in the time production task. In contrast, no effect of STN-DBS was observed in the time bisection or time reproduction tasks. These findings suggest that the STN is involved in the representation process of time duration and that the role of the STN in the sense of time may be limited to the exteriorization of memories formed by experience.

Temporal scaling and computing time in neural circuits: Should we stop watching the clock and look for its gears?

Timing underlies a variety of functions, from walking to perceiving causality. Neural timing models typically fall into one of two categories-"ramping" and "population-clock" theories. According to ramping models, individual neurons track time by gradually increasing or decreasing their activity as an event approaches. To time different intervals, ramping neurons adjust their slopes, ramping steeply for short intervals and vice versa. In contrast, according to "population-clock" models, multiple neurons track time as a group, and each neuron can fire nonlinearly. As each neuron changes its rate at each point in time, a distinct pattern of activity emerges across the population. To time different intervals, the brain learns the population patterns that coincide with key events. Both model categories have empirical support. However, they often differ in plausibility when applied to certain behavioral effects. Specifically, behavioral data indicate that the timing system has a rich computational capacity, allowing observers to spontaneously compute novel intervals from previously learned ones. In population-clock theories, population patterns map to time arbitrarily, making it difficult to explain how different patterns can be computationally combined. Ramping models are viewed as more plausible, assuming upstream circuits can set the slope of ramping neurons according to a given computation. Critically, recent studies suggest that neurons with nonlinear firing profiles often scale to time different intervals-compressing for shorter intervals and stretching for longer ones. This "temporal scaling" effect has led to a hybrid-theory where, like a population-clock model, population patterns encode time, yet like a ramping neuron adjusting its slope, the speed of each neuron's firing adapts to different intervals. Here, we argue that these "relative" population-clock models are as computationally plausible as ramping theories, viewing population-speed and ramp-slope adjustments as equivalent. Therefore, we view identifying these "speed-control" circuits as a key direction for evaluating how the timing system performs computations. Furthermore, temporal scaling highlights that a key distinction between different neural models is whether they propose an absolute or relative time-representation. However, we note that several behavioral studies suggest the brain processes both scales, cautioning against a dichotomy.

A perceptual glitch in serial perception generates temporal distortions

Precisely estimating event timing is essential for survival, yet temporal distortions are ubiquitous in our daily sensory experience. Here, we tested whether the relative position, duration, and distance in time of two sequentially-organized events-standard S, with constant duration, and comparison C, with duration varying trial-by-trial-are causal factors in generating temporal distortions. We found that temporal distortions emerge when the first event is shorter than the second event. Importantly, a significant interaction suggests that a longer inter-stimulus interval (ISI) helps to counteract such serial distortion effect only when the constant S is in the first position, but not if the unpredictable C is in the first position. These results imply the existence of a perceptual bias in perceiving ordered event durations, mechanistically contributing to distortion in time perception. We simulated our behavioral results with a Bayesian model and replicated the finding that participants disproportionately expand first-position dynamic (unpredictable) short events. Our results clarify the mechanisms generating time distortions by identifying a hitherto unknown duration-dependent encoding inefficiency in human serial temporal perception, something akin to a strong prior that can be overridden for highly predictable sensory events but unfolds for unpredictable ones.

Memory decay enhances central bias in time perception

Temporal expectations are essential for appropriately interacting with the environment, but they can be biased. This tendency, called central bias, places higher weights on expected rather than actual duration distributions when perceiving incoming sensory stimuli. In particular, the central bias is strengthened in order to decrease total response error when incoming sensory stimuli are unclear. In the present study, we investigated whether the central bias was enhanced via memory decay. For this, we used a delayed reproduction task, manipulating retention periods by introducing delays between the sample interval and the reproduction phase (0.4, 2, 4 s in Experiment 1; 0.4, 2, 8 s in Experiments 2 and 3). Through three experiments, we found the gradual strengthening of the central bias as a function of the retention period (i.e., short-term memory decay). This suggests that the integration of temporal expectation, generated from past trials and stored sensory stimuli, in a current trial occurs in the reproduction phase in the delayed reproduction task.

Mice make temporal inferences about novel locations based on previously learned spatiotemporal contingencies

Animals learn multiple spatiotemporal contingencies and organize their anticipatory responses accordingly. The representational/computational capacity that underlies such spatiotemporally guided behaviors is not fully understood. To this end, we investigated whether mice make temporal inferences of novel locations based on previously learned spatiotemporal contingencies. We trained 18 C57BL/6J mice to anticipate reward after three different intervals at three different locations and tested their temporal expectations of a reward at five locations simultaneously, including two locations that were not previously associated with reward delivery but adjacent to the previously trained locations. If mice made spatiotemporal inferences, they were expected to interpolate between duration pairs associated with previously reinforced hoppers surrounding the novel hopper. We found that the maximal response rate at the novel locations indeed fell between the two intervals reinforced at the surrounding hoppers. We argue that this pattern of responding might be underlain by spatially constrained Bayesian computations.

Revealing human sensitivity to a latent temporal structure of changes

Precisely timed behavior and accurate time perception plays a critical role in our everyday lives, as our wellbeing and even survival can depend on well-timed decisions. Although the temporal structure of the world around us is essential for human decision making, we know surprisingly little about how representation of temporal structure of our everyday environment impacts decision making. How does the representation of temporal structure affect our ability to generate well-timed decisions? Here we address this question by using a well-established dynamic probabilistic learning task. Using computational modeling, we found that human subjects' beliefs about temporal structure are reflected in their choices to either exploit their current knowledge or to explore novel options. The model-based analysis illustrates a large within-group and within-subject heterogeneity. To explain these results, we propose a normative model for how temporal structure is used in decision making, based on the semi-Markov formalism in the active inference framework. We discuss potential key applications of the presented approach to the fields of cognitive phenotyping and computational psychiatry.

Mental control of uncertainty

Can you reduce uncertainty by thinking? Intuition suggests that this happens through the elusive process of attention: if we expend mental effort, we can increase the reliability of our sensory data. Models based on "rational inattention" formalize this idea in terms of a trade-off between the costs and benefits of attention. This paper surveys the origin of these models in economics, their connection to rate-distortion theory, and some of their recent applications to psychology and neuroscience. We also report new data from a numerosity judgment task in which we manipulate performance incentives. Consistent with rational inattention, people are able to improve performance on this task when incentivized, in part by increasing the reliability of their sensory data.

Perceptual confidence of visual stimulus features is associated with duration perception

It has been shown that the perceived duration of an object in the subsecond range is closely associated with its nontemporal perceptual properties, the mechanism under which remains unclear. Previous studies have revealed a modulatory effect of early visual feature processing on the apparent duration. Here, we further examined the relationship between perceptual confidence and subjective time by asking participants to simultaneously perform temporal and nontemporal perceptual judgments. The results revealed a significant effect on confidence levels. When participants' confidence in judging the coherent motion direction or relative dot numerosity increases, their perceived duration of the stimulus also appears longer. These results are discussed in the context of perceptual evidence accumulation and evaluation for the decision-making of perceptual properties. They suggest a profound contribution of object processing to the computation of subjective time and provide further insights into the mechanism of event timing.

A virtual reality time reproduction task for rodents

Estimates of the duration of time intervals and other magnitudes exhibit characteristic biases that likely result from error minimization strategies. To investigate such phenomena, magnitude reproduction tasks are used with humans and other primates. However, such behavioral tasks do not exist for rodents, one of the most important animal orders for neuroscience. We, therefore, developed a time reproduction task that can be used with rodents. It involves an animal reproducing the duration of a timed visual stimulus by walking along a corridor. The task was implemented in virtual reality, which allowed us to ensure that the animals were actually estimating time. The hallway did not contain prominent spatial cues and movement could be de-correlated from optic flow, such that the animals could not learn a mapping between stimulus duration and covered distance. We tested the reproduction of durations of several seconds in three different stimulus ranges. The gerbils reproduced the durations with a precision similar to experiments on humans. Their time reproductions also exhibited the characteristic biases of magnitude estimation experiments. These results demonstrate that our behavioral paradigm provides a means to study time reproduction in rodents.

Contraction bias in temporal estimation

When asked to compare the perceptual features of two serially presented objects, participants are often biased to over- or under-estimate the difference in magnitude between the stimuli. Overestimation occurs consistently when a) the two stimuli are relatively small in magnitude and the first stimulus is larger in magnitude than the second; or b) the two stimuli are relatively large in magnitude and the first stimulus is smaller in magnitude than the second; underestimation consistently occurs in the complementary cases. This systematic perceptual bias, known as the contraction bias, was demonstrated for a multitude of perceptual features and in various modalities. Here, we tested whether estimation of time-duration is affected by the contraction bias. In each trial of three experiments (n = 20 each), participants compared the duration of two visually presented stimuli. Findings revealed over- and under-estimation effects as predicted by the contraction bias. Here, we discuss this asymmetry and describe how these findings can be explained via a Bayesian inference framework.

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.

Individual beliefs about temporal continuity explain variation of perceptual biases

Perception of magnitudes such as duration or distance is often found to be systematically biased. The biases, which result from incorporating prior knowledge in the perceptual process, can vary considerably between individuals. The variations are commonly attributed to differences in sensory precision and reliance on priors. However, another factor not considered so far is the implicit belief about how successive sensory stimuli are generated: independently from each other or with certain temporal continuity. The main types of explanatory models proposed so far-static or iterative-mirror this distinction but cannot adequately explain individual biases. Here we propose a new unifying model that explains individual variation as combination of sensory precision and beliefs about temporal continuity and predicts the experimentally found changes in biases when altering temporal continuity. Thus, according to the model, individual differences in perception depend on beliefs about how stimuli are generated in the world.

Inducing Cortical Plasticity to Manipulate and Consolidate Subjective Time Interval Production

OBJECTIVES

Time awareness may change depending on the mental state or disease conditions, although each individual perceives his/her own sense of time as stable and accurate. Nevertheless, the processes that consolidate altered duration production remain unclear. The present study aimed to manipulate the subjective duration production via memory consolidation through the modulation of neural plasticity.

MATERIALS AND METHODS

We first performed false feedback training of duration or length production and examined the period required for natural recovery from the altered production. Next, persistent neural plasticity was promoted by quadripulse transcranial magnetic stimulation (QPS) over the right dorsolateral prefrontal cortex (DLPFC), temporoparietal junction (TPJ), and primary motor cortex (M1). We conducted the same feedback training in the individual and studied how the time course of false learning changed.

RESULTS

We observed that altered duration production after false feedback returned to baseline within two hours. Next, immediate exposure to false feedback during neural plasticity enhancement revealed that in individuals who received QPS over the right DLPFC, but not over TPJ or M1, false duration production was maintained for four hours; furthermore, the efficacy persisted for at least one week.

CONCLUSION

These findings suggest that, while learned altered duration production decays over several hours, QPS over the right DLPFC enables the consolidation of newly learned duration production.

Influence of Motor and Cognitive Tasks on Time Estimation

The passing of time can be precisely measured by using clocks, whereas humans’ estimation of temporal durations is influenced by many physical, cognitive and contextual factors, which distort our internal clock. Although it has been shown that temporal estimation accuracy is impaired by non-temporal tasks performed at the same time, no studies have investigated how concurrent cognitive and motor tasks interfere with time estimation. Moreover, most experiments only tested time intervals of a few seconds. In the present study, participants were asked to perform cognitive tasks of different difficulties (look, read, solve simple and hard mathematical operations) and estimate durations of up to two minutes, while walking or sitting. The results show that if observers pay attention only to time without performing any other mental task, they tend to overestimate the durations. Meanwhile, the more difficult the concurrent task, the more they tend to underestimate the time. These distortions are even more pronounced when observers are walking. Estimation biases and uncertainties change differently with durations depending on the task, consistent with a fixed relative uncertainty. Our findings show that cognitive and motor systems interact non-linearly and interfere with time perception processes, suggesting that they all compete for the same resources.

Impulsivity and risk-seeking as Bayesian inference under dopaminergic control

Bayesian models successfully account for several of dopamine (DA)'s effects on contextual calibration in interval timing and reward estimation. In these models, tonic levels of DA control the precision of stimulus encoding, which is weighed against contextual information when making decisions. When DA levels are high, the animal relies more heavily on the (highly precise) stimulus encoding, whereas when DA levels are low, the context affects decisions more strongly. Here, we extend this idea to intertemporal choice and probability discounting tasks. In intertemporal choice tasks, agents must choose between a small reward delivered soon and a large reward delivered later, whereas in probability discounting tasks, agents must choose between a small reward that is always delivered and a large reward that may be omitted with some probability. Beginning with the principle that animals will seek to maximize their reward rates, we show that the Bayesian model predicts a number of curious empirical findings in both tasks. First, the model predicts that higher DA levels should normally promote selection of the larger/later option, which is often taken to imply that DA decreases 'impulsivity,' and promote selection of the large/risky option, often taken to imply that DA increases 'risk-seeking.' However, if the temporal precision is sufficiently decreased, higher DA levels should have the opposite effect-promoting selection of the smaller/sooner option (higher impulsivity) and the small/safe option (lower risk-seeking). Second, high enough levels of DA can result in preference reversals. Third, selectively decreasing the temporal precision, without manipulating DA, should promote selection of the larger/later and large/risky options. Fourth, when a different post-reward delay is associated with each option, animals will not learn the option-delay contingencies, but this learning can be salvaged when the post-reward delays are made more salient. Finally, the Bayesian model predicts correlations among behavioral phenotypes: Animals that are better timers will also appear less impulsive.

Phrase Depicting Immoral Behavior Dilates Its Subjective Time Judgment

Intuitive moral emotions play a major role in forming our opinions and moral decisions. However, it is not yet known how we perceive the subjective time of moral-related information. In this study, we compared subjective durations of phrases depicting immoral, disgust, or neutral behaviors in a duration bisection task and found that phrases depicting immoral behavior were perceived as lasting longer than the neutral and disgusting phrases. By contrast, the subjective duration of the disgusting phrase, unlike the immoral phrase, was comparable to the neutral phrase. Moreover, the lengthening effect of the immoral phrase relative to the neutral phrase was significantly correlated to the anonymously prosocial tendency of the observer. Our findings suggest that immoral phrases induce embodied moral reaction, which alters emotional state and subsequently lengthens subjective time.

Distributed coding of duration in rodent prefrontal cortex during time reproduction

As we interact with the external world, we judge magnitudes from sensory information. The estimation of magnitudes has been characterized in primates, yet it is largely unexplored in nonprimate species. Here, we use time interval reproduction to study rodent behavior and its neural correlates in the context of magnitude estimation. We show that gerbils display primate-like magnitude estimation characteristics in time reproduction. Most prominently their behavioral responses show a systematic overestimation of small stimuli and an underestimation of large stimuli, often referred to as regression effect. We investigated the underlying neural mechanisms by recording from medial prefrontal cortex and show that the majority of neurons respond either during the measurement or the reproduction of a time interval. Cells that are active during both phases display distinct response patterns. We categorize the neural responses into multiple types and demonstrate that only populations with mixed responses can encode the bias of the regression effect. These results help unveil the organizing neural principles of time reproduction and perhaps magnitude estimation in general.

The Spread of the Lengthening Time Effect of Emotions in Memory: A Test in the Setting of the Central Tendency Effect

The aim of the present study was to test how the perception of an emotional stimulus colors the temporal context of judgment and modifies the participant's perception of the current neutral duration. Participants were given two ready-set-go tasks consisting of a distribution of short (0.5-0.9 s) or long sample intervals (0.9-1.3 s) with an overlapping 0.9-s interval. Additional intervals were introduced in the temporal distribution. These were neutral for the two temporal tasks in a control condition and emotional for the short, but not the long temporal task in an emotion condition. The results indicated a replication of a kind of Vierordt's law in the control condition, i.e., the temporal judgment toward the mean of the distribution of sample intervals (central tendency effect). However, there was a shift in the central tendency effect in the emotion condition indicating a general bias in the form of an overestimation of current intervals linked to the presence of a few emotional stimuli among the previous intervals. This finding is entirely consistent with timing mechanisms driven by prior duration context, particularly experience of prior emotional duration.

Medial Entorhinal Cortex Excitatory Neurons Are Necessary for Accurate Timing

The hippocampal region has long been considered critical for memory of time, and recent evidence shows that network operations and single-unit activity in the hippocampus and medial entorhinal cortex (MEC) correlate with elapsed time. However, whether MEC activity is necessary for timing remains largely unknown. Here we expressed DREADDs (designer receptors exclusively activated by designer drugs) under the CaMKIIa promoter to preferentially target MEC excitatory neurons for chemogenetic silencing, while freely moving male rats reproduced a memorized time interval by waiting inside a region of interest. We found that such silencing impaired the reproduction of the memorized interval and led to an overestimation of elapsed time. Trial history analyses under this condition revealed a reduced influence of previous trials on current waiting times, suggesting an impairment in maintaining temporal memories across trials. Moreover, using GLM (logistic regression), we show that decoding behavioral performance from preceding waiting times was significantly compromised when MEC was silenced. In addition to revealing an important role of MEC excitatory neurons for timing behavior, our results raise the possibility that these neurons contribute to such behavior by holding temporal information across trials.SIGNIFICANCE STATEMENT Medial temporal lobe (MTL) structures are implicated in processing temporal information. However, little is known about the role MTL structures, such as the hippocampus and the entorhinal cortex, play in perceiving or reproducing temporal intervals. By chemogenetically silencing medial entorhinal cortex (MEC) excitatory activity during a timing task, we show that this structure is necessary for the accurate reproduction of temporal intervals. Furthermore, trial history analyses suggest that silencing MEC disrupts memory mechanisms during timing. Together, these results suggest that MEC is necessary for timing behavior, possibly by representing the target interval in memory.

Neural implementations of Bayesian inference

Bayesian inference has emerged as a general framework that captures how organisms make decisions under uncertainty. Recent experimental findings reveal disparate mechanisms for how the brain generates behaviors predicted by normative Bayesian theories. Here, we identify two broad classes of neural implementations for Bayesian inference: a modular class, where each probabilistic component of Bayesian computation is independently encoded and a transform class, where uncertain measurements are converted to Bayesian estimates through latent processes. Many recent experimental neuroscience findings studying probabilistic inference broadly fall into these classes. We identify potential avenues for synthesis across these two classes and the disparities that, at present, cannot be reconciled. We conclude that to distinguish among implementation hypotheses for Bayesian inference, we require greater engagement among theoretical and experimental neuroscientists in an effort that spans different scales of analysis, circuits, tasks, and species.

The rhythm aftereffect induced by adaptation to the decelerating rhythm

Rhythm perception can be distorted following prolonged exposure to an isochronous rhythm. It has been suggested that this might arise from the neural adaptation of temporal interval selective neurons. However, the rhythm in our daily life is not always isochronous, and the mechanism that rules the anisochronous rhythm is unclear. Here, we used a sensory adaptation paradigm to investigate whether rhythm perception can be affected by adaptation to the anisochronous rhythm. In Experiments 1 and 2, the direction of tempo change (accelerating vs. decelerating) judgment task and the rhythmic isochronism (isochronous vs. anisochronous) judgment task were used to evaluate participants' perception of rhythms, respectively. We found that after adaptation to a decelerating rhythm, participants tended to perceive the subsequent isochronous rhythm as accelerating. In Experiment 3, visual test rhythms followed the auditory adapting rhythm. In this situation, we did not find any adaptation effects on subsequent rhythm perception. Our results suggest that adaptation to the decelerating rhythm can induce a modality-specific rhythm aftereffect, which is consistent with the temporal order contingent duration aftereffect. It implies a unified timing mechanism for duration and rhythm perception.

Conceptually plausible Bayesian inference in interval timing

In a world that is uncertain and noisy, perception makes use of optimization procedures that rely on the statistical properties of previous experiences. A well-known example of this phenomenon is the central tendency effect observed in many psychophysical modalities. For example, in interval timing tasks, previous experiences influence the current percept, pulling behavioural responses towards the mean. In Bayesian observer models, these previous experiences are typically modelled by unimodal statistical distributions, referred to as the prior. Here, we critically assess the validity of the assumptions underlying these models and propose a model that allows for more flexible, yet conceptually more plausible, modelling of empirical distributions. By representing previous experiences as a mixture of lognormal distributions, this model can be parametrized to mimic different unimodal distributions and thus extends previous instantiations of Bayesian observer models. We fit the mixture lognormal model to published interval timing data of healthy young adults and a clinical population of aged mild cognitive impairment patients and age-matched controls, and demonstrate that this model better explains behavioural data and provides new insights into the mechanisms that underlie the behaviour of a memory-affected clinical population.

The origin of Vierordt's law: The experimental protocol matters

In 1868, Karl Vierordt discovered one type of errors in time perception-an overestimation of short duration and underestimation of long durations, known as Vierordt's law. Here we reviewed the original study in its historical context and asked whether Vierordt's law is a result of an unnatural experimental randomization protocol. Using iterative Bayesian updating, we simulated the original results with high accuracy. Importantly, the model also predicted that a slowly changing random-walk sequence produces less central tendency than a random sequence with the same durations. This was validated by a duration reproduction experiment from two sequences (random and random walk) with the same sampled distribution. The results showed that trial-wise variation influenced the magnitude of Vierordt's law. We concluded that Vierordt's law is caused by an unnatural yet widely used experimental protocol.

Temporal Context Actively Shapes EEG Signatures of Time Perception

Our subjective perception of time is optimized to temporal regularities in the environment. This is illustrated by the central tendency effect: When estimating a range of intervals, short intervals are overestimated, whereas long intervals are underestimated to reduce the overall estimation error. Most models of interval timing ascribe this effect to the weighting of the current interval with previous memory traces after the interval has been perceived. Alternatively, the perception of the duration could already be flexibly tuned to its temporal context. We investigated this hypothesis using an interval reproduction task in which human participants (both sexes) reproduced a shorter and longer interval range. As expected, reproductions were biased toward the subjective mean of each presented range. EEG analyses showed that temporal context indeed affected neural dynamics during the perception phase. Specifically, longer previous durations decreased contingent negative variation and P2 amplitude and increased beta power. In addition, multivariate pattern analysis showed that it is possible to decode context from the transient EEG signal quickly after both onset and offset of the perception phase. Together, these results suggest that temporal context creates dynamic expectations which actively affect the perception of duration.SIGNIFICANCE STATEMENT The subjective sense of duration does not arise in isolation, but is informed by previous experiences. This is demonstrated by abundant evidence showing that the production of duration estimates is biased toward previously experienced time intervals. However, it is yet unknown whether this temporal context actively affects perception or only asserts its influence in later, postperceptual stages as proposed by most current formal models of this task. Using an interval reproduction task, we show that EEG signatures flexibly adapt to the temporal context during perceptual encoding. Furthermore, interval history can be decoded from the transient EEG signal even when the current duration was identical. Thus, our results demonstrate that context actively influences perception.

Temporal Binding in Multisensory and Motor-Sensory Contexts: Toward a Unified Model

Our senses receive a manifold of sensory signals at any given moment in our daily lives. For a coherent and unified representation of information and precise motor control, our brain needs to temporally bind the signals emanating from a common causal event and segregate others. Traditionally, different mechanisms were proposed for the temporal binding phenomenon in multisensory and motor-sensory contexts. This paper reviews the literature on the temporal binding phenomenon in both multisensory and motor-sensory contexts and suggests future research directions for advancing the field. Moreover, by critically evaluating the recent literature, this paper suggests that common computational principles are responsible for the temporal binding in multisensory and motor-sensory contexts. These computational principles are grounded in the Bayesian framework of uncertainty reduction rooted in the Helmholtzian idea of unconscious causal inference.

A common dynamic prior for time in duration discrimination

Estimation of time depends heavily on both global and local statistical context. Durations that are short relative to the global distribution are systematically overestimated; durations that are locally preceded by long durations are also overestimated. Context effects are prominent in duration discrimination tasks, where a standard duration and a comparison duration are presented on each trial. In this study, we compare and test two models that posit a dynamically updating internal reference that biases time estimation on global and local scales in duration discrimination tasks. The internal reference model suggests that the internal reference operates during postperceptual stages and only interacts with the first presented duration. In contrast, a Bayesian account of time estimation implies that any perceived duration updates the internal reference and therefore interacts with both the first and second presented duration. We implemented both models and tested their predictions in a duration discrimination task where the standard duration varied from trial to trial. Our results are in line with a Bayesian perspective on time estimation. First, the standard systematically biased estimation of the comparison, such that shorter standards increased the likelihood of reporting that the comparison was shorter. Second, both the previous standard and comparison systematically biased time estimation of subsequent trials in the same direction. Third, more precise observers showed smaller biases. In sum, our findings suggest a common dynamic prior for time that is updated by each perceived duration and where the relative weighting of old and new observations is determined by their relative precision.

Rational inattention and tonic dopamine

Slow-timescale (tonic) changes in dopamine (DA) contribute to a wide variety of processes in reinforcement learning, interval timing, and other domains. Furthermore, changes in tonic DA exert distinct effects depending on when they occur (e.g., during learning vs. performance) and what task the subject is performing (e.g., operant vs. classical conditioning). Two influential theories of tonic DA-the average reward theory and the Bayesian theory in which DA controls precision-have each been successful at explaining a subset of empirical findings. But how the same DA signal performs two seemingly distinct functions without creating crosstalk is not well understood. Here we reconcile the two theories under the unifying framework of 'rational inattention,' which (1) conceptually links average reward and precision, (2) outlines how DA manipulations affect this relationship, and in so doing, (3) captures new empirical phenomena. In brief, rational inattention asserts that agents can increase their precision in a task (and thus improve their performance) by paying a cognitive cost. Crucially, whether this cost is worth paying depends on average reward availability, reported by DA. The monotonic relationship between average reward and precision means that the DA signal contains the information necessary to retrieve the precision. When this information is needed after the task is performed, as presumed by Bayesian inference, acute manipulations of DA will bias behavior in predictable ways. We show how this framework reconciles a remarkably large collection of experimental findings. In reinforcement learning, the rational inattention framework predicts that learning from positive and negative feedback should be enhanced in high and low DA states, respectively, and that DA should tip the exploration-exploitation balance toward exploitation. In interval timing, this framework predicts that DA should increase the speed of the internal clock and decrease the extent of interference by other temporal stimuli during temporal reproduction (the central tendency effect). Finally, rational inattention makes the new predictions that these effects should be critically dependent on the controllability of rewards, that post-reward delays in intertemporal choice tasks should be underestimated, and that average reward manipulations should affect the speed of the clock-thus capturing empirical findings that are unexplained by either theory alone. Our results suggest that a common computational repertoire may underlie the seemingly heterogeneous roles of DA.

Variation in the "coefficient of variation": Rethinking the violation of the scalar property in time-duration judgments

The coefficient of variation (CV), also known as relative standard deviation, has been used to measure the constancy of the Weber fraction, a key signature of efficient neural coding in time perception. It has long been debated whether or not duration judgments follow Weber's law, with arguments based on examinations of the CV. However, what has been largely ignored in this debate is that the observed CVs may be modulated by temporal context and decision uncertainty, thus questioning conclusions based on this measure. Here, we used a temporal reproduction paradigm to examine the variation of the CV with two types of temporal context: full-range mixed vs. sub-range blocked intervals, separately for intervals presented in the visual and auditory modalities. We found a strong contextual modulation of both interval-duration reproductions and the observed CVs. We then applied a two-stage Bayesian model to predict those variations. Without assuming a violation of the constancy of the Weber fraction, our model successfully predicted the central-tendency effect and the variation in the CV. Our findings and modeling results indicate that both the accuracy and precision of our timing behavior are highly dependent on the temporal context and decision uncertainty. And, critically, they advise caution with using variations of the CV to reject the constancy of the Weber fraction of duration estimation.

Stopwatch training improves cognitive functions in patients with Parkinson's disease

Parkinson's disease (PD) impairs various cognitive functions, including time perception. Dysfunctional time perception in PD is poorly understood, and no study has investigated the rehabilitation of time perception in patients with PD. We aimed to induce the recovery of time perception in PD patients and investigated the potential relationship between recovery and cognitive functions/domains other than time perception. Sixty patients with PD (27 females) and 20 healthy controls (10 females) were recruited. The participants underwent a feedback training protocol for 4 weeks to improve the accuracy of subjective spatial distance or time duration using a ruler or stopwatch, respectively. They participated in three tests at weekly intervals, each comprising 10 types of cognitive tasks and assessments. After duration feedback training for 1 month, performance on the Go/No-go task, Stroop task, and impulsivity assessment improved in patients with PD, while no effect was observed after distance feedback training. Additionally, the effect of training on duration production correlated with extended reaction time and improved accuracy in the Go/No-go and Stroop tasks. These findings suggest that time perception is functionally linked to inhibitory systems. If the feedback training protocol can modulate and maintain time perception, it may improve various cognitive/psychiatric functions in patients with PD. It may also be useful in the treatment of diseases other than PD that cause dysfunctions in temporal processing.

Dissociable neural indices for time and space estimates during virtual distance reproduction

The perception and measurement of spatial and temporal dimensions have been widely studied. Yet, whether these two dimensions are processed independently is still being debated. Additionally, whether EEG components are uniquely associated with time or space, or whether they reflect a more general measure of magnitude quantity remains unknown. While undergoing EEG, subjects performed a virtual distance reproduction task, in which they were required to first walk forward for an unknown distance or time, and then reproduce that distance or time. Walking speed was varied between estimation and reproduction phases, to prevent interference between distance or time in each estimate. Behaviorally, subject performance was more variable when reproducing time than when reproducing distance, but with similar patterns of accuracy. During estimation, EEG data revealed the contingent negative variation (CNV), a measure previously associated with timing and expectation, tracked the probability of the upcoming interval, for both time and distance. However, during reproduction, the CNV exclusively oriented to the upcoming temporal interval at the start of reproduction, with no change across spatial distances. Our findings indicate that time and space are neurally separable dimensions, with the CNV both serving a supramodal role in temporal and spatial expectation, yet an exclusive role in preparing duration reproduction.

Temporal bisection is influenced by ensemble statistics of the stimulus set

Although humans are well capable of precise time measurement, their duration judgments are nevertheless susceptible to temporal context. Previous research on temporal bisection has shown that duration comparisons are influenced by both stimulus spacing and ensemble statistics. However, theories proposed to account for bisection performance lack a plausible justification of how the effects of stimulus spacing and ensemble statistics are actually combined in temporal judgments. To explain the various contextual effects in temporal bisection, we develop a unified ensemble-distribution account (EDA), which assumes that the mean and variance of the duration set serve as a reference, rather than the short and long standards, in duration comparison. To validate this account, we conducted three experiments that varied the stimulus spacing (Experiment 1), the frequency of the probed durations (Experiment 2), and the variability of the probed durations (Experiment 3). The results revealed significant shifts of the bisection point in Experiments 1 and 2, and a change of the sensitivity of temporal judgments in Experiment 3-which were all well predicted by EDA. In fact, comparison of EDA to the extant prior accounts showed that using ensemble statistics can parsimoniously explain various stimulus set-related factors (e.g., spacing, frequency, variance) that influence temporal judgments.

Statistical Learning Model of the Sense of Agency

A sense of agency (SoA) is the experience of subjective awareness regarding the control of one's actions. Humans have a natural tendency to generate prediction models of the environment and adapt their models according to changes in the environment. The SoA is associated with the degree of the adaptation of the prediction models, e.g., insufficient adaptation causes low predictability and lowers the SoA over the environment. Thus, identifying the mechanisms behind the adaptation process of a prediction model related to the SoA is essential for understanding the generative process of the SoA. In the first half of the current study, we constructed a mathematical model in which the SoA represents a likelihood value for a given observation (sensory feedback) in a prediction model of the environment and in which the prediction model is updated according to the likelihood value. From our mathematical model, we theoretically derived a testable hypothesis that the prediction model is updated according to a Bayesian rule or a stochastic gradient. In the second half of our study, we focused on the experimental examination of this hypothesis. In our experiment, human subjects were repeatedly asked to observe a moving square on a computer screen and press a button after a beep sound. The button press resulted in an abrupt jump of the moving square on the screen. Experiencing the various stochastic time intervals between the action execution (button-press) and the consequent event (square jumping) caused gradual changes in the subjects' degree of their SoA. By comparing the above theoretical hypothesis with the experimental results, we concluded that the update (adaptation) rule of the prediction model based on the SoA is better described by a Bayesian update than by a stochastic gradient descent.

Numerical averaging in mice

Rodents can be trained to associate different durations with different stimuli (e.g., light/sound). When the associated stimuli are presented together, maximal responding is observed around the average of individual durations (akin to averaging). The current study investigated whether mice can also average independently trained numerosities. Mice were initially trained to make 10 or 20 lever presses on a single (run) lever to obtain a reward and each fixed-ratio schedule was signaled either with an auditory or visual stimulus. Then, mice were trained to press another lever to obtain the reward after they responded on the run lever for the minimum number of presses [Fixed Consecutive Number (FCN)-10 or -20 trials] signaled by the corresponding discriminative stimulus. Following this training, FCN trials with the compound stimulus were introduced to test the counting behavior of mice when they encountered conflicting information regarding the number of responses required to obtain the reward. Our results showed that the numbers of responses on these compound test trials were around the average of the number of responses in FCN-10 and FCN-20 trials particularly when the auditory stimulus was associated with a fewer number of required responses. The counting strategy explained the behavior of the majority of the mice in the FCN-Compound test trials (as opposed to the timing strategy). The number of responses in FCN-Compound trials was accounted for equally well by the arithmetic, geometric, and Bayesian averages of the number of responses observed in FCN-10 and FCN-20 trials.