Time Perception: A Review on Psychological, Computational and Robotic Models
TTime Perception: A Review on Psychological, Computational andRobotic Models
Hamit Basgol , Inci Ayhan , Emre Ugur Department of Cognitive Science, Bogazici University Department of Psychology, Bogazici University Department of Computer Engineering, Bogazici University
Animals exploit time to survive in the world. Temporal information is required for higher-levelcognitive abilities such as planning, decision making, communication and e ff ective coopera-tion. Since time is an inseparable part of cognition, there is a growing interest in the artificialintelligence approach to subjective time, which has a possibility of advancing the field. Thecurrent survey study aims to provide researchers with an interdisciplinary perspective on timeperception. Firstly, we introduce a brief background from the psychology and neuroscienceliterature, covering the characteristics and models of time perception and the related abilities.Secondly, we summarize the emergent computational and robotic models of time perception. Ageneral overview to the literature reveals that a substantial amount of timing models are basedon a dedicated time processing like the emergence of a clock-like mechanism from the neuralnetwork dynamics and reveal a relationship between the embodiment and time perception. Wealso notice that most models of timing are developed for either sensory timing (i.e. the ability ofassessment of an interval) or motor timing (i.e. ability to reproduce an interval). The number oftiming models capable of retrospective timing, which is the ability to track time without payingattention, is insu ffi cient. In this light, we discuss the possible research directions to promoteinterdisciplinary collaboration for time perception. Introduction
Time, according to Kant (Burnham & Young, 2007), alongwith space, is a main parameter constituting the possibilityof knowledge. Since time conveys information regardingthe current and future state of the environment, biologicalsystems can organize their functions, behaviors, and cogni-tive abilities according to temporal information (Mihailovi´c,Balaž, & Kapor, 2017). It was shown that a wide range ofanimals is capable of time-place learning which is the abil-ity to associate the subjective place and time for the avoid-ance from predators, localization of resources, and there-fore, gaining a survival advantage (Mulder, Gerkema, & derZee, 2013). Moreover, it was found that vertebrates havingsmaller bodies and higher metabolic rates perceive time pass-ing slower in comparison to ones having larger bodies andlower metabolic rates because perceiving in higher temporalresolution poses an energetic cost (Healy, McNally, Ruxton,
Hamit Basgol, [email protected] Ayhan, [email protected] Ugur, [email protected]
Cooper, & Jackson, 2013). The di ff erence in subjective timeperception as a function of body size and metabolic rate af-fects the amount of saved energy, and accordingly, providesa survival advantage to animals (Healy et al., 2013). Thesefindings are not surprising because we know that animalsnavigate not only in space but also in time in order to showrobust and adaptive behaviors. Thus, it can be concluded thatanimals do not live in a three-dimensional world but rather ina four-dimensional one, involving time.Animals are robust and adaptive biological systems. Fromthis perspective, according to Pfeifer, Lungarella, and Iida(2007), understanding the mechanisms underlying the bio-logical processes might be a source of inspiration for devel-oping robust and adaptive systems to environmental changesand perturbations. In this light, embodied artificial intelli-gence takes inspiration from biological systems and their in-teractions with their environment. Studying how biologicalsystems acquire temporal information and how they use itto sca ff old sensory, motor, and cognitive processes is an es-sential topic for further research in embodied artificial in-telligence, cognitive robotics and computational psychology.This type of research might reveal two positive outcomes.The first outcome is the exploitation of temporal informationby artificial intelligence systems. As emphasized by Mani-adakis and Trahanias (2011) and Maniadakis, Wittmann, and a r X i v : . [ c s . A I] A ug HAMIT BASGOL , INCI AYHAN , EMRE UGUR Encoding TypeModality Type
Time Perception in Natural Cognitive Systems
Sensory TimingMotor TimingProspective TimingRetrospective Timing
Models
Algorithmic LevelImplementationallevel Dedicated ModelsIntrinsic ModelsInternal Clock Theory
Abilities Characteristics
Multi-modalityMultiple TimescalesScalar Property
Relationships
ActionDecision MakingLanguageMagnitudes Pacemaker-accumulator ModelsMultiple-oscillator Models
Figure 1 . A mind map for natural cognitive systems of timeperceptionTrahanias (2011), the use of temporal information in artificialsystems has been limited, although it is necessary to developintelligent systems that e ffi ciently interact with their environ-ments. For example, in human-robot interaction scenarios,intentions of agents’ behaviors and their causes are not di-rectly observable. Think about a shared work-space where arobot should collaborate with di ff erent human partners, eachwith di ff erent working styles. Even though it is the very task,some people might operate in a rush because of perceivedtime pressure or a personality trait. The di ff erentiation be-tween these two possibilities requires the acquisition of finetemporal dynamics of behaviors. Therefore, the value of thistype of knowledge is tremendous for autonomous systems.On the other hand, time perception tasks in animal and hu-man timing can be utilized to figure out whether algorithmsdeveloped by artificial intelligence researchers can exploittemporal information and, if they can, how these algorithmsachieve this ability (Deverett, Faulkner, Fortunato, Wayne, &Leibo, 2019).The second outcome of studying how biological systemscomputationally use temporal information is obtaining plau-sible hypotheses and remarkable insights about the timeperception mechanisms in biological systems (Addyman,French, & Thomas, 2016; Deverett et al., 2019; N. F. Hardy& Buonomano, 2016; Maniadakis et al., 2011). In fact, thereis a growing interest in developing computational and roboticmodels that can use temporal information (Addyman et al.,2016; Deverett et al., 2019; Duran & Sandamirskaya, 2017;Hourdakis & Trahanias, 2018; Koskinopoulou, Maniadakis,& Trahanias, 2018; Maniadakis & Trahanias, 2012a, 2014,2015; Maniadakis et al., 2011; Roseboom et al., 2019). Areview study integrating knowledge about time perceptionacross all disciplines, including psychology, cognitive sci-ence, neuroscience and artificial intelligence, on the otherhand, seems to be lacking. Thus, here, we report recent find-ings in the literature and discuss possible research directionsto promote interdisciplinary collaboration in the future. Duration ReproductionEmergentModelsCognitiveModels
Computational andRobotic Models ofTime Perception
ACT-RSOAR Disembodied Emergent Models
ModelingApproach Skills, Tasks,Properties
SensoryTimingMotorTimingOther Robotic Models
Text
Intrinsic Models Duration ComparisonDedicated ModelsEmbodiedEmergent Models
Methods,Principles,Approaches
Reinforcement LearningPerceptual ContentEvolutionary OptimizationMemory DecayDynamic-Neural FieldsState-DependentNetworksOscillationsPopulation ClocksPacemaker-Accumulator RetrospectiveTimingProspectiveTiming TemporalRecallTemporalPrediction
Figure 2 . A mind map for computational and robotic modelsof time perceptionThis review study is composed of three sections. In thefirst section, we briefly discuss the necessary concepts re-garding the use and processing of temporal information innatural cognitive systems (see mind map in Figure 1). In sec-tion two, we investigate the computational and robotic mod-els of time perception. We categorize these models into twogroups, namely cognitive and emergent models, and limit ourdiscussion to the emergent models of time perception (seemind map in Figure 2). In the final section, we make a gen-eral discussion regarding the current status of the literatureand present a set of possible research questions.
Time Perception in Natural Cognitive Systems
Here we briefly discuss the distinguishing characteristicsof time perception in animals, including humans. We thenelaborate on the classical time perception models explain-ing how animals use temporal information. Additionally, weemphasize the connection between time and other cognitiveabilities and the maturation of time perception throughout thedevelopment. These topics will help us to refine our discus-sion about computational and robotic models of time percep-tion.
Characteristics of Time PerceptionMulti-modality of time perception.
Time perceptionhas several distinguishing characteristics. One characteris-tic of time perception is that subjective time perception isformed by the interaction between di ff erent sensory modal-ities (Bausenhart, de la Rosa, & Ulrich, 2014; Vroomen &Keetels, 2010). For example, think about a person talkingon TV. Physically, mouth movements and language are outof sync; however, we perceive them as if they happen at thesame time. This phenomenon is called the temporal ventril-oquism (Bausenhart et al., 2014) and shows the fact that timeperception is multi-modal . IME PERCEPTION Timescales of time perception.
Animals can use tem-poral information in di ff erent timescales. For this reason,time perception is investigated in at least four timescales,namely microsecond timing , millisecond timing , second tim-ing and circadian timing , each of which contributes to dif-ferent abilities in organisms’ lives (Buhusi & Meck, 2005).For example, it was shown that timing up to millisecondsis crucial for producing speech (Schirmer, 2004) and mo-tor control (Sober, Sponberg, Nemenman, & Ting, 2018),whereas timing between seconds to minutes is essential forworking memory maintenance (Brody, Hernández, Zainos,& Romo, 2003) and the production of action sequences (Bor-toletto, Cook, & Cunnington, 2011). Controlling the sleep-wake cycle and metabolism, circadian timing depends onthe day-night cycle (Buhusi & Meck, 2005; Czeisler et al.,1999). The literature for each timescale is very detailed andcannot be covered in a single review study. For the sake ofbrevity, we restrict our discussion to milliseconds-to-secondsand seconds-to-hours. The scalar property of time perception.
An interest-ing feature of the perceptual discrimination is that it dependson the ratio between two values, which is called the
Weber’slaw . Weber’s law is seen in quantity discrimination in di ff er-ent domains such as number, length, and duration and revealsitself as a scalar property in duration discrimination (see Fig-ure 3) (Matell & Meck, 2004). The scalar property defines astrict mathematical relationship between the estimations (tar-get duration) and the interval being estimated (standard dura-tion). It refers to the fact that as the duration to be estimatedincreases, the deviation of estimations from the standard du-ration increases linearly . For the scalar property, “the stan-dard deviations of time estimates grow as a constant fractionof the mean,” (Ferrara, Lejeune, & Wearden, 1997, p. 218)meaning that the coe ffi cient of variation statistic (standarddeviation / mean or CV) remains constant. This property hasbeen observed in duration estimation performances of severalanimals such as rats and pigeons (Buhusi et al., 2009; Leje-une & Wearden, 2006; Malapani & Fairhurst, 2002). Forvery short ( <
100 ms) and long durations ( >
100 s) and inparticular for the challenging tasks, on the other hand, devia-tions from the scalar property have also been observed (Leje-une & Wearden, 2006). For instance, Ferrara et al. (1997)conducted a study with two conditions in which participantswere to detect whether the target duration is the same as thestandard duration (see 3). For the easy condition, target du-rations were set to be around 600 ms with 150 ms increments(150, 300, 450, , 750, 900, 1050), whereas for the hardcondition, with smaller increments (75 ms) (375, 450, 525, , 675, 750, 825). Surprisingly, the group in the hard con-dition was more sensitive to the di ff erence in the two stimulusdurations than that in the easy condition. These result sug-gest that the sensitivity of the timing system varies accord-ing to the discrimination di ffi culty of two temporal intervals. This contradicts with the scalar property, predicting the samesensitivity rate for all temporal discriminations.Despite its distinguishing characteristics, the ability totime is not isolated. In fact, it sca ff olds other perceptual,motor and cognitive processes. In the next section, we willtry to shed light on the relationship between time perceptionand other cognitive abilities. Time perception and related cognitive abilities.
Timehas an important role in performing actions. It was foundthat the duration between action execution and the expectedsensory input a ff ects the sense of agency (Stetson, Cui, Mon-tague, & Eagleman, 2006), which in turn a ff ects the per-ceived duration in between (Haggard, Clark, & Kalogeras,2002; Moore & Obhi, 2012). The former was observedin the sensory-motor temporal calibration paradigm , whilethe latter evidence was observed in the intentional bind-ing paradigm . In the sensory-motor temporal recalibrationparadigm, researchers put an artificial lag between a buttonpress (action) and a beep sound (e ff ect). After the training,the lag between the action and the e ff ect is removed and par-ticipants start perceiving as if the e ff ect occurred before theaction (Stetson et al., 2006). An opposite e ff ect was seenin the intentional binding paradigm . When people think thatthey are responsible for the e ff ect, they perceive that the dura-tion between the button pressing (action) and the beep sound(e ff ect) is closer than they actually are (Haggard et al., 2002;Moore & Obhi, 2012). These two paradigms show that timeplays a role in forming the sense of agency and connectingthe action (cause) and e ff ect into one another.In addition to the binding of an action and its e ff ect, timeis a property that people consider in decision making (Klap-proth, 2008). For example, the classical tasks shown in Fig-ure 4A and Figure 4B require the ability of making decisionby estimating time. Time is also important for decision mak-ing in a real-world context, which can be seen in Figure 4E.In their seminal work, Leclerc, Schmitt, and Dube (1995)showed that people tend to decide for events whose durationsare certain rather than suspicious. It is also important to notethat time determines the value of outcomes. In fact, for anagent, immediate and delayed outcomes do not have the samevalue, which is called the temporal discounting (Critchfield& Kollins, 2001). It is believed that this a personality traita ff ecting people’s ability to make long-term plans (Simons,Vansteenkiste, Lens, & Lacante, 2004).Investigating the connection between language and timeperception, J. Wearden (2008) focused on the speech con-trol and metaphor comprehension. The former is an exam-ple of how time perception a ff ects language understandingand use and the latter is an example of how language af-fects perceiving time. The research suggested that durationdiscrimination problems in speech result in speech percep-tion and production problems (Tallal, 2004); children hav-ing poor reading abilities also have poor temporal judgment HAMIT BASGOL , INCI AYHAN , EMRE UGUR Figure 3 . The figure is adapted from (J. Wearden, Denovan, & Haworth, 1997) and shows an abstract depiction of scalarproperty. In a temporal generalization task , animals receive a standard and a target stimulus and are trained to press yes whenthe standard stimulus is the same as the target stimulus. In the figure, di ff erent experimental groups (standard stimulus witha duration of 2, 4, 6, and 8 seconds) are given in the x-axis. (A) The maximum proportion of yes responses is convergedto the real duration and the variance of the proportion of yes responses increases as the duration to be estimated increases.(B) Moreover, the increase in variance is linearly proportional to the estimated duration. This is the scalar property of timeperception.capabilities (May, Williams, & Dunlap, 1988) and train-ing for temporal discrimination improves phonetic identifi-cation (Szymaszek, Dacewicz, Urban, & Szelag, 2018). Itis also claimed that language determines how we perceivetime. Boroditsky (2001) observed that English people per-ceive time as if it flows horizontally, whereas Mandarin peo-ple thought that it flows vertically. Moreover, Hendricks andBoroditsky (2017), in an experimental study, showed thatlearning a new metaphor to talk about time leads people toform its non-linguistic representations. Time perception and magnitude perception.
A stim-ulus has measurable properties, namely magnitudes, such asits volume in space, number and duration. There is a sub-stantial amount of research showing that the magnitude per-ception skills are not isolated from one another. For example,Brannon, Lutz, and Cordes (2006) found that infants who areat their six months of age show the same sensitivity to num-ber, time, and area in a discrimination task. Xuan, Zhang,He, and Chen (2007) showed that the error in temporal judg-ment is a ff ected by other magnitudes such as number, sizeand luminance. The relationship between magnitudes leadsresearchers to think that there can be a common magnituderepresentation system in the brain. This idea was theorizedby Walsh (Bueti & Walsh, 2009; Walsh, 2003) and called atheory of magnitude (ATOM) . According to this theory, time,space and number are sensory-motor decision variables thatare used for action execution. For this reason, they are pro-cessed in a common magnitude system located in the inferiorparietal cortex. Coming from birth, this system is hardwiredby the evolutionary process (Walsh, 2003; Winter, Marghetis,& Matlock, 2015). ATOM proposes a map between mag-nitudes from birth, while other researchers suggest that thismap might be established after birth. Cantlon (2012) listedthe possible explanations as to how the mapping between dif-ferent magnitudes is established. The map might be formedvia statistical associations throughout the development (e.g.the longer the distance one walks, the longer the duration it passes) or in the conceptual domain through the analogicalreasoning or building metaphorical relationships (Borodit-sky, 2000). The map might be generated because similar in-tensity rates of di ff erent magnitudes are processed within thesame system (e.g. a bright light activates the same represen-tation with a loud tone) (Cantlon, 2012; Gibson, 1969) or itmight be a side e ff ect of the development. According to thishypothesis, in the earlier years of infancy, infants experiencesynesthesia-like experiences due to the abundant connectionsin the brain. Throughout the development, connections be-tween magnitudes are kept while others are pruned (Maurer,Gibson, & Spector, n.d.; Spector & Maurer, 2009). Anotherpossibility would be that the ability to use one magnitudemight be evolved from the other, which leads the system toshare the same representations and computational resources(Cantlon, 2012).Timing is not isolated from the other cognitive abilitiesand magnitude types. Thus, many models and theories aredeveloped to achieve an integration (N. A. Taatgen, Van Rijn,& Anderson, 2007; Walsh, 2003). At the same time, timingis not stable or static from birth, either, but rather, it matu-rates and changes throughout the development. In the nextsubsection, we will give a brief outline on the developmentof time perception. The development of time perception.
In the course ofdevelopment, the timing abilities of human babies show sub-stantial changes (McCormack, 2015). Despite these changes,though, in the early years of their lives, they still hold re-markable skills. For example, the evidence showed thatinfants form temporal predictions (Colombo & Richman,2002) and that they are sensitive to the interval between twostimuli (Brannon, Libertus, Meck, & Woldor ff , 2008; Bran-non, Roussel, Meck, & Woldor ff , 2004). Further researchrevealed that the ability of infants to discriminate di ff erentdurations develops throughout the course of their develop-ment. It was observed that 3-month-old infants can dis-criminate durations with 1:3 (Gava, Valenza, Di Bono, & IME PERCEPTION Duration Comparison t t delay Duration Production delayt t Estimating t is anexample for sensorytiming Producing t is anexample for motortiming Prospective Timing
Estimating t by payingattention to time explicit encoding t RetrospectiveTiming
Estimating t withoutpaying attention to time implicit encoding t Temporal Recalland Temporal Prediction t t Estimating t is temporal recall and estimating t is temporalprediction A B C D E
Figure 4 . The figure shows interval timing abilities and related tasks. (A) In a classical duration comparison task, the agent isasked to decide which stimulus is longer or shorter (t and t ). The task requires estimating the duration of t and t . Durationestimation for one sensory stimulus is called sensory timing. (B) In a classical duration reproduction task, an agent is givena target duration that should be produced by marking the start and the end of the event by pressing a button. Producing t requires motor timing ability. (C) One can estimate the duration of an event by paying attention or (D) without knowing. E)In addition to these abilities, one can estimate when an event occurred and when an would occur.Tosatto, 2012), 5- to 6-month-old infants with 1:2 (VanMarle& Wynn, 2006), 10 month-old infants with 2:3 ratio (Bran-non, Suanda, & Libertus, 2007) (t :t in Figure 4A). That is,although infants can process temporal information from thebirth, they maturate to distinguish more complex proportionsthroughout the childhood (Allman, Pelphrey, & Meck, 2012).Up to this point, we provided a brief outline about the timeperception. In the following subsections, we elaborate on thebasic timing abilities and temporal information processingmodels. Time perception tasks and abilities.
Duration is a fea-ture of sensory stimulus having a start and an end. Abilityto tell duration in seconds-to-hours range is considered as interval timing (Oprisan & Buhusi, 2014), although the termcan have a broader meaning encompassing milliseconds-to-seconds range (Paton & Buonomano, 2018). Studies con-ducted for investigating the abilities of animals in intervaltiming revealed important tasks (see Figure 4).Interval timing tasks can be grouped into two majorclasses according to the use of temporal information. Whiletasks requiring the estimation of sensory stimuli are namedas sensory timing tasks, tasks requiring the regeneration ofduration information are called as motor timing tasks. Thatis, sensory timing is about how much time is passed, whilemotor timing is about when or how long a behavior is shown.For motor timing, temporal information should be repro-duced by motor commands (Buonomano & Laje, 2010). InFigure 4A and Figure 4B, basic tasks for sensory and motortiming are shown.A further categorization between timing tasks can bemade by concerning the type of encoding. Animals can en-code temporal relationships of environmental dynamics un-consciously. This is called implicit encoding of temporalinformation and assessed using a retrospective timing taskin which subjects are not pre-informed that they would beasked to estimate a duration (Block, Grondin, & Zakay, 2018; Grondin, 2010) (see Figure 4D). If subjects know that theywould be asked to estimate a duration, the task is a prospec-tive timing task (see Figure 4C) (Block et al., 2018; Grondin,2010). For example, if subjects are asked to guess how longthe computer has been open, this is a retrospective timingtask because subjects do not deliberately track the duration.Since they implicitly encode it, they should guess by count-ing on their memory. If subjects are asked to wait and delib-erately track how long the computer will be open until it isclosed, this is a prospective timing task because subjects cangive their attention to the temporal information.In addition to the encoding of time, whether the estimatedduration is in the past or in the future is another conceptualdistinction (see Figure 4E). For the past, we can define aterm called temporal recall (already named as timing when by Maniadakis and Trahanias (2016)), which is the abilityto estimate when an event occurred. On the other hand, forthe future, temporal prediction is the ability to use learnedtemporal dynamics to assess when an event would occur orbe completed.In the subsequent sections, We will evaluate computa-tional and robotic models by asking whether the target modelmentions explicit or implicit encoding (prospective and ret-rospective timing), whether the current model is capable ofrepresenting or regenerating the duration (sensory and motortiming) and whether the model shows scalar property (seeFigure 4). Before reviewing these models, we will inves-tigate temporal information processing models that aim toexplain performances in human and animal timing.
Temporal Information Processing Models
Explaining how animals process temporal information isthe central tenet of time perception research. In the literature,two types of models, namely dedicated and intrinsic models ,are the two competing explanations (Ivry & Schlerf, 2008).
HAMIT BASGOL , INCI AYHAN , EMRE UGUR As for the dedicated models, specialized functions contribut-ing to temporal information processing are localized on thesame part, or di ff erent functions are localized on the di ff erentparts of the brain. On the other hand, intrinsic models pos-tulate that temporal information processing does not dependon specific brain regions but is a function of neural popula-tions (Ivry & Schlerf, 2008). Dedicated and intrinsic mod-els consider the biological basis of timing; in other words,they are in the implementational level of explanation. Onthe other hand, these models are influenced by an informa-tion processing model in the algorithmic level. This model isput forward by internal clock theory suggesting that there arespecialized processes and representations for timing. Sincethe theory assumes specialized brain areas for timing, it has aclose relationship with dedicated models of time perception(Church, 1984; Meck, 1984). In the next subsection, we willinvestigate the relationship between the internal clock theoryand the dedicated models of time perception. Internal clock theory and dedicated models.
Accord-ing to the internal clock theory, a mechanism resembling aclock turns physical time into the subjective experience oftime. This theory was put forward as a result of the studiesconducted by Treisman (1963) in psychophysics and Gib-bon et al. (Gibbon, 1977; Gibbon, Church, & Meck, 1984)in animal learning. An internal clock is formed with clock,memory and decision phases (Church, 1984) (see Figure 5).In the clock phase, a module named pacemaker generatesrhythmic pulses and sends them to an accumulator througha switch which determines the frequency of passing pulses.In the memory phase, rhythmic pulses generated in the clockphase are sent to the working and reference memories. Whileworking memory stores the current amount of pulses gener-ated by the pacemaker, reference memory stores the earlieramount of pulses that have been learnt. In the decision phase,pulses in the working and reference memories are comparedto decide whether they correspond to the same temporal in-terval (Allman, Teki, Gri ffi ths, & Meck, 2014). The internalclock theory o ff ers an explanation about how animals learna duration in a fixed-time interval operant conditioning pro-cedure (Skinner, 1990), in which an animal learns to pressa button at certain temporal intervals to receive reward. Inthe initial trials of the procedure, the animal starts pressingthe button randomly. As the experiment unfolds, the ani-mal stores the required pulses to press the button in referencememory and presses the button when enough pulses are ac-cumulated. Since the amount of pulses are compared, theanimal’s temporal estimations obey the Weber’s law.Specialized functions proposed by the internal clock the-ory inspire dedicated models of time perception, which as-sume that these functions are realized in the brain. Ac-cording to the specialized timing models , so-called internalclock is hypothesized to be located in one part of the brain,such as cerebellum (Ivry, Spencer, Zelaznik, & Diedrich- Pacemaker Switch AccumulatorReferenceMemoryWorkingMemory Comparator
ClockMemoryDecision
YES NO
Figure 5 . The information processing model of the internalclock theorysen, 2002), basal ganglion (Harrington, Haaland, & Her-manowitz, 1998), supplementary motor area (Macar, Coull,& Vidal, 2006) or right prefrontal cortex (Lewis & Miall,2006); whereas for the distributed timing models , functionsof internal clock are distributed in the brain (Ivry & Schlerf,2008).There is a substantial amount of work in favor of the in-ternal clock theory. Recall that the theory assumes a pace-maker that generates pulses and an accumulator that storesthem (see Figure 5). Treisman, Faulkner, Naish, and Brogan(1990) and Treisman and Brogan (1992) found that repetitivevisual and auditory stimuli can a ff ect the frequency of pulsesemitted by the pacemaker and therefore change the perceivedduration as if it lasted longer. Meck (1983) showed that thepharmacological manipulations selectively change the per-formance of memory and decision processes in the internalclock. His work pointed out that the increased dopaminelevel extends the perceived duration by increasing the num-ber of pulses emitted by the pacemaker. According to Gibbon(1992), an internal clock that shows variance in the encod-ing and retrieval phases can show the scalar property. Fur-ther evidence for the theory is related to a property of tem-poral representations. Since the internal clock is a generaltime-keeping mechanism, the theory assumes that temporalrepresentations are amodal. In theory, amodal representa-tions should pass one modality to another without notableperformance di ff erences. One evidence for this was foundby Keele, Pokorny, Corcos, and Ivry (1985), who showedthat the accuracies with which participants time the sameinterval with a finger, foot or by observation are correlatedwith each other. In other words, people being successful insensory timing are also successful at motor timing and viceversa. On the other hand, many influential work questionsthe amodal nature of temporal representations. For exam-ple, it was shown that auditory stimuli are experienced longerthan visual stimuli, even though they have the same duration(J. H. Wearden, Edwards, Fakhri, & Percival, 1998). It was IME PERCEPTION ff erent mechanisms for sensoryand motor timing (Buonomano & Laje, 2010). In additionto the modality-dependent temporal representations, subjec-tive time is also multi-modal (Bausenhart et al., 2014; Chen& Vroomen, 2013; Vroomen & Keetels, 2010). It must bepointed out that the internal clock is a high-level and genericcognitive mechanism. Recent research comes up with con-siderable challenges with this idea by selectively manipulat-ing perceived duration of stimuli across visual space (Ay-han, Bruno, Nishida, & Johnston, 2009; Johnston, Arnold, &Nishida, 2006). This type of manipulation suggests a pos-sibility of an inherent association between space and timeand thus validates a modality-specific timing mechanism inthe brain. Moreover, following this research line, Gulhan andAyhan (2019) questioned whether a time pathway specializedfor processing time as a property of visual information existsand found an evidence for the relationship between sensoryprocessing and time perception in higher level motion areas.That is, for brief time intervals, namely milliseconds, therecan be a modality-dependent neural pathway for processingtime, which connects early visual system to higher level cor-tical areas (Ayhan & Ozbagci, 2020; Gulhan & Ayhan, 2019).Apart from the possibility of modality-dependency andmulti-modality of temporal representations, another limita-tion of the internal clock theory is that the assumed internalclock needs a reset point and can only encode the durationof the stimulus explicitly (Gibbon, 1977; Treisman, 1963).Thus, it gives a priority to the prospective estimation of time.Finally, the localization of the internal clock in the brain isstill a matter of debate (for candidate brain areas, refer All-man et al. (2014)). Internal clock theory, despite its limita-tions, supports an intuitive mechanism that counts time.There is another group of models trying to explain timeperception without depending on a clock-like mechanism,which is intrinsic models (Ivry & Schlerf, 2008). Since theypropose that neural groups can process temporal information,they are generally immune to the problems that are faced byinternal clock theory. Intrinsic models.
Intrinsic models state that time per-ception does not depend on specialized brain regions. The-ories relying on intrinsic models collaborate intensely withneurocomputational models to investigate the underlyingmechanisms of time perception. Relevant to our discussion,these models will be detailed in the following sections.An intrinsic model which does not have a computationalimplementation is the energy readout theory proposed byPariyadath and Eagleman (2007). Pariyadath and Eagle-man explain their theory within the context of an oddballparadigm, in which subjects are presented with a sequence ofstandard and target stimuli as in Figure 3. In this paradigm,target stimulus presented much less frequently than the stan-dard, is called the oddball stimulus. Surprisingly, oddballstimulus is perceived longer than the more frequent stim- ulus (Tse, Intriligator, Rivest, & Cavanagh, 2004; Ulrich,Nitschke, & Rammsayer, 2006). According to the energyreadout theory , the magnitude of neural activation codes theduration of stimulus and determines whether the stimulus isperceived as shorter or longer. Since predictability leads toa suppressed neural activation, subjective duration of the fre-quent stimulus is shortened.Intrinsic models consider neural populations as the pri-mary actor of time perception. For this reason, they are betterat explaining modality- and task-based performance di ff er-ences in timing (Spencer, Karmarkar, & Ivry, 2009). On theother hand, these models cannot explain performance tran-sitions between modalities and are limited to milliseconds(Ivry & Schlerf, 2008). In sum, they assume that neuronsheld in the ordinary cognitive tasks might be used for tempo-ral processing (Ivry & Schlerf, 2008; Karmarkar & Buono-mano, 2007).Having provided a brief summary about time perceptionmodels and summarized how animals process temporal in-formation, in the next section, we will investigate the com-putational and robotic models of time perception. Computational and Robotic Models of Time Perception
Investigating how animals process temporal informationand mimicking the same principles by computational androbotic models enable us a chance to develop robust andadaptive systems. Also, time perception tasks that are usedto study how animals perceive time can be used to evaluatethe capabilities of computational agents and understand thembetter. It is important to note that the relationship is not one-sided. Investigations with computational agents might revealpossible hypotheses and significant insights about how ani-mals use temporal information in the environment.According to Vernon, Metta, and Sandini (2007), com-putational models can be classified into two major classes:cognitive and emergent models. While cognitive models fo-cus on the information processing and symbol manipulationto explain cognition, emergent models focus on the abilitiesthat are emerged from the relationship between autonomoussystems and their environment. The embodiment is not cru-cial for cognitive models, whereas, for emergent models, theembodiment is a must. Another explanation of emergent ap-proach can be found in the cognitive science literature. Ac-cording to McClelland et al. (2010), emergent approach isbased on the idea that operations of sub-cognitive processesresult in behavior; thus, tries to model cognitive processesat a sub-symbolic level. Since we consider emergent modelsof time perception in this review, we accepted the definitionof McClelland et al. (2010) to include neurocomputationalmodels of time perception. For cognitive models of timeperception, you may refer to Anamalamudi, Surampudi, andMaganti (2014) and Komosinski and Kups (2015).In addition to emergence, embodiment is another property
HAMIT BASGOL , INCI AYHAN , EMRE UGUR Time Perception Models
EmergentModels CognitiveModels
Embodied EmergentModels Disembodied EmergentModelsDisembodied EmergentDedicated Models Disembodied EmergentIntrinsic Models focus on emergence of abilitiesfrom interactions between sub-cognitive units (McCelland, 2010)focus on agent-environmentinteraction (Vernon, 2007) focus information processing andsymbol manipulation (McCelland,2010; Vernon, 2007)consider that embodiment is not animportant property for cognition(Vernon, 2007)are embodied andemergentgive importance onagent-environmentrelationships are not embodied but emergentbecause they assume sub-cognitive units like neurons.are neurocomputational andneural network modelspropose specializedfunctions andmodules for timeperception do not proposespecialized functions ormodules for timeperception
Disembodied EmergentModelsDisembodied EmergentIntrinsic ModelsDisembodied EmergentDedicated Models
Figure 6 . Embodied and disembodied models of time perceptionof computational models. We accepted that embodied mod-els are the models forming their experience through “sensoryand bodily interaction with their environment” (Mainzer,2009, p. 303) and disembodied models are the models thatdo not focus on experience formation. Relying on this defi-nition, we grouped emergent models as embodied emergentmodels and disembodied emergent models . Recall that timeperception models are grouped into two classes in the liter-ature, namely dedicated and intrinsic models. This gives usa chance to further categorize disembodied emergent modelsinto two kinds as disembodied emergent dedicated models and disembodied emergent intrinsic models . The categoriza-tion we employed is given in Figure 6 and a summary ofcomputational and robotic models to be considered is givenin Table 1.
Disembodied Emergent Models
In this section, we will discuss disembodied and emer-gent models of time perception (see Figure 6). These modelsare neurocomputational and neural network-based models .Emergent models assuming specialized functions are con-sidered as dedicated models, whereas those focusing on thetemporal processing abilities of neurons are considered asintrinsic models.
Disembodied emergent dedicated models.
Dedicatedmodels of time perception assume that temporal informationprocessing depends on specialized systems or functions inthe brain (Ivry & Schlerf, 2008). Two types of disembodiedemergent dedicated models can be defined depending on howthe internal clock transforms physical time into subjectivetime. These models are pacemaker-accumulator models andmultiple-oscillator models. They assume di ff erent physicalrealizations that result in a clock-like function. Pacemaker-accumulator models.
Pacemaker-accumulator models are currently the most prevalentmodels in the literature (Addyman et al., 2016; Simen, Rivest, Ludvig, Balci, & Killeen, 2013). This model familyassumes that an internal clock forms time perception. Whatpacemaker-accumulator models specifically assume is thata pacemaker generates pulses and an accumulator collectsthem. This idea was realized by cognitive architectures(Addyman et al., 2016; Pape & Urbas, 2008; N. Taatgen,Van Rijn, & Anderson, 2004; N. A. Taatgen et al., 2007)and by mathematical models (Gibbon, 1992; Killeen &Taylor, 2000) in the literature. Since the pacemaker-accumulator model and the internal clock theory sharesimilar assumptions, the same disadvantage applies to both.As we have encountered in the literature, the number ofemergent realizations of the pacemaker-accumulator modelis insu ffi cient. An emergent version of the pacemaker-accumulator model was proposed by Roseboom et al.(2019). We will discuss this model in the next subsection. Perception-based model.
Pacemaker-accumulator mod-els do not assume a relationship between sensory informa-tion and time perception, even though temporal informationis acquired through sensory modalities. Roseboom et al.(2019) proposed an interesting idea that counting salient vi-sual change is the primary mechanism of time perception. Totest this idea, they adopted a transfer learning approach byusing a deep image classifier, namely AlexNet (Krizhevsky,Sutskever, & Hinton, 2012). To find the salient change, theycalculated the Euclidian distance between the activation val-ues of layers formed for each frame per video and accu-mulated a salient change if the distance exceeds a dynami-cally set threshold. They then turned accumulated changesinto subjective time estimation via regression. If the changecalculated from the successive activations of ImageNet isseen as a pace generated by a pacemaker, this model canbe considered as an emergent realization of the pacemaker-accumulator model. Roseboom et al. (2019) observed thatthe model showed good performance in duration estimation.Moreover, the performance was improved further when theyfed the network only with screen locations that people lookat. The model is capable of prospective sensory timing and
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The Emergent Computational and Robotic Models of Time Perception
Cat Name Mechanism SP ST MT PT RT CommentDEDM Perception-based model(Roseboom et al., 2019) Counting salient change (cid:52) (cid:52) - (cid:52) - accounts the e ff ect ofperceptual content ontime estimation.Multiple oscillator models:BF (Miall, 1989) Oscillations in di ff erentfrequencies (cid:55) (cid:52) - (cid:52) - the first multipleoscillator model of timeperception.Multiple oscillator models:SBF (Buhusi & Oprisan,2013) Tracking oscillations inmemory (cid:52) (cid:52) - (cid:52) - the firstperceptron-basedrealization ofmultiple-oscillatormodels.Memory decay models:GAMIT-net (Addyman &Mareschal, 2014) Exploiting memorydecay process for timing (cid:52) (cid:52) - (cid:52) (cid:52) shows wide range ofabilities.Evolutionary models:Neuro-evolutionaryoptimization (Maniadakis &Trahanias, 2016) Universal timing module (cid:55) (cid:52) - (cid:52) - the first model capableof telling when an eventhappened.DEIM Synfire chain model (Haß,Blaschke, Rammsayer, &Herrmann, 2008) Synchronous firing ofchains (cid:52) (cid:52) - (cid:52) - considersmillisecond-basedinterval timing.Positive-feedback model(Gavornik, Shuler,Loewenstein, Bear, &Shouval, 2009) Reward modulatedplasticity - (cid:52) - (cid:52) - does not assume aspecial neuron type.State-dependent networkand population clockmodels (N. Hardy &Buonomano, 2018;Karmarkar & Buonomano,2007) State-dependent changesin neural properties (cid:52) (cid:52) (cid:52) (cid:52) - assume thatstate-dependent neuralproperties are exploitedfor temporal estimation.EEM Memory decay models:Developmental roboticsmodel (Addyman, French,Mareschal, & Thomas,2011) Exploiting memorydecay process (cid:52) (cid:52) - (cid:52) - the first embodiedmodel.Evolutionary models:Duration comparison(Maniadakis & Trahanias,2012a) Inverse ramping activity - (cid:52) - (cid:52) - a self-organizing systemdeveloped with minimalassumptions.Evolutionary models:Duration comparison andproduction (Maniadakis,Hourdakis, & Trahanias,2014) Clock-like mechanismcounting imperfectoscillations - (cid:52) (cid:52) (cid:52) - the possibility of theintegration betweendedicated and intrinsicrepresentations.Evolutionary models:Duration comparison,production andcategorization (Maniadakis& Trahanias, 2015) Clock-like mechanismcounting imperfectoscillations - (cid:52) (cid:52) (cid:52) - shows the possibility ofthe integration betweendedicated and intrinsicrepresentations.0 HAMIT BASGOL , INCI AYHAN , EMRE UGUR Cat Name Mechanism SP ST MT PT RT CommentDeep reinforcementlearning models:Feedforward agent(Deverett et al., 2019) Autostigmergic behavior (cid:55) - (cid:52) (cid:52) - shows the possibility ofusing environment tostore temporalinformation.Deep reinforcementlearning models: Recurrentagent (Deverett et al., 2019) Ramping and inverseramping activity - - (cid:52) (cid:52) - shows that areinforcement learningagent can processtemporal information.Dynamic neural field basedmodel (Duran &Sandamirskaya, 2017) Accumulation ofmemory trace - - (cid:52) (cid:52) - a realization of anintrinsic model in amobile robot.ORM Temporal prediction model(Hourdakis & Trahanias,2018) Learning temporalfeatures of actions - (cid:52) - (cid:52) - one of the first studies inthe field.Action learning model(Koskinopoulou et al.,2018) Learningspatio-temporal featuresof actions - - (cid:52) (cid:52) - one of the first studies inthe field. Note:
Abbreviations used in the table are as follows, Cat: Categories, DEDM: Disembodied Emergent DedicatedModels, DEIM: Disembodied, Emergent Intrinsic Models, EEM: Embodied Emergent Models, ORM: Other RoboticModels, SP: Scalar Property, ST: Sensory Timing, MT: Motor Timing, PT: Prospective Timing, RT: RetrospectiveTiming. (cid:52) : model shows the property or ability. (cid:55) : model does not show the property or ability. -: model does notaim for capturing the property or abilitymimicking the scalar property but does not address retrospec-tive timing and motor timing abilities. Being a vision-basedmodel depending on AlexNet, the extendability of findingsmight be seen limited. Authors mentioned the possibilityof using classifiers depending on other modalities for mod-eling time, which implies a possible research direction forinterval timing. Recently, Fountas et al. (2020) extended themodel proposed by Roseboom et al. (2019) and developed anintegrative model of episodic memory and time perceptionto capture the e ff ects of attention, cognitive load and scenetype on time perception. To do this, they integrated seman-tic and episodic memory with time perception in a predic-tive processing model that was composed of bottom-up andtop-down processes. However, the model is not emergentas it uses hierarchical Bayesian modeling to estimate salientchanges and exploits experimental data for parameter fitting. Multiple-oscillator models.
Multiple-oscillator modelsassume that functions of the internal clock are realized by theoscillatory areas emitting oscillations in di ff erent frequenciesin the brain (Matell & Meck, 2004). These models are cat-egorized into two kinds as Beat Frequency (BF) and
Stri-atal Beat Frequency (SBF) models (Buhusi & Oprisan, 2013;Matell & Meck, 2004; Miall, 1989). The BF model, devel-oped by Miall (1989), assumes more than one oscillator, eachof which oscillates in di ff erent frequencies and resets into thesame level when a new stimulus arrives. Phases of oscillators estimate the duration of the stimulus. However, the BF failsto satisfy the scalar property. To represent the scalar propertyin an oscillator model, Buhusi and Oprisan (2013) developedthe SBF model to explain how mice learn a specific durationin a fixed-time interval schedule. The model is a perceptronformed with input neurons called oscillation and output neu-rons called memory. Oscillatory neurons oscillate and sendactivation to memory neurons in each trial. A trial is eithera reinforced or a normal trial as in the conditioning scheduleand a reinforced trial is a trial when reward is received. Whenthe current activation is the same as in reinforced trials, mem-ory neurons are activated. Therefore, the system learns whenthe reward comes from its activation. They showed that thescalar property is introduced by applying noise to the param-eters of the model. Moreover, Buhusi and Oprisan (2013)simulated the e ff ects of dopaminergic and cholinergic drugson interval timing, which was suggested by Meck (1983).Like other models inspired by the internal clock theory, theSBF cannot explain retrospective timing because oscillatorsneed a predefined starting point. Memory decay models.
They hold the view that inter-val timing ability is grounded on memory decay processes.
Memory decay was put forward to explain how forgettingoccurs. According to the decay theory, as the time passes,the information in the short term memory fades away and, asa result, forgetting occurs. Addyman and Mareschal (2014)
IME PERCEPTION ff ects of working memory load and attention on interval tim-ing. Despite all of the advantages and explanatory capabili-ties of GAMIT-net, however, it is not clear whether the mem-ory decay process is the responsible mechanism of forgetting(Lewandowsky, Oberauer, & Brown, 2009). Disembodied emergent intrinsic models.
Disembod-ied emergent intrinsic models are disembodied emergentmodels accepting that neurons can process temporal infor-mation without a specialized brain mechanism. They explainhow neuron groups process temporal information and mightsuppose special neuron types for temporal information pro-cessing. They seem to be limited to the millisecond scale (10and 100 ms) (Block & Gruber, 2014; Ivry & Schlerf, 2008;Paton & Buonomano, 2018).
Synfire chain model.
Synfire chain model, assumingspecial neuron types, was developed by Haß et al. (2008),who proposed that neuron groups that are organized as chainsfire synchronously to represent temporal information. Eachchain is composed of neurons sending activation from oneanother. The varying lengths of chains determine the tempo-ral estimation error of the chain. According to the model, therepresentation of time is achieved via combining the tem-poral estimations of di ff erent chains. The model can tracktime prospectively and shows the scalar property due to thecumulative error in the combination of temporal estimations.Although the model was not developed for motor timing, it isextendable. The model is not capable of retrospective timingbecause chains forming the model needs a starting point totrack time. Positive-feedback model.
Positive-feedback model triesto explain how mice learn a specific duration in a fixed-timeinterval schedule by exploiting the correlation between thevisual stimuli that occurs when they receive reward and theduration passed (Gavornik et al., 2009). This correlationis learned with a mechanism that involves recurrently con-nected neurons that can show reward-dependent plasticity .After the training, the model shows sustained activity untilthe reward is received. The model is based on prospectivesensory timing and not capable of retrospective timing.
State-dependent network and population clock models.
These models assume that temporal information processingis a result of recurrently connected neural populations. While the state-dependent network model was developed for sen-sory timing (Karmarkar & Buonomano, 2007), the popu-lation clock model was developed for motor timing abili-ties (Buonomano & Laje, 2010). According to the state-dependent network model, neural populations code tempo-ral information via their synaptic, cellular, and structuralproperties . Event-related stimuli lead to short-term plastic-ity ; in other words, change in the hidden state of the neuralpopulation and activation patterns (N. F. Hardy & Buono-mano, 2016). The change in the state of the neural popu-lation can be used to detect the duration of an event. Themodel transforms temporal information into spatial infor-mation with the help of short-term plasticity (Karmarkar &Buonomano, 2007). To illustrate the process, imagine skip-ping a stone where each bounce leads to a change in the wa-ter, as a result, patterns in the water can be used to detecta property of the stone. There are several studies that wereconducted to examine the explanatory capabilities of state-dependent network models in interval timing (Buonomano &Maass, 2009; Buonomano & Merzenich, 1995; N. Hardy &Buonomano, 2018; Pérez & Merchant, 2018). In their sem-inal work, Karmarkar and Buonomano (2007) developed aneurocomputational model, which was composed of recur-rently connected 400 excitatory and 100 inhibitory neurons.Each neuron could show short-term synaptic plasticity andinhibitory postsynaptic potential. In their simulation, Kar-markar and Buonomano (2007) visualized dynamics of twonetworks, one of which received one auditory stimulus andthe other received two auditory stimuli 100 ms apart. Theyobserved that networks’ dynamics di ff er in such a way thatthey encode the stimulus history. Since the temporal infor-mation is converted to spatial information, it is easier to re-ceive the stimulus history by a read-out neuron.According to the population clock model, two systemswork hand in hand to process temporal information. One ofthese systems is the population clock composed of neuronsshowing activation patterns as a result of the incoming stimu-lus; the second is the read-out neuron reading activation pat-terns of neurons. If a motor command is activated in a giventime, neural activations in the population clock for that timepoint should be higher. N. Hardy and Buonomano (2018) de-veloped a neurocomputational model to test whether sequen-tial activation of neurons can encode temporal informationfor motor patterns. To achieve this, they trained an RNN thathas excitatory and inhibitory connections between neuronsfor generating a 5-sec target trajectory and receiving a 50ms input as a trigger. It turned out that RNN successfullyproduce the given trajectory and its temporal decisions obeyWeber’s law (N. Hardy & Buonomano, 2018). Both state-dependent and population clock models have an ability totime prospectively, but it seems that they cannot track timeretrospectively.Up to this point, we have discussed disembodied emer-2 HAMIT BASGOL , INCI AYHAN , EMRE UGUR gent models. The capability of processing and representingtemporal information emerges from the dynamics of intrinsicmodels; however, these models are not embodied because, inthe simplest case, they do not consider an agent that receivessensory information and takes action. In the next subsection,we will cover embodied emergent models of time perception. Embodied Emergent Models
We have not yet mentioned the relationship between beingembodied and capable of perceiving time, even though theliterature shows that there is a strong relationship betweenembodiment and temporal experience. For example, recentresearch showed that bodily and emotional states a ff ect timeperception (Wittmann, 2013). Moreover, some researchersconsider that temporal representation is formed via bodilyand emotional states (Craig & Craig, 2009; Di Lernia et al.,2018). For Craig and Craig (2009), the posterior side of theinsular cortex integrates bodily states and motivational fac-tors to form temporal representations. A study conducted byAddyman et al. (2017) showed that interval timing dependson the development of the motor system and it is believedthat the supplementary motor area has a specialized placein forming the relationship between behavior and temporalrepresentations (Coull, Vidal, & Burle, 2016; Merchant &Yarrow, 2016). Overall, accumulated research points out thatthe embodiment is important for time perception (for a gen-eral examination regarding the relationship between tempo-ral cognition and embodied cognition, see Kranjec and Chat-terjee (2010)). In this section, we will explain the embodiedemergent models of time perception.In the literature, there are four approaches studying timeperception from an embodied perspective, namely an ap-proach based on memory decay processes suggested by Ad-dyman et al. (2011), evolutionary optimization proposed byManiadakis, Trahanias, and Tani (2009), Maniadakis et al.(2011) and Maniadakis and Trahanias (2012a, 2015, 2016), deep reinforcement learning introduced by Deverett et al.(2019) and Dynamic-Neural Fields o ff ered by Duran andSandamirskaya (2017). Memory decay models.
Addyman et al. (2011) devel-oped the first embodied model in order to explain the emer-gence of interval timing ability in development. The modelassumes that memory decay can be turned into duration in-formation with the help of sensory-motor processes. For ex-ample, a baby trying to reach a toy has a memory of toydecaying over time, and at the same time, reaching behavior.Throughout the development, the duration of motor behaviorand memory decay are associated and the association is re-used for interval timing. Addyman et al. (2011) tested thishypothesis with an RNN model. The input was simulatedvia visual and auditory information derived from a Gaus-sian’s distribution and the output was one-hot encoded armmovement. The model is a prospective sensory timing model and shows the scalar property. The model cannot explainretrospective timing and does not aim for modeling motortiming; however, it was shown in a later study (Addyman& Mareschal, 2014) that the memory decay process is ex-pandable to retrospective timing. The model receives actioninformation as one-hot encoded vectors and sensory informa-tion as fading Gaussian distribution. These simulation-baseddecisions might make it di ffi cult to generalize the model’sfindings to real life. As is mentioned earlier, it is not clearwhether the memory decay process is the responsible mech-anism of forgetting (Lewandowsky et al., 2009). It is impor-tant to note that the model, in principle, builds a map betweendistance (or length) and duration based on action performed,which might relate this model to hypotheses trying to explainthe relationship between magnitudes.The model developed by Addyman et al. (2011) hadstrong theoretical priors and was modeled with simplesimulation-based decisions to test their assumption about therole of memory-decay processes in forming interval timing.On the other hand, Maniadakis et al. (Maniadakis et al.,2014; Maniadakis & Trahanias, 2012a, 2015) suggested evo-lutionary optimization as a method to develop models thathave little or no assumption in order to investigate possibletime perception mechanisms. Evolutionary models.
Maniadakis et al. (Maniadakiset al., 2014; Maniadakis & Trahanias, 2012a) developed a continuous-time recurrent neural network (CTRNN) for sen-sory and motor timing using an evolutionary optimizationprocedure. In these studies (Maniadakis et al., 2014; Ma-niadakis & Trahanias, 2012a), a mobile robot having a dis-tance sensor for navigation, light sensor for passing one taskto another, and a sound sensor for detecting the stimuluswas used. Simulation environments used in these studies in-cluded a long corridor and agents in use had three layers re-ceiving the sensory observation and generating motor output.While Maniadakis and Trahanias (2012a) trained the modelonly with a sensory timing task, namely duration compari-son , Maniadakis et al. (2014) extended the same idea to mo-tor timing task, namely duration reproduction (refer Figure4). For duration comparison, the mobile robot had to de-cide which stimulus is longer than the other by turning leftor right at the end of the corridor. For duration reproduction,the mobile robot had to continue its movement for the dura-tion of the stimulus given. In the first study, Maniadakis etal. Maniadakis and Trahanias (2012a) trained the model foronly duration comparison and observed that neural activa-tion patterns show inverse ramping activity to decide whichstimulus is longer than the other. Moreover, they observedthat the developed system is not similar to a clock (Gibbon,1977; Gibbon et al., 1984; Treisman, 1963).In a further study, Maniadakis et al. (Maniadakis et al.,2014) trained the network for also duration reproduction andobserved that, in comparison to the earlier study (Maniadakis
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13& Trahanias, 2012a), neurons showed imperfect oscillatoryactivations that are counted by a clock-like mechanism andramping activity. The oscillatory activity in the network con-firms the assumptions of multiple-oscillator models. Mani-adakis et al. (2014) also investigated the relationship betweenembodiment and time perception. They observed from theneural dynamics that neurons responsible for action execu-tion were also used for interval timing. The model developedby (Maniadakis et al., 2014; Maniadakis & Trahanias, 2012a)is successful at prospective sensory timing and models ofManiadakis et al. (2014) are successful at prospective motortiming. Researchers (Maniadakis et al., 2014; Maniadakis &Trahanias, 2012a) did not share whether the model’s deci-sions obey the Weber’s law and do not aim for retrospectivetiming. A recent study conducted by Maniadakis and Traha-nias (2015) added past characterization skill to the model.It is the ability to decide whether an event occurs in thenear or the distant past. Since both abilities relate to thepast and, therefore, memory processes, past characterizationshares similarities with retrospective timing. After trainingthe model, Maniadakis and Trahanias (2015) concluded thatthe network exploited a clock-like mechanism counting os-cillatory activations and exploiting amplitudes of oscillatoryactivations as a temporal information source. This is con-trary to the assumptions of pacemaker-accumulator modelsand internal clock theory which assumed that a pace corre-sponds to one static temporal unit (Gibbon et al., 1984). Theclock developed by the system had a count-up mechanism that works during counting the duration and a count-downmechanism that works during the reproduction of the dura-tion. Moreover, neurons used for ordinary tasks were alsoused for representing time. Since the model shows proper-ties of both intrinsic and dedicated models of time percep-tion, they concluded that both models might be realized inartificial brains.Maniadakis and Trahanias (2016) took one step further bydeveloping a model that can assess when an event occurred,which di ff ers from the abilities that require duration estima-tion of a presented stimulus. While the former is an abilityof long-term interval timing , the latter is considered as short-term interval timing . To model both short- and long-terminterval timing in the same system, they developed a disem-bodied model that can tell how long an event took place and when an event occurred by adopting an incremental neuro-evolutionary optimization approach, involving two phases.In the first training phase, they trained the model to assesshow long an event took place, whereas in the second, whenan event occurred. The system received oscillations in fourdi ff erent frequencies as input, conforming with the assump-tions of the SBF model (Buhusi & Oprisan, 2013) (recall thatSBF is a multiple-oscillator model). Receiving the oscilla-tory signals, a universal time source generated a compositetime representation that was later sent to working memory module, which also received a static signal representing thatevent continues and an event id identifying events. As a re-sult of the first training phase, the system yielded the esti-mated time of six events. In the second phase, Maniadakisand Trahanias (2016) trained the model for tracking when anevent occurred by feeding it with the time interval betweenthe occurrence of the event and the current time. The modeldeveloped in the first phase was a prospective sensory timingmodel that can track time for more than one event, which isan improvement over for interval timing models. However,the model does not show the scalar property. When it comesto the second phase, the model can be considered a retro-spective sensory timing model that can continuously trackthe passage of time and store temporal information for di ff er-ent events. Maniadakis and Trahanias (2016) do not aim tocapture the relationship between the perceptual content andtime perception. However, it is widely accepted that timeperception is multi-modal (Bausenhart et al., 2014; Vroomen& Keetels, 2010) and a ff ected by perceptual content (Rose-boom et al., 2019). The use of a universal timing modulesupports two approaches to mechanisms of time perception,one of which is the amodality of temporal representationsand the second is the validity of dedicated models of timeperception.Since evolutionary optimization provides an opportunityto develop models with little or no assumption, it is an unbi-ased way of exploring possible time perception mechanisms.In addition to the use evolutionary optimization as an un-biased estimate of time perception mechanisms, reinforce-ment learning can be used to model agents in an end-to-endmanner to get insight about possible time perception mech-anisms. Recently, Petter, Gershman, and Meck (2018) pro-posed integration between reinforcement learning and inter-val timing by showing their similarities. In the next subsec-tion, we will review a recent study (Deverett et al., 2019) in-vestigating interval timing in reinforcement learning agents. Deep reinforcement learning based models.
Deverettet al. (2019) investigated interval timing in deep reinforce-ment learning . They used a duration reproduction task simi-lar to the task employed by Maniadakis et al. (2014) (see Fig-ure 4). The agent was an eye gaze receiving reward by mov-ing on a two-dimensional environment, which had cues thatappear to inform the agent about the current phase of the trial.In each trial, the gaze of the agent was fixated on the centerof the screen and the GO cue appeared. After a small delay,the READY cue appeared and the interval to be produced bythe agent was given. Then, the SET cue appeared and theagent was expected to reproduce the interval by reaching theGO location. The agent was based on A3C (AsynchronousAdvantage Actor-Critic) (Mnih et al., 2016). It was com-posed of ResNet architecture (He, Zhang, Ren, & Sun, 2016)coupled with a multi-layer perceptron receiving the currentframe of the environment, a controller network receiving in-4
HAMIT BASGOL , INCI AYHAN , EMRE UGUR put from ResNet, and policy and value networks connectedto the controller. By using two types of controllers, twotypes of agents were generated. Each agent had either afeed-forward neural network (feed-forward agent) or a long-short term memory (LSTM) network (recurrent agent). Aftertraining, surprisingly, each agent learned the task, althoughthe feed-forward agent learned slower and had poorer gener-alization. Deverett et al. (2019) investigated the hidden layerof LSTM of the recurrent agent with principal componentanalysis (PCA). They found that it shows an accumulatingpattern until the duration reproduction phase starts and a re-ducing pattern while the model produces the interval. Thisactivation is similar to the count-up and count-down mecha-nism observed by Maniadakis and Trahanias (2015) and Du-ran and Sandamirskaya (2017). On the other hand, the feed-forward agent’s activations did not show a systematic pattern.To reveal how the agent solves the task, researchers investi-gated the behaviors of the agent while solving the task andobserved that the agent developed an autostigmergic behav-ior to use the environment as a temporal information source.Deverett et al. (2019) showed the importance of recurrentinformation processing for developing a clock-like mecha-nism in the brain and a possible behavioral strategy that canbe used to count time. From the coupling of environment andagent, the system can generate a memory-like mechanismthat works like a clock. Whether feed-forward agents trainedby evolutionary optimization for the same duration reproduc-tion task show a similar autostigmergic behavior observed byDeverett et al. (2019) is an attractive question. Models of De-verett et al. (2019) are capable of prospective motor timingand the feed-forward model’s temporal estimations seem toobey scalar property. We think that the same reinforcementlearning algorithm can be applied to other timing tasks. Dynamic neural field (DNF) based model.
DNF isa mathematical formulation about how neural populationswork. Assuming the principles of DNF, Duran and San-damirskaya (2017) developed a model that can learn and rep-resent the duration of action and tested their model in a mo-bile robot. The mobile robot had to navigate between loca-tions while avoiding objects in a two-dimensional environ-ment. The model was based on elementary behaviors thatrepresent the relationship between neural states and actions.Each elementary behavior had three DNFs, namely intentionDNF, condition of satisfaction DNF (CoS) and condition ofdissatisfaction DNF (CoD). While intention DNF signifiesthe beginning of an action and sets attractors for sensory-motor dynamics, CoS checks whether the action is completedand CoD checks whether the current behavior is aborted ifthe goal could not be achieved. These DNFs were connectedto each other with a node called t that regulates the competi-tion between CoS and CoD. In the earlier trials of training, t gives an advantage to CoS because the duration of action isunknown, whereas in the later trials, t gives an advantage to CoD because action (therefore temporal dynamics of action)is learned. Researchers showed that the model could repre-sent, store, and update temporal information. Also, it coulddetect anomalies by checking unusual di ff erences in time.The model learned the duration of action by accumulatingnew memories; consistent memories control the behavior ofthe agent, whereas inconsistent memories did not. Accordingto Duran and Sandamirskaya (2017), the model instantiatesa state-dependent network because how time is representedis dependent on the current situation of the network, namelythe accumulation principles of the memory trace. As withthe majority of models discussed in this section (Deverett etal., 2019; Maniadakis & Trahanias, 2015, 2016), the modelshowed a ramping activity. It is important to note that themodel shows the possibility of the realization of intrinsicmodels of time perception in robots in order to extend theircapabilities from milliseconds to seconds. Other robotic models.
In this section, we examine themodels mentioned in Figure 6. There are other robotic mod-els that do not comply with our categorization. For learningthe temporal dynamics of actions, Hourdakis and TrahaniasHourdakis and Trahanias (2018) developed a computationalmodel, which was composed of two components, namelytask progress and control. The former is responsible for de-tecting how much of a given task is completed, whereas thelatter tracks the time of primitive motions of the action. Onthe other hand, for learning both spatial and temporal dy-namics of an action, Koskinopoulou et al. (2018) extendedthe learning from demonstration (LfD) framework, which isusually used to teach robots spatial information of actions,to include temporal information. This extends model’s ca-pabilities to executing action at variable speeds and formingtemporal plans.
Discussion and Conclusion
The importance of temporal cognition for artificial sys-tems having higher-level cognitive abilities has been men-tioned in the literature (Kranjec & Chatterjee, 2010; Mani-adakis & Trahanias, 2011, 2012b; Maniadakis et al., 2011;Ziemke, 2003). In this review study, we presented time per-ception abilities in natural and artificial cognitive systems.One of the most important discussions in the literatureis whether time is processed and represented by intrinsicor dedicated systems. Considering the embodied models oftime perception, we could list several mechanisms: oscilla-tory activations that are counted by a clock-like mechanism(Maniadakis et al., 2014; Maniadakis & Trahanias, 2015) andramping activity in neural activations (Deverett et al., 2019;Duran & Sandamirskaya, 2017; Maniadakis et al., 2014). Itseems that embodied models tend to validate dedicated mod-els of time perception proposing an internal clock trackingtime. However, the clock proposed in these models devi-ates from the original dedicated models. For example, Mani-
IME PERCEPTION ff erent abilities.In addition to the importance of multiple time-scales incognitive life, it can be seen from the Table 1 that retrospec-tive timing, learning temporal features of the environmentimplicitly, is largely unexplored by emergent and embod-ied models. In addition to retrospective timing, how peoplelearn complex temporal dynamics of action sequences is notdiscovered scientifically by computational models, althoughthere exist robotic models developed for practical aspects(Hourdakis & Trahanias, 2018; Koskinopoulou et al., 2018).It is necessary to note that temporal abilities that are dis-cussed in this review are highly limited and only representa small proportion of the field. For example, we did not in-clude the verbal estimation of time (Block et al., 2018) andprocessing temporal information of sequences (N. F. Hardy& Buonomano, 2016), partly because of the sparsity of emer- gent models in these aspects. We also could not spareenough time to discuss more cognitive-related abilities suchas mental time travel, reasoning about the future and time-dependent organizations of memory. It is exciting that fur-ther studies can investigate new abilities in artificial systemsand gain insights about how natural systems can solve theseproblems. It is important to note that some artificial agentsinvestigated in this review is unifunctional. For instance, themodels developed by Roseboom et al. (2019), Addyman etal. (2011), and Maniadakis and Trahanias (2016) are capableof sensory timing, whereas the models developed by Dev-erett et al. (2019) and Duran and Sandamirskaya (2017) arecapable of motor timing. It is highly probable that similaralgorithms can be extended to accomplish a wider range oftime perception tasks and abilities to get insights about timeperception mechanisms.In their inspirational work, in comparison to the majorityof models we investigated, Roseboom et al. (2019) suggestedthat tracking salient change in the perceptual content mightbe a mechanism of interval timing and reported that it is in-deed possible to ground interval timing on sensory informa-tion. Whether the very same idea can be extended to roboticagents that will operate in the real world is an appealing ques-tion to discuss.Being essential part of cognitive life, perceiving othermagnitudes relates to the perception of time. Perhaps, arti-ficial agents that are trained incrementally or holistically forusing di ff erent magnitudes can be assessed for possible over-lapping mechanisms to understand the relationship betweenmagnitudes in the brain. The evolutionary optimization ap-proach proposed by (Maniadakis et al., 2014; Maniadakis &Trahanias, 2012a) can be used for a minimally-biased explo-ration. On the other hand, ATOM (Walsh, 2003) can be eval-uated in an embodied system. It is also possible that onecan build a bridge between sensory-motor decision variables(Walsh, 2003) and the use of space to estimate intervals basedon decaying memory trace over time (Addyman et al., 2011,2017). This might connect time, space, and number basedon actions resulting in embodied timing models capable ofusing magnitudes for action selection and control.The scalar property shows exciting challenges to com-putational and robotic models of time perception. It is amathematical property that temporal estimations of animalsshare (Buhusi & Meck, 2005; Ferrara et al., 1997; Lejeune& Wearden, 2006; Malapani & Fairhurst, 2002; Matell &Meck, 2004; J. Wearden et al., 1997). However, from an ap-plication point of view, as long as temporal estimations areaccurate enough, considering the scalar property in artificialsystems might not be necessary. On the other hand, froma scientific point of view, considering the scalar property inartificial systems makes it easier to generalize results to bio-logical systems as an insight.In this study, we discussed time perception through the6 HAMIT BASGOL , INCI AYHAN , EMRE UGUR lens of a wide range of disciplines. Considering the role oftime in natural cognitive systems, we consider time percep-tion as a present challenge to be met by artificial intelligenceand a possible way to develop robust and adaptive systems.We also believe that developing computational and roboticsystems reveal significant insights into how biological timeperception emerges. References Addyman, C., French, R., Mareschal, D., & Thomas, E. (2011).Learning to perceive time: A connectionist, memory-decaymodel of the development of interval timing in infants. In
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