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Time Perception 1 TIME PERCEPTION 1 Time Perception: A Review on Psychological, Computational and Robotic Models Hamit Basgol, Inci Ayhan, and Emre Ugur Abstract—Animals exploit time to survive in the world. Tem- Learning to Time Prospective Behavioral Timing poral information is required for higher-level cognitive abilities Algorithmic Level Encoding Type Theory of Timing Retrospective such as planning, decision making, communication, and effective Internal Timing cooperation. Since time is an inseparable part of cognition, Clock Theory there is a growing interest in the artificial intelligence approach Models Abilities to subjective time, which has a possibility of advancing the field. The current survey study aims to provide researchers Dedicated Models with an interdisciplinary perspective on time perception. Firstly, Implementational Time Perception Sensory Timing Level Modality Type we introduce a brief background from the psychology and Intrinsic Models in Natural Motor Timing Cognitive neuroscience literature, covering the characteristics and models Systems of time perception and related abilities. Secondly, we summa- Language rize the emergent computational and robotic models of time Multi-modality Action perception. A general overview to the literature reveals that a Relationships Characteristics Multiple Timescales Decision Making substantial amount of timing models are based on a dedicated Scalar Property time processing like the emergence of a clock-like mechanism Magnitudes from the neural network dynamics and reveal a relationship between the embodiment and time perception. We also notice Fig. 1. Mind map for natural cognitive systems of time perception that most models of timing are developed for either sensory timing (i.e. ability to assess an interval) or motor timing (i.e. ability to reproduce an interval). The number of timing models and accordingly, provides a survival advantage to animals capable of retrospective timing, which is the ability to track time [5]. These findings are not surprising because we know that without paying attention, is insufficient. In this light, we discuss the possible research directions to promote interdisciplinary animals navigate not only in space but also in time in order to collaboration in the field of time perception. show robust and adaptive behaviors. Thus, it can be concluded that animals do not live in a three-dimensional world but rather in a four-dimensional one, involving time. I. INTRODUCTION Animals are robust and adaptive biological systems. From this perspective, according to Pfeifer et al. [6], understanding Time, according to Kant [1], along with space, is a main the mechanisms underlying the biological processes might be parameter constituting the possibility of knowledge. Since a source of inspiration for developing robust and adaptive sys- time conveys information regarding the current and future tems to the environmental changes and perturbations. In this state of the environment, biological systems can organize context, embodied artificial intelligence takes inspiration from their functions, behaviors, and cognitive abilities according to biological systems. Studying how biological systems acquire temporal information [2]. Animals can quantify the elapsed temporal information and how they use it to achieve sensory, time with or without the external stimuli (sensing), store this motor, and cognitive processes is an essential topic for further information in the memory (memorizing), and anticipate future research in embodied artificial intelligence, cognitive robotics arXiv:2007.11845v3 [cs.AI] 25 Dec 2020 states of the environment (predicting) [3]. It was shown that and computational psychology. This type of research might a wide range of animals is capable of time-place learning, reveal two positive outcomes: The first one is the exploitation which is the ability to associate the subjective place and time of temporal information by artificial intelligence systems. As for the avoidance from predators, localization of resources, and emphasized by Maniadakis et al. [7], [8], the use of temporal gaining a survival advantage [4]. Moreover, it was found that information in artificial systems has been limited, although vertebrates having smaller bodies and higher metabolic rates it is necessary to develop intelligent systems that efficiently perceive time passing slower in comparison to ones having interact with their environments. For example, in human-robot larger bodies and lower metabolic rates because perceiving in interaction scenarios, intentions of agents’ behaviors, and their higher temporal resolution poses an energetic cost [5]. The causes are not directly observable. Think about a shared work- difference in subjective time perception as a function of body space where a robot should collaborate with different human size and metabolic rate affects the amount of saved energy, partners, each with different working styles. Even though it is H. Basgol is an MA Student in Department of Cognitive Science at Bogazici the very task, some people might operate in a rush because of University, Turkey (e-mail: [email protected]). perceived time pressure or a personality trait. The differenti- Inci Ayhan is with Department of Psychology in Bogazici University, ation between these two possibilities requires the acquisition Istanbul, Turkey (e-mail: [email protected]). Emre Ugur is with Department of Computer Engineering in Bogazici of fine temporal dynamics of behaviors. Therefore, the value University, Istanbul, Turkey (e-mail: [email protected]). of this type of knowledge is tremendous for autonomous TIME PERCEPTION 2 Other humans. We emphasize the connection between time and Robotic Models Duration Comparison Disembodied Emergent other cognitive abilities, the maturation of time perception Emergent Models Models Duration Reproduction Embodied Retrospective Timing throughout the development, and time perception tasks and Emergent Models Skills, Prospective Timing abilities. In the next subsection, we elaborate on the classical Models Tasks, Properties Sensory Timing time perception models explaining how animals use temporal Motor Timing information. These topics will help us to refine our discussion Cognitive Temporal Prediction about computational and robotic models of time perception. Models Computational and Robotic Temporal Recall Models of Time Pacemaker-Accumulator Perception Artificial Neural A. Characteristics of Time Perception Oscillations Networks Perceptual Content Evolutionary 1) Multi-modality of time perception: Time perception has Methods Optimization Memory Decay Approaches Neural Engineering several distinguishing characteristics. One of them is that sub- State-Dependent Framework Networks Dynamic jective time perception is formed by the interaction between Population Clocks Neural Fields different sensory modalities [20], [21]. For example, think Reinforcement Delay Network Learning about a person talking on TV. Physically, mouth movements and language are out of sync; however, we perceive them Fig. 2. Mind map for computational and robotic models of time perception as if they happen simultaneously. This phenomenon is called the temporal ventriloquism [20] and shows the fact that time systems. Timing is also crucial for user satisfaction. A recent perception is multi-modal. report reveals that the temporal precision in the timing of 2) Timescales of time perception: Animals can use tempo- robots’ behaviors affects user experience ratings more than ral information in different timescales, which can be divided to the spatial precision [9]. On the other hand, time perception four, namely microsecond timing, millisecond timing, second tasks in animal and human timing can be utilized to figure timing, and circadian timing, each of which contributes to dif- out whether algorithms developed by artificial intelligence ferent abilities in organisms’ lives [22]. For example, timing up researchers can exploit temporal information and, if they can, to milliseconds was shown to be crucial for producing speech how these algorithms achieve this ability [10]. [23] and motor control [24], whereas timing between seconds The second outcome of computationally studying how bio- to minutes is essential for working memory maintenance [25] logical systems use temporal information is obtaining plausible and the production of action sequences [26]. Depending on hypotheses and remarkable insights about the time perception the day-night cycle, circadian timing regulates the sleep-wake mechanisms in biological systems [11], [10], [12], [8]. In cycle and metabolism [22], [27]. In this paper, we restrict our this manner, researchers may develop models for specific discussion to milliseconds-to-seconds and seconds-to-hours. timing tasks devised in animal and human timing literature 3) The scalar property of time perception: The discrimina- to shed light on possible timing mechanisms. In fact, there is tion of two perceptual quantities depends on the ratio between a growing interest in developing computational and robotic them, which is called the Weber’s law. Weber’s law is seen models that can use temporal information [11], [10], [13], in different domains such as number, length, and duration and [14], [15], [8], [16], [17], [18], [19]. A review study integrat- reveals itself as a scalar property in duration discrimination ing knowledge about time perception across all disciplines, (see Fig. 3) [29]. The scalar property defines a strict mathemat- including psychology, cognitive science,
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