Neurobiology of Interval Timing (Advances in Experimental Medicine and Biology, Volume 829)

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This work led to the proposition that different mechanisms underlie the timing of biological motion animate stimuli and visual motion inanimate stimuli , providing additional arguments against generalizing results from traditional laboratory studies to real-life timing contexts Lacquaniti et al. Further, these studies sketch interval timing as a multifaceted process, in which perspective and the nature of the action that needs to be timed could have significant impact on perceived duration.

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For example, Garsoffky, Huff and Schwan showed that, depending on semantic temporal gaps in videos showing series of everyday actions performed by human actors, the duration of a specific action was under- or overestimated. Videos in the long temporal gap condition consisted of clips of temporally distant actions and the target action was systematically underestimated, while in the short temporal gap condition videos consisted of clips of actions that are temporally closer together in the stream of events and caused the target duration to be overestimated in duration.

In the current study, we aimed to investigate interval perception in naturalistic contexts, while retaining optimal experimental control. Specifically, we asked whether common effects found in traditional laboratory studies, the scalar property and context effects, can be generalized to timing in real-world settings. Furthermore, we aimed to explore possible effects of perspective on time perception. To this end, participants were asked to reproduce the duration of an action demonstrated in a video. Each video showed an animated person performing six different everyday actions filmed from first- or third-person perspective for an example, see Figure 1.

After watching the video participants were asked to reproduce the duration of the action e. Importantly, participants were not explicitly instructed when to start or end timing. Exemplary depiction of the action drink in the short video condition. Animated videos were obtained from videos of an actress doing the same everyday actions with real objects and wearing a motion capture suit top. The two bottom panels show the animated human reference model as seen from third- middle and first-person perspective bottom based on the human template video.

Twenty-three students enrolled in the Psychology programme of the University of Groningen mean age: Sample size was based on past research e. All participants had normal or corrected-to-normal vision. Videos of an animated human reference model see below for details performing six different actions recorded from third- and first-person perspectives and performed over shorter or longer durations served as stimuli. All action-related objects were located on a table before and put back on the table after the actions were performed. Importantly, video length was not correlated with the speed of the action e.

Animated videos were based on video recordings of a human actress performing each of the six actions over different time spans Figure 1 , top row. Finally, the scene and the animated human reference model were generated with MMM-based animated characters and 3D object models e. We chose to use an animated human reference model instead of human actors to control for confounding factors like variations in background noise or emotions conveyed by facial expressions e.

With 6 actions, 2 perspectives, and 2 length condition, a total of 24 animated videos were created to be used as stimuli. Participants were provided with instructions informing them that they would be asked to reproduce the duration of an action observed in the video presented on that trial. Each experimental trial started with the presentation of a short text describing the action that would be presented e. After the end of the video the screen went blank for 1 s, followed by a grey circle presented in the centre of the screen.

This circle indicated that participants could reproduce the duration of the action by pressing down the spacebar. As a visual aid, the grey circled turned white while the spacebar was pressed down i. One additional trial sampled randomly from the 24 available videos served as a practice trial at the beginning of the experiment. Data from this trial were not analysed. Importantly, no explicit instructions or visual or auditory aids were provided to indicate when an interval was supposed to start or end; the start- and endpoints of a specific action had to be determined by the participants themselves.

However, it was explicitly stated in the instructions that the start- and endpoint of the action would not necessarily coincide with the start and end of the video. Videos were presented in random order. Each video was presented four times, resulting in a total of 96 trials.

The experiment was programmed in OpenSesame version 3. During SEC extraction, videos are examined and segmented according to spatiotemporal hand-object relations and actions can be categorized e. Based on this segmentation process, we defined the duration of the main action as lasting from the first contact with the involved object until letting go of that object, resulting in the following durations ordered from shortest to longest : 0. The data analyses focused on three main questions: 1 Do the local and global context influence the perceived duration; 2 Is there an effect of perspective on perceived duration; 3 Is the scalar property observed in these data, operationalized by two different measures discussed below.

To test whether including a fixed factor improved the LMM, we performed model comparisons using likelihood ratio tests.

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Participant and action were always entered as random intercepts. After model comparison, we sequentially added random slopes for participant and the fixed factors, and action and the fixed factors excluding objective duration , to the model to test whether this affected the results. In all LMM analyses, we found that the random slopes did not change the effects of the fixed factors qualitatively. Therefore, we will report the results of the simpler random intercept models here. For both significant and non-significant fixed factors in the LMMs, we used Bayesian analyses to quantify the evidence in favour of the alternative hypothesis.

The evidence for H 1 over H 0 will be denoted as BF First, we tested the data for context effects. To test whether there was a global pull towards the subjective mean, an LMM was estimated with bias the difference between the reproduction and the objective duration as dependent variable and objective lag as fixed factor. Whereas perfect reproduction would yield a bias that is consistently 0 over durations, a pull towards the mean would result in a negative effect of duration on bias.

To investigate local context effects, we tested the effect of the previous n-1, n-2, … subjective duration i. Reproduced action duration was entered as dependent variable.

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Objective duration of the current trial, perspective, and previous subjective or objective trial duration were entered as predictors. Following Taatgen and van Rijn , we iteratively compared more complex models e. The same model comparison approach was used to test for effects of perspective. To test the data for the scalar property, following Wearden and Lejeune , the coefficient of determination r 2 was determined by correlating the standard deviation of the reproduced action duration S , averaged over all participants, with the mean reproduced duration M of each action in the long and short condition separately i.

Figure 2 and Figure 3A depict the mean reproduced action durations for each action in the short and long version i. Visual inspection of the results in Figure 2 suggests that shorter durations were overestimated, whereas longer durations were underestimated. Estimated action durations. Coloured dots indicate mean reproduced durations for each action short indicated with [s], long with [l] , averaged over all participants. Grey dots depict the objective duration as defined by the action segmentation algorithm.

Generally, shorter durations were overestimated and longer durations underestimated, demonstrating typical context effects. Estimated action durations a and variance associated with estimated durations b for the short and long version of the 6 different actions.

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Reproduced durations differ from the objective durations diagonal dashed line : shorter durations were overestimated, whereas longer durations were underestimated, demonstrating context effects. Panel B depicts the standard deviation over subjective duration for all 12 actions. Calculated coefficients of variation triangles did not differ significantly from each other.

For theoretical reasons, and following Taatgen and van Rijn , we did not test for an influence of N-3 without including N These results support the hypothesis that reproduced action durations deviate systematically from the objective durations, with a pull towards the mean. Alternatively, however, the effect of the previous trial on the current reproduction could potentially be explained by attentional fluctuations or performance drift over the course of the experiment.

It could, for example, reflect a change in the willingness of the participant to hold down the response key. To disentangle the influence of the subjective N-1 and these overall performance fluctuations, we calculated the relative bias i. If the N-1 effect depends on performance fluctuations, we would expect that the bias in the current trial depends on the bias in the previous trial e. If, however, the N-1 effect depends on the actual subjective duration in the previous trial, we would expect that the current bias reflects the magnitude of this subjective duration e.

We created a mixed model with bias as the dependent variable, and objective duration, previous subjective duration and previous bias as fixed factors. Thus, whereas performance drift seems to play a role, it does not account for the effect of the previous reproduction on the current reproduction. We also tested for the effect of the objective N Supported by a decisive Bayes Factor, it can be concluded that manipulating whether participants saw an action in first- or third-person perspective did not influence perceived durations in the current experimental setup.

Consequently, data was pooled over perspective for subsequent analyses. To assess whether the scalar property held in the current data, we addressed the correlation between the standard deviations and the mean reproduced durations and tested whether subjective duration predicted coefficients of variation. Do the general laws of interval timing, derived from scores of experiments using static and highly artificial stimuli, generalize to more real-world like settings?

Although some studies using dynamic stimuli suggest that interval timing can be affected when more realistic stimuli are used, this study demonstrates that two basic time perception laws hold, even when naturalistic stimuli are used. These results pave the way for integrating interval timing theories in computational or quantitative theories of complex cognitive behaviour studied in real-world settings. For example, when operating complex machinery, many intervals need to be tracked simultaneously as different aspects of complex machines may need attention at different intervals, or when speaking in front of a group of individuals, specific intervals might be associated with different aspects of interaction.

This research demonstrates that in these cases, the global context effect will cause overestimation of the shortest duration and underestimation of the longest, local context effects predict sequential dependencies on a trial-by-trial basis, and the scalar property suggests that the error in shorter duration will be smaller than the error in longer durations.

Taking these effects into account can explain additional variance when studying complex tasks, providing researchers with a more direct picture of the non-temporal aspects of the task under study. Before turning to the effect of context and the scalar property, one aspect of the empirical data needs to be discussed as it deviates from the results obtained with more standard stimuli. As can be seen in Figure 3 , Panel B, the average coefficient of variation is around.

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  5. These values are notably larger than reported in a review of coefficients of variations by Gibbon, Malapani, Dale and Gallistel In this review, durations between 2 and 8 seconds have an average coefficient of variation below. A major difference is that in the current experiment on- and offsets of the duration were, on purpose, not clearly defined as distinct events, so one possible explanation of the higher variance could be that participants encountered difficulties in determining or remembering the exact on- and offset of an action.

    To shed more light on this matter, a future experiment could experimentally manipulate whether distinctiveness of on- and offsets has an effect on how well the interval marked by those events can be reproduced. Context Effects. A consistent finding in studies on interval perception that use multiple, slightly different interval durations is the context effect.

    The duration of the previous trial i. Data from the current study exhibited similar effects of temporal context. Figure 3A shows the typical pattern of global context effects: shorter durations are systematically overestimated while longer durations are underestimated.

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    The analysis of local context effects revealed that not the objective duration of the previously presented stimulus, but the subjective previous duration influences our current interval perception. Since the previous subjective duration was in fact the previous interval reproduction, it may be a better measure of how participants perceived and stored a given interval than the objectively measured duration of the previous interval.

    Furthermore, any given subjective N-1 trial comprises the subjective N-2 trial the N-1 of the N-1 trial , which itself comprises the subjective N-3 trial, and so on. These results demonstrate that in naturalistic tasks, empirical estimates of previously perceived durations, instead of objective duration, is a more powerful predictor of subsequent behaviour. Scalar Property. Data from the current study is in conformity with the scalar property of time perception.

    We found that variation in interval reproduction linearly increased with interval duration, and that the coefficient of variation did not differ across interval durations see Figure 3. In principle, violations of, or large variations in, the coefficient of variation can hint at participants using counting strategies while performing interval timing tasks Allman et al. This was not the case in the current study.

    These results indicate that even though the onsets and offsets might be more difficult to perceive, timing sensitivity is stable and will play a similar role in ecologically valid settings as it does in laboratory studies. The present data showed no sign of an effect of first- versus third-person perspective. That is, in our experiment, participants only passively viewed actions being performed — they did not perform actions themselves. Although the Bayes Factor provided decisive evidence against an effect of perspective in our setup, we prefer to refrain from making strong claims about general effects of perspective see also the introduction until methods that elicit stronger effects of perspective i.

    Timing is extremely important in many tasks and settings, and this study demonstrates that deviations to veridical timing as observed in the laboratory also affect timing in the real world. We established that findings from artificial laboratory studies can be generalized to more real-world like settings and highlighted that, as in many domains, any percept is influenced by and embedded in context. Taken together, this study paves the way for studying interval timing as a component of complex, everyday cognitive performance.

    The funding agency had no involvement in the design of the study, the analysis of the data, writing of the report, or in the decision to submit the article for publication. All authors contributed to the study design, which was programmed and developed by Sabine Scholz. Videos were recorded by E. Aksoy, M. This behavior is a necessary non-autonomically without extrinsic encouragement or reward consequence of the IDyOT architecture. Cherry concluded that this mechanism was statistical in nature, and that the brain stored transition probabilities, to be Musical entrainment can be extremely complicated, with able to estimate maximum-likelihood to guide perception and irregular rhythmic structures spanning cycles of several seconds, overcome noisy signals.

    This was assumed to account for the e.

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    The comprehension of speech. However, between phrases, sophistication is hard to motivate from a purely biological no expectations could be generated, and participants were equally evolutionary perspective see e. The IDyOT prediction mechanism accords with this. Entraining IDyOT In addition to spatial information, listeners can also use other co-operate successfully in the world, humans must be able stimulus features, such as pitch, to orientate attention toward to synchronize movement.

    Synchronization requires accurate particular events Woods et al. Shinn-Cunningham, Crucially, our perception of temporal invariance and capacity In the visual modality, Posner et al. Efficiency, in attentional mechanism coupled with adaptive expectation of this context, is a survival trait. Entrainment capacity in non-humans has been supposed Crucial to the temporal aspect of IDyOT developed below, to correlate with the capacity for vocal learning Patel, ; time itself is also a modulatory factor for attentional orientation. Schachner et al. Speidel and Nelson, , which entails speech perception ERP evidence demonstrates that sounds presented at attended even prior to the development of semantic association and of times elicit a larger N1 than sounds at unattended times Lange speech production.

    A reason for entrainment to be related to et al. Coull and Nobre all these things would be cognitive efficiency, according with report the first direct comparison between the neural the underlying principle in IDyOT. Attending to speech, as to correlates of spatial vs. If periods of attention temporal cues when a target will appear and spatial cues can be appropriately timed, by predicting when the next unit of where it will appear similarly improve reaction time, but that information from an interlocutor will appear, such as orienting hemispheric asymmetry is evident between the two conditions.

    Nobre , p. Further, shared entrainment subject of empirical investigation. Early work by Klemmer would be a necessary feature of effective sustained conversation, , proposed a model of the relationship between because synchronized prediction in a listener greatly increases reaction time and an information-theoretic measure of time the likelihood of successful information transmission.

    Models of uncertainty. In processing language, preschool children and musical and language entrainment are similar, though language adults employ temporally selective attention to preferentially seems to be more tolerant of expectation breach: an equally process the initial portions of words in continuous speech. Doing hierarchical system of beats for linguistic synchronization is a so is an effective listening strategy since word-initial segments are given in phonology e. Humans can entrain to a beat, even when it is irregular or 3.

    Entrainment variable, and many find it difficult not to do so, when presented Our argument, then, is that patterns of events in the world afford with music that they find engaging. Regularity and periodicity are ; Cross, ; Repp, ; Fitch, , ; London, therefore invariant qualities in perception over time, a fact ; Merchant et al. In music, the notion of perceptual exhibit synchronization via reflex response e.

    Grahn Shmulevich and Povel, More generally, the occurrence gives a useful survey of related research in neuroscience. Furthermore, an argument for the evidence for timer-based control, while Large and Jones evolutionary adaptive quality of entrainment can be made in argue for oscillators. See Hass and Durstewitz for a wider terms of social interaction and cohesion. To interact and to survey of contending models.

    Evidence from music, beyond the Frontiers in Psychology www. Effects are also seen in production: even a timer, repeatedly triggered. Thus, at more abstract levels of infant babbling shows syllable timing patterns characteristic of modeling, the distinction is only semantic, and the effect can the language being learned Levitt and Wang, Then, a given temporal interval may be expectation and predictability play a significant role.

    Information represented by a parameter, forming a closed system with the content has effects both globally, with average speech rate oscillator or timer that accepts it. These approaches have the current segment, both for syllables Aylett and Turk, been investigated on the neuroscientific level by, for example, and words Bell et al. Vuust et al. First, speakers affect each other presents neuroscientific evidence for a theoretical model with a as regards the word- or segment-level timings discussed above: similar motivation to that presented here.

    As such, the present both speech rate and information density converge amongst work may offer a more detailed explanatory account of the interlocutors Giles et al. Second, conversational participants are apparently and the affective effects of expectation in pitch and rhythm, in experts in timing at the level of utterances or turns segments context of our definition of entrainment.

    There has been further during which one speaker holds the conversational floor. Sacks debate elsewhere over the relationship in the literature e. Stivers et al. Rhythm and Meter in Language cross-linguistic and cross-cultural: speakers and hearers manage Speech naturally shows regularities in timing, their nature the timing of these transitions to avoid overlap, and minimize varying across languages.

    Until recently the view was that silences; and experiments suggest that disruptions in natural these rhythmic differences stem from isochrony—an even interaction timings are noticed by infants as young as 3 months distribution of certain segment types over time—with individual Striano et al. Heldner et al. For example, whereas Italian speakers simple feedback vocalizations e. We must therefore However, empirical evidence does not uphold this strict predict the end and content of turns as we hear them, to typological division, with some languages falling somewhere begin our own response see Levinson and Torreira, ; between syllable- and stress-timed e.

    Levinson, Expectation is therefore key to turn-taking: Instead, research suggests that all languages are effectively stress- EEG experiments show correlates of turn-end anticipation timed and that the apparent typological differences can be Magyari et al. However, complexity, and variability of duration of vowels and consonants experiments suggest that this expectation is driven by factors Dauer, ; Grabe and Low, ; Patel and Daniele, ; at many levels. Grosjean and Hirt show that prosody Patel, These differences lead to the impression of different helps listeners predict when a turn is going to end, although rhythmic classes and perhaps, via their effects on perception its utility depends on language and on position in the sentence.

    In machine For listeners, this is one mechanism by which attentional classification tasks, Noguchi and Den and Ward and resources can be directed toward predicted salient timepoints to Tsukahara , among others, show success in predicting efficiently process complex auditory stimuli. For musicians, and backchannel points using prosody; but in a general turn- indeed any form of movement associated with musical stimuli, end detection task, Schlangen showed that combining entrainment is necessary for the co-ordination of physical acoustic, lexical and syntactic information improved accuracy, action.

    While prosody contributes information, then, which shed light on the underlying biological mechanism of lexico-syntactic or higher levels must contribute as much if not rhythmic perception. Neuroimaging studies have discovered more. Differing both within and between speakers—with this expectation based EEG responses to trains of identical pulses are reported by on information at a variety of levels.

    IDyOT theory proposes that Brochard et al. Snyder and Large and that which affords musical meter perception, which is the topic of Iversen et al. Rhythm and Meter in Music the later study it is also demonstrated that the priming of A distinction commonly made in the literature is that between an endogenous meter has a predictable effect on subsequent musical meter and rhythm, although there is debate over the auditory responses. Nozaradan et al. London , meter. Rhythm therefore refers to the arrangement of Where a stronger sense of meter is induced, participants events in time, and in that sense can be considered as something could more accurately detect rhythmic deviations.

    In the same that exists in the world and is directly available to our sensory experiment, the authors also provided evidence suggesting the system. London strongly situates meter as the whole. In psychological terms, conflicting musical stimuli. Syncopation is the intentional rhythm involves the structure of the temporal stimulus, while rhythmic articulation of less salient metrical timepoints, which meter involves our perception and cognition of such stimuli. The The experience of meter can, therefore, be considered as a notion of a continuous oscillation in attentional energy process of categorical perception, where the surface details of the provides an account, importantly one with an empirically temporal stimuli, such as the particular structure of the rhythmic grounded underlying mechanism, of the commonly held view pattern, or any expressive performance timing, are perceived with that meter concerns regular patterns of strong and weak reference to a hierarchical organization of regular beats.

    The beats. Entraining IDyOT 3. Affective Responses to Expectation in This entails a representation in which a norm the standard Timing beat, isochronous or otherwise is directly implied, but in which Huron argues that prediction, experienced as expectation, variation may be quantified so that further prediction and is a driver of musical affect. Huron proposes that the feeling associated affect may be modeled. Such a representation is the of uncertainty, which corresponds with entropy in a predictive subject of the next section. The Theory of Conceptual Spaces of music. The formalism is based on betweenness, from which a However, anticipation of what is coming next followed by notion of conceptual similarity is derived.

    Another key aspect is the entrainment that notion of betweenness, in whose terms is defined similarity, allows groups of humans to perform music together, in perfect represented as not necessarily Euclidean distance. This allows but flexible, consistent time, in ways which have never been models of cognitive behaviors to apply geometrical reasoning demonstrated in other species. An archetypal example is a color is necessary for efficient speech communication see Section space with the dimensions hue, saturation, and brightness.

    Each 3. For for exercising of that capacity are favored. Thus, a capacity example, hue is circular, whereas brightness and saturation which is, presumably, grounded in fundamental cyclic behaviors correspond with measured points along finite linear scales. Since speech and social bonding are note that the values on a dimension need not be numbers— interlinked, and social bonding is crucial to human survival in though how an appropriate algebra is then defined is not the wild, one can postulate a tight feedback loop between these discussed.

    This account places neither integral as opposed to separable dimensions, meaning that every music nor language as the progenitor: it would be the basis of dimension must take a value to be well formed. Each domain has a distance measure, which may be resources. However, in both speech could be a space comprising the above domain of color and a and language, affect is manipulated, intentionally or otherwise, by domain representing the perceptually salient features of a given both time and pitch—as in the frustrating denial of expectation set of shapes.

    Kant proposes a theory of incongruity similarity is directly related to not necessarily Euclidean for positive affective response in humor, and something similar proximity. Such spatial representations naturally afford to this may apply here; however, we reserve this discussion for reasoning in terms of spatial regions. For example, in the future work. For purely et al. A Geometrical Formalization of Meter and 4. Further explanation is given in which metrical structure may be variable in perception. Forth by Wiggins b and Wiggins and Forth The simpler space, cognitive architecture.

    GWT is primarily intended to account meter-p, represents the periodic components of well-formed for conscious experience, and that is relevant to some aspects hierarchical structures that correspond with metric entrainment. However, it is the underlying mechanism It can accommodate all theoretically possible forms of metrical that is of interest here, in our references to both theories. The model of sequences, performing Markovian prediction from principal affordance of the geometry is direct computation of context Wiggins and Forth, Conceptually, each generator similarity between musical rhythms with respect to a metrical maintains a buffer of perceptual input which may include mis- interpretation.

    In a genre classification task, exemplars of a range perceptions and alternative perceptions due to the possibility of dance music styles were projected as points in each space. A buffered sequence The overall general spaces are quite high-dimensional, but is flushed into the Global Workspace when it meets a chunking current thinking is that any individual actually uses a subspace, criterion as described below. Figure 1 gives an overview; see attuned to their enculturation. Thus, someone enculturated Wiggins b , Wiggins and Forth for more detail. The experience.

    IDyOT is focused on sequence, and this is in part dimensionality of the spaces depends, also, on the number of due to the musical focus of its ancestor, IDyOM Information metrical levels instantiated in the overall metrical structure. Dynamics of Music: Pearce, ; Pearce and Wiggins, Therefore, musically less structured rhythms inhabit a lower IDyOM models human predictions of what will happen in dimensional space; and, conversely, each space may be extended an auditory sequence, and takes account of information about by the addition of new dimensions corresponding to higher-level musical time in making its predictions.

    It is the most successful groupings or lower-level beat subdivisions. While it is possible to over a body of data viewed as a fixed corpus: it has no interaction instantiate the representation to the point at which specific real with the world; it has no real-time element. The focus of this times are included, and thus actual performances are represented, paper is to extend the IDyOT model with timing, to show how these times may be abstracted out.

    In this case, a point in the it accounts for musical meter, potentially in real time. The geometry input, if some exists, that it receives. If there is no input, of the space then allows us to distinguish groove, inconsistent the generators freewheel Fink et al. In the current paper, we focus away from the regularized rhythm, the second is a cloud around on the perceptual input and synchronization. The previous buffer now Frontiers in Psychology www. Generators synchronized to perceptual input sample, given previously buffered perceptual input if any , from a first-order, multidimensional Markov model to predict the next symbol in sequence, which is matched with the input.

    Predicted symbols that match are buffered by each generator until it is selected on grounds of its information profile. This allows the resulting chunk of sequence to be stored in the memory, to become part of the statistical model and thence to be used subsequently. The model entails that at least some generators must layer, providing semantics for the symbols of the first.

    The process of their sensory input inspired by human biology ; higher-level structure generation is explained in Figure 2. Chunking is the basic process by which layer, and tethering to the level below, eventually bottoming IDyOT manages its information, by analogy with human out in actual percepts. Using this, a consolidation phase perceptual chunking Gobet et al. Once a chunk has allows membership of categories to be optimized, by local entered the Global Workspace, it is added to the memory and adjustment, in terms of the predictive accuracy of the overall becomes available to the generators for prediction.

    This generates model. Theoretically, the layering of models and its associated a positive feedback loop in which the chunks inform the statistical abstraction into categories can proceed arbitrary far up the model that in turn causes chunking, reinforcing the model. For clarity here, we restrict our example Each chunk, having been recorded, is associated with a to the number of layers necessary to describe simple musical symbol in the next-higher-level of the model, which in turn rhythms.

    Each symbol corresponds with a point in of which those in Figure 3 are simplified examples, in parallel, a conceptual space associated with its own layer, and each such tied together by observed co-occurrences of feature values point corresponds with a region or subspace of the conceptual expressed in multidimensional perceptual input sequences.

    Thus, two representations grow in determined by the chunking process, and constrained to predict parallel: the first symbolic and explicitly sequential, driven by only to the subsequent symbol at each level and in each data, providing evidence from which the second is derived; and modality. Note, however, that the subsequent symbol may Frontiers in Psychology www. In reality, the voice input would be an audio signal, but for the purposes of example, we start at the abstract and approximate phoneme level.

    C Five steps in the construction of the memory structure shown in B. A generator is associated with each level of each viewpoint, and with each alternative reading of the structure though ambiguity is not shown here: see Wiggins and Forth, , for details. Rather than move data around, new input, once matched perceptually, is added directly to the memory, which serves as the substrate of the Global Workspace. As each chunk is constructed, there is a peak of information content, which constitutes attentional energy in the system. It is compared here with the conventional music-theoretic 44 meter: the notation is restricted to quaver eighth-note values, to avoid giving the impression of a priori metrical structure.

    The score fragment denotes an experienced rock rhythm. The learned model of meter implies stronger or weaker anticipation over the relevant time periods, the whole being parameterized by the current basic unit. The model of the current rhythm also learned, in the short term also adds predictions. This is an example where an expectation of the background model is denied and the resulting feeling of the missing beat is predicted.

    The figure illustrates how the temporal expectations of with, and conditioned by, more concrete ones, and each higher- the different metrical levels fit together to produce weaker and level symbol will subtend more than one lower level symbol. The differences between generator outputs is caused either The IDyOT generators make predictions of what will be by their predicting from different parts of the memory structure perceived next, expressed as distributions over the relevant e. Each generator also makes a prediction of when the choices licensed by the distributions with which they work.

    Because more predictors from different levels predict what would musicologically be strong 4. Rhythm and Timing Expectation in beats, the prediction at these points is correspondingly stronger, IDyOT and, in terms of qualia, this affords the experience of metrical, Figure 3 illustrates the pattern of structures that is learned as a hierarchical rhythm. The model Section 3. Once such a space is are more frequent than on weak ones, and because a balanced established, new time intervals can be represented within it, and tree representation of the structures is more information-efficient thence abstraction away from time interval to tempo becomes a as a representation than other kinds of representation.

    Thus, the straightforward projection operation on the space, rather than a properties of the data to which IDyOT is exposed conspire with matter of timing from the raw data alone, which would be difficult its information-based criteria to provide a theoretical account to handle without the prior knowledge encoded in the metrical for the development of meter in humans. Any rhythm that model. A hypothetical Mechanism Underlying communication with multiple individuals, who may have Entrainment variation in speed or in regularity in their own speech, and who Entrainment in IDyOT is a direct consequence of attentional will certainly vary in speech speed from one to another; and for dynamics.

    The turn-end timing simultaneously. Exactly the same hierarchical understanding of attention becomes distributed activation in process can apply in both modalities. Thus, IDyOT affords a method by which sequences of time The mechanism with which IDyOT makes predictions of time periods may be derived from a base level of measured temporal is the novel contribution of this paper. We consider temporal units, which allows the construction of the metrical space from predictions to be generated by the same kind of statistical process tabula rasa.

    Exposure to sufficient metrical data will cause that governs the prediction of other attributes, such as the the construction of hierarchical representations of meter, the likelihood of particular musical pitches or phonemes of speech. Temporal predictions are The relationship between the basic unit, and the structures hypothesized as drivers or regulators, coordinating, but also composed upon it by chunking, may be expressed by locating a influenced by, the generation of predictive distributions in rhythm as a point in the conceptual space defined in Section 3.

    The interaction between generated expectations and rhythmic input, even when it is not obviously coherent, into sensory input leads to the construction of representations in a percept of one single rhythm as in polyrhythms the entire memory, which in turn conditions subsequent expectations. Although the actual point at all. Thus, the entire IDyOT Global Workspace resonates mechanism is the subject of much debate for an overview see with the resultant temporal beat of its input, or descends Hass and Durstewitz, , we assume a neuronal representation into confusion when multiple conflicting rhythmic inputs are of the passing of time to be available in the brain.

    We assume a present. Consider a regular, Western rock may appear obvious. However, considering the question of beat, as illustrated in Figure 3, as processed by an IDyOT why and how this may be the case illustrates and supports with extensive exposure to this kind of relatively foursquare our wider position regarding the importance of prediction rhythm.

    First, we discuss predictions at the metrical level. At this Analogous to the derivation of intervallic representations of level, the predictions of the part of the model representing pitch from absolute representations of pitch, an intervallic the current rhythm are mostly in line with those of the more representation of time is more compact in terms of both alphabet general metrical predictions, and therefore the expectations are size and resulting statistical model than a monotonic time-line.

    This translation, directly affording comparison, forming the basis for corresponds with a human feeling the beat strongly. However, the identification of higher-level structure. This rhythm, therefore, creates its musical effect Multiple independent IDyOT generators continuously predict by subverting the metrical expectation of the listener, and sensory input, at each level of the metrical hierarchy induced by IDyOT is able to predict this effect: unexpected occurrences the chunking process.

    There must be a sufficient number, making draw attention, and thus the listener is kept interested in the predictions at sufficient frequency, to be useful to the organism in beat. Entraining IDyOT resources. In the auditory domain, we take the lower bound of imagined, rather than being a response elicited by actual sound, 20 ms the approximate minimum IOI at which listeners can and how the intrinsic experience of pulse can continue beyond reliably discern the correct ordering of two successive onsets: an audio stimulus. Perhaps most important, it explains how untrained temporal resolution.

    Following the global workspace theory, we mechanism. The strength of predictions is determined between generators is mediated. The finite resources in Arabic, Indian and African musics, and the complexity of of cognition act as a global constraint on temporal structure, rhythm in language from everyday argot to the most carefully which in the limit tend toward maximizing efficiency.

    Therefore, performed poetry or rap. In both 5. A perennial problem for evolutionary accounts of biological Thus, conceptual space representations are learned because development is that of distinguishing them from Just-So Stories they are efficient, and they are constrained by embodiment, and Kipling, , because they are untestable. Here, we propose therefore take a common form across a species, but are variable a methodology in which computational models of cognitive across culture.

    Thence, we hypothesize that the mechanism process afford a means of testing hypotheses about evolutionary underlying entrainment is a process of modeling observable development. While it is clear that in silico simulation is not the patterns, which may in a natural organism be associated with same as running in vivo experiments over evolutionary time, it the cause of the patterns, and thus given meaning.

    The specific mechanism proposed is an extension of the event- To see this, one must understand that the computational by-event prediction used in extant statistical models of music and model in question is not merely a predictor from data. That is, language. As each event is detected, the next one is predicted, it is not an attempt to neutrally machine-learn structure in data the prediction being expressed as a distribution over the symbols and classify on that basis, or to search for arbitrary correlations.

    In IDyOT, differently, this Rather, it is in its own right an overarching theory about the distribution changes with time, time being substantially more functional process of mind, which may be decomposed into granular than the inter-event interval. It can be calculated as several related aspects, one of which timing is the current topic. Instead of merely determining the observed likelihood of Different aspects of the theory are testable in different ways, and each of the possible symbols in context, IDyOT treats each piece only though a comprehensive programme of experimentation— of evidence differently, counting not only the symbols, but also first concentrating on individual aspects in isolation, then in the expected time of occurrence.

    The result may be viewed as an combination—can a full understanding of the wider theory be overlay of distributions in time, one for each symbol, with the established. From the current perspective, then, IDyOT is a overall distribution across the alphabet at any point calculated theory; the aspect under scrutiny is its timing mechanism, and by looking up the value of each symbol at that point. This is this drives our current hypothesis formation. Once the model has been shown to be an by Fitch as a primary cognitive construct, emerges as acceptable predictor of empirical observations of the behaviors an epiphenomenon of our more general notion of entrainment: it claims to capture, its parameters may be changed so as to it results from the superposition of multiple, regular strong simulate the effect of changes known to have occurred in the expectations.

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    Importantly, this theory explains how pulse can be relevant species over evolutionary time: e. The left side of the figure shows the time distribution for each symbol as generated from observed experience. These distributions may be notionally superposed, giving the bottom right diagram—however, note that this is for the purposes of illustration only: it is not intended to represent a combined distribution of any kind. The resulting model is similar to a Markov renewal process Ross, , but extends the idea to hierarchical structure.

    For can supply useful answers to carefully posed questions that have a example, an IDyOT with greater hierarchical depth of processing, bearing on the evolution of the aspects of present-day organisms or more training examples, may be used to predict listeners with that the model is shown to simulate. In music, an IDyOT exposed to a large corpus The IDyOT model affords more than one opportunity for may process musical structure at a higher level than an IDyOT exploration of human rhythmic behavior in language and exposed to a small corpus, in the same way that expert listeners music, and its evolution.

    First, the model must predict human tend to perceive music in terms of more semiotic structure; in this behavior as currently observed, in both modalities. In addition to modeling listeners with more to study the effects of combining music with language, or less musical training, IDyOT may be used to model the musical for example, in lyrics. Second, the model should be used perception and expectations of listeners with different cultural to generate behavioral predictions, from which surprising backgrounds.

    These can then metricization, to test whether an encultured IDyOT exhibits the be tested against human behavior, further developing the same subjective metricization behavior as similarly encultured model and adding to knowledge of that behavior. Thirdly, humans. Exposing trained IDyOTs to humans. Entraining IDyOT associated with observed turn-taking and of human judgments example.

    Rather than predicting neural response to anomalies, in end-of-turn prediction experiments. Similarly, it should be one may also predict human cognition at the behavioral level, by able to generate expressive timing for synthesized speech that exposing a trained IDyOT to garden-path sentences, as discussed correlates with human affective response to timing deviations. In this later case, incrementally, as follows. Consider the following discourse one would test whether IDyOT produces temporal responses fragments1 : comparable to humans e. And finally, rather than testing ambiguous or 1.

    There was a bank at the corner. There was a bang, catching my attention. This eagerly predictive Cohort Theory Marslen-Wilson, and not unsuccessful literature e. IDyOT theory predicts this and models the and Plumbley, affords a rich vein of models against effect of the change in time explicitly, as illustrated in Figure 4. Similarly, Note, however, that, on balance, semantic implication is usually psychological Povel and Essens, and neuroscientific Patel somewhat stronger in disambiguating, as discussed by Wiggins and Iversen, comparators exist.

    In the domain of music, IDyOT may be run as a 6. Predicting Behavior from IDyOT participant in a tapping synchronization study, with the Following Honing , once a model has been validated, the hypothesis that human-human pairings are indistinguishable researcher should push the model toward the extremes of its from human-computer or computer-computer pairings.

    This parameters, to discover unexpected predictions about human sort of experiment would not only confirm the accuracy of the behavior. Correspondence with Neural Function Our methodology is to model cognitive function abstracted high-level expectation from top-down knowledge. However, it is useful to consider cognitive In addition to modeling production and synchronization, predictions in context of their hypothetical neurophysiological as in a tapping study, IDyOT may be used to simulate implementation, even though they are separated from it.

    These by testing whether the high level patterns captured by IDyOT are representations, though not literal recordings of sensory reflective of schematic perception of rhythmic variations, or of experience, are very high-dimensional, because they connect generalization and classification of linguistic information. This, we claim, is a necessary requirement dynamics of information processing. Entraining IDyOT between correlated sensory features may be limited; and so on. This, in its own right, may retention of detail in symbol creation can be varied, and be expected to elucidate the quality of the model in respect their effect on the predictions of the system studied.

    The to these capacities; subsequently, in careful comparison with most interesting possibility here is modeling the evolution of similar extinct species, it may be possible to chart a path relating the neocortex: in the style of Bown and Wiggins , an increase in brain size with the development of successively more evolutionary computation system may be set up that allows advanced cognitive capacities. Thus, evolution may be simulated quite literally and associate meaning with words that is, sequences of in silico, albeit at a functional level, and the relationship between phonemes.

    But there is no evidence that they can compose biological affordances and effects studied in ways that are not words into meaningful phrase interpretations; indeed, quite the accessible in vivo. Our model would produce this effect when limited to only a few layers of chunking above the audio: sequences of 7. On the other hand, In this paper, we have presented a novel model of timing in our theory affords much deeper construction when more layers a predictive cognitive architecture.

    We have described in some are allowed Wiggins and Forth, These restrictions would be expected to limit the ability of the system to learn, and thence to predict. Evolving IDyOTs section; MP supplied the linguistic grounding; GW invented From a modeling perspective, evolution may be thought of as a the core model and wrote the sections summarizing it, and long-term parameter search within the IDyOT architecture and those on timing, using illustrations suggested by MP, and neural processing framework.

    When multiple IDyOTs exist in a genetic implementation. The rest of the writing was a team effort. Studies could be constructed such that IDyOTs with different temporal-predictive capacities will compete to The authors are supported by the projects Lrn2Cre8 and survive, while the parameters of well-synced models are passed ConCreTe, which acknowledge the financial support of the on to future generations by simulated breeding. The algorithmic Future and Emerging Technologies FET programme within the parameters and probabilistic weightings underlying predictive Seventh Framework Programme for Research of the European processing may be randomly varied across agents to see which Commission, under FET grant numbers and , variations yield the most adaptive IDyOTs.

    Then, again, those respectively. Thanks to Sarah Hawkins and Dan Stowell for whose predictions facilitate accurate communication or behavior stimulating related discussions and useful information. The smooth signal redundancy hypothesis: a functional explanation for relationships between redundancy, prosodic Abercrombie, D.

    Institute for Logic, Language and Computation (ILLC) - ABC - University of Amsterdam

    Elements of General Phonetics. Edinburgh: Edinburgh prominence, and duration in spontaneous speech. Speech 47, 31— Listeners modulate temporally selective Baars, B. A Cognitive Theory of Consciousness. Cambridge, MA: attention during natural speech processing. Astheimer, L.

    Temporally selective attention supports Effects of disfluencies, predictability, and utterance position on word speech processing in 3- to 5-year-old children. A theory of musical meter. Music Percept. Social origins of rhythm? Rebuschat, M.