The specious interaction of time and numerosity perception

The Mechanisms and Neural Signature of Time-averaged Numerosity Perception

The animal brain is endowed with an innate sense of number allowing to intuitively perceive the approximate quantity of items in a scene, or "numerosity." This ability is not limited to items distributed in space, but also to events unfolding in time and to the average numerosity of dynamic scenes. How the brain computes and represents the average numerosity over time, however, remains unclear. Here, we investigate the mechanisms and EEG signature of the perception of average numerosity over time. To do so, we used stimuli composed of a variable number (3-12) of briefly presented dot arrays (50 msec each) and asked participants to judge the average numerosity of the sequence. We first show that the weight of different portions of the stimuli in determining the judgment depends on how many arrays are included in the sequence itself: the longer the sequence, the lower the weight of the latest arrays. Second, we show systematic adaptation effects across stimuli in consecutive trials. Importantly, the EEG results highlight two processing stages whereby the amplitude of occipital ERPs reflects the adaptation effect (∼300 msec after stimulus onset) and the accuracy and precision of average numerosity judgments (∼450-700 msec). These two stages are consistent with processes involved with the representation of perceived average numerosity and with perceptual decision-making, respectively. Overall, our findings provide new evidence showing how the visual system computes the average numerosity of dynamic visual stimuli, and support the existence of a dedicated, relatively low-level perceptual mechanism mediating this process.

The divisive normalization model of visual number sense: model predictions and experimental confirmation

Our intuitive sense of number allows rapid estimation for the number of objects (numerosity) in a scene. How does the continuous nature of neural information processing create a discrete representation of number? A neurocomputational model with divisive normalization explains this process and existing data; however, a successful model should not only explain existing data but also generate novel predictions. Here, we experimentally test novel predictions of this model to evaluate its merit for explaining mechanisms of numerosity perception. We did so by consideration of the coherence illusion: the underestimation of number for arrays containing heterogeneous compared to homogeneous items. First, we established the existence of the coherence illusion for homogeneity manipulations of both area and orientation of items in an array. Second, despite the behavioral similarity, the divisive normalization model predicted that these two illusions should reflect activity in different stages of visual processing. Finally, visual evoked potentials from an electroencephalography experiment confirmed these predictions, showing that area and orientation coherence modulate brain responses at distinct latencies and topographies. These results demonstrate the utility of the divisive normalization model for explaining numerosity perception, according to which numerosity perception is a byproduct of canonical neurocomputations that exist throughout the visual pathway.

Measuring temporal bias in sequential numerosity comparison

While several methods have been proposed to assess the influence of continuous visual cues in parallel numerosity estimation, the impact of temporal magnitudes on sequential numerosity judgments has been largely ignored. To overcome this issue, we extend a recently proposed framework that makes it possible to separate the contribution of numerical and non-numerical information in numerosity comparison by introducing a novel stimulus space designed for sequential tasks. Our method systematically varies the temporal magnitudes embedded into event sequences through the orthogonal manipulation of numerosity and two latent factors, which we designate as "duration" and "temporal spacing". This allows us to measure the contribution of finer-grained temporal features on numerosity judgments in several sensory modalities. We validate the proposed method on two different experiments in both visual and auditory modalities: results show that adult participants discriminated sequences primarily by relying on numerosity, with similar acuity in the visual and auditory modality. However, participants were similarly influenced by non-numerical cues, such as the total duration of the stimuli, suggesting that temporal cues can significantly bias numerical processing. Our findings highlight the need to carefully consider the continuous properties of numerical stimuli in a sequential mode of presentation as well, with particular relevance in multimodal and cross-modal investigations. We provide the complete code for creating sequential stimuli and analyzing participants' responses.

Near-optimal integration of the magnitude information of time and numerosity

Magnitude information is often correlated in the external world, providing complementary information about the environment. As if to reflect this relationship, the perceptions of different magnitudes (e.g. time and numerosity) are known to influence one another. Recent studies suggest that such magnitude interaction is similar to cue integration, such as multisensory integration. Here, we tested whether human observers could integrate the magnitudes of two quantities with distinct physical units (i.e. time and numerosity) as abstract magnitude information. The participants compared the magnitudes of two visual stimuli based on time, numerosity, or both. Consistent with the predictions of the maximum-likelihood estimation model, the participants integrated time and numerosity in a near-optimal manner; the weight of each dimension was proportional to their relative reliability, and the integrated estimate was more reliable than either the time or numerosity estimate. Furthermore, the integration approached a statistical optimum as the temporal discrepancy of the acquisition of each piece of information became smaller. These results suggest that magnitude interaction arises through a similar computational mechanism to cue integration. They are also consistent with the idea that different magnitudes are processed by a generalized magnitude system.

The more numerous the longer: how the integration between numerosity and time leads to a common neural response

If you are stuck in a traffic jam, the more numerous the queuing cars are, the longer you expect to wait. Time and numerosity are stimulus dimensions often associated in the same percept and whose interaction can lead to misjudgements. At brain level it is unclear to which extent time and numerosity recruit same/different neural populations and how their perceptual integration leads to changes in these populations' responses. Here we used high-spatial-resolution functional magnetic resonance imaging with neural model-based analyses to investigate how the topographic representations of numerosity and time change when these dimensions are varied together on the same visual stimulus in a congruent (the more numerous the items, the longer the display time) or incongruent manner. Compared to baseline conditions, where only one dimension was changed at a time, the variation of both stimulus dimensions led to changes in neural population responses that became more sensitive either to the two features or to one of them. Magnitude integration led also to degradation of topographies and shifts in response preferences. These changes were more pronounced in the comparison between parietal and frontal maps. Our results while pointing to partially distinct representations of time and numerosity show a common neural response to magnitude integration.

The nature of magnitude integration: Contextual interference versus active magnitude binding

Magnitude dimensions such as duration and numerosity have been shown to systematically interact, biasing each other in a congruent fashion: the more numerous a set of items is, the longer it is perceived to last in time. This integration between dimensions plays an important role in defining how we perceive magnitude. So far, however, the nature of magnitude integration remains unclear. Is magnitude integration a contextual interference, occurring whenever different types of information are concurrently available in the visual field, or does it involve an active “binding” of the different dimensions of the same object? To address these possibilities, we measured the integration bias induced by numerosity on perceived duration, in two cases: with duration and numerosity conveyed by distinct stimuli, or by the same stimulus. We show that a congruent integration effect can be observed only when the two magnitudes belong to the same stimulus. Instead, when the two magnitudes are conveyed by distinct stimuli, we observed an opposite effect. These findings demonstrate for the first time that a congruent integration occurs only between the dimensions of the same stimulus, suggesting the involvement of an active mechanism integrating the different dimensions of the same object in a unified percept.