Statistical regularities reduce perceived numerosity

Zhao, Jiaying; Yu, Ru Qi

doi:10.1016/j.cognition.2015.09.018

Cited by 45 publications

(44 citation statements)

References 27 publications

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“…There was no interaction effect between the number of red dots and function type (β = −0.02). Taking together, our results indicate that perceived numerosity is reduced to a greater extent by compositional functions compared to non-compositional functions, a finding that agrees with the results of Zhao and Yu (2016): structural regularity distorts the units of perception, making them appear less numerous. Even though the non-compositional functions we used were in fact structured (as measured by forecastability), they produced a weaker effect on numerosity relative to compositional functions, arguably because their structure is less "intuitive" (i.e., they lack the inductive bias needed to easily perceive this structure).…”

Section: Methodssupporting

confidence: 89%

Compositional Inductive Biases in Function Learning

Schulz

Tenenbaum

Duvenaud

et al. 2016

Preprint

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How do people recognize and learn about complex functional structure? Taking inspiration from other areas of cognitive science, we propose that this is achieved by harnessing compositionality: complex structure is decomposed into simpler building blocks. We formalize this idea within the framework of Bayesian regression using a grammar over Gaussian process kernels, and compare this approach with other structure learning approaches. Participants consistently chose compositional (over non-compositional) extrapolations and interpolations of functions. Experiments designed to elicit priors over functional patterns revealed an inductive bias for compositional structure. Compositional functions were perceived as subjectively more predictable than non-compositional functions, and exhibited other signatures of predictability, such as enhanced memorability and reduced numerosity. Taken together, these results support the view that the human intuitive theory of functions is inherently compositional.

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Section: Methodssupporting

confidence: 89%

Compositional Inductive Biases in Function Learning

Schulz

Tenenbaum

Duvenaud

et al. 2016

Preprint

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“…Interestingly, this effect does not require an explicit spatial connection. Illusory contours connecting objects as well as statistical regularity in the color of neighboring objects is sufficient to create a more abstract "connection" between the objects and reduce perceived numerosity (Kirjakovski & Matsumoto, 2016;Zhao & Yu, 2016). Connectedness affects numerosity representations in extrastriate cortical areas and operates on signals associated with perceived numerosity rather than lower level representations in primary visual cortex.…”

Section: Introductionmentioning

confidence: 99%

Similarly oriented objects appear more numerous

2020

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Several non-numerical factors influence the numerical estimation of visual arrays, including the spacing of items and whether they are arranged randomly or symmetrically. Here we report a novel numerosity illusion we term the coherence illusion. When items in an array have a coherent orientation (all pointing in the same direction) they seem to be more numerous than when items are oriented randomly. Participants show parametric effects of orientation coherence in three distinct numerical judgment tasks. These findings are not predicted by any current model of numerical estimation. We discuss array entropy as a possible framework for explaining both the coherence illusion and the previously reported regular-random illusion.

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“…When dot arrays are seen as grouped, the degree to which they're clustered increases underestimation (Im, Zhong, & Halberda, 2016). Even sub-conscious processes like statistical learning of co-occurrence in colored dot arrays can lead to underestimation (Zhao & Yu, 2016). In the stimuli presented here, it is possible that perception of grouping among dots on various trials led to underestimation.…”

Section: Resultsmentioning

confidence: 80%

Mapping visual features onto numbers

Brockbank¹,

Vul²

2019

Preprint

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Modern society frequently requires that we express our subjective senses in objective, shared formal systems; this entails mapping multiple internal variables onto a common scale. Here we ask whether we accomplish this feat in the case of estimating number by learning a single mapping between explicit numbers and one integrated subjective estimate of numerosity, or if we separately map different perceptual features onto numbers. We present people with arrays of dots and ask them to report how many dots there are; we rely on the systematic under/overestimation of number at higher quantities to estimate error in the mapping function. By comparing how this error changes over time, as the mapping fluctuates for different visual cues to numerosity, we can evaluate whether these cues share a single mapping, or are mapped onto number individually. We find that area, size, and density all share a common mapping, indicating that people obtain a unified subjective estimate of numerosity before mapping it onto the formal number line.

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Statistical regularities reduce perceived numerosity

Cited by 45 publications

References 27 publications

Compositional Inductive Biases in Function Learning

Compositional Inductive Biases in Function Learning

Similarly oriented objects appear more numerous

Mapping visual features onto numbers

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