Increasing entropy reduces perceived numerosity throughout the lifespan

Qu, Chuyan; DeWind, Nicholas K.; Brannon, Elizabeth M.

doi:10.1016/j.cognition.2022.105096

Cited by 12 publications

(19 citation statements)

References 61 publications

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“…More complex decisional assumptions could be introduced in an attempt to model the effects of task instructions that are known to bias decisions on magnitude judgment ( Castaldi et al, 2019 ; Cicchini et al, 2016 ). More assumptions about top-down semantic influences may also explain recent coherence illusion results in orientation or color ( DeWind et al, 2020 ; Qu et al, 2022 ), for instance, if observers are drawn to focus on a particular feature of the stimulus when comparing two dot arrays.…”

Section: Discussionmentioning

confidence: 99%

A visual sense of number emerges from divisive normalization in a simple center-surround convolutional network

Park

Huber

2022

eLife

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Many species of animals exhibit an intuitive sense of number, suggesting a fundamental neural mechanism for representing numerosity in a visual scene. Recent empirical studies demonstrate that early feedforward visual responses are sensitive to numerosity of a dot array but substantially less so to continuous dimensions orthogonal to numerosity, such as size and spacing of the dots. However, the mechanisms that extract numerosity are unknown. Here we identified the core neurocomputational principles underlying these effects: (1) center-surround contrast filters; (2) at different spatial scales; with (3) divisive normalization across network units. In an untrained computational model, these principles eliminated sensitivity to size and spacing, making numerosity the main determinant of the neuronal response magnitude. Moreover, a model implementation of these principles explained both well-known and relatively novel illusions of numerosity perception across space and time. This supports the conclusion that the neural structures and feedforward processes that encode numerosity naturally produce visual illusions of numerosity. Together, these results identify a set of neurocomputational properties that gives rise to the ubiquity of the number sense in the animal kingdom.

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Section: Discussionmentioning

confidence: 99%

A visual sense of number emerges from divisive normalization in a simple center-surround convolutional network

Park

Huber

2022

eLife

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“…Indeed, this persists even when subjects try to ignore the lines completely and focus only on the circles (see also : Kirjakovski & Matsumoto 2016). Conversely, collections of items which cohere in color (Qu et al 2022) and/or orientation (DeWind et al 2020) are irresistibly perceived to be more numerous than collections which don't, ceteris paribus. Critically, these illusions persist even when participants know what's happening, with the effects influencing the Weber fraction they can reliably discriminate.…”

Section: Evidence For An Ansmentioning

confidence: 99%

Compositionality and constituent structure in the analogue mind

Clarke

2023

Philosophical Perspectives

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I argue that analogue mental representations possess a canonical decomposition into privileged constituents from which they compose. I motivate this suggestion, and rebut arguments to the contrary, through reflection on the approximate number system, whose representations are widely expected to have an analogue format. I then argue that arguments for the compositionality and constituent structure of these analogue representations generalize to other analogue mental representations posited in the human mind, such as those in early vision and visual imagery.

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“…Tokita et al, 2013 ). This understanding of the ANS is sometimes referred to as a “direct ANS model” (Qu et al, 2022 ). The direct ANS model of numerosity estimation often seems to serve as a default theory in the field of numerical cognition (Dehaene, 2011 ; Halberda et al, 2008 ; Hyde, 2011 ; Spelke & Kinzler, 2007 ).…”

Section: Introductionmentioning

confidence: 99%

“…The direct ANS model of numerosity estimation often seems to serve as a default theory in the field of numerical cognition (Dehaene, 2011 ; Halberda et al, 2008 ; Hyde, 2011 ; Spelke & Kinzler, 2007 ). Competing, but to our experience less prevalent in literature, are “indirect models,” which assume that a numerosity percept arises from perceiving indirect surrogate cues (e.g., the spatial distribution of stimulus pattern; Qu et al, 2022 ). Only recently, alternative perspectives or extensions of the direct model have been proposed (Allïk & Tuulmets, 1991 ; Clarke & Beck, 2021 ; Gebuis et al, 2016 ; Gevers et al, 2016 ; Leibovich, Katzin, Harel, & Henik, 2017a ; Lourenco & Aulet, 2022 ; Walsh, 2003 ; Zorzi & Testolin, 2018 ).…”

Section: Introductionmentioning

confidence: 99%

“…Only recently, alternative perspectives or extensions of the direct model have been proposed (Allïk & Tuulmets, 1991 ; Clarke & Beck, 2021 ; Gebuis et al, 2016 ; Gevers et al, 2016 ; Leibovich, Katzin, Harel, & Henik, 2017a ; Lourenco & Aulet, 2022 ; Walsh, 2003 ; Zorzi & Testolin, 2018 ). These perspectives differ in their general view of whether number is a distinct feature and privileged entity in perception or a construct of surrogate perceptional cues (Lourenco & Aulet, 2022 ; Qu et al, 2022 ). Furthermore, they distinguish themselves in the question whether the “number sense” is innate (Spelke & Kinzler, 2007 ), emerges from general, not domain specific abilities, based on exposition and interaction with the environment (Zorzi & Testolin, 2018 ) or is nonexistent at all (Gebuis et al, 2016 ).…”

Section: Introductionmentioning

confidence: 99%

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The role of spatial information in an approximate cross-modal number matching task

Ziegler

Stricker

Drewing

2023

Atten Percept Psychophys

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The approximate number system (ANS) is thought to be an innate cognitive system that allows humans to perceive numbers (>4) in a fuzzy manner. One assumption of the ANS is that numerosity is represented amodally due to a mechanism, which filters out nonnumerical information from stimulus material. However, some studies show that nonnumerical information (e.g., spatial parameters) influence the numerosity percept as well. Here, we investigated whether there is a cross-modal transfer of spatial information between the haptic and visual modality in an approximate cross-modal number matching task. We presented different arrays of dowels (haptic stimuli) to 50 undergraduates and asked them to compare haptically perceived numerosity to two visually presented dot arrays. Participants chose which visually presented array matched the numerosity of the haptic stimulus. The distractor varied in number and displayed a random pattern, whereas the matching (target) dot array was either spatially identical or spatially randomized (to the haptic stimulus). We hypothesized that if a “numerosity” percept is based solely on number, neither spatially identical nor spatial congruence between the haptic and the visual target arrays would affect the accuracy in the task. However, results show significant processing advantages for targets with spatially identical patterns and, furthermore, that spatial congruency between haptic source and visual target facilitates performance. Our results show that spatial information was extracted from the haptic stimuli and influenced participants’ responses, which challenges the assumption that numerosity is represented in a truly abstract manner by filtering out any other stimulus features.

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Increasing entropy reduces perceived numerosity throughout the lifespan

Cited by 12 publications

References 61 publications

A visual sense of number emerges from divisive normalization in a simple center-surround convolutional network

A visual sense of number emerges from divisive normalization in a simple center-surround convolutional network

Compositionality and constituent structure in the analogue mind

The role of spatial information in an approximate cross-modal number matching task

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