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

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.

Arithmetic operations without symbols are unimpaired in adults with math anxiety.

This study characterises a previously unstudied facet of a major causal model of math anxiety. The model posits that impaired "basic number abilities" can lead to math anxiety, but what constitutes a basic number ability remains underdefined. Previous work has raised the idea that our perceptual ability to represent quantities approximately without using symbols constitutes one of the basic number abilities.

The effect of abstract representation and response feedback on serial dependence in numerosity perception.

Serial dependence entails an attractive bias based on the recent history of stimulation, making the current stimulus appear more similar to the preceding one. Although serial dependence is ubiquitous in perception, its nature and mechanisms remain unclear. Here, in two independent experiments, we test the hypothesis that this bias originates from high-level processing stages at the level of abstract information processing (Exp.

Flawed stimulus design in additive-area heuristic studies.

In a series of recently published studies purportedly on the "additive-area heuristic," Yousif & Keil (2019, 2020) argue for a systematic distortion in the perception of the cumulative area of an item array and further claim that previous findings of numerical cognition and magnitude perception in general are "at risk" (Yousif & Keil, 2021). This commentary describes serious stimulus design flaws present in all of Yousif and colleagues experiments that prevent from making such conclusions. Specifically, item arrays used in those studies demonstrate a skewed correlational structure between selected magnitude dimensions and exhibit unbalanced ranges across different magnitude dimensions of interest.

Decoding of Electroencephalogram Signals Shows No Evidence of a Neural Signature for Subitizing in Sequential Numerosity.

Numerosity perception is largely governed by two mechanisms. The first so-called subitizing system allows one to enumerate a small number of items (up to three or four) without error. The second system allows only an approximate estimation of larger numerosities.

Context-Dependent Modulation of Early Visual Cortical Responses to Numerical and Nonnumerical Magnitudes.

Whether and how the brain encodes discrete numerical magnitude differently from continuous nonnumerical magnitude is hotly debated. In a previous set of studies, we orthogonally varied numerical (numerosity) and nonnumerical (size and spacing) dimensions of dot arrays and demonstrated a strong modulation of early visual evoked potentials (VEPs) by numerosity and not by nonnumerical dimensions. Although very little is known about the brain's response to systematic changes in continuous dimensions of a dot array, some authors intuit that the visual processing stream must be more sensitive to continuous magnitude information than to numerosity.

The neural basis of counting sequences.

Sequence processing is critical for complex behavior, and counting sequences hold a unique place underlying human numerical development. Despite this, the neural bases of counting sequences remain unstudied. We hypothesized that counting sequences in adults would involve representations in sensory, order, magnitude, and linguistic codes that implicate regions in auditory, supplementary motor, posterior parietal, and inferior frontal areas, respectively.

Disentangling feedforward versus feedback processing in numerosity representation.

Numerosity is a fundamental aspect of the external environment, needed to guide our behavior in an effective manner. Previous studies show that numerosity processing involves at least two temporal stages (~100 and ~150 msec after stimulus onset) in early visual cortex. One possibility is that the two stages reflect an initial feedforward processing followed by feedback signals from higher-order cortical areas that underlie segmentation of visual inputs into perceptual units that define numerosity.

Failure to replicate the benefit of approximate arithmetic training for symbolic arithmetic fluency in adults.

Previous research reported that college students' symbolic addition and subtraction fluency improved after training with non-symbolic, approximate addition and subtraction. These findings were widely interpreted as strong support for the hypothesis that the Approximate Number System (ANS) plays a causal role in symbolic mathematics, and that this relation holds into adulthood. Here we report four experiments that fail to find evidence for this causal relation.

Is thirty-two three tens and two ones? The embedded structure of cardinal numbers.

The acquisition and representation of natural numbers have been a central topic in cognitive science. However, a key question in this topic about how humans acquire the capacity to understand that numbers make 'infinite use of finite means' (or that numbers are generative) has been left unanswered. While previous theories rely on the idea of the successor principle, we propose an alternative hypothesis that children's understanding of the syntactic rules for building complex numerals-or numerical syntax-is a crucial foundation for the acquisition of number concepts.

Attractive serial dependence between memorized stimuli.

Attractive serial dependence - a bias whereby the current stimulus appears more similar to the previous ones - is thought to reflect a stability mechanism integrating past and current visual signals. Prior work suggests that serial dependence originates from both perceptual and cognitive mechanisms, but the conditions under which this attractive bias occurs remain to be studied. In particular, whether serial dependence can occur solely from memory interference remains unclear.

Neural Dynamics of Serial Dependence in Numerosity Perception.

Serial dependence-an attractive perceptual bias whereby a current stimulus is perceived to be similar to previously seen ones-is thought to represent the process that facilitates the stability and continuity of visual perception. Recent results demonstrate a neural signature of serial dependence in numerosity perception, emerging very early in the time course during perceptual processing. However, whether such a perceptual signature is retained after the initial processing remains unknown.

Spontaneous repulsive adaptation in the absence of attractive serial dependence.

Despite noisy and discontinuous input, vision is remarkably stable and continuous. Recent work suggests that such a remarkable feat is enabled by an active stabilization process integrating information over time, resulting in attractive serial dependence. However, precise mechanisms underlying serial dependence are still unknown.

Serial dependence generalizes across different stimulus formats, but not different sensory modalities.

Visual perception is thought to be supported by a stabilization mechanism integrating information over time, resulting in a systematic attractive bias in experimental contexts. Previous studies show that this effect, whereby a current stimulus appears more similar to the one previous to it, depends on attention, suggesting an active high-level mechanism that modulates perception. Here, we test the hypothesis that such a mechanism generalizes across different stimulus formats or sensory modalities, effectively abstracting from the low-level properties of the stimuli.

Serial dependence in numerosity perception.

Our conscious experience of the external world is remarkably stable and seamless, despite the intrinsically discontinuous and noisy nature of sensory information. Serial dependencies in visual perception-reflecting attractive biases making a current stimulus to appear more similar to previous ones-have been recently hypothesized to be involved in perceptual continuity. However, while these effects have been observed across a variety of visual features and at the neural level, several aspects of serial dependence and how it generalizes across visual dimensions is still unknown.

Early Numerosity Encoding in Visual Cortex Is Not Sufficient for the Representation of Numerical Magnitude.

Recent studies have demonstrated that the numerosity of visually presented dot arrays is represented in low-level visual cortex extremely early in latency. However, whether or not such an early neural signature reflects the perceptual representation of numerosity remains unknown. Alternatively, such a signature may indicate the raw sensory representation of the dot-array stimulus before becoming the perceived representation of numerosity.

Looking for more food or more people? Task context influences basic numerosity perception.

Approximate numerical magnitude (or numerosity) is thought to represent one of the fundamental sensory properties driving perceptual choices. Recent studies indicate that numerosity judgment on a dot array is primarily driven by its numerical magnitude, largely independent from its other non-numerical visual dimensions. Nevertheless, these findings do not preclude the possibility that non-numerical cues such as size or spacing of a dot array influence numerosity judgment.

Numerical encoding in early visual cortex.

The ability to estimate numerosity in a visual array arose early in evolution, develops early in human development, and is correlated with mathematical ability. Previous work with visually presented arrays indicates that the intraparietal sulcus (IPS) represents number. However, it is not clear if the number signal originates in IPS or is propagated from earlier visual areas.

Attractive Serial Dependence in the Absence of an Explicit Task.

Attractive serial dependence refers to an adaptive change in the representation of sensory information, whereby a current stimulus appears to be similar to a previous one. The nature of this phenomenon is controversial, however, as serial dependence could arise from biased perceptual representations or from biased traces of working memory representation at a decisional stage. Here, we demonstrated a neural signature of serial dependence in numerosity perception emerging early in the visual processing stream even in the absence of an explicit task.

Direct and rapid encoding of numerosity in the visual stream.

The target article dismisses all prior work purporting to demonstrate that number is a conceptual primitive. Here, we take issue with their misrepresentation of our recent line of work on numerosity perception, which demonstrates rapid and direct encoding of numerosity and undermines the thesis of the target article that "continuous magnitudes are more automatic and basic than numerosities" (sect. 1, para.

Spatiotemporal feature integration shapes approximate numerical processing.

Numerosity perception involves a complex cascade of processing stages comprising an early sensory representation stage followed by a later stage providing a conceptual representation of numerical magnitude. While much recent work has focused on understanding how nonnumerical spatial features (e.g.

Developmental trajectory of neural specialization for letter and number visual processing.

Adult neuroimaging studies have demonstrated dissociable neural activation patterns in the visual cortex in response to letters (Latin alphabet) and numbers (Arabic numerals), which suggest a strong experiential influence of reading and mathematics on the human visual system. Here, developmental trajectories in the event-related potential (ERP) patterns evoked by visual processing of letters, numbers, and false fonts were examined in four different age groups (7-, 10-, 15-year-olds, and young adults). The 15-year-olds and adults showed greater neural sensitivity to letters over numbers in the left visual cortex and the reverse pattern in the right visual cortex, extending previous findings in adults to teenagers.