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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. Taken together, these results identify a set of neurocomputational properties that gives rise to the ubiquity of the number sense in the animal kingdom. 

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. Indeed, several recent studies tested how participants with math anxiety estimate and compare non-symbolic quantities. However, little is known about how participants with math anxiety perform arithmetic operations (addition and subtraction) on non-symbolic quantities. This is an important question because poor arithmetic performance on symbolic numbers is one of the primary signatures of high math anxiety. To test the question, we recruited 92 participants and asked them to complete a math anxiety survey, two measures of working memory, a timed symbolic arithmetic test, and a non-symbolic “approximate arithmetic” task. We hypothesised that if impaired ability to perform operations was a potential causal factor to math anxiety, we should see relationships between math anxiety and both symbolic and approximate arithmetic. However, if math anxiety relates to precise or symbolic representation, only a relationship between math anxiety and symbolic arithmetic should appear. Our results show no relationship between math anxiety and the ability to perform operations with approximate quantities, suggesting that difficulties performing perceptually based arithmetic operations do not constitute a basic number ability linked to math anxiety. 

Abstract 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. To address this possibility, we measured VEPs of participants viewing dot arrays that changed exclusively in one nonnumerical magnitude dimension at a time (size or spacing) while holding numerosity constant and compared this to a condition where numerosity was changed while holding size and spacing constant. We found reliable but small neural sensitivity to exclusive changes in size and spacing; however, exclusively changing numerosity elicited a much more robust modulation of the VEPs. Together with previous work, these findings suggest that sensitivity to magnitude dimensions in early visual cortex is context dependent: The brain is moderately sensitive to changes in size and spacing when numerosity is held constant, but sensitivity to these continuous variables diminishes to a negligible level when numerosity is allowed to vary at the same time. Neurophysiological explanations for the encoding and context dependency of numerical and nonnumerical magnitudes are proposed within the framework of neuronal normalization. 

Abstract 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. Here, we investigate the neural bases of the two systems using sequentially presented numerosity. Sequential numerosity (i.e., the number of events presented over time) starts as a subitizable set but may eventually transition into a larger numerosity in the approximate estimation range, thus offering a unique opportunity to investigate the neural signature of that transition point, or subitizing boundary. If sequential numerosity is encoded by two distinct perceptual mechanisms (i.e., for subitizing and approximate estimation), neural representations of the sequentially presented items crossing the subitizing boundary should be sharply distinguishable. In contrast, if sequential numerosity is encoded by a single perceptual mechanism for all numerosities and subitizing is achieved through an external postperceptual mechanism, no such differences in the neural representations should indicate the subitizing boundary. Using the high temporal resolution of the EEG technique incorporating a multivariate decoding analysis, we found results consistent with the latter hypothesis: No sharp representational distinctions were observed between items across the subitizing boundary, which is in contrast with the behavioral pattern of subitizing. The results support a single perceptual mechanism encoding sequential numerosities, whereas subitizing may be supported by a postperceptual attentional mechanism operating at a later processing stage. 

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. Here, we address this question by investigating the neural dynamics of serial dependence using a recently developed technique that allowed a reactivation of hidden memory states. Participants performed a numerosity discrimination task during EEG recording, with task-relevant dot array stimuli preceded by a task-irrelevant stimulus inducing serial dependence. Importantly, the neural network storing the representation of the numerosity stimulus was perturbed (or pinged) so that the hidden states of that representation can be explicitly quantified. The results first show that a neural signature of serial dependence emerges early in the brain signals, starting soon after stimulus onset. Critical to the central question, the pings at a later latency could successfully reactivate the biased representation of the initial stimulus carrying the signature of serial dependence. These results provide one of the first pieces of empirical evidence that the biased neural representation of a stimulus initially induced by serial dependence is preserved throughout a relatively long period.