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. 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.

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. 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.

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. In an fMRI scanner, participants heard four-number sequences in a 2 × 2 × 2 design. The sequences were adjacent or not (e.g., 5, 6, 7, 8 vs. 5, 6, 7, 9), ordered or not (e.g., 5, 6, 7, 8 vs. 8, 5, 7, 6), and were spoken by a voice of consistent or variable identity. Then, neural substrates of counting sequences were identified by testing for the effect of consecutiveness (ordered nonadjacent versus ordered adjacent, e.g., 5, 6, 7, 9 > 5, 6, 7, 8) in the hypothesized brain regions. Violations to consecutiveness elicited brain activity in the right inferior frontal gyrus (IFG) and the supplementary motor area (SMA). In contrast, no such activation was observed in the auditory cortex, despite violations in voice identity recruiting strong activity in that region. Also, no activation was observed in the inferior parietal lobule, despite a robust effect of orderedness observed in that brain region. These findings indicate that listening to counting sequences do not automatically elicit sensory or magnitude codes but suggest that the precise increments in the sequence are tracked by the mechanism for processing ordered associations in the SMA and by the mechanism for binding individual lexical items into a cohesive whole in the IFG.

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. 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.

Numerosity representation is encoded in human subcortex.

Certain numerical abilities appear to be relatively ubiquitous in the animal kingdom, including the ability to recognize and differentiate relative quantities. This skill is present in human adults and children, as well as in nonhuman primates and, perhaps surprisingly, is also demonstrated by lower species such as mosquitofish and spiders, despite the absence of cortical computation available to primates. This ubiquity of numerical competence suggests that representations that connect to numerical tasks are likely subserved by evolutionarily conserved regions of the nervous system. Here, we test the hypothesis that the evaluation of relative numerical quantities is subserved by lower-order brain structures in humans. Using a monocular/dichoptic paradigm, across four experiments, we show that the discrimination of displays, consisting of both large (5-80) and small (1-4) numbers of dots, is facilitated in the monocular, subcortical portions of the visual system. This is only the case, however, when observers evaluate larger ratios of 3:1 or 4:1, but not smaller ratios, closer to 1:1. This profile of competence matches closely the skill with which newborn infants and other species can discriminate numerical quantity. These findings suggest conservation of ontogenetically and phylogenetically lower-order systems in adults' numerical abilities. The involvement of subcortical structures in representing numerical quantities provokes a reconsideration of current theories of the neural basis of numerical cognition, inasmuch as it bolsters the cross-species continuity of the biological system for numerical abilities.

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. Across three psychophysical experiments, we demonstrate that suppressing high-level modulatory signals on early cortical activity via visual backward masking completely abolishes the serial dependence effect, indicating the critical role of cortical feedback processing on serial dependence. Moreover, we show that the absence of modulatory feedback results in a robust repulsive aftereffect, as in perceptual adaptation, after only 50 ms of stimulation, indicating the presence of a local neurocomputational process for an automatic and spontaneous recalibration of the stimulus representation. These findings collectively illustrate the interplay between two contrasting cortical mechanisms at short timescales that serve as a basis for our perceptual experience.

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. Here, we addressed this question by using the connectedness illusion, whereby arrays with pairwise connected dots are perceived to be less numerous compared with arrays containing isolated dots. Using EEG and fMRI in two independent experiments, we measured neural responses to dot-array stimuli comprising 16 or 32 dots, either isolated or pairwise connected. The effect of connectedness, which reflects the segmentation of the visual stimulus into perceptual units, was observed in the neural activity after 150 msec post stimulus onset in the EEG experiment and in area V3 in the fMRI experiment using a multivariate pattern analysis. In contrast, earlier neural activity before 100 msec and in area V2 was strictly modulated by numerosity regardless of connectedness, suggesting that this early activity reflects the sensory representation of a dot array before perceptual segmentation. Our findings thus demonstrate that the neural representation for numerosity in early visual cortex is not sufficient for visual number perception and suggest that the perceptual encoding of numerosity occurs at or after the segmentation process that takes place later in area V3.

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. Furthermore, a psychophysical experiment revealed that numerosity perception is biased by a previously presented stimulus in an attractive way, not by repulsive adaptation. These results suggest that serial dependence is a perceptual phenomenon starting from early levels of visual processing and occurring independently from a decision process, which is consistent with the view that these biases smooth out noise from neural signals to establish perceptual continuity.

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. In marked contrast, 7- and 10-year-olds did not show this dissociable neural pattern. Furthermore, the contrast of familiar stimuli (letters or numbers) versus unfamiliar ones (false fonts) showed stark ERP differences between the younger (7- and 10-year-olds) and the older (15-year-olds and adults) participants. These results suggest that both coarse (familiar versus unfamiliar) and fine (letters versus numbers) tuning for letters and numbers continue throughout childhood and early adolescence, demonstrating a profound impact of uniquely human cultural inventions on visual cognition and its development.

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. Here we explore the behavioral signature of serial dependence in numerosity perception by assessing how the perceived numerosity of dot-array stimuli is biased by a task-irrelevant "inducer" stimulus presented before task-relevant stimuli. First, although prior work suggests that numerosity perception starts in the subcortex, the current study rules out a possible involvement of subcortical processing in serial dependence, confirming that the effect likely starts in the visual cortex. Second, we show that the effect is coarsely spatially localized to the position of the inducer stimulus. Third, we demonstrate that the effect is present even with a stimulus presentation procedure minimizing the involvement of post-perceptual processes, but only when participants actively pay attention to the inducer stimulus. Overall, these results provide a comprehensive characterization of serial dependencies in numerosity perception, demonstrating that attractive biases occur by means of spatially localized attentional modulations of early sensory activity.

Numerosity processing in early visual cortex.

While parietal cortex is thought to be critical for representing numerical magnitudes, we recently reported an event-related potential (ERP) study demonstrating selective neural sensitivity to numerosity over midline occipital sites very early in the time course, suggesting the involvement of early visual cortex in numerosity processing. However, which specific brain area underlies such early activation is not known. Here, we tested whether numerosity-sensitive neural signatures arise specifically from the initial stages of visual cortex, aiming to localize the generator of these signals by taking advantage of the distinctive folding pattern of early occipital cortices around the calcarine sulcus, which predicts an inversion of polarity of ERPs arising from these areas when stimuli are presented in the upper versus lower visual field. Dot arrays, including 8-32dots constructed systematically across various numerical and non-numerical visual attributes, were presented randomly in either the upper or lower visual hemifields. Our results show that neural responses at about 90ms post-stimulus were robustly sensitive to numerosity. Moreover, the peculiar pattern of polarity inversion of numerosity-sensitive activity at this stage suggested its generation primarily in V2 and V3. In contrast, numerosity-sensitive ERP activity at occipito-parietal channels later in the time course (210-230ms) did not show polarity inversion, indicating a subsequent processing stage in the dorsal stream. Overall, these results demonstrate that numerosity processing begins in one of the earliest stages of the cortical visual stream.

Rapid and Direct Encoding of Numerosity in the Visual Stream.

Humans are endowed with an intuitive number sense that allows us to perceive and estimate numerosity without relying on language. It is controversial, however, as to whether there is a neural mechanism for direct perception of numerosity or whether numerosity is perceived indirectly via other perceptual properties. In this study, we used a novel regression-based analytic method, which allowed an assessment of the unique contributions of visual properties, including numerosity, to explain visual evoked potentials of participants passively viewing dot arrays. We found that the human brain is uniquely sensitive to numerosity and more sensitive to changes in numerosity than to changes in other visual properties, starting extremely early in the visual stream: 75 ms over a medial occipital site and 180 ms over bilateral occipitoparietal sites. These findings provide strong evidence for the existence of a neural mechanism for rapidly and directly extracting numerosity information in the human visual pathway.

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., density, area) influence numerosity perception in this processing cascade, little is known about how the spatiotemporal properties of the stimuli affect numerosity processing. Whether numerosity information is integrated over space and time in the processing cascade is an important question as it can provide insights into how the system dedicated for numerosity interacts with other perceptual systems. To address these issues, in four independent experiments, we asked participants to judge the numerosities of various different kinds of dynamically presented dot arrays, such as dots randomly changing in their locations, moving in smooth trajectories, or flickering on and off. The results revealed a systematic overestimation of dynamically presented dot arrays, which implicates the existence of spatiotemporal integration mechanisms, both at the early sensory representation stage and the later conceptual representation stage. The results also revealed the influence of motion and color processing areas on numerosity processing. The findings thus provide empirical evidence that numerosity perception arises from a complex interaction between multiple perceptual mechanisms in the visual stream, and that it is shaped by the integration of spatiotemporal properties of visual stimuli.

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. 2).

Non-symbolic approximate arithmetic training improves math performance in preschoolers.

Math proficiency at early school age is an important predictor of later academic achievement. Thus, an important goal for society should be to improve math readiness in preschool-age children, especially in low-income children who typically arrive in kindergarten with less mathematical competency than their higher income peers. The majority of existing research-based math intervention programs target symbolic verbal number concepts in young children. However, very little attention has been paid to the preverbal intuitive ability to approximately represent numerical quantity, which is hypothesized to be an important foundation for full-fledged mathematical thinking. Here, we tested the hypothesis that repeated engagement of non-symbolic approximate addition and subtraction of large arrays of items results in improved math skills in very young children, an idea that stems from our previous studies in adults. In the current study, 3- to 5-year-olds showed selective improvements in math skills after multiple days of playing a tablet-based non-symbolic approximate arithmetic game compared with children who played a memory game. These findings, collectively with our previous reports, suggest that mental manipulation of approximate numerosities provides an important tool for improving math readiness, even in preschoolers who have yet to master the meaning of number words.

Experience-dependent hemispheric specialization of letters and numbers is revealed in early visual processing.

Recent fMRI research has demonstrated that letters and numbers are preferentially processed in distinct regions and hemispheres in the visual cortex. In particular, the left visual cortex preferentially processes letters compared with numbers, whereas the right visual cortex preferentially processes numbers compared with letters. Because letters and numbers are cultural inventions and are otherwise physically arbitrary, such a double dissociation is strong evidence for experiential effects on neural architecture. Here, we use the high temporal resolution of ERPs to investigate the temporal dynamics of the neural dissociation between letters and numbers. We show that the divergence between ERP traces to letters and numbers emerges very early in processing. Letters evoked greater N1 waves (latencies 140-170 msec) than did numbers over left occipital channels, whereas numbers evoked greater N1s than letters over the right, suggesting letters and numbers are preferentially processed in opposite hemispheres early in visual encoding. Moreover, strings of letters, but not single letters, elicited greater P2 ERP waves (starting around 250 msec) than numbers did over the left hemisphere, suggesting that the visual cortex is tuned to selectively process combinations of letters, but not numbers, further along in the visual processing stream. Additionally, the processing of both of these culturally defined stimulus types differentiated from similar but unfamiliar visual stimulus forms (false fonts) even earlier in the processing stream (the P1 at 100 msec). These findings imply major cortical specialization processes within the visual system driven by experience with reading and mathematics.

Neural connectivity patterns underlying symbolic number processing indicate mathematical achievement in children.

In early childhood, humans learn culturally specific symbols for number that allow them entry into the world of complex numerical thinking. Yet little is known about how the brain supports the development of the uniquely human symbolic number system. Here, we use functional magnetic resonance imaging along with an effective connectivity analysis to investigate the neural substrates for symbolic number processing in young children. We hypothesized that, as children solidify the mapping between symbols and underlying magnitudes, important developmental changes occur in the neural communication between the right parietal region, important for the representation of non-symbolic numerical magnitudes, and other brain regions known to be critical for processing numerical symbols. To test this hypothesis, we scanned children between 4 and 6 years of age while they performed a magnitude comparison task with Arabic numerals (numerical, symbolic), dot arrays (numerical, non-symbolic), and lines (non-numerical). We then identified the right parietal seed region that showed greater blood-oxygen-level-dependent signal in the numerical versus the non-numerical conditions. A psychophysiological interaction method was used to find patterns of effective connectivity arising from this parietal seed region specific to symbolic compared to non-symbolic number processing. Two brain regions, the left supramarginal gyrus and the right precentral gyrus, showed significant effective connectivity from the right parietal cortex. Moreover, the degree of this effective connectivity to the left supramarginal gyrus was correlated with age, and the degree of the connectivity to the right precentral gyrus predicted performance on a standardized symbolic math test. These findings suggest that effective connectivity underlying symbolic number processing may be critical as children master the associations between numerical symbols and magnitudes, and that these connectivity patterns may serve as an important indicator of mathematical achievement.

Parietal functional connectivity in numerical cognition.

The parietal cortex is central to numerical cognition. The right parietal region is primarily involved in basic quantity processing, while the left parietal region is additionally involved in precise number processing and numerical operations. Little is known about how the 2 regions interact during numerical cognition. We hypothesized that functional connectivity between the right and left parietal cortex is critical for numerical processing that engages both basic number representation and learned numerical operations. To test this hypothesis, we estimated neural activity using functional magnetic resonance imaging in participants performing numerical and arithmetic processing on dot arrays. We first found task-based functional connectivity between a right parietal seed and the left sensorimotor cortex in all task conditions. As we hypothesized, we found enhanced functional connectivity between this right parietal seed and both the left parietal cortex and neighboring right parietal cortex, particularly during subtraction. The degree of functional connectivity also correlated with behavioral performance across individual participants, while activity within each region did not. These results highlight the role of parietal functional connectivity in numerical processing. They suggest that arithmetic processing depends on crosstalk between and within the parietal cortex and that this crosstalk contributes to one's numerical competence.

Neural broadening or neural attenuation? Investigating age-related dedifferentiation in the face network in a large lifespan sample.

Previous studies have found that cortical responses to different stimuli become less distinctive as people get older. This age-related dedifferentiation may reflect the broadening of the tuning curves of category-selective neurons (broadening hypothesis) or it may be due to decreased activation of category-selective neurons (attenuation hypothesis). In this study, we evaluated these hypotheses in the context of the face-selective neural network. Over 300 participants, ranging in age from 20 to 89 years, viewed images of faces, houses, and control stimuli in a functional magnetic resonance imaging session. Regions within the core face network and extended face network were identified in individual subjects. Activation in many of these regions became significantly less face-selective with age, confirming previous reports of age-related dedifferentiation. Consistent with the broadening hypothesis, this dedifferentiation in the fusiform face area (FFA) was driven by increased activation to houses. In contrast, dedifferentiation in the extended face network was driven by decreased activation to faces, consistent with the attenuation hypothesis. These results suggest that age-related dedifferentiation reflects distinct processes in different brain areas. More specifically, dedifferentiation in FFA activity may be due to broadening of the tuning curves for face-selective neurons, while dedifferentiation in the extended face network reflects reduced face- or emotion-selective activity.

Training the approximate number system improves math proficiency.

Humans and nonhuman animals share an approximate number system (ANS) that permits estimation and rough calculation of quantities without symbols. Recent studies show a correlation between the acuity of the ANS and performance in symbolic math throughout development and into adulthood, which suggests that the ANS may serve as a cognitive foundation for the uniquely human capacity for symbolic math. Such a proposition leads to the untested prediction that training aimed at improving ANS performance will transfer to improvement in symbolic-math ability. In the two experiments reported here, we showed that ANS training on approximate addition and subtraction of arrays of dots selectively improved symbolic addition and subtraction. This finding strongly supports the hypothesis that complex math skills are fundamentally linked to rudimentary preverbal quantitative abilities and provides the first direct evidence that the ANS and symbolic math may be causally related. It also raises the possibility that interventions aimed at the ANS could benefit children and adults who struggle with math.