Neuronal correlates of a visual "sense of number" in primate parietal and prefrontal cortices

Sharpening the number sense: Developmental trends in numerosity perception

Numerosity perception, the ability to process and estimate the number of objects in a set without explicitly counting, has been widely studied, and one well-established finding is that children become more accurate at perceiving numerosity with age. The question remains, however, what the underlying cognitive processes and mechanisms are that drive this improvement. Some authors have suggested that this is due to an increased numerical precision (i.e., the sharpening hypothesis), whereas others have proposed that the more accurate performance is due to the improved ability to inhibit non-numerical features of the display such as object size and spacing of items (i.e., the filtering hypothesis). The current study examined the developmental trajectory of numerosity perception across three age groups (M = 5.65, M = 11.03, and M = 20.10 years). As expected, more accurate performance was observed with age. Regression and analyses of variance revealing the contribution of numerical and non-numerical predictors in performance show that the performance in all age groups was primarily driven by numerical information and that its contribution increased with age. In addition, a consistent bias toward non-numerical features was observed in all age groups. These results support the sharpening hypothesis for children from 5 years of age to early adulthood, suggesting that from this age onward children increasingly focus on numerical information as they get older. These results have important implications for the understanding of the development and specific improvements of numerical perception.

Effects of feature-based attention on numerosity perception

One of the most remarkable human cognitive abilities is the "sense of number," that is, the almost instantaneous perception of numerosity information in the visual environment. While numerosity perception mirrors primary sensory processing in many aspects, little is known whether and how numerosity perception is influenced by selective attention to numerosity. Here, we investigated the effects of feature-based attention on numerosity perception using the visual search paradigm and the adaptation paradigm, respectively. In the visual search experiment, participants identified the presence of a numerosity-defined outlier among an array of distractors, while in the numerosity adaptation experiment, participants attended to a random dot field whose numerosity either matched or differed from the adaptor. We found a "semiparallel" search pattern in which attention was captured by the numerosity-defined outliers in a time-consuming, rather than an instantaneous manner. Interestingly, reduced numerosity adaptation aftereffects were observed when the attended numerosity matched the numerosity of the adaptor, indicating weakened perceptual representation of numerosity induced by feature-based attention. Our findings show, for the first time, that numerosity serves as a unique unit of nonspatial feature-based attention and that numerosity perception was modulated by feature-based attention via a distinctive mechanism that differed from other primary visual features.

Numerical cognition across the lifespan: A selective review of key developmental stages and neural, cognitive, and affective underpinnings

Numerical cognition constitutes a set of hierarchically related skills and abilities that develop-and may subsequently begin to decline-over developmental time. An innate "number sense" has long been argued to provide a foundation for the development of increasingly complex and applied numerical cognition, such as symbolic numerical reference, arithmetic, and financial literacy. However, evidence for a direct link between basic perceptual mechanisms that allow us to determine numerical magnitude (e.g., "how many" objects are in front of us and whether some of these are of a "greater" or "lesser" quantity), and later symbolic applications for counting and mathematics, has recently been challenged. Understanding how one develops an increasingly precise sense of number and which neurocognitive mechanisms support arithmetic development and achievement is crucial for developing successful mathematics curricula, supporting individual financial literacy and decision-making, and designing appropriate intervention and remediation programs for mathematical learning disabilities as well as mathematics anxiety. The purpose of this review is to provide a broad overview of the cognitive, neural, and affective underpinnings of numerical cognition-spanning the earliest hours of infancy to senior adulthood-and highlight gaps in our knowledge that remain to be addressed.

Neuronal mechanisms enhancing selectivity of the innate number sense via learning

In their feature article, Lorenzi et al. (2025) compiled extensive biological evidence on the ontogenetic origins of the number sense. Drawing on both behavioral and neurobiological data, they convincingly argue that the "number sense" is fundamentally innate and present from birth in numerically competent animals, including humans. At the same time, the authors acknowledge the role of learning and experience in shaping numerical cognition. This commentary builds on the idea of learning-induced changes to the number sense, extending the concept of an innate number sense to one that is modifiable through learning and experience. It summarizes evidence from single-neuron recordings and proposes neurophysiological mechanisms underlying these learning-induced changes in numerical cognition.

Is there an innate sense of number in the brain?

The approximate number system or «sense of number» is a crucial, presymbolic mechanism enabling animals to estimate quantities, which is essential for survival in various contexts (eg estimating numerosities of social companions, prey, predators, and so on). Behavioral studies indicate that a sense of number is widespread across vertebrates and invertebrates. Specific brain regions such as the intraparietal sulcus and prefrontal cortex in primates, or equivalent areas in birds and fish, are involved in numerical estimation, and their activity is modulated by the ratio of quantities. Data gathered across species strongly suggest similar evolutionary pressures for number estimation pointing to a likely common origin, at least across vertebrates. On the other hand, few studies have investigated the origins of the sense of number. Recent findings, however, have shown that numerosity-selective neurons exist in newborn animals, such as domestic chicks and zebrafish, supporting the hypothesis of an innateness of the approximate number system. Control-rearing experiments on visually naïve animals further support the notion that the sense of number is innate and does not need any specific instructive experience in order to be triggered.

The calculating brain

The human brain possesses neural networks and mechanisms enabling the representation of numbers, basic arithmetic operations, and mathematical reasoning. Without the ability to represent numerical quantity and perform calculations, our scientifically and technically advanced culture would not exist. However, the origins of numerical abilities are grounded in an intuitive understanding of quantity deeply rooted in biology. Nevertheless, more advanced symbolic arithmetic skills require a cultural background with formal mathematical education. In the past two decades, cognitive neuroscience has seen significant progress in understanding the workings of the calculating brain through various methods and model systems. This review begins by exploring the mental and neuronal representations of nonsymbolic numerical quantity and then progresses to symbolic representations acquired in childhood. During arithmetic operations (addition, subtraction, multiplication, and division), these representations are processed and transformed according to arithmetic rules and principles, leveraging different mental strategies and types of arithmetic knowledge that can be dissociated in the brain. Although it was once believed that number processing and calculation originated from the language faculty, it is now evident that mathematical and linguistic abilities are primarily processed independently in the brain. Understanding how the healthy brain processes numerical information is crucial for gaining insights into debilitating numerical disorders, including acquired conditions like acalculia and learning-related calculation disorders such as developmental dyscalculia.

Zero-shot counting with a dual-stream neural network model

To understand a visual scene, observers need to both recognize objects and encode relational structure. For example, a scene comprising three apples requires the observer to encode concepts of "apple" and "three." In the primate brain, these functions rely on dual (ventral and dorsal) processing streams. Object recognition in primates has been successfully modeled with deep neural networks, but how scene structure (including numerosity) is encoded remains poorly understood. Here, we built a deep learning model, based on the dual-stream architecture of the primate brain, which is able to count items "zero-shot"-even if the objects themselves are unfamiliar. Our dual-stream network forms spatial response fields and lognormal number codes that resemble those observed in the macaque posterior parietal cortex. The dual-stream network also makes successful predictions about human counting behavior. Our results provide evidence for an enactive theory of the role of the posterior parietal cortex in visual scene understanding.

Neural Basis of Number Sense in Larval Zebrafish

Number sense, the ability to discriminate the quantity of objects, is crucial for survival. To understand how neurons work together and develop to mediate number sense, we used two-photon fluorescence light sheet microscopy to capture the activity of individual neurons throughout the brain of larval Danio rerio, while displaying a visual number stimulus to the animal. We identified number-selective neurons as early as 3 days post-fertilization and found a proportional increase of neurons tuned to larger quantities after 3 days. We used machine learning to predict the stimulus from the neuronal activity and observed that the prediction accuracy improves with age. We further tested ethanol's effect on number sense and found a decrease in number-selective neurons in the forebrain, suggesting cognitive impairment. These findings are a significant step towards understanding neural circuits devoted to discrete magnitudes and our methodology to track single-neuron activity across the whole brain is broadly applicable to other fields in neuroscience.

Bistable perception of symbolic numbers

Numerals, that is, semantic expressions of numbers, enable us to have an exact representation of the amount of things. Visual processing of numerals plays an indispensable role in the recognition and interpretation of numbers. Here, we investigate how visual information from numerals is processed to achieve semantic understanding. We first found that partial occlusion of some digital numerals introduces bistable interpretations. Next, by using the visual adaptation method, we investigated the origin of this bistability in human participants. We showed that adaptation to digital and normal Arabic numerals, as well as homologous shapes, but not Chinese numerals, biases the interpretation of a partially occluded digital numeral. We suggest that this bistable interpretation is driven by intermediate shape processing stages of vision, that is, by features more complex than local visual orientations, but more basic than the abstract concepts of numerals.

Inferior parietal cortex represents relational structures for explicit transitive inference

The human brain is distinguished by its ability to perform explicit logical reasoning like transitive inference. This study investigated the functional role of the inferior parietal cortex in transitive inference with functional MRI. Participants viewed premises describing abstract relations among items. They accurately recalled the relationship between old pairs of items, effectively inferred the relationship between new pairs of items, and discriminated between true and false relationships for new pairs. First, the inferior parietal cortex, but not the hippocampus or lateral prefrontal cortex, was associated with transitive inference. The inferior parietal activity and functional connectivity were modulated by inference (new versus old pairs) and discrimination (true versus false pairs). Moreover, the new/old and true/false pairs were decodable from the inferior parietal representation. Second, the inferior parietal cortex represented an integrated relational structure (ordered and directed series). The inferior parietal activity was modulated by serial position (larger end versus center pairs). The inferior parietal representation was modulated by symbolic distance (adjacent versus distant pairs) and direction (preceding versus following pairs). It suggests that the inferior parietal cortex may flexibly integrate observed relations into a relational structure and use the relational structure to infer unobserved relations and discriminate between true and false relations.

Recruitment of the premotor cortex during arithmetic operations by the monkey

Arithmetic operations are complex mental processes rooted in the abstract concept of numerosity. Despite the significance, the neural architecture responsible for these operations has remained largely uncharted. In this study, we explored the presence of specific neuronal activity in the dorsal premotor cortex of the monkey dedicated to numerical addition and subtraction. Our findings reveal that many of these neural activities undergo a transformation, shifting their coding from arithmetic to motor representations. These motor representations include information about which hand to use and the number of steps involved in the action. We consistently observed that cells related to the right-hand encoded addition, while those linked to the left-hand encoded subtraction, suggesting that arithmetic operations and motor commands are intertwining with each other. Furthermore, we used a multivariate decoding technique to predict the monkey's behaviour based on the activity of these arithmetic-related cells. The classifier trained to discern arithmetic operations, including addition and subtraction, not only predicted the arithmetic decisions but also the subsequent motor actions of the right and left-hand. These findings imply a cognitive extension of the motor cortex's function, where inherent neural systems are repurposed to facilitate arithmetic operations.

A number sense as an emergent property of the manipulating brain

The ability to understand and manipulate numbers and quantities emerges during childhood, but the mechanism through which humans acquire and develop this ability is still poorly understood. We explore this question through a model, assuming that the learner is able to pick up and place small objects from, and to, locations of its choosing, and will spontaneously engage in such undirected manipulation. We further assume that the learner's visual system will monitor the changing arrangements of objects in the scene and will learn to predict the effects of each action by comparing perception with a supervisory signal from the motor system. We model perception using standard deep networks for feature extraction and classification. Our main finding is that, from learning the task of action prediction, an unexpected image representation emerges exhibiting regularities that foreshadow the perception and representation of numbers and quantity. These include distinct categories for zero and the first few natural numbers, a strict ordering of the numbers, and a one-dimensional signal that correlates with numerical quantity. As a result, our model acquires the ability to estimate numerosity, i.e. the number of objects in the scene, as well as subitization, i.e. the ability to recognize at a glance the exact number of objects in small scenes. Remarkably, subitization and numerosity estimation extrapolate to scenes containing many objects, far beyond the three objects used during training. We conclude that important aspects of a facility with numbers and quantities may be learned with supervision from a simple pre-training task. Our observations suggest that cross-modal learning is a powerful learning mechanism that may be harnessed in artificial intelligence.

Adaptation to numerosity affects the pupillary light response

We recently showed that the gain of the pupillary light response depends on numerosity, with weaker responses to fewer items. Here we show that this effect holds when the stimuli are physically identical but are perceived as less numerous due to numerosity adaptation. Twenty-eight participants adapted to low (10 dots) or high (160 dots) numerosities and subsequently watched arrays of 10-40 dots, with variable or homogeneous dot size. Luminance was constant across all stimuli. Pupil size was measured with passive viewing, and the effects of adaptation were checked in a separate psychophysical session. We found that perceived numerosity was systematically lower, and pupillary light responses correspondingly smaller, following adaptation to high rather than low numerosities. This is consistent with numerosity being a primary visual feature, spontaneously encoded even when task irrelevant, and affecting automatic and unconscious behaviours like the pupillary light response.

Visuo-frontal interactions during social learning in freely moving macaques

Social interactions represent a ubiquitous aspect of our everyday life that we acquire by interpreting and responding to visual cues from conspecifics1. However, despite the general acceptance of this view, how visual information is used to guide the decision to cooperate is unknown. Here, we wirelessly recorded the spiking activity of populations of neurons in the visual and prefrontal cortex in conjunction with wireless recordings of oculomotor events while freely moving macaques engaged in social cooperation. As animals learned to cooperate, visual and executive areas refined the representation of social variables, such as the conspecific or reward, by distributing socially relevant information among neurons in each area. Decoding population activity showed that viewing social cues influences the decision to cooperate. Learning social events increased coordinated spiking between visual and prefrontal cortical neurons, which was associated with improved accuracy of neural populations to encode social cues and the decision to cooperate. These results indicate that the visual-frontal cortical network prioritizes relevant sensory information to facilitate learning social interactions while freely moving macaques interact in a naturalistic environment.

Neurobiology of numerical learning

Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying numerical cognition in different species have long been appreciated, genetic and molecular techniques have more recently expanded the knowledge about the mechanisms underlying numerical learning. In this review, we discuss the status of the research related to the neurobiological bases of numerical abilities. We consider how genetic factors have been associated with mathematical capacities and how these link to the current knowledge of brain regions underlying these capacities in human and non-human animals. We further discuss the extent to which significant variations in the levels of specific neurotransmitters may be used as potential markers of individual performance and learning difficulties and take into consideration the therapeutic potential of brain stimulation methods to modulate learning and improve interventional outcomes. The implications of this research for formulating a more comprehensive view of the neural basis of mathematical learning are discussed.

Magnitude shifts spatial attention from left to right in rhesus monkeys as in the human mental number line

Humans typically represent numbers and quantities along a left-to-right continuum. Early perspectives attributed number-space association to culture; however, recent evidence in newborns and animals challenges this hypothesis. We investigate whether the length of an array of dots influences spatial bias in rhesus macaques. We designed a touch-screen task that required monkeys to remember the location of a target. At test, monkeys maintained high performance with arrays of 2, 4, 6, or 10 dots, regardless of changes in the array's location, spacing, and length. Monkeys remembered better left targets with 2-dot arrays and right targets with 6- or 10-dot arrays. Replacing the 10-dot array with a long bar, yielded more accurate performance with rightward locations, consistent with an underlying left-to-right oriented magnitude code. Our study supports the hypothesis of a spatially oriented mental magnitude line common to humans and animals, countering the idea that this code arises from uniquely human cultural learning.

Sequential neuronal processing of number values, abstract decision, and action in the primate prefrontal cortex

Decision-making requires processing of sensory information, comparing the gathered evidence to make a judgment, and performing the action to communicate it. How neuronal representations transform during this cascade of representations remains a matter of debate. Here, we studied the succession of neuronal representations in the primate prefrontal cortex (PFC). We trained monkeys to judge whether a pair of sequentially presented displays had the same number of items. We used a combination of single neuron and population-level analyses and discovered a sequential transformation of represented information with trial progression. While numerical values were initially represented with high precision and in conjunction with detailed information such as order, the decision was encoded in a low-dimensional subspace of neural activity. This decision encoding was invariant to both retrospective numerical values and prospective motor plans, representing only the binary judgment of "same number" versus "different number," thus facilitating the generalization of decisions to novel number pairs. We conclude that this transformation of neuronal codes within the prefrontal cortex supports cognitive flexibility and generalizability of decisions to new conditions.

Human brain representations of internally generated outcomes of approximate calculation revealed by ultra-high-field brain imaging

Much of human culture's advanced technology owes its existence to the ability to mentally manipulate quantities. Neuroscience has described the brain regions overall recruited by numerical tasks and the neuronal codes representing individual quantities during perceptual tasks. Nevertheless, it remains unknown how quantity representations are combined or transformed during mental computations and how specific quantities are coded in the brain when generated as the result of internal computations rather than evoked by a stimulus. Here, we imaged the brains of adult human subjects at 7 Tesla during an approximate calculation task designed to disentangle in- and outputs of the computation from the operation itself. While physically presented sample numerosities were distinguished in activity patterns along the dorsal visual pathway and within frontal and occipito-temporal regions, a representation of the internally generated result was most prominently detected in higher order regions such as angular gyrus and lateral prefrontal cortex. Behavioral precision in the task was related to cross-decoding performance between sample and result representations in medial IPS regions. This suggests the transformation of sample into result may be carried out within dorsal stream sensory-motor integration regions, and resulting outputs maintained for task purposes in higher-level regions in a format possibly detached from sensory-evoked inputs.

Convergent Circuit Computation for Categorization in the Brains of Primates and Songbirds

Categorization is crucial for behavioral flexibility because it enables animals to group stimuli into meaningful classes that can easily be generalized to new circumstances. A most abstract quantitative category is set size, the number of elements in a set. This review explores how categorical number representations are realized by the operations of excitatory and inhibitory neurons in associative telencephalic microcircuits in primates and songbirds. Despite the independent evolution of the primate prefrontal cortex and the avian nidopallium caudolaterale, the neuronal computations of these associative pallial circuits show surprising correspondence. Comparing cellular functions in distantly related taxa can inform about the evolutionary principles of circuit computations for cognition in distinctly but convergently realized brain structures.

Visual number sense for real-world scenes shared by deep neural networks and humans

Recently, visual number sense has been identified from deep neural networks (DNNs). However, whether DNNs have the same capacity for real-world scenes, rather than the simple geometric figures that are often tested, is unclear. In this study, we explore the number perception of scenes using AlexNet and find that numerosity can be represented by the pattern of group activation of the category layer units. The global activation of these units increases with the number of objects in the scene, and the variations in their activation decrease accordingly. By decoding the numerosity from this pattern, we reveal that the embedding coefficient of a scene determines the likelihood of potential objects to contribute to numerical perception. This was demonstrated by the more optimized performance for pictures with relatively high embedding coefficients in both DNNs and humans. This study for the first time shows that a distinct feature in visual environments, revealed by DNNs, can modulate human perception, supported by a group-coding mechanism.

The role of non-numerical information in the perception of temporal numerosity

Numerosity perception refers to the ability to make rapid but approximate estimates of the quantity of elements in a set (spatial numerosity) or presented sequentially (temporal numerosity). Whether numerosity is directly perceived or indirectly recomputed from non-numerical features is a highly debated issue. In the spatial domain, area and density have been suggested as the main parameters through which numerosity would be recomputed. In the temporal domain, stimuli duration and temporal frequency could be similarly exploited to retrieve numerosity. By adapting a psychophysical technique previously exploited in the spatial domain, we investigated whether temporal visual numerosity is directly perceived. Adult participants observed sequences of visual impulses sampled from a stimulus space spanning several levels of temporal frequency and duration (and hence numerosity), and then reproduced the sequence as accurately as possible via a series of keypresses. Crucially, participants were not asked to reproduce any particular property (such as number of impulses) but were free to choose any available cue (such as total duration, or temporal frequency). The results indicate that while the overall sequence duration was barely considered, numerosity and temporal frequency were both spontaneously used as the main cues to reproduce the sequences, with a slight but significant dominance of numerosity. Overall, the results are in line with previous literature suggesting that numerosity is directly encoded, even for temporal sequences, but a non-numerical feature (temporal frequency) is also used in reproducing sequences.

The neural correlates of individual differences in numerosity perception: A voxel-based morphometry study

Numerosity perception is a fundamental cognitive function in humans and animals. Using an individual difference approach with a comprehensive dataset (N = 249), we performed a voxel-based morphometry analysis to unravel the neuroanatomical substrates associated with individual differences in numerosity perception sensitivity, measured by a classical non-symbolic numerical judgment task. Results showed that greater gray matter volume (GMV) in the left cerebellum, right temporal pole, and right parahippocampal was positively correlated to higher perceptual sensitivity to numerosity. In contrast, the GMV in the left intraparietal sulcus, and bilateral precentral/postcentral gyrus was negatively correlated to the sensitivity of numerosity perception. These findings indicate that a wide range of brain structures, rather than a specific anatomical structure or circuit, forms the neuroanatomical basis of numerosity perception, lending support to the emerging network view of the neural representation of numerosity. This work contributes to a more comprehensive understanding of how the brain processes numerical information.

•Unveils neuroanatomical basis of numerosity perception •Discovers positive and negative greater GMV correlations •Links GMV in a wide range of brain regions to numerical sensitivity •Supports the network view of the neural representation of numerosity perception

Learning-induced reorganization of number neurons and emergence of numerical representations in a biologically inspired neural network

Number sense, the ability to decipher quantity, forms the foundation for mathematical cognition. How number sense emerges with learning is, however, not known. Here we use a biologically-inspired neural architecture comprising cortical layers V1, V2, V3, and intraparietal sulcus (IPS) to investigate how neural representations change with numerosity training. Learning dramatically reorganized neuronal tuning properties at both the single unit and population levels, resulting in the emergence of sharply-tuned representations of numerosity in the IPS layer. Ablation analysis revealed that spontaneous number neurons observed prior to learning were not critical to formation of number representations post-learning. Crucially, multidimensional scaling of population responses revealed the emergence of absolute and relative magnitude representations of quantity, including mid-point anchoring. These learnt representations may underlie changes from logarithmic to cyclic and linear mental number lines that are characteristic of number sense development in humans. Our findings elucidate mechanisms by which learning builds novel representations supporting number sense.

Neural representations of economic decision variables in human posterior parietal cortex

Decision making has been intensively studied in the posterior parietal cortex in non-human primates on a single neuron level. In humans decision making has mainly been studied with psychophysical tools or with fMRI. Here, we investigated how single neurons from human posterior parietal cortex represent numeric values informing future decisions during a complex two-player game. The tetraplegic study participant was implanted with a Utah electrode array in the anterior intraparietal area (AIP). We played a simplified variant of Black Jack with the participant while neuronal data was recorded. During the game two players are presented with numbers which are added up. Each time a number is presented the player has to decide to proceed or to stop. Once the first player stops or the score reaches a limit the turn passes on to the second player who tries to beat the score of the first player. Whoever is closer to the limit (without overshooting) wins the game. We found that many AIP neurons selectively responded to the face value of the presented number. Other neurons tracked the cumulative score or were selectively active for the upcoming decision of the study participant. Interestingly, some cells also kept track of the opponent's score. Our findings show that parietal regions engaged in hand action control also represent numbers and their complex transformations. This is also the first demonstration of complex economic decisions being possible to track in single neuron activity in human AIP. Our findings show how tight are the links between parietal neural circuits underlying hand control, numerical cognition and complex decision-making.

Implicit Processing of Numerical Order: Evidence from a Continuous Interocular Flash Suppression Study

Processing the ordered relationships between sequential items is a key element in many cognitive abilities that are important for survival. Specifically, order may play a crucial role in numerical processing. Here, we assessed the existence of a cognitive system designed to implicitly evaluate numerical order, by combining continuous flash suppression with a priming method in a numerical enumeration task. In two experiments and diverse statistical analysis, targets that required numerical enumeration were preceded by an invisibly ordered or non-ordered numerical prime sequence. The results of both experiments showed that enumeration for targets that appeared after an ordered prime was significantly faster, while the ratio of the prime sequences produced no significant effect. The findings suggest that numerical order is processed implicitly and affects a basic cognitive ability: enumeration of quantities.

Shared Neural Activity But Distinct Neural Dynamics for Cognitive Control in Monkey Prefrontal and Parietal Cortex

To better understand how prefrontal networks mediate forms of cognitive control disrupted in schizophrenia, we translated a variant of the AX continuous performance task that measures specific deficits in the human disease to 2 male monkeys and recorded neurons in PFC and parietal cortex during task performance. In the task, contextual information instructed by cue stimuli determines the response required to a subsequent probe stimulus. We found parietal neurons encoding the behavioral context instructed by cues that exhibited nearly identical activity to their prefrontal counterparts (Blackman et al., 2016). This neural population switched their preference for stimuli over the course of the trial depending on whether the stimuli signaled the need to engage cognitive control to override a prepotent response. Cues evoked visual responses that appeared in parietal neurons first, whereas population activity encoding contextual information instructed by cues was stronger and more persistent in PFC. Increasing cognitive control demand biased the representation of contextual information toward the PFC and augmented the temporal correlation of task-defined information encoded by neurons in the two areas. Oscillatory dynamics in local field potentials differed between cortical areas and carried as much information about task conditions as spike rates. We found that, at the single-neuron level, patterns of activity evoked by the task were nearly identical between the two cortical areas. Nonetheless, distinct population dynamics in PFC and parietal cortex were evident. suggesting differential contributions to cognitive control.SIGNIFICANCE STATEMENT We recorded neural activity in PFC and parietal cortex of monkeys performing a task that measures cognitive control deficits in schizophrenia. This allowed us to characterize computations performed by neurons in the two areas to support forms of cognitive control disrupted in the disease. Subpopulations of neurons in the two areas exhibited parallel modulations in firing rate; and as a result, all patterns of task-evoked activity were distributed between PFC and parietal cortex. This included the presence in both cortical areas of neurons reflecting proactive and reactive cognitive control dissociated from stimuli or responses in the task. However, differences in the timing, strength, synchrony, and correlation of information encoded by neural activity were evident, indicating differential contributions to cognitive control.

Omit needless words: Sentence length perception

Short sentences improve readability. Short sentences also promote social justice through accessibility and inclusiveness. Despite this, much remains unknown about sentence length perception-an important factor in producing readable writing. Accordingly, we conducted a psychophysical study using procedures from Signal Detection Theory to examine sentence length perception in naive adults. Participants viewed real-world full-page text samples and judged whether a bolded target sentence contained more or fewer than 17 words. The experiment yielded four findings. First, naïve adults perceived sentence length in real-world text samples quickly (median = 300-400 ms) and precisely (median = ~90% correct). Second, flipping real-world text samples upside-down generated no reaction-time cost and nearly no loss in the precision of sentence length perception. This differs from the large inversion effects that characterize other highly practiced, real-world perceptual tasks involving canonically oriented stimuli, most notably face perception and reading. Third, participants significantly underestimated the length of mirror-reversed sentences-but not upside-down, nor standard sentences. This finding parallels participants' familiarity with commonly occurring left-justified right-ragged text, and suggests a novel demonstration of left-lateralized anchoring in scene syntax. Fourth, error patterns demonstrated that participants achieved their high speed, high precision sentence-length judgments by heuristically counting text lines, not by explicitly counting words. This suggests practical advice for writing instructors to offer students. When copy editing, students can quickly and precisely identify their long sentences via a line-counting heuristic, e.g., "a 17-word sentence spans about 1.5 text lines". Students can subsequently improve a long sentence's readability and inclusiveness by omitting needless words.

Visual adaptation reveals multichannel coding for numerosity

Visual numerosity is represented automatically and rapidly, but much remains unknown about the computations underlying this perceptual experience. For example, it is unclear whether numerosity is represented with an opponent channel or multichannel coding system. Within an opponent channel system, all numerical values are represented via the relative activity of two pools of neurons (i.e., one pool with a preference for small numerical values and one pool with a preference for large numerical values). However, within a multichannel coding system, all numerical values are represented directly, with separate pools of neurons for each (discriminable) numerical value. Using an adaptation paradigm, we assessed whether the visual perception of number is better characterized by an opponent channel or multichannel system. Critically, these systems make distinct predictions regarding the pattern of aftereffects exhibited when an observer is adapted to an intermediate numerical value. Opponent channel coding predicts no aftereffects because both pools of neurons adapt equally. By contrast, multichannel coding predicts repulsive aftereffects, wherein numerical values smaller than the adapter are underestimated and those larger than the adapter are overestimated. Consistent with multichannel coding, visual adaptation to an intermediate value (50 dots) yielded repulsive aftereffects, such that participants underestimated stimuli ranging from 10-50 dots, but overestimated stimuli ranging from 50-250 dots. These findings provide novel evidence that the visual perception of number is supported by a multichannel, not opponent channel, coding system, and raise important questions regarding the contributions of different cortical regions, such as the ventral and lateral intraparietal areas, to the representation of number.

Number comparison under the Ebbinghaus illusion

A series of studies show interest in how visual attributes affect the estimate of object numbers in a scene. In comparison tasks, it is suggested that larger patches are perceived as more numerous. However, the inequality of density, which changes inversely with the area when numerosity remains constant, may mediate the influence of area on numerosity perception. This study aims to explore the role of area and density in the judgment of numerosity. The Ebbinghaus illusion paradigm was adopted to induce differences in the perceived, rather than the physical, area of the two patches to be compared. Participants were asked to compare the area, density, and the number of the two patches in three tasks. To this end, no PSE (point of subjective equality) bias was found in number comparison with randomly distributed dots, although a significant difference was revealed in the perceived area of the two patches. No PSE bias was found in the density comparison, either. For a comparison, density and number tasks were also conducted with regularly distributed dots. No PSE bias was found in density comparison. By contrast, significant PSE bias showed up in number comparison, and larger patches appeared to be more numerous than smaller patches. The density mechanism was proposed as the basis for number comparison with regular patterns. The individual Weber fractions for regular patterns were not correlated with those for random patterns in the number task, but they were correlated with those for both patterns in the density task. To summarize, numerosity is directly sensed, and numerosity perception is not affected by area inequality induced by the Ebbinghaus illusion. In contrast, density and area are combined to infer numerosity when the approximate numerosity mechanism is disrupted by dot distribution.

Number neurons in the nidopallium of young domestic chicks

Numerosity, that is, the number of items in a set, is a significant aspect in the perception of the environment. Behavioral and in silico experiments suggest that number sense belongs to a core knowledge system and can be present already at birth. However, neurons sensitive to the number of visual items have been so far described only in the brain of adult animals. Therefore, it remained unknown to what extent their selectivity would depend on visual learning and experience. We found number neurons in the caudal nidopallium (a higher associative area functionally similar to the mammalian prefrontal cortex) of very young, numerically naïve domestic chicks. This result suggests that numerosity perception is possibly an inborn feature of the vertebrate brain.

Numerical cognition is ubiquitous in the animal kingdom. Domestic chicks are a widely used developmental model for studying numerical cognition. Soon after hatching, chicks can perform sophisticated numerical tasks. Nevertheless, the neural basis of their numerical abilities has remained unknown. Here, we describe number neurons in the caudal nidopallium (functionally equivalent to the mammalian prefrontal cortex) of young domestic chicks. Number neurons that we found in young chicks showed remarkable similarities to those in the prefrontal cortex and caudal nidopallium of adult animals. Thus, our results suggest that numerosity perception based on number neurons might be an inborn feature of the vertebrate brain.

Attention drives human numerosity-selective responses

Numerosity, the set size of a group of items, helps guide behavior and decisions. Previous studies have shown that neural populations respond selectively to numerosities. How numerosity is extracted from the visual scene is a longstanding debate, often contrasting low-level visual with high-level cognitive processes. Here, we investigate how attention influences numerosity-selective responses. The stimuli consisted of black and white dots within the same display. Participants' attention was focused on either black or white dots, while we systematically changed the numerosity of black, white, and total dots. Using 7 T fMRI, we show that the numerosity-tuned neural populations respond only when attention is focused on their preferred numerosity, irrespective of the unattended or total numerosities. Without attention, responses to preferred numerosity are suppressed. Unlike traditional effects of attention in the visual cortex, where attention enhances already existing responses, these results suggest that attention is required to drive numerosity-selective responses.

Emerged human-like facial expression representation in a deep convolutional neural network

Recent studies found that the deep convolutional neural networks (DCNNs) trained to recognize facial identities spontaneously learned features that support facial expression recognition, and vice versa. Here, we showed that the self-emerged expression-selective units in a VGG-Face trained for facial identification were tuned to distinct basic expressions and, importantly, exhibited hallmarks of human expression recognition (i.e., facial expression confusion and categorical perception). We then investigated whether the emergence of expression-selective units is attributed to either face-specific experience or domain-general processing by conducting the same analysis on a VGG-16 trained for object classification and an untrained VGG-Face without any visual experience, both having the identical architecture with the pretrained VGG-Face. Although similar expression-selective units were found in both DCNNs, they did not exhibit reliable human-like characteristics of facial expression perception. Together, these findings revealed the necessity of domain-specific visual experience of face identity for the development of facial expression perception, highlighting the contribution of nurture to form human-like facial expression perception.

A connectome-based neuromarker of nonverbal number acuity and arithmetic skills

The approximate number system (ANS) is vital for survival and reproduction in animals and is crucial for constructing abstract mathematical abilities in humans. Most previous neuroimaging studies focused on identifying discrete brain regions responsible for the ANS and characterizing their functions in numerosity perception. However, a neuromarker to characterize an individual's ANS acuity is lacking, especially one based on whole-brain functional connectivity (FC). Here, based on the resting-state functional magnetic resonance imaging (rs-fMRI) data obtained from a large sample, we identified a distributed brain network (i.e. a numerosity network) using a connectome-based predictive modeling (CPM) analysis. The summed FC strength within the numerosity network reliably predicted individual differences in ANS acuity regarding behavior, as measured using a nonsymbolic number-comparison task. Furthermore, in an independent dataset of the Human Connectome Project (HCP), we found that the summed FC strength within the numerosity network also specifically predicted individual differences in arithmetic skills, but not domain-general cognitive abilities. Therefore, our findings revealed that the identified numerosity network could serve as an applicable neuroimaging-based biomarker of nonverbal number acuity and arithmetic skills.

Neurons in the Dorso-Central Division of Zebrafish Pallium Respond to Change in Visual Numerosity

We found a region of the zebrafish pallium that shows selective activation upon change in the numerosity of visual stimuli. Zebrafish were habituated to sets of small dots that changed in individual size, position, and density, while maintaining their numerousness and overall surface. During dishabituation tests, zebrafish faced a change in number (with the same overall surface), in shape (with the same overall surface and number), or in size (with the same shape and number) of the dots, whereas, in a control group, zebrafish faced the same stimuli as during the habituation. Modulation of the expression of the immediate early genes c-fos and egr-1 and in situ hybridization revealed a selective activation of the caudal part of the dorso-central division of the zebrafish pallium upon change in numerosity. These findings support the existence of an evolutionarily conserved mechanism for approximate magnitude and provide an avenue for understanding its underlying molecular correlates.

Electrophysiological Signatures of Numerosity Encoding in a Delayed Match-to-Sample Task

The number of elements in a small set of items is appraised in a fast and exact manner, a phenomenon called subitizing. In contrast, humans provide imprecise responses when comparing larger numerosities, with decreasing precision as the number of elements increases. Estimation is thought to rely on a dedicated system for the approximate representation of numerosity. While previous behavioral and neuroimaging studies associate subitizing to a domain-general system related to object tracking and identification, the nature of small numerosity processing is still debated. We investigated the neural processing of numerosity across subitizing and estimation ranges by examining electrophysiological activity during the memory retention period in a delayed numerical match-to-sample task. We also assessed potential differences in the neural signature of numerical magnitude in a fully non-symbolic or cross-format comparison. In line with behavioral performance, we observed modulation of parietal-occipital neural activity as a function of numerosity that differed in two ranges, with distinctive neural signatures of small numerosities showing clear similarities with those observed in visuospatial working memory tasks. We also found differences in neural activity related to numerical information in anticipation of single vs. cross-format comparison, suggesting a top-down modulation of numerical processing. Finally, behavioral results revealed enhanced performance in the mixed-format conditions and a significant correlation between task performance and symbolic mathematical skills. Overall, we provide evidence for distinct mechanisms related to small and large numerosity and differences in numerical encoding based on task demands.

Spontaneous representation of numerosity zero in a deep neural network for visual object recognition

Conceiving "nothing" as a numerical value zero is considered a sophisticated numerical capability that humans share with cognitively advanced animals. We demonstrate that representation of zero spontaneously emerges in a deep learning neural network without any number training. As a signature of numerical quantity representation, and similar to real neurons from animals, numerosity zero network units show maximum activity to empty sets and a gradual decrease in activity with increasing countable numerosities. This indicates that the network spontaneously ordered numerosity zero as the smallest numerical value along the number line. Removal of empty-set network units caused specific deficits in the network's judgment of numerosity zero, thus reflecting these units' functional relevance. These findings suggest that processing visual information is sufficient for a visual number sense that includes zero to emerge and explains why cognitively advanced animals with whom we share a nonverbal number system exhibit rudiments of numerosity zero.

The macaque ventral intraparietal area has expanded into three homologue human parietal areas

The macaque ventral intraparietal area (VIP) in the fundus of the intraparietal sulcus has been implicated in a diverse range of sensorimotor and cognitive functions such as motion processing, multisensory integration, processing of head peripersonal space, defensive behavior, and numerosity coding. Here, we exhaustively review macaque VIP function, cytoarchitectonics, and anatomical connectivity and integrate it with human studies that have attempted to identify a potential human VIP homologue. We show that human VIP research has consistently identified three, rather than one, bilateral parietal areas that each appear to subsume some, but not all, of the macaque area's functionality. Available evidence suggests that this human "VIP complex" has evolved as an expansion of the macaque area, but that some precursory specialization within macaque VIP has been previously overlooked. The three human areas are dominated, roughly, by coding the head or self in the environment, visual heading direction, and the peripersonal environment around the head, respectively. A unifying functional principle may be best described as prediction in space and time, linking VIP to state estimation as a key parietal sensorimotor function. VIP's expansive differentiation of head and self-related processing may have been key in the emergence of human bodily self-consciousness.

Overlapping Neuronal Population Responses in the Human Parietal Cortex during Visuospatial Attention and Arithmetic Processing

Engagement of posterior parietal cortex (PPC) in visuospatial attention and arithmetic processing has been extensively documented using neuroimaging methods. Numerous studies have suggested a close connection between visuospatial attention and arithmetic processing. However, the extant evidence in humans stems from neuroimaging methods that have relied on group analyses without much knowledge about the profile of neurophysiological engagement within localized neuronal populations at the individual brain level. Hence, it has remained unclear if the overlap of two functions in the PPC is the product of averaging, or they truly stem from a common profile of activity within the same neuronal populations in the human PPC. In the current study, we leveraged the anatomical precision and high signal-to-noise ratio of intracranial electrocorticography and probed the engagement of discrete PPC neuronal populations in seven neurosurgical patients (n = 179 total PPC sites covered; 26 sites on average per individual participant). We aimed to study the extent of parietal activations within each individual brain during visuospatial attention versus arithmetic tasks and the profile of electrophysiological responses within a given recording site during these tasks. Our findings indicated that about 40% of PPC sites did not respond to either visuospatial attention or arithmetic stimuli-or episodic memory conditions that were used as an adjunct control condition. Of those that were activated during either visuospatial attention or arithmetic conditions, a large majority showed overlapping responses during both visuospatial attention and arithmetic conditions. Most interestingly, responses during arithmetic processing were greatest in sites along the intraparietal sulcus region showing preference to contralateral, instead of ipsilateral, visual probes in the visuospatial attention task. Our results provide novel data about the relationship between numerical and spatial orientation at the neuronal population level and shed light on the complex functional organization of the PPC that could not be attained with noninvasive methods.

The Sense of Number in Fish, with Particular Reference to Its Neurobiological Bases

Simple Summary

The ability to deal with quantity, both discrete (numerosities) and continuous (spatial or temporal extent) developed from an evolutionarily conserved system for approximating numerical magnitude. Non-symbolic number cognition based on an approximate sense of magnitude has been documented in a variety of vertebrate species, including fish. Fish, in particular zebrafish, are widely used as models for the investigation of the genetics and molecular mechanisms of behavior, and thus may be instrumental to development of a neurobiology of number cognition. We review here the behavioural studies that have permitted to identify numerical abilities in fish, and the current status of the research related to the neurobiological bases of these abilities with special reference to zebrafish. Combining behavioural tasks with molecular genetics, molecular biology and confocal microscopy, a role of the retina and optic tectum in the encoding of continuous magnitude in larval zebrafish has been reported, while the thalamus and the dorso-central subdivision of pallium in the encoding of discrete magnitude (number) has been documented in adult zebrafish. Research in fish, in particular zebrafish, may reveal instrumental for identifying and characterizing the molecular signature of neurons involved in quantity discrimination processes of all vertebrates, including humans.

Abstract

It is widely acknowledged that vertebrates can discriminate non-symbolic numerosity using an evolutionarily conserved system dubbed Approximate Number System (ANS). Two main approaches have been used to assess behaviourally numerosity in fish: spontaneous choice tests and operant training procedures. In the first, animals spontaneously choose between sets of biologically-relevant stimuli (e.g., conspecifics, food) differing in quantities (smaller or larger). In the second, animals are trained to associate a numerosity with a reward. Although the ability of fish to discriminate numerosity has been widely documented with these methods, the molecular bases of quantities estimation and ANS are largely unknown. Recently, we combined behavioral tasks with molecular biology assays (e.g c-fos and egr1 and other early genes expression) showing that the thalamus and the caudal region of dorso-central part of the telencephalon seem to be activated upon change in numerousness in visual stimuli. In contrast, the retina and the optic tectum mainly responded to changes in continuous magnitude such as stimulus size. We here provide a review and synthesis of these findings.

The pupil responds spontaneously to perceived numerosity

Although luminance is the main determinant of pupil size, the amplitude of the pupillary light response is also modulated by stimulus appearance and attention. Here we ask whether perceived numerosity modulates the pupillary light response. Participants passively observed arrays of black or white dots of matched physical luminance but different physical or illusory numerosity. In half the patterns, pairs of dots were connected by lines to create dumbbell-like shapes, inducing an illusory underestimation of perceived numerosity; in the other half, connectors were either displaced or removed. Constriction to white arrays and dilation to black were stronger for patterns with higher perceived numerosity, either physical or illusory, with the strength of the pupillary light response scaling with the perceived numerosity of the arrays. Our results show that even without an explicit task, numerosity modulates a simple automatic reflex, suggesting that numerosity is a spontaneously encoded visual feature.

Mathematical learning deficits originate in early childhood from atypical development of a frontoparietal brain network

Mathematical learning deficits are defined as a neurodevelopmental disorder (dyscalculia) in the International Classification of Diseases. It is not known, however, how such deficits emerge in the course of early brain development. Here, we conducted functional and structural magnetic resonance imaging (MRI) experiments in 3- to 6-year-old children without formal mathematical learning experience. We followed this sample until the age of 7 to 9 years, identified individuals who developed deficits, and matched them to a typically developing control group using comprehensive behavioral assessments. Multivariate pattern classification distinguished future cases from controls with up to 87% accuracy based on the regional functional activity of the right posterior parietal cortex (PPC), the network-level functional activity of the right dorsolateral prefrontal cortex (DLPFC), and the effective functional and structural connectivity of these regions. Our results indicate that mathematical learning deficits originate from atypical development of a frontoparietal network that is already detectable in early childhood.

Children With Dyscalculia Show Hippocampal Hyperactivity During Symbolic Number Perception

Dyscalculia is a learning disability affecting the acquisition of arithmetical skills in children with normal intelligence and age-appropriate education. Two hypotheses attempt to explain the main cause of dyscalculia. The first hypothesis suggests that a problem with the core mechanisms of perceiving (non-symbolic) quantities is the cause of dyscalculia (core deficit hypothesis), while the alternative hypothesis suggests that dyscalculics have problems only with the processing of numerical symbols (access deficit hypothesis). In the present study, the symbolic and non-symbolic numerosity processing of typically developing children and children with dyscalculia were examined with functional magnetic resonance imaging (fMRI). Control (n = 15, mean age: 11.26) and dyscalculia (n = 12, mean age: 11.25) groups were determined using a wide-scale screening process. Participants performed a quantity comparison paradigm in the fMRI with two number conditions (dot and symbol comparison) and two difficulty levels (0.5 and 0.7 ratio). The results showed that the bilateral intraparietal sulcus (IPS), left dorsolateral prefrontal cortex (DLPFC) and left fusiform gyrus (so-called “number form area”) were activated for number perception as well as bilateral occipital and supplementary motor areas. The task difficulty engaged bilateral insular cortex, anterior cingulate cortex, IPS, and DLPFC activation. The dyscalculia group showed more activation in the left orbitofrontal cortex, left medial prefrontal cortex, and right anterior cingulate cortex than the control group. The dyscalculia group showed left hippocampus activation specifically for the symbolic condition. Increased left hippocampal and left-lateralized frontal network activation suggest increased executive and memory-based compensation mechanisms during symbolic processing for dyscalculics. Overall, our findings support the access deficit hypothesis as a neural basis for dyscalculia.

Learning exact enumeration and approximate estimation in deep neural network models

A system for approximate number discrimination has been shown to arise in at least two types of hierarchical neural network models-a generative Deep Belief Network (DBN) and a Hierarchical Convolutional Neural Network (HCNN) trained to classify natural objects. Here, we investigate whether the same two network architectures can learn to recognise exact numerosity. A clear difference in performance could be traced to the specificity of the unit responses that emerged in the last hidden layer of each network. In the DBN, the emergence of a layer of monotonic 'summation units' was sufficient to produce classification behaviour consistent with the behavioural signature of the approximate number system. In the HCNN, a layer of units uniquely tuned to the transition between particular numerosities effectively encoded a thermometer-like 'numerosity code' that ensured near-perfect classification accuracy. The results support the notion that parallel pattern-recognition mechanisms may give rise to exact and approximate number concepts, both of which may contribute to the learning of symbolic numbers and arithmetic.

Neural basis of approximate number in congenital blindness

Although humans are unique among animals in their ability to manipulate symbolic numbers, we share with other species an approximate number sense that allows us to estimate and compare the number of objects or events in a set, such as the number of apples in a tree. Our ability to discriminate the numerosity of two sets decreases as the ratio between them becomes smaller (e.g., 8 vs 16 items is harder to discriminate than 8 vs 32 items). The intraparietal sulcus (IPS) plays a key role in this numerical approximation. Neuronal populations within the IPS code for numerosity, with stimuli of different numerosities eliciting discriminable spatial patterns of activity. The developmental origins of these IPS number representations are not known. Here, we tested the hypothesis that representations of number in the IPS require visual experience with object sets, by working with individuals blind from birth. While undergoing fMRI, congenitally blind (n = 17) and blindfolded sighted (n = 25) participants judged which of two sequences of beeps was more numerous. In both sighted and blind individuals, patterns of activity in the IPS discriminated among different numerosities (4, 8, 16 vs 32), with better discrimination in the IPS of the blind group. In both groups, decoding performance decreased as the ratio between numerosities decreased (e.g., 8 vs 16 was less discriminable than 8 vs 32). These findings suggest that number representations in the IPS either have innate precursors, or that auditory or tactile experience with sets is sufficient for typical development.

Towards a standardization of non-symbolic numerical experiments: GeNEsIS, a flexible and user-friendly tool to generate controlled stimuli

Several studies have suggested that vertebrate and invertebrate species may possess a number sense, i.e. an ability to process in a non-symbolic and non-verbal way the numerousness of a set of items. However, this hypothesis has been challenged by the presence of other non-numerical continuous physical variables, which vary along with numerosity (i.e., any change in the number of visual physical elements in a set naturally involves a related change in visual features such as area, density, contour length and convex hull of the stimulus). It is therefore necessary to control and manipulate the continuous physical information when investigating the ability of humans and other animals to perceive numerousness. During decades of research, different methods have been implemented in order to address this issue, which has implications for experiment replicability and inter-species comparisons, since no general standardized procedure is currently being used. Here we present the ‘Generation of Numerical Elements Images Software’ (GeNEsIS) for the creation of non-symbolic numerical arrays in a standardized and user-friendly environment. The main aim of this tool is to provide researchers in the field of numerical cognition a manageable and precise instrument to produce visual numerical arrays controlled for all the continuous variables. Additionally, we implemented the ability to actively guide stimuli presentation during habituation/dishabituation and dual-choice comparison tasks used in human and comparative research.

The Evolutionary History of Brains for Numbers

Humans and other animals share a number sense', an intuitive understanding of countable quantities. Having evolved independent from one another for hundreds of millions of years, the brains of these diverse species, including monkeys, crows, zebrafishes, bees, and squids, differ radically. However, in all vertebrates investigated, the pallium of the telencephalon has been implicated in number processing. This suggests that properties of the telencephalon make it ideally suited to host number representations that evolved by convergent evolution as a result of common selection pressures. In addition, promising candidate regions in the brains of invertebrates, such as insects, spiders, and cephalopods, can be identified, opening the possibility of even deeper commonalities for number sense.

Developmental Changes in ANS Precision Across Grades 1-9: Different Patterns of Accuracy and Reaction Time

The main aim of this study was to analyze the patterns of changes in Approximate Number Sense (ANS) precision from grade 1 (mean age: 7.84 years) to grade 9 (mean age: 15.82 years) in a sample of Russian schoolchildren. To fulfill this aim, the data from a longitudinal study of two cohorts of children were used. The first cohort was assessed at grades 1-5 (elementary school education plus the first year of secondary education), and the second cohort was assessed at grades 5-9 (secondary school education). ANS precision was assessed by accuracy and reaction time (RT) in a non-symbolic comparison test ("blue-yellow dots" test). The patterns of change were estimated via mixed-effect growth models. The results revealed that in the first cohort, the average accuracy increased from grade 1 to grade 5 following a non-linear pattern and that the rate of growth slowed after grade 3 (7-9 years old). The non-linear pattern of changes in the second cohort indicated that accuracy started to increase from grade 7 to grade 9 (13-15 years old), while there were no changes from grade 5 to grade 7. However, the RT in the non-symbolic comparison test decreased evenly from grade 1 to grade 7 (7-13 years old), and the rate of processing non-symbolic information tended to stabilize from grade 7 to grade 9. Moreover, the changes in the rate of processing non-symbolic information were not explained by the changes in general processing speed. The results also demonstrated that accuracy and RT were positively correlated across all grades. These results indicate that accuracy and the rate of non-symbolic processing reflect two different processes, namely, the maturation and development of a non-symbolic representation system.

Neuroethology of number sense across the animal kingdom

Many species from diverse and often distantly related animal groups (e.g. monkeys, crows, fish and bees) have a sense of number. This means that they can assess the number of items in a set - its 'numerosity'. The brains of these phylogenetically distant species are markedly diverse. This Review examines the fundamentally different types of brains and neural mechanisms that give rise to numerical competence across the animal tree of life. Neural correlates of the number sense so far exist only for specific vertebrate species: the richest data concerning explicit and abstract number representations have been collected from the cerebral cortex of mammals, most notably human and nonhuman primates, but also from the pallium of corvid songbirds, which evolved independently of the mammalian cortex. In contrast, the neural data relating to implicit and reflexive numerical representations in amphibians and fish is limited. The neural basis of a number sense has not been explored in any protostome so far. However, promising candidate regions in the brains of insects, spiders and cephalopods - all of which are known to have number skills - are identified in this Review. A comparative neuroscientific approach will be indispensable for identifying evolutionarily stable neuronal circuits and deciphering codes that give rise to a sense of number across phylogeny.