A network of topographic numerosity maps in human association cortex

The interplay between spatial and non-spatial grouping cues over approximate number perception

Humans and animals share the cognitive ability to quickly extract approximate number information from sets. Main psychophysical models suggest that visual approximate numerosity relies on segmented units, which can be affected by Gestalt rules. Indeed, arrays containing spatial grouping cues, such as connectedness, closure, and even symmetry, are underestimated compared to ungrouped arrays with equal low-level features. Recent evidence suggests that non-spatial cues, such as color-similarity, also trigger numerosity underestimation. However, in natural vision, several grouping cues may coexist in the scene. Notably, conjunction of grouping cues (color and closure) reduces perceived numerosity following an additive rule. To test whether the conjunction-effect holds for other Gestalt cues, we investigated the effect of connectedness and symmetry over numerosity perception both in isolation and, critically, in conjunction with luminance similarity. Participants performed a comparison-task between a reference and a test stimulus varying in numerosity. In Experiment 1, test stimuli contained two isolated groupings (connectedness or luminance), a conjunction (connectedness and luminance), and a neutral condition (no groupings). Results show that point of subjective equality was higher in both isolated grouping conditions compared to the neutral condition. Furthermore, in the conjunction condition, the biases from isolated grouping cues added linearly, resulting in a numerosity underestimation equal to the sum of the isolated biases. In Experiment 2 we found that conjunction of symmetry and luminance followed the same additive rule. These findings strongly suggest that both spatial and non-spatial isolated cues affect numerosity perception. Crucially, we show that their conjunction effect extends to symmetry and connectedness.

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.

Cortical quantity representations of visual numerosity and timing overlap increasingly into superior cortices but remain distinct

Many sensory brain areas are organized as topographic maps where neural response preferences change gradually across the cortical surface. Within association cortices, 7-Tesla fMRI and neural model-based analyses have also revealed many topographic maps for quantities like numerosity and event timing, often in similar locations. Numerical and temporal quantity estimations also show behavioral similarities and even interactions. For example, the duration of high-numerosity displays is perceived as longer than that of low-numerosity displays. Such interactions are often ascribed to a generalized magnitude system with shared neural responses across quantities. Anterior quantity responses are more closely linked to behavior. Here, we investigate whether common quantity representations hierarchically emerge by asking whether numerosity and timing maps become increasingly closely related in their overlap, response preferences, and topography. While the earliest quantity maps do not overlap, more superior maps overlap increasingly. In these overlapping areas, some intraparietal maps have consistently correlated numerosity and timing preferences, and some maps have consistent angles between the topographic progressions of numerosity and timing preferences. However, neither of these relationships increases hierarchically like the amount of overlap does. Therefore, responses to different quantities are initially derived separately, then progressively brought together, without generally becoming a common representation. Bringing together distinct responses to different quantities may underlie behavioral interactions and allow shared access to comparison and action planning systems.

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.

Neurocognitive Assessment of Mathematics-Related Capacities in Neurosurgical Patients

A precise neuropsychological assessment is of the utmost importance for neurosurgical patients undergoing the surgical excision of cerebral lesions. The assessment of mathematical abilities is usually limited to arithmetical operations while other fundamental visuo-spatial aspects closely linked to mathematics proficiency, such as the perception of numerical quantities and geometrical reasoning, are completely neglected. We evaluated these abilities with two objective and reproducible psychophysical tests, measuring numerosity perception and non-symbolic geometry, respectively. We tested sixteen neuro-oncological patients before the operation and six after the operation with classical neuropsychological tests and with two psychophysical tests. The scores of the classical neuropsychological tests were very heterogeneous, possibly due to the distinct location and histology of the tumors that might have spared (or not) brain areas subserving these abilities or allowed for plastic reorganization. Performance in the two non-symbolic tests reflected, on average, the presumed functional role of the lesioned areas, with participants with parietal and frontal lesions performing worse on these tests than patients with occipital and temporal lesions. Single-case analyses not only revealed some interesting exceptions to the group-level results (e.g., patients with parietal lesions performing well in the numerosity test), but also indicated that performance in the two tests was independent of non-verbal reasoning and visuo-spatial working memory. Our results highlight the importance of assessing non-symbolic numerical and geometrical abilities to complement typical neuropsychological batteries. However, they also suggest an avoidance of reliance on an excessively rigid localizationist approach when evaluating the neuropsychological profile of oncological patients.

Individual risk attitudes arise from noise in neurocognitive magnitude representations

Humans are generally risk averse, preferring smaller certain over larger uncertain outcomes. Economic theories usually explain this by assuming concave utility functions. Here, we provide evidence that risk aversion can also arise from relative underestimation of larger monetary payoffs, a perceptual bias rooted in the noisy logarithmic coding of numerical magnitudes. We confirmed this with psychophysics and functional magnetic resonance imaging, by measuring behavioural and neural acuity of magnitude representations during a magnitude perception task and relating these measures to risk attitudes during separate risky financial decisions. Computational modelling indicated that participants use similar mental magnitude representations in both tasks, with correlated precision across perceptual and risky choices. Participants with more precise magnitude representations in parietal cortex showed less variable behaviour and less risk aversion. Our results highlight that at least some individual characteristics of economic behaviour can reflect capacity limitations in perceptual processing rather than processes that assign subjective values to monetary outcomes.

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

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.

The more numerous the longer: how the integration between numerosity and time leads to a common neural response

If you are stuck in a traffic jam, the more numerous the queuing cars are, the longer you expect to wait. Time and numerosity are stimulus dimensions often associated in the same percept and whose interaction can lead to misjudgements. At brain level it is unclear to which extent time and numerosity recruit same/different neural populations and how their perceptual integration leads to changes in these populations' responses. Here we used high-spatial-resolution functional magnetic resonance imaging with neural model-based analyses to investigate how the topographic representations of numerosity and time change when these dimensions are varied together on the same visual stimulus in a congruent (the more numerous the items, the longer the display time) or incongruent manner. Compared to baseline conditions, where only one dimension was changed at a time, the variation of both stimulus dimensions led to changes in neural population responses that became more sensitive either to the two features or to one of them. Magnitude integration led also to degradation of topographies and shifts in response preferences. These changes were more pronounced in the comparison between parietal and frontal maps. Our results while pointing to partially distinct representations of time and numerosity show a common neural response to magnitude integration.

Mechanisms of speed encoding in the human middle temporal cortex measured by 7T fMRI

Perception of dynamic scenes in our environment results from the evaluation of visual features such as the fundamental spatial and temporal frequency components of a moving object. The ratio between these two components represents the object's speed of motion. The human middle temporal cortex hMT+ has a crucial biological role in the direct encoding of object speed. However, the link between hMT+ speed encoding and the spatiotemporal frequency components of a moving object is still under explored. Here, we recorded high resolution 7T blood oxygen level-dependent BOLD responses to different visual motion stimuli as a function of their fundamental spatial and temporal frequency components. We fitted each hMT+ BOLD response with a 2D Gaussian model allowing for two different speed encoding mechanisms: (1) distinct and independent selectivity for the spatial and temporal frequencies of the visual motion stimuli; (2) pure tuning for the speed of motion. We show that both mechanisms occur but in different neuronal groups within hMT+, with the largest subregion of the complex showing separable tuning for the spatial and temporal frequency of the visual stimuli. Both mechanisms were highly reproducible within participants, reconciling single cell recordings from MT in animals that have showed both encoding mechanisms. Our findings confirm that a more complex process is involved in the perception of speed than initially thought and suggest that hMT+ plays a primary role in the evaluation of the spatial features of the moving visual input.

The two-network framework of number processing: a step towards a better understanding of the neural origins of developmental dyscalculia

Developmental dyscalculia is a specific learning disorder that persists over lifetime and can have an enormous impact on personal, health-related, and professional aspects of life. Despite its central importance, the origin both at the cognitive and neural level is not yet well understood. Several classification schemas of dyscalculia have been proposed, sometimes together with an associated deficit at the neural level. However, these explanations are (a) not providing an exhaustive framework that is at levels with the observed complexity of developmental dyscalculia at the behavioral level and (b) are largely mono-causal approaches focusing on gray matter deficits. We suggest that number processing is instead the result of context-dependent interaction of two anatomically largely separate, distributed but overlapping networks that function/cooperate in a closely integrated fashion. The proposed two-network framework (TNF) is the result of a series of studies in adults on the neural correlates underlying magnitude processing and arithmetic fact retrieval, which comprised neurofunctional imaging of various numerical tasks, the application of probabilistic fiber tracking to obtain well-defined connections, and the validation and modification of these results using disconnectome mapping in acute stroke patients. Emerged from data in adults, it represents the endpoint of the acquisition and use of mathematical competencies in adults. Yet, we argue that its main characteristics should already emerge earlier during development. Based on this TNF, we develop a classification schema of phenomenological subtypes and their underlying neural origin that we evaluate against existing propositions and the available empirical data.

Number selective sensorimotor neurons in the crow translate perceived numerosity into number of actions

Translating a perceived number into a matching number of self-generated actions is a hallmark of numerical reasoning in humans and animals alike. To explore this sensorimotor transformation, we trained crows to judge numerical values in displays and to flexibly plan and perform a matching number of pecks. We report number selective sensorimotor neurons in the crow telencephalon that signaled the impending number of self-generated actions. Neuronal population activity during the sensorimotor transformation period predicted whether the crows mistakenly planned fewer or more pecks than instructed. During sensorimotor transformation, both a static neuronal code characterized by persistently number-selective neurons and a dynamic code originating from neurons carrying rapidly changing numerical information emerged. The findings indicate there are distinct functions of abstract neuronal codes supporting the sensorimotor number system.

Visual P2p component responds to perceived numerosity

Numerosity perception is a key ability for human and non-human species, probably mediated by dedicated brain mechanisms. Electrophysiological studies revealed the existence of both early and mid-latency components of the Electrophysiological (EEG) signal sensitive to numerosity changes. However, it is still unknown whether these components respond to physical or perceived variation in numerical attributes. We here tackled this point by recording electrophysiological signal while participants performed a numerosity adaptation task, a robust psychophysical method yielding changes in perceived numerosity judgments despite physical numerosity invariance. Behavioral measures confirmed that the test stimulus was consistently underestimated when presented after a high numerous adaptor while perceived as veridical when presented after a neutral adaptor. Congruently, EEG results revealed a potential at around 200 ms (P2p) which was reduced when the test stimulus was presented after the high numerous adaptor. This result was much prominent over the left posterior cluster of electrodes and correlated significantly with the amount of adaptation. No earlier modulations were retrievable when changes in numerosity were illusory while both early and mid-latency modulations occurred for physical changes. Taken together, our results reveal that mid-latency P2p mainly reflects perceived changes in numerical attributes, while earlier components are likely to be bounded to the physical characteristics of the stimuli. These results suggest that short-term plastic mechanisms induced by numerosity adaptation may involve a relatively late processing stage of the visual hierarchy likely engaging cortical areas beyond the primary visual cortex. Furthermore, these results also indicate mid-latency electrophysiological correlates as a signature of the internal representation of numerical information.

Assessing the ecological validity of numerosity-selective neuronal populations with real-world natural scenes

Animals and humans are able to quickly and effortlessly estimate the number of items in a set: their numerosity. Numerosity perception is thought to be critical to behavior, from feeding to escaping predators to human mathematical cognition. Virtually, all scientific studies on numerosity mechanisms use well controlled but artificial stimuli to isolate the numerosity dimension from other physical quantities. Here, we probed the ecological validity of these artificial stimuli and evaluate whether an important component in numerosity processing, the numerosity-selective neural populations, also respond to numerosity of items in real-world natural scenes. Using 7T MRI and natural images from a wide range of categories, we provide evidence that the numerosity-tuned neuronal populations show numerosity-selective responses when viewing images from a real-world natural scene. Our findings strengthen the role of numerosity-selective neurons in numerosity perception and provide an important link to their function in numerosity perception in real-world settings.

An evaluation of how connectopic mapping reveals visual field maps in V1

Abstract

Functional gradients, in which response properties change gradually across the cortical surface, have been proposed as a key organising principle of the brain. However, the presence of these gradients remains undetermined in many brain regions. Resting-state neuroimaging studies have suggested these gradients can be reconstructed from patterns of functional connectivity. Here we investigate the accuracy of these reconstructions and establish whether it is connectivity or the functional properties within a region that determine these “connectopic maps”. Different manifold learning techniques were used to recover visual field maps while participants were at rest or engaged in natural viewing. We benchmarked these reconstructions against maps measured by traditional visual field mapping. We report an initial exploratory experiment of a publicly available naturalistic imaging dataset, followed by a preregistered replication using larger resting-state and naturalistic imaging datasets from the Human Connectome Project. Connectopic mapping accurately predicted visual field maps in primary visual cortex, with better predictions for eccentricity than polar angle maps. Non-linear manifold learning methods outperformed simpler linear embeddings. We also found more accurate predictions during natural viewing compared to resting-state. Varying the source of the connectivity estimates had minimal impact on the connectopic maps, suggesting the key factor is the functional topography within a brain region. The application of these standardised methods for connectopic mapping will allow the discovery of functional gradients across the brain.

Protocol registration

The stage 1 protocol for this Registered Report was accepted in principle on 19 April 2022. The protocol, as accepted by the journal, can be found at 10.6084/m9.figshare.19771717.

Intracranial recordings show evidence of numerosity tuning in human parietal cortex

Numerosity is the set size of a group of items. Numerosity perception is a trait shared across numerous species. Numerosity-selective neural populations are thought to underlie numerosity perception. These neurons have been identified primarily using electrical recordings in animal models and blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) in humans. Here we use electrical intracranial recordings to investigate numerosity tuning in humans, focusing on high-frequency transient activations. These recordings combine a high spatial and temporal resolution and can bridge the gap between animal models and human recordings. In line with previous studies, we find numerosity-tuned responses at parietal sites in two out of three participants. Neuronal populations at these locations did not respond to other visual stimuli, i.e. faces, houses, and letters, in contrast to several occipital sites. Our findings further corroborate the specificity of numerosity tuning of in parietal cortex, and further link fMRI results and electrophysiological recordings.

What has vision science taught us about functional MRI?

In the domain of human neuroimaging, much attention has been paid to the question of whether and how the development of functional magnetic resonance imaging (fMRI) has advanced our scientific knowledge of the human brain. However, the opposite question is also important; how has our knowledge of the visual system advanced our understanding of fMRI? Here, we discuss how and why scientific knowledge about the human and animal visual system has been used to answer fundamental questions about fMRI as a brain measurement tool and how these answers have contributed to scientific discoveries beyond vision science.

Visual timing-tuned responses in human association cortices and response dynamics in early visual cortex

Quantifying the timing (duration and frequency) of brief visual events is vital to human perception, multisensory integration and action planning. Tuned neural responses to visual event timing have been found in association cortices, in areas implicated in these processes. Here we ask how these timing-tuned responses are related to the responses of early visual cortex, which monotonically increase with event duration and frequency. Using 7-Tesla functional magnetic resonance imaging and neural model-based analyses, we find a gradual transition from monotonically increasing to timing-tuned neural responses beginning in the medial temporal area (MT/V5). Therefore, across successive stages of visual processing, timing-tuned response components gradually become dominant over inherent sensory response modulation by event timing. This additional timing-tuned response component is independent of retinotopic location. We propose that this hierarchical emergence of timing-tuned responses from sensory processing areas quantifies sensory event timing while abstracting temporal representations from spatial properties of their inputs.

Early visual cortical responses increase with event duration and frequency, while later timing-tuned responses quantify event timing. Here, the authors show timing tuning gradually emerges up the visual hierarchy, and separates temporal and spatial event features.

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.

Auditory timing-tuned neural responses in the human auditory cortices

Perception of sub-second auditory event timing supports multisensory integration, and speech and music perception and production. Neural populations tuned for the timing (duration and rate) of visual events were recently described in several human extrastriate visual areas. Here we ask whether the brain also contains neural populations tuned for auditory event timing, and whether these are shared with visual timing. Using 7T fMRI, we measured responses to white noise bursts of changing duration and rate. We analyzed these responses using neural response models describing different parametric relationships between event timing and neural response amplitude. This revealed auditory timing-tuned responses in the primary auditory cortex, and auditory association areas of the belt, parabelt and premotor cortex. While these areas also showed tonotopic tuning for auditory pitch, pitch and timing preferences were not consistently correlated. Auditory timing-tuned response functions differed between these areas, though without clear hierarchical integration of responses. The similarity of auditory and visual timing tuned responses, together with the lack of overlap between the areas showing these responses for each modality, suggests modality-specific responses to event timing are computed similarly but from different sensory inputs, and then transformed differently to suit the needs of each modality.

Children perform better on left than right targets in an ordinal task

Francis Galton first reported that humans mentally organize numbers from left to right on a mental number line (1880). This spatial-numerical association was long considered to result from writing and reading habits. More recently though, newborns and animals showed a left-to-right oriented spatial numerical association challenging the primary role assigned to culture in determining the link between number and space. Despite growing evidence supporting the intrinsic association between number and space in different species, its adaptive value is still largely unknown. Here we tested for an advantage in identification of left versus right target positions in 3- to 6-year-old children. Children watched as a toy was hidden under one of 10 linearly arranged identical cups and were then asked to help a stuffed animal retrieve the toy. On each trial, the toy was hidden in the 2nd, 3rd, or 4th cup, from the left or right. To prevent children from staring at the target cup, they were asked to pick up the stuffed animal from under their chair after witnessing the hiding of the toy and then to help the stuffed animal find the toy. Older children were more accurate than younger children. Children exhibited a serial position effect, with performance higher for more exterior targets. Remarkably, children also showed a left bias: they remembered the left targets better than the right targets. Only the youngest children were dramatically influenced by the location of the experimenter during search. Additional analyses support the hypothesis that children used a left-to-right oriented searching strategy in this spatial/ordinal task.

Numerosity perception is tuned to salient environmental features

Numerosity perception is a key ability to guide behavior. However, current models propose that number units encode an abstract representation of numerosity regardless of the non-numerical attributes of the stimuli, suggesting rather coarse environmental tuning. Here we investigated whether numerosity systems spontaneously adapt to all visible items, or to subsets segregated by salient attributes such as color or pitch. We measured perceived numerosity after participants adapted to highly numerous stimuli with color either matched to or different from the test. Matched colors caused a 25% underestimation of numerosity, while different colors had virtually no effect. This was true both for physically different colors, and for the same colors perceived as different, via a color-assimilation illusion. A similar result occurred in the acoustic domain, where adaptation magnitude was halved when the adaptor and test differed in pitch. Taken together, our results support the idea that numerosity perception is selectively tuned to salient environmental attributes.

Numerosity tuning in human association cortices and local image contrast representations in early visual cortex

Human early visual cortex response amplitudes monotonically increase with numerosity (object number), regardless of object size and spacing. However, numerosity is typically considered a high-level visual or cognitive feature, while early visual responses follow image contrast in the spatial frequency domain. We find that, at fixed contrast, aggregate Fourier power (at all orientations and spatial frequencies) follows numerosity closely but nonlinearly with little effect of object size, spacing or shape. This would allow straightforward numerosity estimation from spatial frequency domain image representations. Using 7T fMRI, we show monotonic responses originate in primary visual cortex (V1) at the stimulus’s retinotopic location. Responses here and in neural network models follow aggregate Fourier power more closely than numerosity. Truly numerosity tuned responses emerge after lateral occipital cortex and are independent of retinotopic location. We propose numerosity’s straightforward perception and neural responses may result from the pervasive spatial frequency analyses of early visual processing.

The authors show that spatial frequency domain Fourier power closely but nonlinearly follows numerosity, simplifying computing numerosity from early visual responses. Monotonic early visual cortex and neural network responses follow Fourier power, while later tuned responses follow numerosity.

Partially Separable Aspects of Spatial and Temporal Estimations in Virtual Navigation as Revealed by Adaptation

Recent studies claim that estimating the magnitude of the spatial and temporal aspects of one's self-motion shows similar characteristics, suggesting shared processing mechanisms between these two dimensions. While the estimation of other magnitude dimensions, such as size, number, and duration, exhibits negative aftereffects after prolonged exposure to the stimulus, it remains to be elucidated whether this could occur similarly in the estimation of the distance travelled and time elapsed during one's self-motion. We sought to fill this gap by examining the effects of adaptation on distance and time estimation using a virtual navigation task. We found that a negative aftereffect occurred in the distance reproduction task after repeated exposure to self-motion with a fixed travel distance. No such aftereffect occurred in the time reproduction task after repeated exposure to self-motion with a fixed elapsed time. Further, the aftereffect in distance reproduction occurred only when the distance of the adapting stimulus was fixed, suggesting that it did not reflect adaptation to time, which varied with distance. The estimation of spatial and temporal aspects of self-motion is thus processed by partially separable mechanisms, with the distance estimation being similar to the estimation of other magnitude dimensions.

Deprivation of Auditory Experience Influences Numerosity Discrimination, but Not Numerosity Estimation

Number sense is the ability to estimate the number of items, and it is common to many species. Despite the numerous studies dedicated to unveiling how numerosity is processed in the human brain, to date, it is not clear whether the representation of numerosity is supported by a single general mechanism or by multiple mechanisms. Since it is known that deafness entails a selective impairment in the processing of temporal information, we assessed the approximate numerical abilities of deaf individuals to disentangle these two hypotheses. We used a numerosity discrimination task (2AFC) and an estimation task, in both cases using sequential (temporal) or simultaneous (spatial) stimuli. The results showed a selective impairment of the deaf participants compared with the controls (hearing) in the temporal numerosity discrimination task, while no difference was found to discriminate spatial numerosity. Interestingly, the deaf and hearing participants did not differ in spatial or temporal numerosity estimation. Overall, our results suggest that the deficit in temporal processing induced by deafness also impacts perception in other domains such as numerosity, where sensory information is conveyed in a temporal format, which further suggests the existence of separate mechanisms subserving the processing of temporal and spatial numerosity.

The role of neural tuning in quantity perception

Perception of quantities, such as numerosity, timing, and size, is essential for behavior and cognition. Accumulating evidence demonstrates neurons processing quantities are tuned, that is, have a preferred quantity amount, not only for numerosity, but also other quantity dimensions and sensory modalities. We argue that quantity-tuned neurons are fundamental to understanding quantity perception. We illustrate how the properties of quantity-tuned neurons can underlie a range of perceptual phenomena. Furthermore, quantity-tuned neurons are organized in distinct but overlapping topographic maps. We suggest that this overlap in tuning provides the neural basis for perceptual interactions between different quantities, without the need for a common neural representational code.

Laminar processing of numerosity supports a canonical cortical microcircuit in human parietal cortex

As neural signals travel through the visual hierarchy, spatial precision decreases and specificity for stimulus features increases.^1-4 A similar hierarchy has been found for laminar processing in V1, where information from the thalamus predominantly targets the central layers, while spatial precision decreases and feature specificity increases toward superficial and deeper layers.^5-17 This laminar processing scheme is proposed to represent a canonical cortical microcircuit that is similar across the cortex.^11,18-21 Here, we go beyond early visual cortex and investigate whether processing of numerosity (the set size of a group of items) across cortical depth in the parietal association cortex follows this hypothesis. Numerosity processing is implicated in many tasks such as multiple object tracking,²² mathematics,^23-25 decision making,²⁶ and dividing attention.²⁷ Neurons in the parietal association cortex are tuned to numerosity, with both a preferred numerosity tuning and tuning width (i.e., specificity).^28-30 We quantified preferred numerosity responses across cortical depth in the parietal association cortex with ultra-high field fMRI and population receptive field-based numerosity modeling.^1,28,31 We find that numerosity responses sharpen, i.e., become increasingly specific, moving away from the central layers. This suggests that the laminar processing scheme for numerosity processing in the parietal cortex is similar to primary visual cortex, providing support for the canonical cortical microcircuit hypothesis beyond primary visual cortex.

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.

Evidence for an A-Modal Number Sense: Numerosity Adaptation Generalizes Across Visual, Auditory, and Tactile Stimuli

Humans and other species share a perceptual mechanism dedicated to the representation of approximate quantities that allows to rapidly and reliably estimate the numerosity of a set of objects: an Approximate Number System (ANS). Numerosity perception shows a characteristic shared by all primary visual features: it is susceptible to adaptation. As a consequence of prolonged exposure to a large/small quantity (“adaptor”), the apparent numerosity of a subsequent (“test”) stimulus is distorted yielding a robust under- or over-estimation, respectively. Even if numerosity adaptation has been reported across several sensory modalities (vision, audition, and touch), suggesting the idea of a central and a-modal numerosity processing system, evidence for cross-modal effects are limited to vision and audition, two modalities that are known to preferentially encode sensory stimuli in an external coordinate system. Here we test whether numerosity adaptation for visual and auditory stimuli also distorts the perceived numerosity of tactile stimuli (and vice-versa) despite touch being a modality primarily coded in an internal (body-centered) reference frame. We measured numerosity discrimination of stimuli presented sequentially after adaptation to series of either few (around 2 Hz; low adaptation) or numerous (around 8 Hz; high adaptation) impulses for all possible combinations of visual, auditory, or tactile adapting and test stimuli. In all cases, adapting to few impulses yielded a significant overestimation of the test numerosity with the opposite occurring as a consequence of adaptation to numerous stimuli. The overall magnitude of adaptation was robust (around 30%) and rather similar for all sensory modality combinations. Overall, these findings support the idea of a truly generalized and a-modal mechanism for numerosity representation aimed to process numerical information independently from the sensory modality of the incoming signals.

Multitask learning over shared subspaces

This paper uses constructs from machine learning to define pairs of learning tasks that either shared or did not share a common subspace. Human subjects then learnt these tasks using a feedback-based approach and we hypothesised that learning would be boosted for shared subspaces. Our findings broadly supported this hypothesis with either better performance on the second task if it shared the same subspace as the first, or positive correlations over task performance for shared subspaces. These empirical findings were compared to the behaviour of a Neural Network model trained using sequential Bayesian learning and human performance was found to be consistent with a minimal capacity variant of this model. Networks with an increased representational capacity, and networks without Bayesian learning, did not show these transfer effects. We propose that the concept of shared subspaces provides a useful framework for the experimental study of human multitask and transfer learning.

How does knowledge gained from previous experience affect learning of new tasks? This question of “Transfer Learning” has been addressed by teachers, psychologists, and more recently by researchers in the fields of neural networks and machine learning. Leveraging constructs from machine learning, we designed pairs of learning tasks that either shared or did not share a common subspace. We compared the dynamics of transfer learning in humans with those of a multitask neural network model, finding that human performance was consistent with a minimal capacity variant of the model. Learning was boosted in the second task if the same subspace was shared between tasks. Additionally, accuracy between tasks was positively correlated but only when they shared the same subspace. Our results highlight the roles of subspaces, showing how they could act as a learning boost if shared, and be detrimental if not.

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.

Topographic numerosity maps cover subitizing and estimation ranges

Numerosity, the set size of a group of items, helps guide behaviour and decisions. Non-symbolic numerosities are represented by the approximate number system. However, distinct behavioural performance suggests that small numerosities, i.e. subitizing range, are implemented differently in the brain than larger numerosities. Prior work has shown that neural populations selectively responding (i.e. hemodynamic responses) to small numerosities are organized into a network of topographical maps. Here, we investigate how neural populations respond to large numerosities, well into the ANS. Using 7 T fMRI and biologically-inspired analyses, we found a network of neural populations tuned to both small and large numerosities organized within the same topographic maps. These results demonstrate a continuum of numerosity preferences that progressively cover both the subitizing range and beyond within the same numerosity map, suggesting a single neural mechanism. We hypothesize that differences in map properties, such as cortical magnification and tuning width, underlie known differences in behaviour.

Individualized cognitive neuroscience needs 7T: Comparing numerosity maps at 3T and 7T MRI

The field of cognitive neuroscience is weighing evidence about whether to move from the current standard field strength of 3 Tesla (3T) to ultra-high field (UHF) of 7T and above. The present study contributes to the evidence by comparing a computational cognitive neuroscience paradigm at 3T and 7T. The goal was to evaluate the practical effects, i.e. model predictive power, of field strength on a numerosity task using accessible pre-processing and analysis tools. Previously, using 7T functional magnetic resonance imaging and biologically-inspired analyses, i.e. population receptive field modelling, we discovered topographical organization of numerosity-selective neural populations in human parietal cortex. Here we show that these topographic maps are also detectable at 3T. However, averaging of many more functional runs was required at 3T to reliably reconstruct numerosity maps. On average, one 7T run had about four times the model predictive power of one 3T run. We believe that this amount of scanning would have made the initial discovery of the numerosity maps on 3T highly infeasible in practice. Therefore, we suggest that the higher signal-to-noise ratio and signal sensitivity of UHF MRI is necessary to build mechanistic models of the organization and function of our cognitive abilities in individual participants.

Tuned neural responses to haptic numerosity in the putamen

The ability to perceive the numerosity of items in the environment is critical for behavior of species across the evolutionary tree. Though the focus of studies of numerosity perception lays on the parietal and frontal cortices, the ability to perceive numerosity by a range of species suggests that subcortical nuclei may be implicated in the process. Recently, we have uncovered tuned neural responses to haptic numerosity in the human cortex. Here, we questioned whether subcortical nuclei are also engaged in perception of haptic numerosity. To that end, we utilized a task of haptic numerosity exploration, together with population receptive field model of numerosity selective responses measured at ultra-high field MRI (7T). We found tuned neural responses to haptic numerosity in the bilateral putamen. Similar to the cortex, the population receptive fields tuning width increased with numerosity. The tuned responses to numerosity in the putamen extend its role in cognition and propose that the motor-sensory loops of the putamen and basal ganglia might take an active part in numerosity perception and preparation for future action.

Zooming-in on higher-level vision: High-resolution fMRI for understanding visual perception and awareness

One of the central questions in visual neuroscience is how the sparse retinal signals leaving our eyes are transformed into a rich subjective visual experience of the world. Invasive physiology studies, which offers the highest spatial resolution, have revealed many facts about the processing of simple visual features like contrast, color, and orientation, focusing on the early visual areas. At the same time, standard human fMRI studies with comparably coarser spatial resolution have revealed more complex, functionally specialized, and category-selective responses in higher visual areas. Although the visual system is the best understood among the sensory modalities, these two areas of research remain largely segregated. High-resolution fMRI opens up a possibility for linking them. On the one hand, it allows studying how the higher-level visual functions affect the fine-scale activity in early visual areas. On the other hand, it allows discovering the fine-scale functional organization of higher visual areas and exploring their functional connectivity with visual areas lower in the hierarchy. In this review, I will discuss examples of successful work undertaken in these directions using high-resolution fMRI and discuss where this method could be applied in the future to advance our understanding of the complexity of higher-level visual processing.

Adaptation to visual numerosity changes neural numerosity selectivity

Perceiving numerosity, i.e. the set size of a group of items, is an evolutionarily preserved ability found in humans and animals. A useful method to infer the neural underpinnings of a given perceptual property is sensory adaptation. Like other primary perceptual attributes, numerosity is susceptible to adaptation. Recently, we have shown numerosity-selective neural populations with a topographic organization in the human brain. Here, we investigated whether numerosity adaptation can affect the numerosity selectivity of these populations using ultra-high field (7 Tesla) functional magnetic resonance imaging (fMRI). Participants viewed stimuli of changing numerosity (1 to 7 dots), which allowed the mapping of numerosity selectivity. We interleaved a low or high numerosity adapter stimulus with these mapping stimuli, repeatedly presenting 1 or 20 dots respectively to adapt the numerosity-selective neural populations. We analyzed the responses using custom-build population receptive field neural models of numerosity encoding and compared estimated numerosity preferences between adaptation conditions. We replicated our previous studies where we found several topographic maps of numerosity-selective responses. We found that overall, numerosity adaptation altered the preferred numerosities within the numerosity maps, resulting in predominantly attractive biases towards the numerosity of the adapter. The differential biases could be explained by the difference between the unadapted preferred numerosity and the numerosity of the adapter, with attractive biases being observed with higher difference. The results could link perceptual numerosity adaptation effects to changes in neural numerosity selectivity.

Topographic maps representing haptic numerosity reveals distinct sensory representations in supramodal networks

Dedicated maps for cognitive quantities such as timing, size and numerosity support the view that topography is a general principle of brain organization. To date, however, all of these maps were driven by the visual system. Here, we ask whether there are supramodal topographic maps representing cognitive dimensions irrespective of the stimulated sensory modality. We measured haptically and visually driven numerosity-selective neural responses using model-based analyses and ultra-high field (7T) fMRI. We found topographically organized neural populations tuned to haptic numerosity. The responses to visual or haptic numerosity shared a similar cortical network. However, the maps of the two modalities only partially overlap. Thus, although both visual and haptic numerosities are processed in a similar supramodal functional network, the underlying neural populations may be related, but distinct. Therefore, we hypothesize that overlap between modality-specific maps facilitates cross-modal interactions and supramodal representation of cognitive quantities.

Topographically organized tuned responses to haptic numerosity were found in the human brain. The responses to visual or haptic numerosity shared a similar large-scale cortical network, yet the maps of the two modalities only partially overlapped, suggesting distinct underlying neural populations.

Disentangling feedforward versus feedback processing in numerosity representation

Numerosity is a fundamental aspect of the external environment, needed to guide our behavior in an effective manner. Previous studies show that numerosity processing involves at least two temporal stages (~100 and ~150 msec after stimulus onset) in early visual cortex. One possibility is that the two stages reflect an initial feedforward processing followed by feedback signals from higher-order cortical areas that underlie segmentation of visual inputs into perceptual units that define numerosity. Alternatively, multiple stages of feedforward processing might progressively refine the input leading to the segmented representation. Here, we distinguish these two hypotheses by exploiting the connectedness illusion (i.e., the systematic underestimation of pairwise-connected dots), backward masking (to suppress feedback signals), and serial dependence (i.e., a perceptual bias making a stimulus appear to be more similar to its preceding one). Our results show that a connected dot array biases the numerosity representation of the subsequent dot array based on its illusory perception, irrespective of whether it is visible or suppressed by masking. These findings demonstrate that feedback processing is not strictly necessary for the perceptual segmentation that gives rise to perceived numerosity, and instead suggest that different stages of feedforward activity presumably carrying low and high spatial frequency information are sufficient to create a numerosity representation in early visual areas.

A Sensorimotor Numerosity System

Incoming sensory input provides information for the planning and execution of actions, which yield motor outcomes that are themselves sensory inputs. One dimension where action and perception strongly interact is numerosity perception. Many non-human animals can estimate approximately the number of external elements as well as their own actions, and neurons have been identified that respond to both. Recent psychophysical adaptation studies on humans also provide evidence for neural mechanisms responding to both the number of externally generated events and self-produced actions. Here we advance the idea that these strong connections may arise from dedicated sensorimotor mechanisms in the brain, part of a more generalized system interfacing action with the processing of other quantitative magnitudes such as space and time.

How visual is the « number sense »? Insights from the blind

Is vision a necessary building block for the foundations of mathematical cognition? A straightforward model to test the causal role visual experience plays in the development of numerical abilities is to study people born without sight. In this review we will demonstrate that congenitally blind people can develop numerical abilities that equal or even surpass those of sighted individuals, despite representing numbers using a qualitatively different representational format. We will also show that numerical thinking in blind people maps onto regions typically involved in visuo-spatial processing in the sighted, highlighting how intrinsic computational biases may constrain the reorganization of numerical networks in case of early visual deprivation. More generally, we will illustrate how the study of arithmetic abilities in congenitally blind people represents a compelling model to understand how sensory experience scaffolds the development of higher-level cognitive representations.

Number Adaptation Can Be Dissociated From Density Adaptation

Rapidly judging the number of objects in a scene is an important perceptual ability. Recent debates have centered on whether number perception is accomplished by dedicated mechanisms and, in particular, on whether number-adaptation aftereffects reflect adaptation of number per se or adaptation of related stimulus properties, such as density. Here, we report an adaptation experiment (N = 8) for which the predictions of number and density theories are diametrically opposed. We found that when a reference stimulus has higher density than an adaptation stimulus but contains fewer elements, adaptation reduces the perceived number of elements in the reference stimulus. This is consistent with number adaptation and inconsistent with density adaptation. Thus, number-adaptation aftereffects are more than a by-product of density adaptation: When density and number are dissociated, adaptation effects are in the direction predicted by adaptation to number, not density.

The role of action intentionality and effector in the subjective expansion of temporal duration after saccadic eye movements

Visual perception is based on periods of stable fixation separated by saccadic eye movements. Although naive perception seems stable (in space) and continuous (in time), laboratory studies have demonstrated that events presented around the time of saccades are misperceived spatially and temporally. Saccadic chronostasis, the "stopped clock illusion", represents one such temporal distortion in which the movement of the clock hand after the saccade is perceived as lasting longer than usual. Multiple explanations for chronostasis have been proposed including action-backdating, temporal binding of the action towards the moment of its effect ("intentional binding") and post-saccadic temporal dilation. The current study aimed to resolve this debate by using different types of action (keypress vs saccade) and varying the intentionality of the action. We measured both perceived onset of the motor action and perceived onset of an auditory tone presented at different delays after the keypress/saccade. The results showed intentional binding for the keypress action, with perceived motor onset shifted forwards in time and the time of the tone shifted backwards. Saccades resulted in the opposite pattern, showing temporal expansion rather than compression, especially with cued saccades. The temporal illusion was modulated by intentionality of the movement. Our findings suggest that saccadic chronostasis is not solely dependent on a backward shift in perceived saccade onset, but instead reflects a temporal dilation. This percept of an effectively "longer" period at the beginning of a new fixation may reflect the pattern of suppressed, and then enhanced, visual processing around the time of saccades.

From ATOM to GradiATOM: Cortical gradients support time and space processing as revealed by a meta-analysis of neuroimaging studies

According to the ATOM (A Theory Of Magnitude), formulated by Walsh more than fifteen years ago, there is a general system of magnitude in the brain that comprises regions, such as the parietal cortex, shared by space, time and other magnitudes. The present meta-analysis of neuroimaging studies used the Activation Likelihood Estimation (ALE) method in order to determine the set of regions commonly activated in space and time processing and to establish the neural activations specific to each magnitude domain. Following PRISMA guidelines, we included in the analysis a total of 112 and 114 experiments, exploring space and time processing, respectively. We clearly identified the presence of a system of brain regions commonly recruited in both space and time that includes: bilateral insula, the pre-supplementary motor area (pre-SMA), the right frontal operculum and the intraparietal sulci. These regions might be the best candidates to form the core magnitude neural system. Surprisingly, along each of these regions but the insula, ALE values progressed in a cortical gradient from time to space. The SMA exhibited an anterior-posterior gradient, with space activating more-anterior regions (i.e., pre-SMA) and time activating more-posterior regions (i.e., SMA-proper). Frontal and parietal regions showed a dorsal-ventral gradient: space is mediated by dorsal frontal and parietal regions, and time recruits ventral frontal and parietal regions. Our study supports but also expands the ATOM theory. Therefore, we here re-named it the 'GradiATOM' theory (Gradient Theory of Magnitude), proposing that gradient organization can facilitate the transformations and integrations of magnitude representations by allowing space- and time-related neural populations to interact with each other over minimal distances.

A parietal region processing numerosity of observed actions: An FMRI study

When observing others' behavior, it is important to perceive not only the identity of the observed actions (OAs), but also the number of times they were performed. Given the mounting evidence implicating posterior parietal cortex in action observation, and in particular that of manipulative actions, the aim of this study was to identify the parietal region, if any, that contributes to the processing of observed manipulative action (OMA) numerosity, using the functional magnetic resonance imaging technique. Twenty‐one right‐handed healthy volunteers performed two discrimination tasks while in the scanner, responding to video stimuli in which an actor performed manipulative actions on colored target balls that appeared four times consecutively. The subjects discriminated between two small numerosities of either OMAs (“Action” condition) or colors of balls (“Ball” condition). A significant difference between the “Action” and “Ball” conditions was observed in occipito‐temporal cortex and the putative human anterior intraparietal sulcus (phAIP) area as well as the third topographic map of numerosity‐selective neurons at the post‐central sulcus (NPC3) of the left parietal cortex. A further region of interest analysis of the group‐average data showed that at the single voxel level the latter area, more than any other parietal or occipito‐temporal numerosity map, favored numerosity of OAs. These results suggest that phAIP processes the identity of OMAs, while neighboring NPC3 likely processes the numerosity of the identified OAs.