Numerosity representation is encoded in human subcortex

High-level visual processing in the lateral geniculate nucleus revealed using goal-driven deep learning

BACKGROUND

The Lateral Geniculate Nucleus (LGN) is an essential contributor to high-level visual processing despite being an early subcortical area in the visual system. Current LGN computational models focus on its basic properties, with less emphasis on its role in high-level vision.

NEW METHOD

We propose a high-level approach for encoding mouse LGN neural responses to natural scenes. This approach employs two deep neural networks (DNNs); namely VGG16 and ResNet50, as goal-driven models. We use these models as tools to better understand visual features encoded in the LGN.

RESULTS

Early layers of the DNNs represent the best LGN models. We also demonstrate that numerosity, as a high-level visual feature, is encoded, along with other visual features, in LGN neural activity. Results demonstrate that intermediate layers are better in representing numerosity compared to early layers. Early layers are better at predicting simple visual features, while intermediate layers are better at predicting more complex features. Finally, we show that an ensemble model of an early and an intermediate layer achieves high neural prediction accuracy and numerosity representation.

COMPARISON WITH EXISTING METHOD(S)

Our approach emphasizes the role of analyzing the inner workings of DNNs to demonstrate the representation of a high-level feature such as numerosity in the LGN, as opposed to the common belief about the simplicity of the LGN.

CONCLUSIONS

We demonstrate that goal-driven DNNs can be used as high-level vision models of the LGN for neural prediction and as an exploration tool to better understand the role of the LGN.

Investigating the Triple Code Model in numerical cognition using stereotactic electroencephalography

The ability to conceptualize numerical quantities is an essential human trait. According to the "Triple Code Model" in numerical cognition, distinct neural substrates encode the processing of visual, auditory, and non-symbolic numerical representations. While our contemporary understanding of human number cognition has benefited greatly from advances in clinical imaging, limited studies have investigated the intracranial electrophysiological correlates of number processing. In this study, 13 subjects undergoing stereotactic electroencephalography for epilepsy participated in a number recognition task. Drawing upon postulates of the Triple Code Model, we presented subjects with numerical stimuli varying in representation type (symbolic vs. non-symbolic) and mode of stimuli delivery (visual vs. auditory). Time-frequency spectrograms were dimensionally reduced with principal component analysis and passed into a linear support vector machine classification algorithm to identify regions associated with number perception compared to inter-trial periods. Across representation formats, the highest classification accuracy was observed in the bilateral parietal lobes. Auditory (spoken and beeps) and visual (Arabic) number formats preferentially engaged the superior temporal cortices and the frontoparietal regions, respectively. The left parietal cortex was found to have the highest classification for number dots. Notably, the putamen exhibited robust classification accuracies in response to numerical stimuli. Analyses of spectral feature maps revealed that non-gamma frequency, below 30 Hz, had greater-than-chance classification value and could be potentially used to characterize format specific number representations. Taken together, our findings obtained from intracranial recordings provide further support and expand on the Triple Code Model for numerical cognition.

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.

Perception of visual variance is mediated by subcortical mechanisms

Variance characterizes the structure of the environment. This statistical concept plays a critical role in evaluating the reliability of evidence for human decision-making. The present study examined the involvement of subcortical structures in the processing of visual variance. To this end, we used a stereoscope to sequentially present two circle arrays in a dichoptic or monocular fashion while participants compared the perceived variance of the two arrays. In Experiment 1, two arrays were presented monocularly to the same eye, dichopticly to different eyes, or binocularly to both eyes. The variance judgment was less accurate in different-eye condition than the other conditions. In Experiment 2, the first circle array was split into a large-variance and a small-variance set, with either the large-variance or small-variance set preceding the presentation of the second circle array in the same eye. The variance of the first array was judged larger when the second array was preceded by the large-variance set in the same eye, showing that the perception of variance was modulated by the visual variance processed in the same eye. Taken together, these findings provide evidence for monocular processing of visual variance, suggesting that subcortical structures capture the statistical structure of the visual world.

Atypical reliance on monocular visual pathway for face and word recognition in developmental dyslexia

Studies with individuals with developmental dyslexia (DD) have documented impaired perception of words and faces, both of which are domains of visual expertise for human adults. In this study, we examined a possible mechanism that might be associated with the impaired acquisition of visual expertise for words and faces in DD, namely, the atypical engagement of the monocular visual pathway. Participants with DD and typical readers (TR) judged whether a pair of sequentially presented unfamiliar faces or nonwords were the same or different, and the pair of stimuli were displayed in an eye-specific fashion using a stereoscope. Based on evidence of greater reliance on subcortical structures early in development, we predicted differences between the groups in the engagement of lower (monocular) versus higher (binocular) regions of the visual pathways. Whereas the TR group showed a monocular advantage for both stimulus types, the DD participants evinced a monocular advantage for faces and words that was much greater than that measured in the TRs. These findings indicate that the DD individuals have enhanced subcortical engagement and that this might arise from the failure to fine-tune cortical correlates mediating the discrimination of homogeneous exemplars in domains of expertise.

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.

Contributions of Lower Structures to Higher Cognition: Towards a Dynamic Network Model

Researchers often attribute higher cognition to the enlargement of cortical regions throughout evolution, reflecting the belief that humans sit at the top of the cognitive pyramid. Implicitly, this approach assumes that the subcortex is of secondary importance for higher-order cognition. While it is now recognized that subcortical regions can be involved in various cognitive domains, it remains unclear how they contribute to computations essential for higher-level cognitive processes such as endogenous attention and numerical cognition. Herein, we identify three models of subcortical-cortical relations in these cognitive processes: (i) subcortical regions are not involved in higher cognition; (ii) subcortical computations support elemental forms of higher cognition mainly in species without a developed cortex; and (iii) higher cognition depends on a whole-brain dynamic network, requiring integrated cortical and subcortical computations. Based on evolutionary theories and recent data, we propose the SEED hypothesis: the Subcortex is Essential for the Early Development of higher cognition. According to the five principles of the SEED hypothesis, subcortical computations are essential for the emergence of cognitive abilities that enable organisms to adapt to an ever-changing environment. We examine the implications of the SEED hypothesis from a multidisciplinary perspective to understand how the subcortex contributes to various forms of higher cognition.

Subcortical encoding of summary statistics in humans

Statistical encoding compresses redundant information from multiple items into a single summary metric (e.g., mean). Such statistical representation has been suggested to be automatic, but at which stage it is extracted is unknown. Here, we examined the involvement of the subcortex in the processing of summary statistics. We presented an array of circles dichoptically or monocularly while matching the number of perceived circles after binocular fusion. Experiments 1 and 2 showed that interocularly suppressed, invisible circles were automatically involved in the summary statistical representation, but only when they were presented to the same eye as the visible circles. This same-eye effect was further observed for consciously processed circles in Experiment 3, in which the estimated mean size of the circles was biased toward the information transmitted by monocular channels. Together, we provide converging evidence that the processing of summary statistics, an assumed high-level cognitive process, is mediated by subcortical structures.

Does auditory numerosity and non-numerical magnitude affect visual non-symbolic numerical representation?

In the present study, we investigated the effects of auditory numerosity and magnitude (loudness) on visual numerosity processing. Participants compared numerosities of two sequential dot arrays. The second dot array was paired with a tone array that was independent of visual comparison. The numerosity (One-tone vs. Multiple-tone) and the non-numerical magnitude of tones (loudness) were manipulated in Experiments 1 and 2, respectively. In Experiment 1, participants' inverse efficiency score (IES), that is, the quotient between response time and accuracy, was significantly smaller in the One-tone and Multiple-tone conditions than that in the No-tone condition, and linear trend analyses showed that the IES decreased with the number of tones. In Experiment 2, the IES in the Loud-tone condition was significantly smaller than that in the No-tone condition, and the IES decreased as the loudness of the tones increased. In Experiment 3, both auditory numerosity and magnitude were manipulated. For soft tones, the IES was smaller in the Multiple-tone condition than in the One-tone condition, whereas no significant difference was found between two conditions in loud tones. In sum, these findings suggest that the visual numerical representation can be spontaneously affected by the numerosity and non-numerical magnitude of stimuli from another modality.

Muscimol-induced inactivation of the ventral prefrontal cortex impairs counting performance in rhesus monkeys

Numbers are one of the three basic concepts of human abstract thinking. When human beings count, they often point to things, one by one, and read numbers in a positive integer column. The prefrontal cortex plays a wide range of roles in executive functions, including active maintenance and achievement of goals, adaptive coding and exertion of general intelligence, and completion of time complexity events. Nonhuman animals do not use number names, such as "one, two, three," or numerals, such as "1, 2, 3" to "count" in the same way as humans do. Our previous study established an animal model of counting in monkeys. Here, we used this model to determine whether the prefrontal cortex participates in counting in monkeys. Two 5-year-old female rhesus monkeys (macaques), weighing 5.0 kg and 5.5 kg, were selected to train in a counting task, counting from 1 to 5. When their counting task performance stabilized, we performed surgery on the prefrontal cortex to implant drug delivery tubes. After allowing the monkeys' physical condition and counting performance to recover, we injected either muscimol or normal saline into their dorsal and ventral prefrontal cortex. Thereafter, we observed their counting task performance and analyzed the error types and reaction time during the counting task. The monkeys' performance in the counting task decreased significantly after muscimol injection into the ventral prefrontal cortex; however, it was not affected after saline injection into the ventral prefrontal cortex, or after muscimol or saline injection into the dorsal prefrontal cortex. The ventral prefrontal cortex of the monkey is necessary for counting performance.

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.

Magnitudes for Nervous Systems: Theoretical Issues and Experimental Evidence

Animals’ negotiations with the environment frequently involve quantitative assessments. However, it is largely unknown how different nervous systems can deal with information about magnitude and perform operations on it. Here we review some of the literature on this topic and discuss a few issues worthy of debate that can guide future research directions. First, we present experimental evidence suggesting that, in addition to the cortical (pallial) brain regions that are widely acknowledged to play a role in magnitude estimation, subcortical (more generally, subpallial) brain regions also play an important role. Second, we discuss interactions between different domains of magnitude and put forward a hypothesis to account for the directionality of associations between discrete and continuous magnitude. Finally, we suggest how the distinction between the concepts of number and discrete quantity should foster more attention to the role of sensory areas and circuits in assessing discrete quantities.

Sub-cortical areas process physical size but not numerical value

A robust finding in the numerical cognition literature is that the physical size and the numerical value of two to-be-compared digits interact, resulting in a size congruity effect (SiCE). The current study focuses on the possible role of prestriate areas in a digit comparison Stroop-like task. In the visual pathway, prestriate areas refer to regions from the retina up to the primary visual cortex (V1). I hypothesized that processing of physical size, but not numerical value, begins already in prestriate areas. This is because physical size is a basic visual feature while the numerical value of a symbol is a learned convention that should be retrieved from long-term memory. Adult participants compared the size or the numerical value of two digits. Without participants' awareness, I projected the digits either to the same eye, or each digit to a different eye. The latter type of presentation prevents prestriate areas from taking part in comparing the digits. Therefore, slower a response time under this condition hints at the involvement of prestriate areas. Evidence confirmed the initial hypothesis, demonstrating slower performance when the stimuli are segregated between the eyes but only for physical size comparisons. This finding suggests that at least the initial processing of physical size, when relevant, is done before, and by different neural substrate than numerical value. The implications of the study and future directions are discussed.

Subcortical Cognition: The Fruit Below the Rind

Cognitive neuroscience has highlighted the cerebral cortex while often overlooking subcortical structures. This cortical proclivity is found in basic and translational research on many aspects of cognition, especially higher cognitive domains such as language, reading, music, and math. We suggest that, for both anatomical and evolutionary reasons, multiple subcortical structures play substantial roles across higher and lower cognition. We present a comprehensive review of existing evidence, which indeed reveals extensive subcortical contributions in multiple cognitive domains. We argue that the findings are overall both real and important. Next, we advance a theoretical framework to capture the nature of (sub)cortical contributions to cognition. Finally, we propose how new subcortical cognitive roles can be identified by leveraging anatomical and evolutionary principles, and we describe specific methods that can be used to reveal subcortical cognition. Altogether, this review aims to advance cognitive neuroscience by highlighting subcortical cognition and facilitating its future investigation. Expected final online publication date for the Annual Review of Neuroscience, Volume 45 is July 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Reduced 2D form coherence and 3D structure from motion sensitivity in developmental dyscalculia

Developmental dyscalculia (DD) is a specific learning disability affecting the development of numerical and arithmetical skills. The origin of DD is typically attributed to the suboptimal functioning of key regions within the dorsal visual stream (parietal cortex) which support numerical cognition. While DD individuals are often impaired in visual numerosity perception, the extent to which they also show a wider range of visual dysfunctions is poorly documented. In the current study we measured sensitivity to global motion (translational and flow), 2D static form (Glass patterns) and 3D structure from motion in adults with DD and control subjects. While sensitivity to global motion was comparable across groups, thresholds for static form and structure from motion were higher in the DD compared to the control group, irrespective of associated reading impairments. Glass pattern sensitivity predicted numerical abilities, and this relation could not be explained by recently reported differences in visual crowding. Since global form sensitivity has often been considered an index of ventral stream function, our findings could indicate a cortical dysfunction extending beyond the dorsal visual stream. Alternatively, they would fit with a role of parietal cortex in form perception under challenging conditions requiring multiple element integration.

Ancient visual channels have a causal role in arithmetic calculations

Humans exhibit complex arithmetic skills, often attributed to our exceptionally large neocortex. However, the past decade has provided ample evidence that the functional domain of the subcortex extends well beyond basic functions. Using a sensitive behavioral method, for the first time, we explored the contributions of lower-order visual monocular channels to symbolic arithmetic operations, addition and subtraction. The pattern of results from 4 different experiments provides converging evidence for a causal relation between mental arithmetic and primitive subcortical regions. The results have major implications for our understanding of the neuroevolutionary development of general numerical abilities–subcortical regions, which are shared across different species, are essential to complex numerical operations. In a bigger conceptual framework, these findings and others call for a shift from the modal view of the exclusive role of the neocortex in high-level cognition to a view that emphasizes the interplay between subcortical and cortical brain networks.

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.

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.

Numerosities and Other Magnitudes in the Brains: A Comparative View

The ability to represent, discriminate, and perform arithmetic operations on discrete quantities (numerosities) has been documented in a variety of species of different taxonomic groups, both vertebrates and invertebrates. We do not know, however, to what extent similarity in behavioral data corresponds to basic similarity in underlying neural mechanisms. Here, we review evidence for magnitude representation, both discrete (countable) and continuous, following the sensory input path from primary sensory systems to associative pallial territories in the vertebrate brains. We also speculate on possible underlying mechanisms in invertebrate brains and on the role played by modeling with artificial neural networks. This may provide a general overview on the nervous system involvement in approximating quantity in different animal species, and a general theoretical framework to future comparative studies on the neurobiology of number cognition.

Visual Cortex Transcranial Direct Current Stimulation for Proliferative Diabetic Retinopathy Patients: A Double-Blinded Randomized Exploratory Trial

Proliferative diabetic retinopathy (PDR) is a severe complication of diabetes. PDR-related retinal hemorrhages often lead to severe vision loss. The main goals of management are to prevent visual impairment progression and improve residual vision. We explored the potential of transcranial direct current stimulation (tDCS) to enhance residual vision. tDCS applied to the primary visual cortex (V1) may improve visual input processing from PDR patients’ retinas. Eleven PDR patients received cathodal tDCS stimulation of V1 (1 mA for 10 min), and another eleven patients received sham stimulation (1 mA for 30 s). Visual acuity (logarithm of the minimum angle of resolution (LogMAR) scores) and number acuity (reaction times (RTs) and accuracy rates (ARs)) were measured before and immediately after stimulation. The LogMAR scores and the RTs of patients who received cathodal tDCS decreased significantly after stimulation. Cathodal tDCS has no significant effect on ARs. There were no significant changes in the LogMAR scores, RTs, and ARs of PDR patients who received sham stimulation. The results are compatible with our proposal that neuronal noise aggravates impaired visual function in PDR. The therapeutic effect indicates the potential of tDCS as a safe and effective vision rehabilitation tool for PDR patients.

Fast saccadic eye-movements in humans suggest that numerosity perception is automatic and direct

Fast saccades are rapid automatic oculomotor responses to salient and ecologically important visual stimuli such as animals and faces. Discriminating the number of friends, foe, or prey may also have an evolutionary advantage. In this study, participants were asked to saccade rapidly towards the more numerous of two arrays. Participants could discriminate numerosities with high accuracy and great speed, as fast as 190 ms. Intermediate numerosities were more likely to elicit fast saccades than very low or very high numerosities. Reaction-times for vocal responses (collected in a separate experiment) were slower, did not depend on numerical range, and correlated only with the slow not the fast saccades, pointing to different systems. The short saccadic reaction-times we observe are surprising given that discrimination using numerosity estimation is thought to require a relatively complex neural circuit, with several relays of information through the parietal and prefrontal cortex. Our results suggest that fast numerosity-driven saccades may be generated on a single feed-forward pass of information recruiting a primitive system that cuts through the cortical hierarchy and rapidly transforms the numerosity information into a saccade command.

Excessive visual crowding effects in developmental dyscalculia

Visual crowding refers to the inability to identify objects when surrounded by other similar items. Crowding-like mechanisms are thought to play a key role in numerical perception by determining the sensory mechanisms through which ensembles are perceived. Enhanced visual crowding might hence prevent the normal development of a system involved in segregating and perceiving discrete numbers of items and ultimately the acquisition of more abstract numerical skills. Here, we investigated whether excessive crowding occurs in developmental dyscalculia (DD), a neurodevelopmental disorder characterized by difficulty in learning the most basic numerical and arithmetical concepts, and whether it is found independently of associated major reading and attentional difficulties. We measured spatial crowding in two groups of adult individuals with DD and control subjects. In separate experiments, participants were asked to discriminate the orientation of a Gabor patch either in isolation or under spatial crowding. Orientation discrimination thresholds were comparable across groups when stimuli were shown in isolation, yet they were much higher for the DD group with respect to the control group when the target was crowded by closely neighbouring flanking gratings. The difficulty in discriminating orientation (as reflected by the combination of accuracy and reaction times) in the DD compared to the control group persisted over several larger target flanker distances. Finally, we found that the degree of such spatial crowding correlated with impairments in mathematical abilities even when controlling for visual attention and reading skills. These results suggest that excessive crowding effects might be a characteristic of DD, independent of other associated neurodevelopmental disorders.

Exemplar learning reveals the representational origins of expert category perception

Irrespective of whether one has substantial perceptual expertise for a class of stimuli, an observer invariably encounters novel exemplars from this class. To understand how novel exemplars are represented, we examined the extent to which previous experience with a category constrains the acquisition and nature of representation of subsequent exemplars from that category. Participants completed a perceptual training paradigm with either novel other-race faces (category of experience) or novel computer-generated objects (YUFOs) that included pairwise similarity ratings at the beginning, middle, and end of training, and a 20-d visual search training task on a subset of category exemplars. Analyses of pairwise similarity ratings revealed multiple dissociations between the representational spaces for those learning faces and those learning YUFOs. First, representational distance changes were more selective for faces than YUFOs; trained faces exhibited greater magnitude in representational distance change relative to untrained faces, whereas this trained-untrained distance change was much smaller for YUFOs. Second, there was a difference in where the representational distance changes were observed; for faces, representations that were closer together before training exhibited a greater distance change relative to those that were farther apart before training. For YUFOs, however, the distance changes occurred more uniformly across representational space. Last, there was a decrease in dimensionality of the representational space after training on YUFOs, but not after training on faces. Together, these findings demonstrate how previous category experience governs representational patterns of exemplar learning as well as the underlying dimensionality of the representational space.

Challenging the neurobiological link between number sense and symbolic numerical abilities

A significant body of research links individual differences in symbolic numerical abilities, such as arithmetic, to number sense, the neurobiological system used to approximate and manipulate quantities without language or symbols. However, recent findings from cognitive neuroscience challenge this influential theory. Our current review presents an overview of evidence for the number sense account of symbolic numerical abilities and then reviews recent studies that challenge this account, organized around the following four assertions. (1) There is no number sense as traditionally conceived. (2) Neural substrates of number sense are more widely distributed than common consensus asserts, complicating the neurobiological evidence linking number sense to numerical abilities. (3) The most common measures of number sense are confounded by other cognitive demands, which drive key correlations. (4) Number sense and symbolic number systems (Arabic digits, number words, and so on) rely on distinct neural mechanisms and follow independent developmental trajectories. The review follows each assertion with comments on future directions that may bring resolution to these issues.

Quantity versus quality: Convergent findings in effort-based choice tasks

Organisms must frequently make cost-benefit decisions based on time, risk, and effort in choosing rewards to pursue. Various tasks have been developed to assess effort-based choice in rats, and experimenters have found largely similar results across tasks and brain regions. In this review, we focus primarily on the convergence of different effort-based choice tasks where quality or quantity of reward are manipulated. In the former, the rat is typically presented with the option to work for a preferred reward or select a less preferred, but freely-available reward. In such paradigms, the rewards are of different identities but are confirmed to differ qualitatively in value by a food preference task when both are freely-available. In the latter task type, rats are required to select between higher magnitude versus lower magnitudes of the same reward, but each with a similar effort requirement. We discuss the strengths/limitations of these paradigms, and describe brain regions that have been probed that result in converging or equivocal findings. Results are also reviewed with reference to a need for future work, and the broader impacts and implications of studies probing the mechanisms of effort.

Asymmetrical interference between number and item size perception provides evidence for a domain specific impairment in dyscalculia

Dyscalculia, a specific learning disability that impacts arithmetical skills, has previously been associated to a deficit in the precision of the system that estimates the approximate number of objects in visual scenes (the so called 'number sense' system). However, because in tasks involving numerosity comparisons dyscalculics' judgements appears disproportionally affected by continuous quantitative dimensions (such as the size of the items), an alternative view linked dyscalculia to a domain-general difficulty in inhibiting task-irrelevant responses. To arbitrate between these views, we evaluated the degree of reciprocal interference between numerical and non-numerical quantitative dimensions in adult dyscalculics and matched controls. We used a novel stimulus set orthogonally varying in mean item size and numerosity, putting particular attention into matching both features' perceptual discriminability. Participants compared those stimuli based on each of the two dimensions. While control subjects showed no significant size interference when judging numerosity, dyscalculics' numerosity judgments were strongly biased by the unattended size dimension. Importantly however, both groups showed the same degree of interference from the unattended dimension when judging mean size. Moreover, only the ability to discard the irrelevant size information when comparing numerosity (but not the reverse) significantly predicted calculation ability across subjects. Overall, our results show that numerosity discrimination is less prone to interference than discrimination of another quantitative feature (mean item size) when the perceptual discriminability of these features is matched, as here in control subjects. By quantifying, for the first time, dyscalculic subjects' degree of interference on another orthogonal dimension of the same stimuli, we are able to exclude a domain-general inhibition deficit as explanation for their poor / biased numerical judgement. We suggest that enhanced reliance on non-numerical cues during numerosity discrimination can represent a strategy to cope with a less precise number sense.

Serial dependence in numerosity perception

Our conscious experience of the external world is remarkably stable and seamless, despite the intrinsically discontinuous and noisy nature of sensory information. Serial dependencies in visual perception-reflecting attractive biases making a current stimulus to appear more similar to previous ones-have been recently hypothesized to be involved in perceptual continuity. However, while these effects have been observed across a variety of visual features and at the neural level, several aspects of serial dependence and how it generalizes across visual dimensions is still unknown. Here we explore the behavioral signature of serial dependence in numerosity perception by assessing how the perceived numerosity of dot-array stimuli is biased by a task-irrelevant "inducer" stimulus presented before task-relevant stimuli. First, although prior work suggests that numerosity perception starts in the subcortex, the current study rules out a possible involvement of subcortical processing in serial dependence, confirming that the effect likely starts in the visual cortex. Second, we show that the effect is coarsely spatially localized to the position of the inducer stimulus. Third, we demonstrate that the effect is present even with a stimulus presentation procedure minimizing the involvement of post-perceptual processes, but only when participants actively pay attention to the inducer stimulus. Overall, these results provide a comprehensive characterization of serial dependencies in numerosity perception, demonstrating that attractive biases occur by means of spatially localized attentional modulations of early sensory activity.

Examining the Triple Code Model in numerical cognition: An fMRI study

The Triple Code Model (TCM) of numerical cognition argues for the existence of three representational codes for number: Arabic digits, verbal number words, and analog nonsymbolic magnitude representations, each subserved by functionally dissociated neural substrates. Despite the popularity of the TCM, no study to date has explored all three numerical codes within one fMRI paradigm. We administered three tasks, associated with each of the aforementioned numerical codes, in order to explore the neural correlates of numerosity processing in a sample of adults (N = 46). Independent task-control contrast analyses revealed task-dependent activity in partial support of the model, but also highlight the inherent complexity of a distributed and overlapping fronto-parietal network involved in all numerical codes. The results indicate that the TCM correctly predicts the existence of some functionally dissociated neural substrates, but requires an update that accounts for interactions with attentional processes. Parametric contrasts corresponding to differences in task difficulty revealed specific neural correlates of the distance effect, where closely spaced numbers become more difficult to discriminate than numbers spaced further apart. A conjunction analysis illustrated overlapping neural correlates across all tasks, in line with recent proposals for a fronto-parietal network of number processing. We additionally provide tentative results suggesting the involvement of format-independent numerosity-sensitive retinotopic maps in the early visual stream, extending previous findings of nonsymbolic stimulus selectivity. We discuss the functional roles of the components associated with the model, as well as the purported fronto-parietal network, and offer arguments in favor of revising the TCM.

Subcortical Facilitation of Behavioral Responses to Threat

Behavioral responses to threat are critical to survival. Several cortical and subcortical brain regions respond selectively to threat. However, the relation of these neural responses and their underlying representations to behavior is unclear. We examined the contribution of lower-order subcortical representations to behavioral responses to threat in adult humans. In Experiments 1 and 2, participants viewed pairs of images presented to the same eye or to different eyes. We observed a monocular advantage, which indicates subcortical facilitation, for ancestral threats (snakes, spiders), but not for modern threats, positive images, or neutral images. In Experiment 3, we presented pairs of snakes or neutral images into the temporal or nasal hemifield. For snakes only, we observed a temporal hemifield advantage, which indicates facilitation by the retino-tectal subcortical pathway. These results advance the current understanding of processing of threat by adult humans by revealing the characteristics of behaviors driven by a lower-order neural mechanism that is specialized for the processing of ancestral threats. The results also contribute to ongoing debates concerning the biological generality of neural mechanisms for processing of complex, emotionally-relevant stimuli by providing evidence for conservation of lower-order neural mechanisms for processing of ancestral threats across both ontogeny and phylogeny.