Sensory and Working Memory Representations of Small and Large Numerosities in the Crow Endbrain

The calculating brain

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

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.

Jackdaws form categorical prototypes based on experience with category exemplars

Categorization represents one cognitive ability fundamental to animal behavior. Grouping of elements based on perceptual or semantic features helps to reduce processing resources and facilitates appropriate behavior. Corvids master complex categorization, yet the detailed categorization learning strategies are less well understood. We trained two jackdaws on a delayed match to category paradigm using a novel, artificial stimulus type, RUBubbles. Both birds learned to differentiate between two session-unique categories following two distinct learning protocols. Categories were either introduced via central category prototypes (low variability approach) or using a subset of diverse category exemplars from which diagnostic features had to be identified (high variability approach). In both versions, the stimulus similarity relative to a central category prototype explained categorization performance best. Jackdaws consistently used a central prototype to judge category membership, regardless of whether this prototype was used to introduce distinct categories or had to be inferred from multiple exemplars. Reliance on a category prototype occurred already after experiencing only a few trials with different category exemplars. High stimulus set variability prolonged initial learning but showed no consistent beneficial effect on later generalization performance. High numbers of stimuli, their perceptual similarity, and coherent category structure resulted in a prototype-based strategy, reflecting the most adaptive, efficient, and parsimonious way to represent RUBubble categories. Thus, our birds represent a valuable comparative animal model that permits further study of category representations throughout learning in different regions of a brain producing highly cognitive behavior.

Input and Output Connections of the Crow Nidopallium Caudolaterale

The avian telencephalic structure nidopallium caudolaterale (NCL) functions as an analog to the mammalian prefrontal cortex. In crows, corvid songbirds, it plays a crucial role in higher cognitive and executive functions. These functions rely on the NCL's extensive telencephalic connections. However, systematic investigations into the brain-wide connectivity of the NCL in crows or other songbirds are lacking. Here, we studied its input and output connections by injecting retrograde and anterograde tracers into the carrion crow NCL. Our results, mapped onto a published carrion crow brain atlas, confirm NCL multisensory connections and extend prior pigeon findings by identifying a novel input from the hippocampal formation. Furthermore, we analyze crow NCL efferent projections to the arcopallium and report newly identified arcopallial neurons projecting bilaterally to the NCL. These findings help to clarify the role of the NCL as central executive hub in the corvid songbird brain.

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

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

Association neurons in the crow telencephalon link visual signs to numerical values

Many animals can associate signs with numerical values and use these signs in a goal-directed way during task performance. However, the neuronal basis of this semantic association has only rarely been investigated, and so far only in primates. How mechanisms of number associations are implemented in the distinctly evolved brains of other animal taxa such as birds is currently unknown. Here, we explored this semantic number-sign mapping by recording single-neuron activity in the crows' nidopallium caudolaterale (NCL), a brain structure critically involved in avian numerical cognition. Crows were trained to associate visual shapes with varying numbers of items in a number production task. The responses of many NCL neurons during stimulus presentation reflected the numerical values associated with visual shapes in a behaviorally relevant way. Consistent with the crow's better behavioral performance with signs, neuronal representations of numerical values extracted from shapes were more selective compared to those from dot arrays. The existence of number association neurons in crows points to a phylogenetic preadaptation of the brains of cognitively advanced vertebrates to link visual shapes with numerical meaning.

Corvids optimize working memory by categorizing continuous stimuli

Working memory (WM) is a crucial element of the higher cognition of primates and corvid songbirds. Despite its importance, WM has a severely limited capacity and is vulnerable to noise. In primates, attractor dynamics mitigate the effect of noise by discretizing continuous information. Yet, it remains unclear whether similar dynamics are seen in avian brains. Here, we show jackdaws (Corvus monedula) have similar behavioral biases as humans; memories are less precise and more biased as memory demands increase. Model-based analysis reveal discrete attractors are evenly spread across the stimulus space. Altogether, our comparative approach suggests attractor dynamics in primates and corvids mitigate the effect of noise by systematically drifting towards specific attractors. By demonstrating this effect in an evolutionary distant species, our results strengthen attractor dynamics as general, adaptive biological principle to efficiently use WM.

Costs and benefits of voluntary attention in crows

Behavioural signatures of voluntary, endogenous selective attention have been found in both mammals and birds, but the relationship between performance benefits at attended and costs at unattended locations remains unclear. We trained two carrion crows (Corvus corone) on a Posner-like spatial cueing task with dissociated cue and target locations, using both highly predictive and neutral central cues to compare reaction time (RT) and detection accuracy for validly, invalidly and neutrally cued targets. We found robust RT effects of predictive cueing at varying stimulus-onset asynchronies (SOA) that resulted from both advantages at cued locations and costs at un-cued locations. Both crows showed cueing effects around 15-25 ms with an early onset at 100 ms SOA, comparable to macaques. Our results provide a direct assessment of costs and benefits of voluntary attention in a bird species. They show that crows are able to guide spatial attention using associative cues, and that the processing advantage at attended locations impairs performance at unattended locations.

Categorical representation of abstract spatial magnitudes in the executive telencephalon of crows

The ability to group abstract continuous magnitudes into meaningful categories is cognitively demanding but key to intelligent behavior. To explore its neuronal mechanisms, we trained carrion crows to categorize lines of variable lengths into arbitrary "short" and "long" categories. Single-neuron activity in the nidopallium caudolaterale (NCL) of behaving crows reflected the learned length categories of visual stimuli. The length categories could be reliably decoded from neuronal population activity to predict the crows' conceptual decisions. NCL activity changed with learning when a crow was retrained with the same stimuli assigned to more categories with new boundaries ("short", "medium," and "long"). Categorical neuronal representations emerged dynamically so that sensory length information at the beginning of the trial was transformed into behaviorally relevant categorical representations shortly before the crows' decision making. Our data show malleable categorization capabilities for abstract spatial magnitudes mediated by the flexible networks of the crow NCL.

Crows protect visual working memory against interference

Working memory, the ability to actively maintain and manipulate information across time, is key to intelligent behavior. Because of the limited capacity of working memory, relevant information needs to be protected against distracting representations. Whether birds can resist distractors and safeguard memorized relevant information is unclear. We trained carrion crows in a delayed match-to-sample task to memorize an image while resisting other, interfering stimuli. We found that the repetition of the sample stimulus during the memory delay improved performance accuracy and accelerated reaction time relative to a reference condition with a neutral interfering stimulus. In contrast, the presentation of the image that constituted the subsequent non-match test stimulus mildly weakened performance. However, the crows' robust performance in this most demanding distractor condition indicates that sample information was actively protected from being overwritten by the distractor. These data show that crows can cognitively control and safeguard behaviorally relevant working memory contents.

Visual adaptation reveals multichannel coding for numerosity

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

Number 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.

In search for consciousness in animals: Using working memory and voluntary attention as behavioral indicators

Whether animals have subjective experiences about the content of their sensory input, i.e., whether they are aware of stimuli, is a notoriously difficult question to answer. If consciousness is present in animals, it must share fundamental characteristics with human awareness. Working memory and voluntary/endogenous attention are suggested as diagnostic features of conscious awareness. Behavioral evidence shows clear signatures of both working memory and voluntary attention as minimal criterium for sensory consciousness in mammals and birds. In contrast, reptiles and amphibians show no sign of either working memory or volitional attention. Surprisingly, some species of teleost fishes exhibit elementary working memory and voluntary attention effects suggestive of possibly rudimentary forms of subjective experience. With the potential exception of honeybees, evidence for conscious processing is lacking in invertebrates. These findings suggest that consciousness is not ubiquitous in the animal kingdom but also not exclusive to humans. The phylogenetic gap between animal taxa argues that evolution does not rely on specific neural substrates to endow distantly related species with basic forms of consciousness.

A brain atlas of the carrion crow (Corvus corone)

Corvidae, passerine songbirds such as jays, crows, and ravens known as corvids, have become model systems for the study of avian cognition. The superior cognitive capabilities of corvids mainly emerge from a disproportionally large telencephalon found in these species. However, a systematic mapping of the neuroanatomy of the corvid brain, and the telencephalon in particular, is lacking so far. Here, we present a brain atlas of the carrion crow, Corvus corone, with special emphasis on the telencephalic pallium. We applied four staining techniques to brain slices (Nissl, myelin, combination of Nissl and myelin, and tyrosine hydroxylase targeting catecholaminergic neurons). This allowed us to identify brain nuclei throughout the brain and delineate the known pallial subdivisions termed hyperpallium, entopallium, mesopallium, nidopallium, arcopallium, and hippocampal complex. The extent of these subdivisions and brain nuclei are described according to stereotaxic coordinates. In addition, 3D depictions of pallial regions were reconstructed from these slices. While the overall organization of the carrion crow's brain matches other songbird brains, the relative proportions and expansions of associative pallial areas differ considerably in agreement with enhanced cognitive skills found in corvids. The presented global organization of the crow brain in stereotaxic coordinates will help to guide future neurobiological studies in corvids.

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.

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.

Behavioral Training Related Neurotransmitter Receptor Expression Dynamics in the Nidopallium Caudolaterale and the Hippocampal Formation of Pigeons

Learning and memory are linked to dynamic changes at the level of synapses in brain areas that are involved in cognitive tasks. For example, changes in neurotransmitter receptors are prerequisite for tuning signals along local circuits and long-range networks. However, it is still unclear how a series of learning events promotes plasticity within the system of neurotransmitter receptors and their subunits to shape information processing at the neuronal level. Therefore, we investigated the expression of different glutamatergic NMDA (GRIN) and AMPA (GRIA) receptor subunits, the GABAergic GABARG2 subunit, dopaminergic DRD1, serotonergic 5HTR1A and noradrenergic ADRA1A receptors in the pigeon's brain. We studied the nidopallium caudolaterale, the avian analogue of the prefrontal cortex, and the hippocampal formation, after training the birds in a rewarded stimulus-response association (SR) task and in a simultaneous-matching-to-sample (SMTS) task. The results show that receptor expression changed differentially after behavioral training compared to an untrained control group. In the nidopallium caudolaterale, GRIN2B, GRIA3, GRIA4, DRD1D, and ADRA1A receptor expression was altered after SR training and remained constantly decreased after the SMTS training protocol, while GRIA2 and DRD1A decreased only under the SR condition. In the hippocampal formation, GRIN2B decreased and GABARG2 receptor expression increased after SR training. After SMTS sessions, GRIN2B remained decreased, GABARG2 remained increased if compared to the control group. None of the investigated receptors differed directly between both conditions, although differentially altered. The changes in both regions mostly occur in favor of the stimulus response task. Thus, the present data provide evidence that neurotransmitter receptor expression dynamics play a role in the avian prefrontal cortex and the hippocampal formation for behavioral training and is uniquely, regionally and functionally associated to cognitive processes including learning and memory.

Executive Functions in Birds

Executive functions comprise of top-down cognitive processes that exert control over information processing, from acquiring information to issuing a behavioral response. These cognitive processes of inhibition, working memory, and cognitive flexibility underpin complex cognitive skills, such as episodic memory and planning, which have been repeatedly investigated in several bird species in recent decades. Until recently, avian executive functions were studied in relatively few bird species but have gained traction in comparative cognitive research following MacLean and colleagues’ large-scale study from 2014. Therefore, in this review paper, the relevant previous findings are collected and organized to facilitate further investigations of these core cognitive processes in birds. This review can assist in integrating findings from avian and mammalian cognitive research and further the current understanding of executive functions’ significance and evolution.

Cell-type specific pallial circuits shape categorical tuning responses in the crow telencephalon

The nidopallium caudolaterale (NCL), an integration centre in the telencephalon of birds, plays a crucial role in representing and maintaining abstract categories and concepts. However, the computational principles allowing pallial microcircuits consisting of excitatory and inhibitory neurons to shape the tuning to abstract categories remain elusive. Here we identified the major pallial cell types, putative excitatory projection cells and inhibitory interneurons, by characterizing the waveforms of action potentials recorded in crows performing a cognitively demanding numerical categorization task. Both cell types showed clear differences in their capacity to encode categorical information. Nearby and functionally coupled putative projection neurons generally exhibited similar tuning, whereas putative interneurons showed mainly opposite tuning. The results favour feedforward mechanisms for the shaping of categorical tuning in microcircuits of the NCL. Our findings help to decipher the workings of pallial microcircuits in birds during complex cognition and to compare them vis-a-vis neocortical processes in mammals.

Neural recordings from the caudolateral nidopallium in crows during a numerosity task suggest there are two subsets of projection neurons and inhibitory interneurons involved in complex cognition.

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 evolution of quantitative sensitivity

The ability to represent approximate quantities appears to be phylogenetically widespread, but the selective pressures and proximate mechanisms favouring this ability remain unknown. We analysed quantity discrimination data from 672 subjects across 33 bird and mammal species, using a novel Bayesian model that combined phylogenetic regression with a model of number psychophysics and random effect components. This allowed us to combine data from 49 studies and calculate the Weber fraction (a measure of quantity representation precision) for each species. We then examined which cognitive, socioecological and biological factors were related to variance in Weber fraction. We found contributions of phylogeny to quantity discrimination performance across taxa. Of the neural, socioecological and general cognitive factors we tested, cortical neuron density and domain-general cognition were the strongest predictors of Weber fraction, controlling for phylogeny. Our study is a new demonstration of evolutionary constraints on cognition, as well as of a relation between species-specific neuron density and a particular cognitive ability.

This article is part of the theme issue ‘Systems neuroscience through the lens of evolutionary theory’.

Electrophysiological Evidence for a Common Magnitude Representation of Spatiotemporal Information in Working Memory

Spatiotemporal interference has attracted increasing attention because it provides a window for studying the neural representation of magnitude in the brain. We aimed to identify the neural basis of spatiotemporal interference using a Kappa effect task in which two circles were presented in sequence with two time intervals and three space distances. Participants reproduced the time intervals while ignoring the space distance when electroencephalogram signals were recorded synchronously. The behavior results showed that production time increased with time interval and space distance. Offset of the time intervals elicited typical P2 and P3b components. Larger parietal P2 and P3b amplitudes were elicited by the combination of longer time intervals and longer space distances. The parietal P2 and P3b amplitudes were positively correlated with the production time, and the corresponding neural source was located in the parietal cortex. The results suggest that the parietal P2 and P3b index updates a common representation of spatiotemporal information in working memory, which provides electrophysiological evidence for the mechanisms underlying spatiotemporal interferences. Our study supports a theory of magnitude, in which different dimensions can be integrated into a common magnitude representation in a generalized magnitude system that is localized at the parietal cortex.

High associative neuron numbers could drive cognitive performance in corvid species

Corvids possess cognitive skills, matching those of non-human primates. However, how these species with their small brains achieve such feats remains elusive. Recent studies suggest that cognitive capabilities could be based on the total numbers of telencephalic neurons. Here we extend this hypothesis further and posit that especially high neuron counts in associative pallial areas drive flexible, complex cognition. If true, avian species like corvids should specifically accumulate neurons in the avian associative areas meso- and nidopallium. To test the hypothesis, we analyzed the neuronal composition of telencephalic areas in corvids and non-corvids (chicken, pigeons, and ostriches - the species with the largest bird brain). The overall number of pallial neurons in corvids was much higher than in chicken and pigeons and comparable to those of ostriches. However, neuron numbers in the associative mesopallium and nidopallium were twice as high in corvids and, in correlation with these associative areas, the corvid subpallium also contained high neuron numbers. These findings support our hypothesis that large absolute numbers of associative pallial neurons contribute to cognitive flexibility and complexity and are key to explain why crows are smart. Since meso/nidopallial and subpallial areas scale jointly, it is conceivable that associative pallio-striatal loops play a similar role in executive decision-making as described in primates. This article is protected by copyright. All rights reserved.

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

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

RUBubbles as a novel tool to study categorization learning

Grouping objects into discrete categories affects how we perceive the world and represents a crucial element of cognition. Categorization is a widespread phenomenon that has been thoroughly studied. However, investigating categorization learning poses several requirements on the stimulus set in order to control which stimulus feature is used and to prevent mere stimulus-response associations or rote learning. Previous studies have used a wide variety of both naturalistic and artificial categories, the latter having several advantages such as better control and more direct manipulation of stimulus features. We developed a novel stimulus type to study categorization learning, which allows a high degree of customization at low computational costs and can thus be used to generate large stimulus sets very quickly. 'RUBubbles' are designed as visual artificial category stimuli that consist of an arbitrary number of colored spheres arranged in 3D space. They are generated using custom MATLAB code in which several stimulus parameters can be adjusted and controlled separately, such as number of spheres, position in 3D-space, sphere size, and color. Various algorithms for RUBubble generation can be combined with distinct behavioral training protocols to investigate different characteristics and strategies of categorization learning, such as prototype- vs. exemplar-based learning, different abstraction levels, or the categorization of a sensory continuum and category exceptions. All necessary MATLAB code is freely available as open-source code and can be customized or expanded depending on individual needs. RUBubble stimuli can be controlled purely programmatically or via a graphical user interface without MATLAB license or programming experience.

Avian pallial circuits and cognition: A comparison to mammals

Cognitive functions are similar in birds and mammals. So, are therefore pallial cellular circuits and neuronal computations also alike? In search of answers, we move in from bird's pallial connectomes, to cortex-like sensory canonical circuits and connections, to forebrain micro-circuitries and finally to the avian "prefrontal" area. This voyage from macro- to micro-scale networks and areas reveals that both birds and mammals evolved similar neural and computational properties in either convergent or parallel manner, based upon circuitries inherited from common ancestry. Thus, these two vertebrate classes evolved separately within 315 million years with highly similar pallial architectures that produce comparable cognitive functions.

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.

Behavioral and Neuronal Representation of Numerosity Zero in the Crow

Different species of animals can discriminate numerosity, the countable number of objects in a set. The representations of countable numerosities have been deciphered down to the level of single neurons. However, despite its importance for human number theory, a special numerical quantity, the empty set (numerosity zero), has remained largely unexplored. We explored the behavioral and neuronal representation of the empty set in carrion crows. Crows were trained to discriminate small numerosities including the empty set. Performance data showed a numerical distance effect for the empty set in one crow, suggesting that the empty set and countable numerosities are represented along the crows' "mental number line." Single-cell recordings in the endbrain region nidopallium caudolaterale (NCL) showed a considerable proportion of NCL neurons tuned to the preferred numerosity zero. As evidenced by neuronal distance and size effects, NCL neurons integrated the empty set in the neural number line. A subsequent neuronal population analysis using a statistical classifier approach showed that the neuronal numerical representations were predictive of the crows' success in the task. These behavioral and neuronal data suggests that the conception of the empty set as a cognitive precursor of a zero-like number concept is not an exclusive property of the cerebral cortex of primates. Zero as a quantitative category cannot only be implemented in the layered neocortex of primates, but also in the anatomically distinct endbrain circuitries of birds that evolved based on convergent evolution.SIGNIFICANCE STATEMENT The conception of "nothing" as number "zero" is celebrated as one of the greatest achievements in mathematics. To explore whether precursors of zero-like concepts can be found in vertebrates with a cerebrum that anatomically differs starkly from our primate brain, we investigated this in carrion crows. We show that crows can grasp the empty set as a null numerical quantity that is mentally represented next to number one. Moreover, we show that single neurons in an associative avian cerebral region specifically respond to the empty set and show the same physiological characteristics as for countable quantities. This suggests that zero as a quantitative category can also be implemented in the anatomically distinct endbrain circuitries of birds that evolved based on convergent evolution.

The Evolutionary History of Brains for Numbers

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

Neuroethology of number sense across the animal kingdom

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

Neural Code of Motor Planning and Execution during Goal-Directed Movements in Crows

The planning and execution of head-beak movements are vital components of bird behavior. They require integration of sensory input and internal processes with goal-directed motor output. Despite its relevance, the neurophysiological mechanisms underlying action planning and execution outside of the song system are largely unknown. We recorded single-neuron activity from the associative endbrain area nidopallium caudolaterale (NCL) of two male carrion crows (Corvus corone) trained to plan and execute head-beak movements in a spatial delayed response task. The crows were instructed to plan an impending movement toward one of eight possible targets on the left or right side of a touchscreen. In a fraction of trials, the crows were prompted to plan a movement toward a self-chosen target. NCL neurons signaled the impending motion direction in instructed trials. Tuned neuronal activity during motor planning categorically represented the target side, but also specific target locations. As a marker of intentional movement preparation, neuronal activity reliably predicted both target side and specific target location when the crows were free to select a target. In addition, NCL neurons were tuned to specific target locations during movement execution. A subset of neurons was tuned during both planning and execution period; these neurons experienced a sharpening of spatial tuning with the transition from planning to execution. These results show that the avian NCL not only represents high-level sensory and cognitive task components, but also transforms behaviorally-relevant information into dynamic action plans and motor execution during the volitional perception-action cycle of birds.SIGNIFICANCE STATEMENT Corvid songbirds have become exciting new models for understanding complex cognitive behavior. As a key neural underpinning, the endbrain area nidopallium caudolaterale (NCL) represents sensory and memory-related task components. How such representations are converted into goal-directed motor output remained unknown. In crows, we report that NCL neurons are involved in the planning and execution of goal-directed movements. NCL neurons prospectively signaled motion directions in instructed trials, but also when the crows were free to choose a target. NCL neurons showed a target-specific sharpening of tuning with the transition from the planning to the execution period. Thus, the avian NCL not only represents high-level sensory and cognitive task components, but also transforms relevant information into action plans and motor execution.

A histological study of the song system of the carrion crow (Corvus corone)

The song system of songbirds (oscines) is one of the best studied neuroethological model systems. So far, it has been treated as a relatively constrained sensorimotor system. Songbirds such as crows, however, are also known for their capability to cognitively control their audio-vocal system. Yet, the neuroanatomy of the corvid song system has never been explored systematically. We aim to close this scientific gap by presenting a stereotactic investigation of the extended song system of the carrion crow (Corvus corone), an oscine songbird of the corvid family that has become an interesting model system for cognitive neuroscience. In order to identify and delineate the song nuclei, the ascending auditory nuclei, and the descending vocal-motor nuclei, four stains were applied. In addition to the classical Nissl-, myelin-, and a combination of Nissl-and-myelin staining, staining for tyrosine hydroxylase was used to reveal the distribution of catecholaminergic neurons (dopaminergic, noradrenergic, and adrenergic) in the song system. We show that the crow brain contains the important song-related nuclei, including auditory input and motor output structures, and map them throughout the brain. Fiber-stained sections reveal putative connection patterns between the crow's song nuclei comparable to other songbirds.

Categorical Auditory Working Memory in Crows

The ability to group sensory data into behaviorally meaningful classes and to maintain these perceptual categories active in working memory is key to intelligent behavior. Here, we show that carrion crows, highly vocal and cognitively advanced corvid songbirds, possess categorical auditory working memory. The crows were trained in a delayed match-to-category task that required them to flexibly match remembered sounds based on the upward or downward shift of the sounds' frequency modulation. After training, the crows instantaneously classified novel sounds into the correct auditory categories. The crows showed sharp category boundaries as a function of the relative frequency interval of the modulation. In addition, the crows generalized frequency-modulated sounds within a category and correctly classified novel sounds kept in working memory irrespective of other acoustic features of the sound. This suggests that crows can form and actively memorize auditory perceptual categories in the service of cognitive control of their goal-directed behaviors.

•

Crows performed a delayed match-to-category task with frequency modulated sounds

•

Crows classified novel sounds into upward or downward modulated sound categories

•

Crows showed sharp category boundaries and within-category generalization

•

Crows can actively memorize auditory perceptual categories for cognitive control

Neural Processes Underlying Tool Use in Humans, Macaques, and Corvids

It was thought that tool use in animals is an adaptive specialization. Recent studies, however, have shown that some non-tool-users, such as rooks and jays, can use and manufacture tools in laboratory settings. Despite the abundant evidence of tool use in corvids, little is known about the neural mechanisms underlying tool use in this family of birds. This review summarizes the current knowledge on the neural processes underlying tool use in humans, macaques and corvids. We suggest a possible neural network for tool use in macaques and hope this might inspire research to discover a similar brain network in corvids. We hope to establish a framework to elucidate the neural mechanisms that supported the convergent evolution of tool use in birds and mammals.

Format-dependent and format-independent representation of sequential and simultaneous numerosity in the crow endbrain

Humans’ symbolic counting skills are built on a primordial ability to approximately estimate the number of items, or numerosity. To date it is debated whether numerosities presented in categorically different formats, that is as temporal sequences versus spatial arrays, are represented abstractly in the brain. To address this issue, we identified the behavioral characteristics and neuronal codes for sequential and simultaneous number formats in crows. We find a format-dependent representation by distinct groups of selective neurons during the sensory encoding stage. However, an abstract and format-independent numerosity code emerges once the encoding phase is completed and numerosities needed to be memorized. These results suggest a successive two-stage code for categorically different number formats and help to reconcile conflicting findings observed in psychophysics and brain imaging.

Numbers are processed as abstract categories, despite considerable variations in presentation formats. By recording single-neuron activity in behaving crows, the authors show successive format-dependent and format-independent numerosity codes in the avian endbrain.

Neural constraints on human number concepts

True counting and arithmetic abilities are unique to humans and are inextricably linked to symbolic competence. However, our unprecedented numerical skills are deeply rooted in our neuronal heritage as primates and vertebrates. In this article, I argue that numerical competence in humans is the result of three neural constraints. First, I propose that the neuronal mechanisms of quantity estimation are part of our evolutionary heritage and can be witnessed across primate and vertebrate phylogeny. Second, I suggest that a basic understanding of number, what numerical quantity means, is innately wired into the brain and gives rise to an intuitive number sense, or number instinct. Third and finally, I argue that symbolic counting and arithmetic in humans is rooted in an evolutionarily and ontogenetically primeval neural system for non-symbolic number representations. These three neural constraints jointly determine the basic processing of number concepts in the human mind.

Time-scale-invariant information-theoretic contingencies in discrimination learning

Animals optimize their behavior to maximize rewards by utilizing cues from the environment. In discrimination learning, cues signal when rewards can and cannot be earned by making a particular response. In our experiment, we trained male mice to press a lever to receive a reward on a random interval schedule. We then introduced a prolonged tone (20, 40, or 80 sec), during which no rewards could be earned. We sought to test our hypothesis that the duration of the tone and frequency of reward during the inter-tone-intervals affect the informativeness of cues and led to differences in discriminative behavior. Learning was expressed as an increase in lever pressing during the intertrial interval (ITI) and, when the informativeness of the cue was high, animals also reduced their lever pressing during the tone. Additionally, we found that the depth of discriminative learning was linearly related to the informativeness of the cues. Our results show that the time-scale invariant information-theoretic definition of contingency applied to excitatory conditioning can also be applied to inhibitory conditioning. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Number detectors spontaneously emerge in a deep neural network designed for visual object recognition

Humans and animals have a "number sense," an innate capability to intuitively assess the number of visual items in a set, its numerosity. This capability implies that mechanisms to extract numerosity indwell the brain's visual system, which is primarily concerned with visual object recognition. Here, we show that network units tuned to abstract numerosity, and therefore reminiscent of real number neurons, spontaneously emerge in a biologically inspired deep neural network that was merely trained on visual object recognition. These numerosity-tuned units underlay the network's number discrimination performance that showed all the characteristics of human and animal number discriminations as predicted by the Weber-Fechner law. These findings explain the spontaneous emergence of the number sense based on mechanisms inherent to the visual system.

Numerical ordering of zero in honey bees

Some vertebrates demonstrate complex numerosity concepts-including addition, sequential ordering of numbers, or even the concept of zero-but whether an insect can develop an understanding for such concepts remains unknown. We trained individual honey bees to the numerical concepts of "greater than" or "less than" using stimuli containing one to six elemental features. Bees could subsequently extrapolate the concept of less than to order zero numerosity at the lower end of the numerical continuum. Bees demonstrated an understanding that parallels animals such as the African grey parrot, nonhuman primates, and even preschool children.

Neurons in the Hippocampus of Crows Lack Responses to Non-spatial Abstract Categories

Lesion studies suggest a role of the avian hippocampus in spatial and episodic memory. However, whether the avian hippocampus is also involved in processing categorical information and non-spatial working memory contents remains unknown. To address this question, we trained two crows in a delayed-match-to-sample test to assess and briefly memorize the number of items in dot displays, i.e., their numerosity. We recorded neuronal activity in hippocampus while crows solved this task. Hardly any hippocampal neurons responded to the category 'numerosity,' during neither sample presentation, nor during the memory delay. This was in striking contrast to previous recordings in the telencephalic association area 'nidopallium caudolaterale' (NCL) of the same crows, in which we previously reported an abundance of numerosity-selective and working memory-selective neurons. Our data suggest that categorical information is not processed in the avian hippocampus.

Evolution of cognitive and neural solutions enabling numerosity judgements: lessons from primates and corvids

Brains that are capable of representing numerosity, the number of items in a set, have arisen repeatedly and independently in different animal taxa. This review compares the cognitive and physiological mechanisms found in a nonhuman primate, the rhesus macaque, and a corvid songbird, the carrion crow, in order to elucidate the evolutionary adaptations underlying numerical competence. Monkeys and corvids are known for their advanced cognitive competence, despite them both having independently and distinctly evolved endbrains that resulted from a long history of parallel evolution. In both species, numerosity is represented as an analogue magnitude by an approximate number system that obeys the Weber-Fechner Law. In addition, the activity of numerosity-selective neurons in the fronto-parietal association cortex of monkeys and the telencephalic associative area nidopallium caudolaterale of crows mirrors the animals' performance. In both species' brains, neuronal activity is tuned to a preferred numerosity, encodes the numerical value in an approximate fashion, and is best represented on a logarithmic scale. Collectively, the data show an impressive correspondence of the cognitive and neuronal mechanisms for numerosity representations across monkeys and crows. This suggests that remotely related vertebrates with distinctly developed endbrains adopted similar physiological solutions to common computational problems in numerosity processing.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Finding numbers in the brain

After listing functional constraints on what numbers in the brain must do, I sketch the two's complement fixed-point representation of numbers because it has stood the test of time and because it illustrates the non-obvious ways in which an effective coding scheme may operate. I briefly consider its neurobiological implementation. It is easier to imagine its implementation at the cell-intrinsic molecular level, with thermodynamically stable, volumetrically minimal polynucleotides encoding the remembered numbers, than at the circuit level, with plastic synapses encoding them.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Neurons in the Endbrain of Numerically Naive Crows Spontaneously Encode Visual Numerosity

Endowed with an elaborate cerebral cortex, humans and other primates can assess the number of items in a set, or numerosity, from birth on [1] and without being trained [2]. Whether spontaneous numerosity extraction is a unique feat of the mammalian cerebral cortex [3-7] or rather an adaptive property that can be found in differently designed and independently evolved neural substrates, such as the avian enbrain [8], is unknown. To address this question, we recorded single-cell activity from the nidopallium caudolaterale (NCL), a high-level avian association brain area [9-11], of numerically naive crows. We found that a proportion of NCL neurons were spontaneously responsive to numerosity and tuned to the number of items, even though the crows were never trained to assess numerical quantity. Our data show that numerosity-selective neuronal responses are spontaneously present in the distinct endbrains of diverge vertebrate taxa. This seemingly hard-wired property of the avian endbrain to extract numerical quantity explains how birds in the wild, or right after hatching, can exploit numerical cues when making foraging or social decisions. It suggests that endbrain circuitries that evolved based on convergent evolution, such as the avian endbrain, give rise to the same numerosity code.

Neurons in the crow nidopallium caudolaterale encode varying durations of visual working memory periods

Adaptive sequential behaviors rely on the bridging and integration of temporally separate information for the realization of prospective goals. Corvids' remarkable behavioral flexibility is thought to depend on the workings of the nidopallium caudolaterale (NCL), a high-level avian associative forebrain area. We trained carrion crows to remember visual items for three alternating delay durations in a delayed match-to-sample task and recorded single-unit activity from the NCL. Sample-selective delay activity, a correlate of visual working memory, was maintained throughout different working memory durations. Delay responses remained selective for the same preferred sample item across blocks with different delay durations. However, selectivity strength decreased with increasing delay durations, mirroring worsened behavioral performance with longer memory delays. Behavioral relevance of delay activity was further evidenced by reduced encoding of the preferred sample item during error trials. In addition, NCL neurons adapted their time-dependent discharges to blocks of different memory durations, so that delay duration could be successfully classified based on population activity a few trials after the delay duration switched. Therefore, NCL neurons not only maintain information from individual trials, but also keep track of the duration for which this information is needed in the context of the task. These results strengthen the role of corvid NCL in maintaining working memory for flexible control of temporally extended goal-directed behavior.