Number neurons in the nidopallium of young domestic chicks

A number sense as an emergent property of the manipulating brain

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

Neurobiology of numerical learning

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

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

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

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.

The neural ingredients for a language of thought are available

The classical notion of a 'language of thought' (LoT), advanced prominently by the philosopher Jerry Fodor, is an influential position in cognitive science whereby the mental representations underpinning thought are considered to be compositional and productive, enabling the construction of new complex thoughts from more primitive symbolic concepts. LoT theory has been challenged because a neural implementation has been deemed implausible. We disagree. Examples of critical computational ingredients needed for a neural implementation of a LoT have in fact been demonstrated, in particular in the hippocampal spatial navigation system of rodents. Here, we show that cell types found in spatial navigation (border cells, object cells, head-direction cells, etc.) provide key types of representation and computation required for the LoT, underscoring its neurobiological viability.

Neural coding of numerousness

Perception of numerousness, i.e. number of items in a set, is an important cognitive ability, which is present in several animal taxa. In spite of obvious differences in neuroanatomy, insects, fishes, reptiles, birds, and mammals all possess a "number sense". Furthermore, information regarding numbers can belong to different sensory modalities: animals can estimate a number of visual items, a number of tones, or a number of their own movements. Given both the heterogeneity of stimuli and of the brains processing these stimuli, it is hard to imagine that number cognition can be traced back to the same evolutionary conserved neural pathway. However, neurons that selectively respond to the number of stimuli have been described in higher-order integration brain centres both in primates and in birds, two evolutionary distant groups. Although most probably not of the same evolutionary origin, these number neurons share remarkable similarities in their response properties. Instead of homology, this similarity might result from computational advantages of the underlying coding mechanism. This means that one might expect numerousness information to undergo similar steps of neural processing even in evolutionary distant neural pathways. Following this logic, in this review we summarize our current knowledge of how numerousness is processed in the brain from sensory input to coding of abstract information in the higher-order integration centres. We also propose a list of key open questions that might promote future research on number cognition.

Crows flexibly apply statistical inferences based on previous experience

Statistical inference, the ability to use limited information to draw conclusions about the likelihood of an event, is critical for decision-making during uncertainty. The ability to make statistical inferences was thought to be a uniquely human skill requiring verbal instruction and mathematical reasoning.1 However, basic inferences have been demonstrated in both preliterate and pre-numerate individuals,2,3,4,5,6,7 as well as non-human primates.8 More recently, the ability to make statistical inferences has been extended to members outside of the primate lineage in birds.9,10 True statistical inference requires subjects use relative rather than absolute frequency of previously experienced events. Here, we show that crows can relate memorized reward probabilities to infer reward-maximizing decisions. Two crows were trained to associate multiple reward probabilities ranging from 10% to 90% to arbitrary stimuli. When later faced with the choice between various stimulus combinations, crows retrieved the reward probabilities associated with individual stimuli from memory and used them to gain maximum reward. The crows showed behavioral distance and size effects when judging reward values, indicating that the crows represented probabilities as abstract magnitudes. When controlling for absolute reward frequency, crows still made reward-maximizing choices, which is the signature of true statistical inference. Our study provides compelling evidence of decision-making by relative reward frequency in a statistical inference task.

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.

Spontaneous supra-modal encoding of number in the infant brain

The core knowledge hypothesis postulates that infants automatically analyze their environment along abstract dimensions, including numbers. According to this view, approximate numbers should be encoded quickly, pre-attentively, and in a supra-modal manner by the infant brain. Here, we directly tested this idea by submitting the neural responses of sleeping 3-month-old infants, measured with high-density electroencephalography (EEG), to decoders designed to disentangle numerical and non-numerical information. The results show the emergence, in approximately 400 ms, of a decodable number representation, independent of physical parameters, that separates auditory sequences of 4 vs. 12 tones and generalizes to visual arrays of 4 vs. 12 objects. Thus, the infant brain contains a number code that transcends sensory modality, sequential or simultaneous presentation, and arousal state.

Executive Control of Sequence Behavior in Pigeons Involves Two Distinct Brain Regions

Executive functions arise from multiple regions of the brain acting in concert. To facilitate such cross-regional computations, the brain is organized into distinct executive networks, like the frontoparietal network. Despite similar cognitive abilities across many domains, little is known about such executive networks in birds. Recent advances in avian fMRI have shown a possible subset of regions, including the nidopallium caudolaterale (NCL) and the lateral part of medial intermediate nidopallium (NIML), that may contribute to complex cognition, forming an action control system of pigeons. We investigated the neuronal activity of NCL and NIML. Single-cell recordings were obtained during the execution of a complex sequential motor task that required executive control to stop executing one behavior and continue with a different one. We compared the neuronal activity of NIML to NCL and found that both regions fully processed the ongoing sequential execution of the task. Differences arose from how behavioral outcome was processed. Our results indicate that NCL takes on a role in evaluating outcome, while NIML is more tightly associated with ongoing sequential steps. Importantly, both regions seem to contribute to overall behavioral output as parts of a possible avian executive network, crucial for behavioral flexibility and decision-making.

Numerosity as a visual property: Evidence from two highly evolutionary distant species

Most animals, from humans to invertebrates, possess an ability to estimate numbers. This evolutionary advantage facilitates animals' choice of environments with more food sources, more conspecifics to increase mating success, and/or reduced predation risk among others. However, how the brain processes numerical information remains largely unknown. There are currently two lines of research interested in how numerosity of visual objects is perceived and analyzed in the brain. The first argues that numerosity is an advanced cognitive ability processed in high-order brain areas, while the second proposes that "numbers" are attributes of the visual scene and thus numerosity is processed in the visual sensory system. Recent evidence points to a sensory involvement in estimating magnitudes. In this Perspective, we highlight this evidence in two highly evolutionary distant species: humans and flies. We also discuss the advantages of studying numerical processing in fruit flies in order to dissect the neural circuits involved in and required for numerical processing. Based on experimental manipulation and the fly connectome, we propose a plausible neural network for number sense in invertebrates.

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.