Single-cell coding of sensory, spatial and numerical magnitudes in primate prefrontal, premotor and cingulate motor cortices

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.

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.

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.

The role of neural tuning in quantity perception

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

A geometric framework for understanding dynamic information integration in context-dependent computation

The prefrontal cortex (PFC) plays a prominent role in performing flexible cognitive functions and working memory, yet the underlying computational principle remains poorly understood. Here, we trained a rate-based recurrent neural network (RNN) to explore how the context rules are encoded, maintained across seconds-long mnemonic delay, and subsequently used in a context-dependent decision-making task. The trained networks replicated key experimentally observed features in the PFC of rodent and monkey experiments, such as mixed selectivity, neuronal sequential activity, and rotation dynamics. To uncover the high-dimensional neural dynamical system, we further proposed a geometric framework to quantify and visualize population coding and sensory integration in a temporally defined manner. We employed dynamic epoch-wise principal component analysis (PCA) to define multiple task-specific subspaces and task-related axes, and computed the angles between task-related axes and these subspaces. In low-dimensional neural representations, the trained RNN first encoded the context cues in a cue-specific subspace, and then maintained the cue information with a stable low-activity state persisting during the delay epoch, and further formed line attractors for sensor integration through low-dimensional neural trajectories to guide decision-making. We demonstrated via intensive computer simulations that the geometric manifolds encoding the context information were robust to varying degrees of weight perturbation in both space and time. Overall, our analysis framework provides clear geometric interpretations and quantification of information coding, maintenance, and integration, yielding new insight into the computational mechanisms of context-dependent computation.

Autocorrelation Structure in the Macaque Dorsolateral, But not Orbital or Polar, Prefrontal Cortex Predicts Response-Coding Strength in a Visually Cued Strategy Task

In previous work, we studied the activity of neurons in the dorsolateral (PFdl), orbital (PFo), and polar (PFp) prefrontal cortex while monkeys performed a strategy task with 2 spatial goals. A cue instructed 1 of 2 strategies in each trial: stay with the previous goal or shift to the alternative goal. Each trial started with a fixation period, followed by a cue. Subsequently, a delay period was followed by a "go" signal that instructed the monkeys to choose one goal. After each choice, feedback was provided. In this study, we focused on the temporal receptive fields of the neurons, as measured by the decay in autocorrelation (time constant) during the fixation period, and examined the relationship with response and strategy coding. The temporal receptive field in PFdl correlated with the response-related but not with the strategy-related modulation in the delay and the feedback periods: neurons with longer time constants in PFdl tended to show stronger and more prolonged response coding. No such correlation was found in PFp or PFo. These findings demonstrate that the temporal specialization of neurons for temporally extended computations is predictive of response coding, and neurons in PFdl, but not PFp or PFo, develop such predictive properties.

Working memory representation of empty sets in the primate parietal and prefrontal cortices

For the brain, representing empty sets as a precursor to zero is a challenge because it requires the active coding of a quantitative category that, by definition, contains no items. Recent neurophysiological recordings show that empty sets are distinctively encoded by neurons in the primate ventral intraparietal area (VIP) and the prefrontal cortex (PFC). However, how empty sets are represented in working memory is unknown. We simultaneously recorded from VIP and PFC while rhesus monkeys performed a delayed numerosity matching task that required the maintenance of numerosities in memory for a brief period. Countable numerosities (1-4) and empty sets ('numerosity 0') were included as stimuli. Single neurons in PFC, and to a lesser extent neurons in VIP, actively encoded empty sets during the delay period. In both cortical areas, empty sets were progressively differentiated from countable numerosities with time during the ongoing trial. Moreover, the tuning of neuron populations in VIP and PFC shifted dynamically towards empty sets so that they became increasingly overrepresented in working memory. Compared to VIP, the prefrontal representation of empty sets was more stable in time and more independent of low level visual features. Moreover, PFC activity correlated better with behavioral performance in empty set trials. These findings suggest that the representation of null quantity in working memory relies more on prefrontal and less on parietal processing. Overall, our results show that empty sets are dynamically and distinctly represented in working memory.

Number faculty is alive and kicking: On number discriminations and number neurons

Leibovich et al. advocate for a single "sense of magnitude" to which a dedicated faculty for number could allegedly be reduced. This conclusion is unjustified as the authors adopt an unnecessarily narrow definition of "number sense," neglect studies that demonstrate non-symbolic numerosity representation, and furthermore ignore abstract number representations in the brain.

Magnitude Codes for Cross-Modal Working Memory in the Primate Frontal Association Cortex

Quantitative features of stimuli may be ordered along a magnitude continuum, or line. Magnitude refers to parameters of different types of stimulus properties. For instance, the frequency of a sound relates to sensory and continuous stimulus properties, whereas the number of items in a set is an abstract and discrete property. In addition, within a stimulus property, magnitudes need to be processed not only in one modality, but across multiple modalities. In the sensory domain, for example, magnitude applies to both to the frequency of auditory sounds and tactile vibrations. Similarly, both the number of visual items and acoustic events constitute numerical quantity, or numerosity. To support goal-directed behavior and executive functions across time, magnitudes need to be held in working memory, the ability to briefly retain and manipulate information in mind. How different types of magnitudes across multiple modalities are represented in working memory by single neurons has only recently been explored in primates. These studies show that neurons in the frontal lobe can encode the same magnitude type across sensory modalities. However, while multimodal sensory magnitude in relative comparison tasks is represented by monotonically increasing or decreasing response functions ("summation code"), multimodal numerical quantity in absolute matching tasks is encoded by neurons tuned to preferred numerosities ("labeled-line code"). These findings indicate that most likely there is not a single type of cross-modal working-memory code for magnitudes, but rather a flexible code that depends on the stimulus dimension as well as on the task requirements.

Independent coding of absolute duration and distance magnitudes in the prefrontal cortex

The estimation of space and time can interfere with each other, and neuroimaging studies have shown overlapping activation in the parietal and prefrontal cortical areas. We used duration and distance discrimination tasks to determine whether space and time share resources in prefrontal cortex (PF) neurons. Monkeys were required to report which of two stimuli, a red circle or blue square, presented sequentially, were longer and farther, respectively, in the duration and distance tasks. In a previous study, we showed that relative duration and distance are coded by different populations of neurons and that the only common representation is related to goal coding. Here, we examined the coding of absolute duration and distance. Our results support a model of independent coding of absolute duration and distance metrics by demonstrating that not only relative magnitude but also absolute magnitude are independently coded in the PF.

NEW & NOTEWORTHY

Human behavioral studies have shown that spatial and duration judgments can interfere with each other. We investigated the neural representation of such magnitudes in the prefrontal cortex. We found that the two magnitudes are independently coded by prefrontal neurons. We suggest that the interference among magnitude judgments might depend on the goal rather than the perceptual resource sharing.

The neuronal code for number

Humans and non-human primates share an elemental quantification system that resides in a dedicated neural network in the parietal and frontal lobes. In this cortical network, 'number neurons' encode the number of elements in a set, its cardinality or numerosity, irrespective of stimulus appearance across sensory motor systems, and from both spatial and temporal presentation arrays. After numbers have been extracted from sensory input, they need to be processed to support goal-directed behaviour. Studying number neurons provides insights into how information is maintained in working memory and transformed in tasks that require rule-based decisions. Beyond an understanding of how cardinal numbers are encoded, number processing provides a window into the neuronal mechanisms of high-level brain functions.

Working Memory in the Service of Executive Control Functions

Working memory is a type of short-term memory which has a crucial cognitive function that supports ongoing and upcoming behaviors, allowing storage of information across delay periods. The content of this memory may typically include tangible information about features such as the shape, color or texture of an object, and its location and motion relative to the body, as well as phonological information. The neural correlate of working memory has been found in different brain areas that are involved in organizing perceptual or motor functions. In particular, neuronal activity in prefrontal areas encodes task-related information corresponding to working memory across delay periods, and lesions in the prefrontal cortex severely affect the ability to retain this type of memory. Recent studies have further expanded the scope and possible role of working memory by showing that information of a more abstract nature (including a behavior-guiding rule, or the occurrence of a conflict in information processing) can also be maintained in short-term memory, and used for adjusting the allocation of executive control in dynamic environments. It has also been shown that neuronal activity in the prefrontal cortex encodes and maintains information about such abstract entities. These findings suggest that the prefrontal cortex plays crucial roles in the organization of goal-directed behavior by supporting many different mnemonic processes, which maintain a wide range of information required for the executive control of ongoing and upcoming behaviors.