Neural Basis of Social Influence of Observing Other's Perception in Dot-Number Estimation

Our perceptions and decisions are often implicitly influenced by observing another's actions. However, it is unclear how observing other people's perceptual decisions without interacting with them can engage the processing of self-other discrepancies and change the observer's decisions. In this study, we employed functional magnetic resonance imaging and a computational model to investigate the neural basis of how unilaterally observing the other's perceptual decisions modulated one's own decisions. The experimental task was to discriminate whether the number of presented dots was higher or lower than a reference number. The participants performed the task solely while unilaterally observing the performance of another "participant," who produced overestimations and underestimations in the same task in separate sessions. Results of the behavioral analysis showed that the participants' decisions were modulated to resemble those of the other. Image analysis based on computational model revealed that the activation in the medial prefrontal cortex was associated with the discrepancy between the inferred participant's and the presented other's decisions. In addition, the number-sensitive region in the superior parietal region showed altered activation patterns after observing the other's overestimations and underestimations. The activity of the superior parietal region was not involved in assessing the observation of other's perceptual decisions, but it was engaged in plain numerosity perception. These results suggest that computational modeling can capture the neuro-behavioral processing of self-other discrepancies in perception followed by the activity modulation in the number-sensitive region in the task of dot-number estimation.

Understanding the Effects of Transcranial Electrical Stimulation in Numerical Cognition: A Systematic Review for Clinical Translation

Atypical development of numerical cognition (dyscalculia) may increase the onset of neuropsychiatric symptoms, especially when untreated, and it may have long-term detrimental social consequences. However, evidence-based treatments are still lacking. Despite plenty of studies investigating the effects of transcranial electrical stimulation (tES) on numerical cognition, a systematized synthesis of results is still lacking. In the present systematic review (PROSPERO ID: CRD42021271139), we found that the majority of reports (20 out of 26) showed the effectiveness of tES in improving both number (80%) and arithmetic (76%) processing. In particular, anodal tDCS (regardless of lateralization) over parietal regions, bilateral tDCS (regardless of polarity/lateralization) over frontal regions, and tRNS (regardless of brain regions) strongly enhance number processing. While bilateral tDCS and tRNS over parietal and frontal regions and left anodal tDCS over frontal regions consistently improve arithmetic skills. In addition, tACS seems to be more effective than tDCS at ameliorating arithmetic learning. Despite the variability of methods and paucity of clinical studies, tES seems to be a promising brain-based treatment to enhance numerical cognition. Recommendations for clinical translation, future directions, and limitations are outlined.

Ensemble perception: Extracting the average of perceptual versus numerical stimuli

Recent research has established that humans can extract the average perceptual feature over briefly presented arrays of visual elements or the average of a rapid temporal sequence of numbers. Here we compared the extraction of the average over briefly presented arrays, for a perceptual feature (orientations) and for numerical values (1-9 digits), using an identical experimental design for the two tasks. We hypothesized that the averaging of numbers, more than of orientations, would be constrained by capacity limitations. Arrays of Gabor elements or digits were simultaneously presented for 300 ms and observers were required to estimate the average on a continuous response scale. In each trial the elements were sampled from normal distributions (of various means) and we varied the set size (4-12). We found that while for orientation the averaging precision remained constant with set size, for numbers it decreased with set size. Using computational modeling we also extracted capacity parameters (the number of elements that are pooled in the average extraction). Despite marked heterogeneity between observers, the capacity for orientations (around eight items) was much larger than for numbers (around four items). The orientation task also had a larger fraction of participants relying on distributed attention to all elements. Our study thus supports the idea that numbers more than perceptual features are subject to capacity or attentional limitations when observers need to evaluate the average over an ensemble of stimuli.

The averaging of numerosities: A psychometric investigation of the mental line

Humans and animals are capable of estimating and discriminating nonsymbolic numerosities via mental representation of magnitudes—the approximate number system (ANS). There are two models of the ANS system, which are similar in their prediction in numerosity discrimination tasks. The log-Gaussian model, which assumes numerosities are represented on a compressed logarithmic scale, and the scalar variability model, which assumes numerosities are represented on a linear scale. In the first experiment of this paper, we contrasted these models using averaging of numerosities. We examined whether participants generate a compressed mean (i.e., geometric mean) or a linear mean when averaging two numerosities. Our results demonstrated that half of the participants are linear and half are compressed; however, in general, the compression is milder than a logarithmic compression. In Experiments 2 and 3, we examined averaging of numerosities in sequences larger than two. We found that averaging precision increases with sequence length. These results are in line with previous findings, suggesting a mechanism in which the estimate is generated by population averaging of the responses each stimulus generates on the numerosity representation.

Distinct strategies for estimating the temporal average of numerical and perceptual information

Humans can estimate global trends in dynamic information presented either as perceptual features or as symbolic codes such as numbers. Previous studies on temporal statistics estimation have shown that observers judge the temporal average of visual attributes according to information from the last few frames of the presentation sequence (in what is referred to as the recency effect). Here, we investigated how humans estimate the temporal average of number vs. orientation using identical stimuli for the two tasks. In Experiment 1, a randomly-selected single-digit number was serially presented at orientations randomly varying over time. In Experiment 2, a texture comprising a random number of Gabor elements was shown at orientations randomly varying over time. In both experiments, observers judged the temporal averages of the numerical values and orientations in separate blocks. Results showed that observers judging the temporal average of orientation relied upon information from later frames as predicted by a typical model of perceptual decision making. By contrast, for the judgement of numerical values, we found that the impacts of each temporal frame were constant or varied little across temporal frames regardless of whether the numerical information was given as digits or by the number of texture elements. The results are interpreted as evidence that distinct computational strategies may be involved in estimating the temporal averages of perceptual features and numerical information.

Anodal High-definition Transcranial Direct Current Stimulation over the Posterior Parietal Cortex Modulates Approximate Mental Arithmetic

The representation and processing of numerosity is a crucial cognitive capacity. Converging evidence points to the posterior parietal cortex (PPC) as primary "number" region. However, the exact role of the left and right PPC for different types of numerical and arithmetic tasks remains controversial. In this study, we used high-definition transcranial direct current stimulation (HD-tDCS) to further investigate the causal involvement of the PPC during approximative, nonsymbolic mental arithmetic. Eighteen healthy participants received three sessions of anodal HD-tDCS at 1-week intervals in counterbalanced order: left PPC, right PPC, and sham stimulation. Results showed an improved performance during online parietal HD-tDCS (vs. sham) for subtraction problems. Specifically, the general tendency to underestimate the results of subtraction problems (i.e., the "operational momentum effect") was reduced during online parietal HD-tDCS. There was no difference between left and right stimulation. This study thus provides new evidence for a causal involvement of the left and right PPC for approximate nonsymbolic arithmetic and advances the promising use of noninvasive brain stimulation in increasing cognitive functions.

Relating categorization to set summary statistics perception

Two cognitive processes have been explored that compensate for the limited information that can be perceived and remembered at any given moment. The first parsimonious cognitive process is object categorization. We naturally relate objects to their category, assume they share relevant category properties, often disregarding irrelevant characteristics. Another scene organizing mechanism is representing aspects of the visual world in terms of summary statistics. Spreading attention over a group of objects with some similarity, one perceives an ensemble representation of the group. Without encoding detailed information of individuals, observers process summary data concerning the group, including set mean for various features (from circle size to face expression). Just as categorization may include/depend on prototype and intercategory boundaries, so set perception includes property mean and range. We now explore common features of these processes. We previously investigated summary perception of low-level features with a rapid serial visual presentation (RSVP) paradigm and found that participants perceive both the mean and range extremes of stimulus sets, automatically, implicitly, and on-the-fly, for each RSVP sequence, independently. We now use the same experimental paradigm to test category representation of high-level objects. We find participants perceive categorical characteristics better than they code individual elements. We relate category prototype to set mean and same/different category to in/out-of-range elements, defining a direct parallel between low-level set perception and high-level categorization. The implicit effects of mean or prototype and set or category boundaries are very similar. We suggest that object categorization may share perceptual-computational mechanisms with set summary statistics perception.

Goal-dependent flexibility in preferences formation from rapid payoff sequences

The formation of attitudes or preferences for alternatives that consist of rapid numerical sequences has been suggested to reflect either a summation or an averaging principle. Previous studies indicate the presence of two mechanisms, accumulators (that mediate summation) and population-coding (that mediate averaging), which operate in preference formation tasks of rapid numerical sequences, and are subject to task-demands and individual differences. Here, we test whether participants can flexibly control the preference mechanism they deploy as a function of the reward contingency. Towards this aim, participants in two studies ( N1 = 21, N2 = 23) made choices between the same sequence alternatives in two task-framing sessions, which made the reward dependent on the sequence-sum or sequence-average, respectively. The results demonstrate that although participants show an overall bias in favour of averaging, they are also remarkably flexible in deploying an averaging or a summation type mechanism that matches the reward contingency

Integration to boundary in decisions between numerical sequences

Integration-to-boundary is a prominent normative principle used in evidence-based decisions to explain the speed-accuracy trade-off and determine the decision-time. Despite its prominence, however, the decision boundary is not directly observed, but rather is theoretically assumed, and there is still an ongoing debate regarding its form: fixed vs. collapsing. The aim of this study is to show that the integration-to-boundary process extends to decisions between rapid pairs of numerical sequences (2 Hz rate), and to determine the boundary type by directly monitoring the noisy accumulated evidence. In a set of two experiments (supplemented by computational modelling), we demonstrate that integration to a collapsing-boundary takes place in such tasks, ruling out non-integration heuristic strategies. Moreover, we show that participants can adaptively adjust their boundaries in response to reward contingencies. Finally, we discuss the implications to decision optimality and the nature of processes and representations in numerical cognition.

Probing the architecture of visual number sense with parietal tRNS

Theoretical accounts of the visual number sense (VNS), i.e., an ability to discriminate approximate numerosities, remain controversial. A proposal that the VNS represents a process of numerosity extraction, leading to an abstract number representation in the brain, has been challenged by the view that the VNS is non-numerical in its essence and amounts to a weighted integration of continuous magnitude features that typically change with numerosity. In the present study, using two-alternative forced-choice paradigm, we aimed to distinguish between these proposals by probing brain areas implicated in the VNS with transcranial random noise stimulation (tRNS). We generated predictions for the stimulation-related changes in behavioural performance which would be compatible with alternative mechanisms proposed for the VNS. First, we investigated whether the superior parietal (SP) area hosts a numerosity code or whether its function is to modulate weighting of continuous stimulus features. We predicted that stimulation may affect the VNS precision if the SP role is representational, and that it may affect decision threshold if its role is modulatory. Second, we investigated whether the intraparietal (IP) area hosts a numerosity code independently of codes for continuous stimulus features, or whether their representations overlap. If the numerosity code is independent, we predicted that IP stimulation may improve the VNS but not continuous magnitude judgements. Our results were consistent with the hypotheses of a modulatory role of the SP and of the independence of the numerosity code in the IP, whereby suggesting that VNS is an emergent abstract property based on continuous magnitude statistics.

Fast and effective: Intuitive processes in complex decisions

Is it possible to carry out complex multi-attribute decisions (which require an estimation of the weighted average) intuitively, without resorting to simplifying heuristics? Over the course of 600 trials, 26 participants had to choose the better-suiting job-candidate, a task requiring comparison of two alternatives over three/four/five dimensions with specified importance weights, with a time constraint forcing intuitive decisions. Participants performed the task fast (mean reaction time (RT) ~ 1.5 s) and with high accuracy (~86%). The participants were classified as users of one of three strategies: Weighted Additive Utility (WADD), Equal Weight rule and Take-The-Best heuristic (TTB). Fifty-nine percent of the participants were classified as users of the compensatory WADD strategy and 29% as users of the non-compensatory TTB. Moreover, the WADD users achieved higher task accuracy without showing time costs. The results provide support for the existence of an automatic compensatory mechanism in weighted average estimations.

Extraction of mean emotional tone from face arrays in social anxiety disorder

BACKGROUND

Social anxiety disorder (SAD) is characterized by intense fear when facing a crowd. Processing biases of crowd-related information have been suggested as contributing to the etiology and maintenance of the disorder. Here we tested whether patients with SAD display aberrant patterns of extracting the mean emotional tone from sets of faces.

METHODS

Twenty-one participants with SAD and 24 unanxious control participants had to determine the average emotion expression of sets of six different morphed faces ranging from happy to angry. In 20% of trials the six faces were randomly sampled from the entire happy-angry range. The remaining 80% of trials, considered the critical trials, had an emotional outlier: five faces were sampled from one-half of the emotional range, whereas the sixth face was sampled from the opposite emotional range.

RESULTS

Participants with SAD were less accurate than controls in extracting the mean emotional tone from sets of faces. Unanxious participants underweighted negative outliers and overweighed positive outliers when extracting the mean, whereas participants with SAD exhibited no such biases.

CONCLUSIONS

Results suggest a possible mechanism associated with the anxiety experienced by socially anxious individuals when facing a crowd.

A Perceptual-Like Population-Coding Mechanism of Approximate Numerical Averaging

Humans possess a remarkable ability to rapidly form coarse estimations of numerical averages. This ability is important for making decisions that are based on streams of numerical or value-based information, as well as for preference formation. Nonetheless, the mechanism underlying rapid approximate numerical averaging remains unknown, and several competing mechanism may account for it. Here, we tested the hypothesis that approximate numerical averaging relies on perceptual-like processes, instantiated by population coding. Participants were presented with rapid sequences of numerical values (four items per second) and were asked to convey the sequence average. We manipulated the sequences' length, variance, and mean magnitude and found that similar to perceptual averaging, the precision of the estimations improves with the length and deteriorates with (higher) variance or (higher) magnitude. To account for the results, we developed a biologically plausible population-coding model and showed that it is mathematically equivalent to a population vector. Using both quantitative and qualitative model comparison methods, we compared the population-coding model to several competing models, such as a step-by-step running average (based on leaky integration) and a midrange model. We found that the data support the population-coding model. We conclude that humans' ability to rapidly form estimations of numerical averages has many properties of the perceptual (intuitive) system rather than the arithmetic, linguistic-based (analytic) system and that population coding is likely to be its underlying mechanism.

Selective overweighting of larger magnitudes during noisy numerical comparison

Humans are often required to compare average magnitudes in numerical data; for example, when comparing product prices on two rival consumer websites. However, the neural and computational mechanisms by which numbers are weighted, integrated and compared during categorical decisions are largely unknown^1,2,3,4,5. Here, we show a systematic deviation from 'optimality' in both visual and auditory tasks requiring averaging of symbolic numbers. Participants comparing numbers drawn from two categories selectively overweighted larger numbers when making a decision, and larger numbers evoked disproportionately stronger decision-related neural signals over the parietal cortex. A representational similarity analysis⁶ showed that neural (dis)similarity in patterns of electroencephalogram activity reflected numerical distance, but that encoding of number in neural data was systematically distorted in a way predicted by the behavioural weighting profiles, with greater neural distance between adjacent larger numbers. Finally, using a simple computational model, we show that although it is suboptimal for a lossless observer, this selective overweighting policy paradoxically maximizes expected accuracy by making decisions more robust to noise arising during approximate numerical integration². In other words, although selective overweighting discards decision information, it can be beneficial for limited-capacity agents engaging in rapid numerical averaging.