Distributed attention model of perceptual averaging

The combination operation of grouping and ensemble coding for structured biological motion crowds in working memory

Massive studies have explored biological motion (BM) crowds processing for their remarkable social significance, primarily focused on uniformly distributed ones. However, real-world BM crowds often exhibit hierarchical structures rather than uniform arrangements. How such structured BM crowds are processed remains a subject of inquiry. This study investigates the representation of structured BM crowds in working memory (WM), recognizing the pivotal role WM plays in our social interactions involving BM. We propose the group-based ensemble hypothesis and test it through a member identification task. Participants were required to discern whether a presented BM belonged to a prior memory display of eight BM, each with distinct walking directions. Drawing on prominent Gestalt principles as organizational cues, we constructed structured groups within BM crowds by applying proximity and similarity cues in Experiments 1 and 2, respectively. In Experiment 3, we deliberately weakened the visibility of stimuli structures by increasing the similarity between subsets, probing the robustness of results. Consistently, our findings indicate that BM aligned with the mean direction of the subsets was more likely to be recognized as part of the memory stimuli. This suggests that WM inherently organizes structured BM crowds into separate ensembles based on organizational cues. In essence, our results illuminate the simultaneous operation of grouping and ensemble encoding mechanisms for BM crowds within WM.

Examining the role of action-driven attention in ensemble processing

Ensemble processing allows the visual system to condense visual information into useful summary statistics (e.g., average size), thereby overcoming capacity limitations to visual working memory and attention. To examine the role of attention in ensemble processing, we conducted three experiments using a novel paradigm that merged the action effect (a manipulation of attention) and ensemble processing. Participants were instructed to make a simple action if the feature of a cue word corresponded to a subsequent shape. Immediately after, they were shown an ensemble display of eight ovals of varying sizes and were asked to report either the average size of all ovals or the size of a single oval from the set. In Experiments 1 and 2, participants were cued with a task-relevant feature, and in Experiment 3, participants were cued with a task-irrelevant feature. Overall, the task-relevant cues that elicited an action influenced reports of average size in the ensemble phase more than the cues that were passively viewed, whereas task-irrelevant cues did not bias the reports of average size. The results of this study suggest that attention influences ensemble processing only when it is directed toward a task-relevant feature.

The functional role of spatial anisotropies in ensemble perception

BACKGROUND

The human brain can rapidly represent sets of similar stimuli by their ensemble summary statistics, like the average orientation or size. Classic models assume that ensemble statistics are computed by integrating all elements with equal weight. Challenging this view, here, we show that ensemble statistics are estimated by combining parafoveal and foveal statistics in proportion to their reliability. In a series of experiments, observers reproduced the average orientation of an ensemble of stimuli under varying levels of visual uncertainty.

RESULTS

Ensemble statistics were affected by multiple spatial biases, in particular, a strong and persistent bias towards the center of the visual field. This bias, evident in the majority of subjects and in all experiments, scaled with uncertainty: the higher the uncertainty in the ensemble statistics, the larger the bias towards the element shown at the fovea.

CONCLUSION

Our findings indicate that ensemble perception cannot be explained by simple uniform pooling. The visual system weights information anisotropically from both the parafovea and the fovea, taking the intrinsic spatial anisotropies of vision into account to compensate for visual uncertainty.

Americans weigh an attended emotion more than Koreans in overall mood judgments

Face ensemble coding is the perceptual ability to create a quick and overall impression of a group of faces, triggering social and behavioral motivations towards other people (approaching friendly people or avoiding an angry mob). Cultural differences in this ability have been reported, such that Easterners are better at face ensemble coding than Westerners are. The underlying mechanism has been attributed to differences in processing styles, with Easterners allocating attention globally, and Westerners focusing on local parts. However, the remaining question is how such default attention mode is influenced by salient information during ensemble perception. We created visual displays that resembled a real-world social setting in which one individual in a crowd of different faces drew the viewer's attention while the viewer judged the overall emotion of the crowd. In each trial, one face in the crowd was highlighted by a salient cue, capturing spatial attention before the participants viewed the entire group. American participants' judgment of group emotion more strongly weighed the attended individual face than Korean participants, suggesting a greater influence of local information on global perception. Our results showed that different attentional modes between cultural groups modulate social-emotional processing underlying people's perceptions and attributions.

Nonadditive integration of visual information in ensemble processing

Statistically summarizing information from a stimulus array into an ensemble representation (e.g., the mean) improves the efficiency of visual processing. However, little is known about how the brain computes the ensemble statistics. Here, we propose that ensemble processing is realized by nonadditive integration, rather than linear averaging, of individual items. We used a linear regression model approach to extract EEG responses to three levels of information: the individual items, their local interactions, and their global interaction. The local and global interactions, representing nonadditive integration of individual items, elicited rapid and independent neural responses. Critically, only the neural representation of the global interaction predicted the precision of the ensemble perception at the behavioral level. Furthermore, spreading attention over the global pattern to enhance ensemble processing directly promoted rapid neural representation of the global interaction. Taken together, these findings advocate a global, nonadditive mechanism of ensemble processing in the brain.

Remembering Sets: Capacity Limit and Time Limit of Ensemble Representations in Working Memory

In a constantly changing visual environment, the ability to extract and store ensemble representations plays a crucial role in efficiently processing and remembering complex visual information. However, how working memory maintains these ensemble representations remains unclear. Therefore, the present study aimed to investigate the limits and characteristics of ensemble representations in working memory using a change detection paradigm. Participants were presented with multiple sets of circles grouped by spatial proximity and were asked to memorize the mean diameter of the circles in each set. Results showed that working memory could stably maintain mean sizes of approximately two sets for at least four seconds. Moreover, the memory performance of ensembles was not affected by the number of circles within a set, suggesting that individual details were not stored in working memory. These results suggest that the visual system can effectively store ensembles in working memory without preserving detailed individual information.

The effect of masks on the emotion perception of a facial crowd

The present study investigated the effect of facial masks on people's ability to perceive emotions in crowds. We presented faces with the bottom halves occluded by masks or full faces without occlusion. In two sequentially presented crowds, we varied the number of faces, emotional valence, and intensity of facial expressions, examining the impact of masks on the perception of crowd emotion. Participants reported which of the two crowds they would avoid based on the crowds' average emotions. The participants' ability to judge the average emotion of a crowd, especially a crowd expressing happiness, was impaired when the crowd wore masks. For faces covered by masks, crowd emotion judgments were more negatively biased than those without masks. However, participants could still distinguish the emotional intensities of a crowd wearing masks above chance. Additionally, participants responded more quickly to a crowd with more people without compromising accuracy, despite the perceptual challenges imposed by facial masks. Our results suggest that under ambiguous social situations in which individuals' emotions are partially hidden by masks, a large group may provide stronger social cues than a small group, thereby promoting communication and regulating social behaviors.

Role of facial familiarity and emotional expression intensity in ensemble emotion perception

When looking at groups of people, we can extract information from the different faces to derive properties of the group, such as its average facial emotion, although how this average is computed remains a matter of debate. Here, we examined whether our participants' personal familiarity with the faces in the group, as well as the intensity of the facial expressions, biased ensemble perception. Participants judged the average emotional expression of ensembles of four different identities whose expressions depicted either neutral, angry, or happy emotions. For the angry and happy expressions, the intensity of the emotion could be either low (e.g., slightly happy) or high (very happy). When all the identities in the ensemble were unfamiliar, the presence of any high intensity emotional face biased ensemble perception towards its emotion. However, when a familiar face was present in the ensemble, perception was biased towards the familiar face's emotion regardless of its intensity. These findings reveal that how we perceive the average emotion of a group is influenced by both the emotional intensity and familiarity of the faces comprising the group, supporting the idea that different faces may be weighted differently in ensemble perception. These findings have important implications for the judgements we make about a group's overall emotional state may be biased by individuals within the group.

Ensemble averaging: What can we learn from skewed feature distributions?

Many studies have shown that observers can accurately estimate the average feature of a group of objects. However, the way the visual system relies on the information from each individual item is still under debate. Some models suggest some or all items sampled and averaged arithmetically. Another strategy implies "robust averaging," when middle elements gain greater weight than outliers. One version of a robust averaging model was recently suggested by Teng et al. (2021), who studied motion direction averaging in skewed feature distributions and found systematic biases toward their modes. They interpreted these biases as evidence for robust averaging and suggested a probabilistic weighting model based on minimization of the virtual loss function. In four experiments, we replicated systematic skew-related biases in another feature domain, namely, orientation averaging. Importantly, we show that the magnitude of the bias is not determined by the locations of the mean or mode alone, but is substantially defined by the shape of the whole feature distribution. We test a model that accounts for such distribution-dependent biases and robust averaging in a biologically plausible way. The model is based on well-established mechanisms of spatial pooling and population encoding of local features by neurons with large receptive fields. Both the loss functions model and the population coding model with a winner-take-all decoding rule accurately predicted the observed patterns, suggesting that the pooled population response model can be considered a neural implementation of the computational algorithms of information sampling and robust averaging in ensemble perception.

The role of motion in visual working memory for dynamic stimuli: More lagged but more precise representations of moving objects

While most visual working memory studies use static stimuli with unchanging features, objects in the real world are often dynamic, introducing significant differences in the surface feature information hitting the retina from the same object over time (e.g., changes in orientation, lighting, shadows). Previous research on dynamic stimuli has shown that change detection is improved if objects obey rules of physical motion, but it is unclear how memory for visual features interacts with object motion. In the current study, we investigated whether object motion facilitates greater temporal integration of continuously changing surface feature information. In a series of experiments, participants were asked to report the final color of continuously changing colored dots that were either moving or stationary on the screen. We found that the reported colors "lagged behind" the physical states of the dots when they were in motion. We also observed that the precision of memory responses was significantly higher for stimuli in the moving condition compared to the stationary condition. Together, these findings suggest that memory representation is improved - but lagged - for moving objects, consistent with the idea that object motion may facilitate integration of object information over longer intervals.

The Relation between Ensemble Coding of Length and Orientation Does Not Depend on Spatial Attention

Most people are good at estimating summary statistics for different features of groups of objects. For instance, people can selectively attend to different features of a group of lines and report ensemble properties such as the mean length or mean orientation and there are reliable individual differences in such ensemble judgment abilities. Our recent study found decisive evidence in support of a correlation between the errors on mean length and mean orientation judgments (r = 0.62). The present study investigates one possible mechanism for this correlation. The ability to allocate spatial attention to single items varies across individuals, and in the recent study, this variability could have contributed to both judgments because the location of lines was unpredictable. Here, we replicate this prior work with arrays of lines with fully predictable spatial locations, to lower the contribution of the ability to distribute attention effectively over all items in a display. We observed a strong positive correlation between errors on the length and orientation averaging tasks (r = 0.65). This provides evidence against individual differences in spatial attention as a common mechanism supporting mean length and orientation judgments. The present result aligns with the growing evidence for at least one ensemble-specific ability that applies across different kinds of features and stimuli.

Ensemble size perception: Its neural signature and the role of global interaction over individual items

To efficiently process complex visual scenes, the visual system often summarizes statistical information across individual items and represents them as an ensemble. However, due to the lack of techniques to disentangle the representation of the ensemble from that of the individual items constituting the ensemble, whether there exists a specialized neural mechanism for ensemble processing and how ensemble perception is computed in the brain remain unknown. To address these issues, we used a frequency-tagging EEG approach to track brain responses to periodically updated ensemble sizes. Neural responses tracking the ensemble size were detected in parieto-occipital electrodes, revealing a global and specialized neural mechanism of ensemble size perception. We then used the temporal response function to isolate neural responses to the individual sizes and their interactions. Notably, while the individual sizes and their local and global interactions were encoded in the EEG signals, only the global interaction contributed directly to the ensemble size perception. Finally, distributed attention to the global stimulus pattern enhanced the neural signature of the ensemble size, mainly by modulating the neural representation of the global interaction between all individual sizes. These findings advocate a specialized, global neural mechanism of ensemble size perception and suggest that global interaction between individual items contributes to ensemble perception.

How are local orientation signals pooled?

Visual perception is capable of pooling multiple local orientation signals into a single more accurate summary orientation. However, there is still a lack of systematic inquiry into which summary statistics are implemented in that process. Here, the task was to recognize in which direction, clockwise or counter-clockwise, the mean orientation of a set of randomly distributed Gabor patches (N = 1, 2, 4, and 8) was rotated from the implicit vertical. The mean orientation discrimination accuracy did not improve with the increase of the number N of elements in proportion to the square-root-N, as could be expected if noisy internal representations were arithmetically averaged. The Proportion of Informative Elements (PIE), defined as the percentage of elements having an orientation different from the vertical, also affected the discrimination precision, violating the arithmetic averaging rules. The decrease in the orientation discrimination precision with the increase of the PIE would suggest that the orientation pooling could be more adequately described by a quadratic or higher power mean. Thus, we parameterized the averaging process for the power parameter of the generalized mean formula. The results indicate that different pooling rules in different trials may apply, for example, the arithmetic mean in some and the maximal deviation rule in others. It is concluded that pooling of orientation information is a relatively inaccurate process for which different perceptual cues and their combination rules can be used.

Modeling mean estimation tasks in within-trial and across-trial contexts

The mean estimation task, which explicitly asks observers to estimate the mean feature value of multiple stimuli, is a fundamental paradigm in research areas such as ensemble coding and cue integration. The current study uses computational models to formalize how observers summarize information in mean estimation tasks. We compare model predictions from our Fidelity-based Integration Model (FIM) and other models on their ability to simulate observed patterns in within-trial weight distribution, across-trial information integration, and set-size effects on mean estimation accuracy. Experiments show non-equal weighting within trials in both sequential and simultaneous mean estimation tasks. Observers implicitly overestimated trial means below the global mean and underestimated trial means above the global mean. Mean estimation performance declined and stabilized with increasing set sizes. FIM successfully simulated all observed patterns, while other models failed. FIM's information sampling structure provides a new way to interpret the capacity limit in visual working memory and sub-sampling strategies. As a model framework, FIM offers task-dependent modeling for various ensemble coding paradigms, facilitating research synthesis across different studies in the literature.

Individual Faces Were Not Discarded During Extracting Mean Emotion Representations

Individuals can perceive the mean emotion or mean identity of a group of faces. It has been considered that individual representations are discarded when extracting a mean representation; for example, the "element-independent assumption" asserts that the extraction of a mean representation does not depend on recognizing or remembering individual items. The "element-dependent assumption" proposes that the extraction of a mean representation is closely connected to the processing of individual items. The processing mechanism of mean representations and individual representations remains unclear. The present study used a classic member-identification paradigm and manipulated the exposure time and set size to investigate the effect of attentional resources allocated to individual faces on the processing of both the mean emotion representation and individual representations in a set and the relationship between the two types of representations. The results showed that while the precision of individual representations was affected by attentional resources, the precision of the mean emotion representation did not change with it. Our results indicate that two different pathways may exist for extracting a mean emotion representation and individual representations and that the extraction of a mean emotion representation may have higher priority. Moreover, we found that individual faces in a group could be processed to a certain extent even under extremely short exposure time and that the precision of individual representations was relatively poor but individual representations were not discarded.

Multivariate summary of a complex scene

The current study investigated how people summarize and represent objects with multiple features to cope with the complexity due to the number of objects and feature dimensions. We presented a set of circles whose color and size were either correlated perfectly (r = 1) or not correlated at all (r = 0). Using a membership identification task, we found that participants formed a statistical representation that included information about conjunctions as well as each color and size dimensions. In addition, we found that participants represented different set boundaries depending on the correlation between features of a set. Lastly, a pair-matching task revealed that participants predicted one feature value from the other feature value based on the correlation between features of a set. Our findings suggest that people represent a multi-feature ensemble statistically as a multivariate feature distribution, which is an efficient strategy to cope with scene complexity.

A method for detection of inattentional feature blindness

In ensemble displays, two principal factors determine the precision with which the mean value of some perceptual attribute, such as size and orientation, can be discriminated: inefficiency and representational noise of each element. Inefficiency is mainly caused by biased inference, or by inattentional (feature) blindness (i.e., some elements or their features are not processed). Here, we define inattentional feature blindness as an inability to perceive the value(s) of certain feature(s) of an object while the presence of the object itself may be registered. Separation of the effects of inattentional (feature) blindness and perceptual noise has escaped traditional analytic methods because of their trade-off effects on the slope of the psychometric discrimination function. Here, we propose a method that can separate the effects of inattentional feature blindness from that of the representational noise. The basic idea is to display a set of elements from which only one contains information relevant for solving the task, while all other elements are "dummies" carrying no useful information because they do not differ from the reference. If the single informative element goes unprocessed, the correct answer can only be given by a random guess. The guess rate can be modeled similarly to the lapse rate, traditionally represented by λ. As an illustration, we present evidence that the presence versus lack of inattentional feature blindness in orientation pooling depends on the feature types present in the display.

Size-distance rescaling in the ensemble representation of range: Study with binocular and monocular cues

According to numerous studies observers can rapidly and precisely evaluate mean or range of the set. Recent studies have shown that the mean size estimated based on sizes of objects rescaled to their distances (Tiurina & Utochkin, 2019). In the current study, we directly tested this rescaling mechanism on the perception of range using binocular and monocular cues. In Experiment 1, a sample set of circles with different angular sizes and in different apparent distances were stereoscopically presented. Participants had to adjust the range of the test set to match the range of the sample set. The main manipulation was the size-distance correlation for sample and test sets: in negative size-distance correlation, the apparent range had to decrease, while in positive correlation - increase. We found the highest underestimation in the condition with the negative sample correlation and positive test correlation, which could be explained only if ensemble summary statistics were estimated after the item's rescaling. In Experiment 2, we used Ponzo-like illusion and spatial positions as a depth cue. Sets were presented with positive, negative or without size-distance correlation on a grey background or the background with Ponzo-like illusion. We found that the range was underestimated in negative correlation and overestimated in positive correlation. Thus, items of ensemble could be automatically rescaled according to their distance, based on both binocular and monocular cues, and ensemble summary statistics estimation is based on perceived sizes.

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.

A direct comparison of central tendency recall and temporal integration in the successive field iconic memory task

The ensemble coding literature suggests the existence of a fast, automatic formation of some ensemble codes. Can statistical representations, such as memory for the central tendency along a particular visual feature dimension, be extracted from information held in the sensory register? Furthermore, can knowledge of early, iconic memory processes be used to determine how central tendency is extracted? We focused on the potential role of visible persistence mechanisms that support temporal integration. We tested whether mean orientation could be accurately recalled from brief visual displays using the successive field task. On separate blocks of trials, participants were asked to report the location of a split element (requiring differentiation of frames), a missing element (requiring integration across frames), and the average orientation of elements pooled across both frames (central tendency recall). Results replicate the expected tradeoff between differentiation and integration performance across inter-frame interval (IFI). In contrast, precision of mean estimates was high and invariant across IFIs. A manipulation of within-frame distributional similarity coupled with simulations using 12 models supported 2-item subsampling. The results argue against the “strategic” interpretation of subsampling since 2-item readout was predicted by information theoretic estimates of STM encoding rate: the 2 items were not from a superset in STM. Most crucially, the results argue against the various early “preattentive/parallel/global pooling” accounts and instead suggest that non-selective readout of information from iconic memory supplies a relatively small amount of item information to STM, and it is only at this point that the computation of ensemble averages begins.

Synergy between research on ensemble perception, data visualization, and statistics education: A tutorial review

In the age of big data, we are constantly inventing new data visualizations to consolidate massive amounts of numerical information into smaller and more digestible visual formats. These data visualizations use various visual features to convey quantitative information, such as spatial position in scatter plots, color saturation in heat maps, and area in dot maps. These data visualizations are typically composed of ensembles, or groups of related objects, that together convey information about a data set. Ensemble perception, or one's ability to perceive summary statistics from an ensemble, such as the mean, has been used as a foundation for understanding and explaining the effectiveness of certain data visualizations. However, research in data visualization has revealed some perceptual biases and conceptual difficulties people face when trying to utilize the information in these graphs. In this tutorial review, we will provide a broad overview of research conducted in ensemble perception, discuss how principles of ensemble encoding have been applied to the research in data visualization, and showcase the barriers graphs can pose to learning statistical concepts, using histograms as a specific example. The goal of this tutorial review is to highlight possible connections between three areas of research-ensemble perception, data visualization, and statistics education-and to encourage research in the practical applications of ensemble perception in solving real-world problems in statistics education.

Somatosensory evoked potentials that index lateral inhibition are modulated according to the mode of perceptual processing: comparing or combining multi-digit tactile motion

Many perceptual studies focus on the brain's capacity to discriminate between stimuli. However, our normal experience of the world also involves integrating multiple stimuli into a single perceptual event. Neural mechanisms such as lateral inhibition are believed to enhance local differences between sensory inputs from nearby regions of the receptor surface. However, this mechanism would seem dysfunctional when sensory inputs need to be combined rather than contrasted. Here, we investigated whether the brain can strategically regulate the strength of suppressive interactions that underlie lateral inhibition between finger representations in human somatosensory processing. To do this, we compared sensory processing between conditions that required either comparing or combining information. We delivered two simultaneous tactile motion trajectories to index and middle fingertips of the right hand. Participants had to either compare the directions of the two stimuli, or to combine them to form their average direction. To reveal preparatory tuning of somatosensory cortex, we used an established event-related potential design to measure the interaction between cortical representations evoked by digital nerve shocks immediately before each tactile stimulus. Consistent with previous studies, we found a clear suppression between cortical activations when participants were instructed to compare the tactile motion directions. Importantly, this suppression was significantly reduced when participants had to combine the same stimuli. These findings suggest that the brain can strategically switch between a comparative and a combinative mode of somatosensory processing, according to the perceptual goal, by preparatorily adjusting the strength of a process akin to lateral inhibition.

Ensemble coding of crowd speed using biological motion

The accurate perception of human crowds is integral to social understanding and interaction. Previous studies have shown that observers are sensitive to several crowd characteristics such as average facial expression, gender, identity, joint attention, and heading direction. In two experiments, we examined ensemble perception of crowd speed using standard point-light walkers (PLW). Participants were asked to estimate the average speed of a crowd consisting of 12 figures moving at different speeds. In Experiment 1, trials of intact PLWs alternated with trials of scrambled PLWs with a viewing duration of 3 seconds. We found that ensemble processing of crowd speed could rely on local motion alone, although a globally intact configuration enhanced performance. In Experiment 2, observers estimated the average speed of intact-PLW crowds that were displayed at reduced viewing durations across five blocks of trials (between 2500 ms and 500 ms). Estimation of fast crowds was precise and accurate regardless of viewing duration, and we estimated that three to four walkers could still be integrated at 500 ms. For slow crowds, we found a systematic deterioration in performance as viewing time reduced, and performance at 500 ms could not be distinguished from a single-walker response strategy. Overall, our results suggest that rapid and accurate ensemble perception of crowd speed is possible, although sensitive to the precise speed range examined.

Ensemble perception includes information from multiple spatial scales

Most visual scenes contain information at different spatial scales, including the local and global, or the detail and gist. Global processes have become increasingly implicated in research examining summary statistical perception, initially as the output of ensemble coding, and more recently as a gating mechanism for selecting which information is included in the averaging process itself. Yet local and global processing are known to be rapidly integrated by the visual system, and it is plausible that global-level information, like spatial organization, may be included as an input during ensemble coding. We tested this hypothesis using an ensemble shape-perception task in which observers evaluated the mean aspect ratios of sets of ellipses. In addition to varying the aspect ratios of the individual shapes, we independently varied the spatial arrangements of the sets so that they had either flat or tall organizations at the global level. We found that observers made precise summary judgments about the average aspect ratios of the sets by integrating information from multiple shapes. More importantly, global flat and tall organizations were incorporated into ensemble judgments about the sets; summary judgments were biased in the directions of the global spatial arrangements on each trial. This global-to-local integration even occurred when the global organizations were masked. Our results demonstrate that the process of summary representation can include information from both the local and global scales. The gist is not just an output of ensemble representation - it can be included as an input to the mechanism itself.

Quality of average representation can be enhanced by refined individual items

Ensemble perception is efficient because it summarizes redundant and complex information. However, it loses the fine details of individual items during the averaging process. Such characteristics of ensemble perception are similar to those of coarse processing. Here, we tested whether extracting an average of a set was similar to coarse processing. To manipulate coarse processing, we used the fast flicker adaptation known as suppressing coarse information processed by the magnocellular pathway. We hypothesized that if computing the average of a set relied on coarse processing, the precision of an averaging task should decrease after adaptation compared to baseline (no-adaptation). Across experiments with various features (orientation in Experiment 1, size in Experiment 2, and facial expression in Experiment 3), we found that suppressing coarse information did not disrupt the performance of the averaging tasks. Rather, adaptation increased the precision of mean representation. The precision of mean representation might have increased because fine information was relatively enhanced after adaptation. Our results suggest that the quality of ensemble representation relies on that of individual items.

Effects of Selective Attention on Mean-Size Computation: Weighted Averaging and Perceptual Enlargement

For efficient use of limited capacity, the visual system summarizes redundant information and prioritizes relevant information, strategies known respectively as ensemble perception and selective attention. Although previous studies showed a close relationship between these strategies, the specific mechanisms underlying the relationship have not been determined. We investigated how attention modulated mean-size computation. Fourteen people participated in this study. We hypothesized that attention biases mean-size computation by increasing the contribution (weighted averaging) and the apparent size (perceptual enlargement) of an attended item. Consistent with this hypothesis, our results showed that estimated mean sizes were biased toward the attended size and overestimated regardless of the attended size, supporting weighted averaging and perceptual enlargement, respectively. Taken together, the observed effects of selective attention on mean-size computation signify a close relationship between the two optimization mechanisms to achieve efficient management of the visual system’s limited capacity.

Roles of saliency and set size in ensemble averaging

Ensemble statistics are often thought of as a reliable impression of numerous items despite limited capacities to consciously represent each individual. However, whether all items equally contribute to ensemble summaries (e.g., mean) and whether they might be affected by known limited-capacity processes, such as focused attention, is still debated. We addressed these questions via a recently described "amplification effect," a systematic bias of perceived mean (e.g., average size) towards the more salient "tail" of a feature distribution (e.g., larger items). In our experiments, observers adjusted the mean orientation of sets of items varying in set size. We made some of the items more salient or less salient by changing their size. While the whole orientation distribution was fixed, the more salient subset could be shifted relative to the set mean or differ in range. We measured the bias away from the set mean and the standard deviation (SD) of errors, as it is known to reflect the physical range from which ensemble information is sampled. We found that bias and SD changes followed the shifts and range changes in salient subsets, providing evidence for amplification. However, these changes were weaker than those expected from sampling only salient items, suggesting that less salient items were also sampled. Importantly, the SD decreased as a function of set size, which is only possible if the number of sampled elements increased with set size. Overall, we conclude that orientation summary statistics are sampled from an entire ensemble and modulated by the amplification effect of attention.

Ensemble perception and focused attention: Two different modes of visual processing to cope with limited capacity

The visual system has a limited capacity for dealing with complex and redundant information in a scene. Here, we propose that a distributed attention mode of processing is necessary for coping with this limit, together with a focused attention mode of processing. The distributed attention mode provides a statistical summary of a scene, whereas the focused attention mode provides relevant information for object recognition. In this paper, we claim that a distributed mode of processing is necessary because (1) averaging performance improves with increased set-sizes, (2) even unselected items are likely to contribute to averaging, and (3) the assumption of variable capacity limits in averaging over different set-sizes is not plausible. We then propose how the averaging process can access multiple items over the capacity limit of focused attention. The visual system can represent multiple items as population responses and read out relevant information using the two modes of attention. It can summarize population responses with a broad application of a Gaussian profile (i.e., distributed attention) and represent its peak as the mean. It can focus on relevant population responses with a narrow application of a Gaussian profile (i.e., focused attention) and select important information for object recognition. The two attention modes of processing provide a framework for incorporating two seemingly opposing fields of study (ensemble perception and selective attention) and a unified theory of a coping strategy with our limited capacity.