Subitizing endures in sequential rather than simultaneous comparison tasks.

Subitizing is the ability to appraise a number of small quantities (up to four) rapidly and precisely. This system, however, can be impaired by distractors presented along with targets to be enumerated. To better understand whether this limitation arises in perceptual circuits or in the response selection stage, we investigated whether subitizing can endure in simultaneous comparison tasks. Participants were asked to compare the number of dots in two sets on the left and right sides of the screen, presented either simultaneously or sequentially. For comparing within the numerosity range (6-32 dots), both the error rate and reaction time increased steadily as the ratio between the two numbers compared approached "1." Namely, a phenomenon labeled the ratio effect was revealed. For comparison with small numbers (<5), the sequential comparison task was errorless despite the ratio, suggesting the feature of subitizing. Individual efficiency (measured by the inverse efficiency score [IES]) did not correlate between number ranges in sequential comparison, suggesting that distinct mechanisms were involved. However, we found that in simultaneous tasks, error rate and efficiency showed an increase as the ratios of the two numbers compared approached "1." This is similar to the ratio effect revealed in the comparison for moderate numbers. Individual efficiency within these two ranges correlated, indicating that the enumeration within these two ranges was based on a single mechanism. These results suggest that subitizing cannot process sets in parallel, and numerosity takes the job whenever subitizing fails.

Sensorimotor mechanisms selective to numerosity derived from individual differences.

We have previously shown that after few seconds of adaptation by finger-tapping, the perceived numerosity of spatial arrays and temporal sequences of visual objects displayed near the tapping region is increased or decreased, implying the existence of a sensorimotor numerosity system (Anobile et al., 2016). To date, this mechanism has been evidenced only by adaptation. Here, we extend our finding by leveraging on a well-established covariance technique, used to unveil and characterize 'channels' for basic visual features such as colour, motion, contrast, and spatial frequency. Participants were required to press rapidly a key a specific number of times, without counting. We then correlated the precision of reproduction for various target number presses between participants. The results showed high positive correlations for nearby target numbers, scaling down with numerical distance, implying tuning selectivity. Factor analysis identified two factors, one for low and the other for higher numbers. Principal component analysis revealed two bell-shaped covariance channels, peaking at different numerical values. Two control experiments ruled out the role of non-numerical strategies based on tapping frequency and response duration. These results reinforce our previous reports based on adaptation, and further suggest the existence of at least two sensorimotor number channels responsible for translating symbolic numbers into action sequences.

Serial Dependence in Perception.

Much evidence has shown that perception is biased towards previously presented similar stimuli, an effect recently termed serial dependence. Serial dependence affects nearly every aspect of perception, often causing gross perceptual distortions, especially for weak and ambiguous stimuli. Despite unwanted side-effects, empirical evidence and Bayesian modeling show that serial dependence acts to improve efficiency and is generally beneficial to the system. Consistent with models of predictive coding, the Bayesian priors of serial dependence are generated at high levels of cortical analysis, incorporating much perceptual experience, but feed back to lower sensory areas. These feedback loops may drive oscillations in the alpha range, linked strongly with serial dependence. The discovery of top-down predictive perceptual processes is not new, but the new, more quantitative approach characterizing serial dependence promises to lead to a deeper understanding of predictive perceptual processes and their underlying neural mechanisms.

The role of non-numerical information in the perception of temporal numerosity.

Numerosity perception refers to the ability to make rapid but approximate estimates of the quantity of elements in a set (spatial numerosity) or presented sequentially (temporal numerosity). Whether numerosity is directly perceived or indirectly recomputed from non-numerical features is a highly debated issue. In the spatial domain, area and density have been suggested as the main parameters through which numerosity would be recomputed. In the temporal domain, stimuli duration and temporal frequency could be similarly exploited to retrieve numerosity. By adapting a psychophysical technique previously exploited in the spatial domain, we investigated whether temporal visual numerosity is directly perceived. Adult participants observed sequences of visual impulses sampled from a stimulus space spanning several levels of temporal frequency and duration (and hence numerosity), and then reproduced the sequence as accurately as possible via a series of keypresses. Crucially, participants were not asked to reproduce any particular property (such as number of impulses) but were free to choose any available cue (such as total duration, or temporal frequency). The results indicate that while the overall sequence duration was barely considered, numerosity and temporal frequency were both spontaneously used as the main cues to reproduce the sequences, with a slight but significant dominance of numerosity. Overall, the results are in line with previous literature suggesting that numerosity is directly encoded, even for temporal sequences, but a non-numerical feature (temporal frequency) is also used in reproducing sequences.

Serial dependence improves performance and biases confidence-based decisions.

Perception depends on both the current sensory input and on the preceding stimuli history, a mechanism referred to as serial dependence (SD). One interesting, and somewhat controversial, question is whether serial dependence originates at the perceptual stage, which should lead to a sensory improvement, or at a subsequent decisional stage, causing solely a bias. Here, we studied the effects of SD in a novel manner by leveraging on the human capacity to spontaneously assess the quality of sensory information. Two noisy-oriented Gabor stimuli were simultaneously presented along with two bars of the same orientation as the Gabor stimuli. Participants were asked to choose which Gabor stimulus to judge and then make a forced-choice judgment of its orientation by selecting the appropriate response bar. On all trials, one of the Gabor stimuli had the same orientation as the Gabor in the same position on the previous trial. We explored whether continuity in orientation and position affected choice and accuracy. Results show that continuity of orientation leads to a persistent (up to four back) accuracy advantage and a higher preference in the selection of stimuli with the same orientation, and this advantage accumulates over trials. In contrast, analysis of the continuity of the selected position indicated that participants had a strong tendency to choose stimuli in the same position, but this behavior did not lead to an improvement in accuracy.

Quantum spin models for numerosity perception.

Humans share with animals, both vertebrates and invertebrates, the capacity to sense the number of items in their environment already at birth. The pervasiveness of this skill across the animal kingdom suggests that it should emerge in very simple populations of neurons. Current modelling literature, however, has struggled to provide a simple architecture carrying out this task, with most proposals suggesting the emergence of number sense in multi-layered complex neural networks, and typically requiring supervised learning; while simple accumulator models fail to predict Weber's Law, a common trait of human and animal numerosity processing. We present a simple quantum spin model with all-to-all connectivity, where numerosity is encoded in the spectrum after stimulation with a number of transient signals occurring in a random or orderly temporal sequence. We use a paradigmatic simulational approach borrowed from the theory and methods of open quantum systems out of equilibrium, as a possible way to describe information processing in neural systems. Our method is able to capture many of the perceptual characteristics of numerosity in such systems. The frequency components of the magnetization spectra at harmonics of the system's tunneling frequency increase with the number of stimuli presented. The amplitude decoding of each spectrum, performed with an ideal-observer model, reveals that the system follows Weber's law. This contrasts with the well-known failure to reproduce Weber's law with linear system or accumulators models.

Crowding results from optimal integration of visual targets with contextual information.

Crowding is the inability to recognize an object in clutter, usually considered a fundamental low-level bottleneck to object recognition. Here we advance and test an alternative idea, that crowding, like predictive phenomena such as serial dependence, results from optimizing strategies that exploit redundancies in natural scenes. This notion leads to several testable predictions: crowding should be greatest for unreliable targets and reliable flankers; crowding-induced biases should be maximal when target and flankers have similar orientations, falling off for differences around 20°; flanker interference should be associated with higher precision in orientation judgements, leading to lower overall error rate; effects should be maximal when the orientation of the target is near that of the average of the flankers, rather than to that of individual flankers. Each of these predictions were supported, and could be simulated with ideal-observer models that maximize performance. The results suggest that while crowding can affect object recognition, it may be better understood not as a processing bottleneck, but as a consequence of efficient exploitation of the spatial redundancies of the natural world.

Visual priming and serial dependence are mediated by separate mechanisms.

Perceptual history influences current perception, readily revealed by visual priming (the facilitation of responses on repeated presentations of similar stimuli) and by serial dependence (systematic biases toward the previous stimuli). We asked whether the two phenomena shared perceptual mechanisms. We modified the standard "priming of pop-out" paradigm to measure both priming and serial dependence concurrently. The stimulus comprised three grating patches, one or two red, and the other green. Participants identified the color singleton (either red or green), and reproduced its orientation. Trial sequences were designed to maximize serial dependence, and long runs of priming color and position. The results showed strong effects of priming, both on reaction times and accuracy, which accumulated steadily over time, as generally reported in the literature. The serial dependence effects were also strong, but did not depend on previous color, nor on the run length. Reaction times measured under various conditions of repetition or change of priming color or position were reliably correlated with imprecision in orientation reproduction, but reliably uncorrelated with magnitude of serial dependence. The results suggest that visual priming and serial dependence are mediated by different neural mechanisms. We propose that priming affects sensitivity, possibly via attention-like mechanisms, whereas serial dependence affects criteria, two orthogonal dimensions in the signal detection theory.

Numerosity perception is tuned to salient environmental features.

Numerosity perception is a key ability to guide behavior. However, current models propose that number units encode an abstract representation of numerosity regardless of the non-numerical attributes of the stimuli, suggesting rather coarse environmental tuning. Here we investigated whether numerosity systems spontaneously adapt to all visible items, or to subsets segregated by salient attributes such as color or pitch. We measured perceived numerosity after participants adapted to highly numerous stimuli with color either matched to or different from the test. Matched colors caused a 25% underestimation of numerosity, while different colors had virtually no effect. This was true both for physically different colors, and for the same colors perceived as different, via a color-assimilation illusion. A similar result occurred in the acoustic domain, where adaptation magnitude was halved when the adaptor and test differed in pitch. Taken together, our results support the idea that numerosity perception is selectively tuned to salient environmental attributes.

Ideal observer analysis for continuous tracking experiments.

Continuous tracking is a newly developed technique that allows fast and efficient data acquisition by asking participants to "track" a stimulus varying in some property (usually position in space). Tracking is a promising paradigm for the investigation of dynamic features of perception and could be particularly well suited for testing ecologically relevant situations difficult to study with classical psychophysical paradigms. The high rate of data collection may be useful in studies on clinical populations and children, who are unable to undergo long testing sessions. In this study, we designed tracking experiments with two novel stimulus features, numerosity and size, proving the feasibility of the technique outside standard object tracking. We went on to develop an ideal observer model that characterizes the results in terms of efficiency of conversion of stimulus strength into responses, and identification of early and late noise sources. Our ideal observer closely modeled results from human participants, providing a generalized framework for the interpretation of tracking data. The proposed model allows to use the tracking paradigm in various perceptual domains, and to study the divergence of human participants from ideal behavior.

Reduced 2D form coherence and 3D structure from motion sensitivity in developmental dyscalculia.

Developmental dyscalculia (DD) is a specific learning disability affecting the development of numerical and arithmetical skills. The origin of DD is typically attributed to the suboptimal functioning of key regions within the dorsal visual stream (parietal cortex) which support numerical cognition. While DD individuals are often impaired in visual numerosity perception, the extent to which they also show a wider range of visual dysfunctions is poorly documented. In the current study we measured sensitivity to global motion (translational and flow), 2D static form (Glass patterns) and 3D structure from motion in adults with DD and control subjects. While sensitivity to global motion was comparable across groups, thresholds for static form and structure from motion were higher in the DD compared to the control group, irrespective of associated reading impairments. Glass pattern sensitivity predicted numerical abilities, and this relation could not be explained by recently reported differences in visual crowding. Since global form sensitivity has often been considered an index of ventral stream function, our findings could indicate a cortical dysfunction extending beyond the dorsal visual stream. Alternatively, they would fit with a role of parietal cortex in form perception under challenging conditions requiring multiple element integration.

Uncertainty and Prior Assumptions, Rather Than Innate Logarithmic Encoding, Explain Nonlinear Number-to-Space Mapping.

Mapping number to space is natural and spontaneous but often nonveridical, showing a clear compressive nonlinearity that is thought to reflect intrinsic logarithmic encoding of numerical values. We asked 78 adult participants to map dot arrays onto a number line across nine trials. Combining participant data, we confirmed that on the first trial, mapping was heavily compressed along the number line, but it became more linear across trials. Responses were well described by logarithmic compression but also by a parameter-free Bayesian model of central tendency, which quantitatively predicted the relationship between nonlinearity and number acuity. To experimentally test the Bayesian hypothesis, we asked 90 new participants to complete a color-line task in which they mapped noise-perturbed color patches to a "color line." When there was more noise at the high end of the color line, the mapping was logarithmic, but it became exponential with noise at the low end. We conclude that the nonlinearity of both number and color mapping reflects contextual Bayesian inference processes rather than intrinsic logarithmic encoding.

Perceptual History Acts in World-Centred Coordinates.

Serial dependence effects have been observed using a variety of stimuli and tasks, revealing that the recent past can bias current percepts, leading to increased similarity between two. The aim of this study is to determine whether this temporal integration occurs in egocentric or allocentric coordinates. We asked participants to perform an orientation reproduction task using grating stimuli while the head was kept at a fixed position, or after a 40° yaw rotation between trials, from left (-20°) to right (+20°), putting the egocentric and allocentric cues in conflict. Under these conditions, allocentric cues prevailed.

The pupil responds spontaneously to perceived numerosity.

Although luminance is the main determinant of pupil size, the amplitude of the pupillary light response is also modulated by stimulus appearance and attention. Here we ask whether perceived numerosity modulates the pupillary light response. Participants passively observed arrays of black or white dots of matched physical luminance but different physical or illusory numerosity. In half the patterns, pairs of dots were connected by lines to create dumbbell-like shapes, inducing an illusory underestimation of perceived numerosity; in the other half, connectors were either displaced or removed. Constriction to white arrays and dilation to black were stronger for patterns with higher perceived numerosity, either physical or illusory, with the strength of the pupillary light response scaling with the perceived numerosity of the arrays. Our results show that even without an explicit task, numerosity modulates a simple automatic reflex, suggesting that numerosity is a spontaneously encoded visual feature.

Perceptual history propagates down to early levels of sensory analysis.

One function of perceptual systems is to construct and maintain a reliable representation of the environment. A useful strategy intrinsic to modern "Bayesian" theories of perception1-6 is to take advantage of the relative stability of the input and use perceptual history (priors) to predict current perception. This strategy is efficient1-7 but can lead to stimuli being biased toward perceptual history, clearly revealed in a phenomenon known as serial dependence.8-14 However, it is still unclear whether serial dependence biases sensory encoding or only perceptual decisions.15,16 We leveraged on the "surround tilt illusion"-where tilted flanking stimuli strongly bias perceived orientation-to measure its influence on the pattern of serial dependence, which is typically maximal for similar orientations of past and present stimuli.7,10 Maximal serial dependence for a neutral stimulus preceded by an illusory one occurred when the perceived, not the physical, orientations of the two stimuli matched, suggesting that the priors biasing current perception incorporate the effect of the illusion. However, maximal serial dependence of illusory stimuli induced by neutral stimuli occurred when their physical (not perceived) orientations were matched, suggesting that priors interact with incoming sensory signals before they are biased by flanking stimuli. The evidence suggests that priors are high-level constructs incorporating contextual information, which interact directly with early sensory signals, not with highly processed perceptual representations.

Subitizing, unlike estimation, does not process sets in parallel.

Enumeration of very small quantities is a common task that we perform everyday. Much research has highlighted that in these conditions humans display fast, near errorless performance, a phenomenon dubbed subitizing. It has been suggested that this regime has a pivotal role in numerosity perception. Here we asked if this system can process multiple sets of items in parallel. At odds with what happens for moderate numerosities, we found a strong impairment caused already by the introduction of a second group of items marked by a different color. Adding shape as a cue provided no benefit. The only case in which subitizing was possible was when the target and distractor group were held constant through the experimental block. These results show the surprising fact that whilst being rapid and errorless, subitizing does not have the capability to disentangle multiple groups of items and deals only with coarse stimulus statistics.

Object identity determines trans-saccadic integration.

Humans make two to four rapid eye movements (saccades) per second, which, surprisingly, does not lead to abrupt changes in vision. To the contrary, we perceive a stable world. Hence, an important question is how information is integrated across saccades. To investigate this question, we used the sequential metacontrast paradigm (SQM), where two expanding streams of lines are presented. When one line is spatially offset, the other lines are perceived as being offset, too. When more lines are offset, all offsets integrate mandatorily; that is, observers cannot report the individual offsets but perceive one integrated offset. Here, we asked observers to make a saccade during the SQM. Even though the saccades caused a highly disrupted motion trajectory on the retina, offsets presented before and after the saccade integrated mandatorily. When observers made no saccade and the streams were displaced on the screen so that a similarly disrupted retinal image occurred as in the previous condition, no integration occurred. We suggest that trans-saccadic integration and perception are determined by object identity in spatiotopic coordinates and not by the retinal image.

Using psychophysical performance to predict short-term ocular dominance plasticity in human adults.

Binocular rivalry has become an important index of visual performance, both to measure ocular dominance or its plasticity, and to index bistable perception. We investigated its interindividual variability across 50 normal adults and found that the duration of dominance phases in rivalry is linked with the duration of dominance phases in another bistable phenomenon (structure from motion). Surprisingly, it also correlates with the strength of center-surround interactions (indexed by the tilt illusion), suggesting a common mechanism supporting both competitive interactions: center-surround and rivalry. In a subset of 34 participants, we further investigated the variability of short-term ocular dominance plasticity, measured with binocular rivalry before and after 2 hours of monocular deprivation. We found that ocular dominance shifts in favor of the deprived eye and that a large portion of ocular dominance variability after deprivation can be predicted from the dynamics of binocular rivalry before deprivation. The single best predictor is the proportion of mixed percepts (phases without dominance of either eye) before deprivation, which is positively related to ocular dominance unbalance after deprivation. Another predictor is the duration of dominance phases, which interacts with mixed percepts to explain nearly 50% of variance in ocular dominance unbalance after deprivation. A similar predictive power is achieved by substituting binocular rivalry dominance phase durations with tilt illusion magnitude, or structure from motion phase durations. Thus, we speculate that ocular dominance plasticity is modulated by two types of signals, estimated from psychophysical performance before deprivation, namely, interocular inhibition (promoting binocular fusion, hence mixed percepts) and inhibition for perceptual competition (promoting longer dominance phases and stronger center-surround interactions).