The development of Bayesian integration in sensorimotor estimation

No evidence for a difference in Bayesian reasoning for egocentric versus allocentric spatial cognition

Bayesian reasoning (i.e. prior integration, cue combination, and loss minimization) has emerged as a prominent model for some kinds of human perception and cognition. The major theoretical issue is that we do not yet have a robust way to predict when we will or will not observe Bayesian effects in human performance. Here we tested a proposed divide in terms of Bayesian reasoning for egocentric spatial cognition versus allocentric spatial cognition (self-centered versus world-centred). The proposal states that people will show stronger Bayesian reasoning effects when it is possible to perform the Bayesian calculations within the egocentric frame, as opposed to requiring an allocentric frame. Three experiments were conducted with one egocentric-allowing condition and one allocentric-requiring condition but otherwise matched as closely as possible. No difference was found in terms of prior integration (Experiment 1), cue combination (Experiment 2), or loss minimization (Experiment 3). The contrast in previous reports, where Bayesian effects are present in many egocentric-allowing tasks while they are absent in many allocentric-requiring tasks, is likely due to other differences between the tasks-for example, the way allocentric-requiring tasks are often more complex and memory intensive.

The distinct development of stimulus and response serial dependence

Serial dependence (SD) is a phenomenon wherein current perceptions are biased by the previous stimulus and response. This helps to attenuate perceptual noise and variability in sensory input and facilitates stable ongoing perceptions of the environment. However, little is known about the developmental trajectory of SD. This study investigates how the stimulus and response biases of the SD effect develop across three age groups. Conventional analyses, in which previous stimulus and response biases were assessed separately, revealed significant changes in the biases over time. Previous stimulus bias shifted from repulsion to attraction, while previous response bias evolved from attraction to greater attraction. However, there was a strong correlation between stimulus and response orientations. Therefore, a generalized linear mixed-effects (GLME) analysis that simultaneously considered both previous stimulus and response, outperformed separate analyses. This revealed that previous stimulus and response resulted in two distinct biases with different developmental trajectories. The repulsion bias of previous stimulus remained relatively stable across all age groups, whereas the attraction bias of previous response was significantly stronger in adults than in children and adolescents. These findings demonstrate that the repulsion bias towards preceding stimuli is established early in the developing brain (at least by around 10 years old), while the attraction bias towards responses is not fully developed until adulthood. Our findings provide new insights into the development of the SD phenomenon and how humans integrate two opposing mechanisms into their perceptual responses to external input during development.

Prior uncertainty impedes discrete locomotor adaptation

The impact of environmental uncertainty on locomotor adaptation remains unclear. Environmental uncertainty could either aid locomotor adaptation by prompting protective control strategies that stabilize movements to assist learning or impede adaptation by reducing error sensitivity and fostering hesitance to pursue corrective movements. To explore this, we investigated participants' adaptation to a consistent force field after experiencing environmental uncertainty in the form of unpredictable balance perturbations. We compared the performance of this group (Perturbation) to the adaptive performance of a group that did not experience any unpredictable perturbations (Non-Perturbation). Perturbations were delivered using a cable-driven robotic device applying lateral forces to the pelvis. We assessed whole-body center of mass (COM) trajectory (COM signed deviation), anticipatory postural adjustments (COM lateral offset), and first step width. The Perturbation group exhibited larger disruptions in COM trajectory (greater COM signed deviations) than the Non-Perturbation group when first walking in the force field. While the COM signed deviations of both groups decreased towards baseline values, only the Non-Perturbation group returned to baseline levels. The Perturbation groups COM signed deviations remained higher, indicating they failed to fully adapt to the force field before the end. The Perturbation group also did not adapt their COM lateral offset to counter the predictable effects of the force field as the Non-Perturbation group did, and their first step width increased more slowly. Our findings suggest that exposure to unpredictable perturbations impeded future sensorimotor adaptations to consistent perturbations.

Bayesian Decision-Making Under Uncertainty in Borderline Personality Disorder

Bayesian decision theory suggests that optimal decision-making should use and weigh prior beliefs with current information, according to their relative uncertainties. However, some characteristics of borderline personality disorder (BPD) patients, such as fast, drastic changes in the overall perception of themselves and others, suggest they may be underrelying on priors. Here, we investigated if BPD patients have a general deficit in relying on or combining prior with current information. We analyzed this by having BPD patients (n = 23) and healthy controls (n = 18) perform a coin-catching sensorimotor task with varying levels of prior and current information uncertainty. Our results indicate that BPD patients learned and used prior information and combined it with current information in a qualitatively Bayesian-like way. Our results show that, at least in a lower-level, nonsocial sensorimotor task, BPD patients can appropriately use both prior and current information, illustrating that potential deficits using priors may not be widespread or domain-general.

Sensory weighting of position and force feedback during pinching

Human hands are complex biomechanical systems that allow for dexterous tasks with many degrees of freedom. Coordination of the fingers is essential for many activities of daily living and involves integrating sensory signals. During this sensory integration, the central nervous system deals with the uncertainty of sensory signals. When handling compliant objects, force and position are related. Interactions with stiff objects result in reduced position changes and increased force changes compared to compliant objects. Literature has shown sensory integration of force and position at the shoulder. Nevertheless, differences in sensory requirements between proximal and distal joints may lead to different proprioceptive representations, hence findings at proximal joints cannot be directly transferred to distal joints, such as the digits. Here, we investigate the sensory integration of force and position during pinching. A haptic manipulator rendered a virtual spring with adjustable stiffness between the index finger and the thumb. Participants had to blindly reproduce a force against the spring. In both visual reference trials and blind reproduction trials, the relation between pinch force and spring compression was constant. However, by covertly changing the spring characteristics in catch trials into an adjusted force-position relation, the participants' weighting of force and position could be revealed. In agreement with previous studies on the shoulder, participants relied more on force sense in trials with higher stiffness. This study demonstrated stiffness-dependent sensory integration of force and position feedback during pinching.

Computational modeling of human multisensory spatial representation by a neural architecture

Our brain constantly combines sensory information in unitary percept to build coherent representations of the environment. Even though this process could appear smooth, integrating sensory inputs from various sensory modalities must overcome several computational issues, such as recoding and statistical inferences problems. Following these assumptions, we developed a neural architecture replicating humans' ability to use audiovisual spatial representations. We considered the well-known ventriloquist illusion as a benchmark to evaluate its phenomenological plausibility. Our model closely replicated human perceptual behavior, proving a truthful approximation of the brain's ability to develop audiovisual spatial representations. Considering its ability to model audiovisual performance in a spatial localization task, we release our model in conjunction with the dataset we recorded for its validation. We believe it will be a powerful tool to model and better understand multisensory integration processes in experimental and rehabilitation environments.

Developmental changes in colour constancy in a naturalistic object selection task

When the illumination falling on a surface change, so does the reflected light. Despite this, adult observers are good at perceiving surfaces as relatively unchanging-an ability termed colour constancy. Very few studies have investigated colour constancy in infants, and even fewer in children. Here we asked whether there is a difference in colour constancy between children and adults; what the developmental trajectory is between six and 11 years; and whether the pattern of constancy across illuminations and reflectances differs between adults and children. To this end, we developed a novel, child-friendly computer-based object selection task. In this, observers saw a dragon's favourite sweet under a neutral illumination and picked the matching sweet from an array of eight seen under a different illumination (blue, yellow, red, or green). This set contained a reflectance match (colour constant; perfect performance) and a tristimulus match (colour inconstant). We ran two experiments, with two-dimensional scenes in one and three-dimensional renderings in the other. Twenty-six adults and 33 children took part in the first experiment; 26 adults and 40 children took part in the second. Children performed better than adults on this task, and their performance decreased with age in both experiments. We found differences across illuminations and sweets, but a similar pattern across both age groups. This unexpected finding might reflect a real decrease in colour constancy from childhood to adulthood, explained by developmental changes in the perceptual and cognitive mechanisms underpinning colour constancy, or differences in task strategies between children and adults. HIGHLIGHTS: Six- to 11-year-old children demonstrated better performance than adults on a colour constancy object selection task. Performance decreased with age over childhood. These findings may indicate development of cognitive strategies used to overcome automatic colour constancy mechanisms.

Novel applications of Bayesian inference clarify sensorimotor uncertainty during stepping movements

The human nervous system relies on sensory information from the feet and legs to control the way we balance and walk. However, even in healthy individuals this sensory information is inherently variable and clouded with uncertainty. Researchers have found that the central nervous system (CNS) estimates body position amid the uncertainty of sensory signals in a way consistent with Bayesian inference. Bayesian inference posits that the brain accounts for variability in sensory data by combining it with learned expectations built from previous movement attempts. While initial findings on this topic are promising, they have neglected to study full-body movements such as gait and balance. The purpose of this research was to determine if the CNS controls balance-related stepping tasks in a way that fits a Bayesian framework. To address this purpose, we created a virtual reality protocol where participants moved their center of mass (CoM) to various targets while relying on uncertain visual cues and compensating for an alternating shift to the cursor position. We showed that as incoming sensory information became less certain, participants relied more on their learned expectation of body position and demonstrated more uncertainty in their responses. Accordingly, as participants learned to control and estimate their CoM position during our mobility task, they relied both on the sensory information they were receiving as well as learned expectations for its location. These results provide further evidence that the CNS is aware of the variability in sensory information and is proficient at compensating for the resultant uncertainty. We aim to apply these findings as a method for measuring the efficacy of interventions targeting sensory function.

An adaptive cue selection model of allocentric spatial reorientation

After becoming disoriented, an organism must use the local environment to reorient and recover vectors to important locations. A new theory, adaptive combination, suggests that the information from different spatial cues is combined with Bayesian efficiency during reorientation. To test this further, we modified the standard reorientation paradigm to be more amenable to Bayesian cue combination analyses while still requiring reorientation in an allocentric (i.e., world-based, not egocentric) frame. Twelve adults and 20 children at ages 5 to 7 years old were asked to recall locations in a virtual environment after a disorientation. Results were not consistent with adaptive combination. Instead, they are consistent with the use of the most useful (nearest) single landmark in isolation. We term this adaptive selection. Experiment 2 suggests that adults also use the adaptive selection method when they are not disoriented but are still required to use a local allocentric frame. This suggests that the process of recalling a location in the allocentric frame is typically guided by the single most useful landmark rather than a Bayesian combination of landmarks. These results illustrate that there can be important limits to Bayesian theories of the cognition, particularly for complex tasks such as allocentric recall.

Whether studying the development of children’s spatial cognition, creating artificial intelligence with human-like capacities, or designing civic spaces, we can benefit from a strong understanding of how humans process the space around them. Here we tested a prominent theory that brings together statistical theory and psychological theory (Bayesian models of perception and memory) but found that it could not satisfactorily explain our data. Our findings suggest that when tracking the spatial relations between objects from different viewpoints, rather than efficiently combining all the available landmarks, people often fall back to the much simpler method of tracking the spatial relation to the nearest landmark.

Bayesian integration during sensorimotor estimation in elite athletes

An experiment was designed to determine the effects of sensory uncertainty on sensorimotor estimation in elite athletes compared to non-athletes. Nineteen elite athletes and 16 non-athletes were required to estimate when and where a cursor arrived at a target location. The cursor position was displayed through its entire trajectory in the certain condition while only briefly in the uncertain condition. Accuracy and variability in time and spatial domains were calculated. A Bayesian analysis using subsets of subjects' total spatial variance was also performed. The results indicated that athletes and non-athletes used estimation strategies consistent with Bayesian integration. The results also showed a decrease in variability for spatial performance for both groups during the uncertain condition compared to the certain condition, especially when the cursor location was further away from the prior mean. This decrease in variability was significantly greater for non-athletes. By concentrating performance around the end-point mean location, an increase in spatial error occurred. More spatial and timing errors were observed in non-athletes than athletes, indicating athletes were more certain about likelihood information or their interpretation of likelihood information than non-athletes. These results suggest that athletic experience may facilitate the use of probabilistic information for optimal sensorimotor estimations.

Immersive virtual reality interferes with default head-trunk coordination strategies in young children

The acquisition of postural control is an elaborate process, which relies on the balanced integration of multisensory inputs. Current models suggest that young children rely on an 'en-block' control of their upper body before sequentially acquiring a segmental control around the age of 7, and that they resort to the former strategy under challenging conditions. While recent works suggest that a virtual sensory environment alters visuomotor integration in healthy adults, little is known about the effects on younger individuals. Here we show that this default coordination pattern is disrupted by an immersive virtual reality framework where a steering role is assigned to the trunk, which causes 6- to 8-year-olds to employ an ill-adapted segmental strategy. These results provide an alternate trajectory of motor development and emphasize the immaturity of postural control at these ages.

Vestibular Stimulation May Drive Multisensory Processing: Principles for Targeted Sensorimotor Therapy (TSMT)

At birth, the vestibular system is fully mature, whilst higher order sensory processing is yet to develop in the full-term neonate. The current paper lays out a theoretical framework to account for the role vestibular stimulation may have driving multisensory and sensorimotor integration. Accordingly, vestibular stimulation, by activating the parieto-insular vestibular cortex, and/or the posterior parietal cortex may provide the cortical input for multisensory neurons in the superior colliculus that is needed for multisensory processing. Furthermore, we propose that motor development, by inducing change of reference frames, may shape the receptive field of multisensory neurons. This, by leading to lack of spatial contingency between formally contingent stimuli, may cause degradation of prior motor responses. Additionally, we offer a testable hypothesis explaining the beneficial effect of sensory integration therapies regarding attentional processes. Key concepts of a sensorimotor integration therapy (e.g., targeted sensorimotor therapy (TSMT)) are also put into a neurological context. TSMT utilizes specific tools and instruments. It is administered in 8-weeks long successive treatment regimens, each gradually increasing vestibular and postural stimulation, so sensory-motor integration is facilitated, and muscle strength is increased. Empirically TSMT is indicated for various diseases. Theoretical foundations of this sensorimotor therapy are discussed.

Central tendency biases must be accounted for to consistently capture Bayesian cue combination in continuous response data

Observers in perceptual tasks are often reported to combine multiple sensory cues in a weighted average that improves precision—in some studies, approaching statistically optimal (Bayesian) weighting, but in others departing from optimality, or not benefitting from combined cues at all. To correctly conclude which combination rules observers use, it is crucial to have accurate measures of their sensory precision and cue weighting. Here, we present a new approach for accurately recovering these parameters in perceptual tasks with continuous responses. Continuous responses have many advantages, but are susceptible to a central tendency bias, where responses are biased towards the central stimulus value. We show that such biases lead to inaccuracies in estimating both precision gains and cue weightings, two key measures used to assess sensory cue combination. We introduce a method that estimates sensory precision by regressing continuous responses on targets and dividing the variance of the residuals by the squared slope of the regression line, “correcting-out” the error introduced by the central bias and increasing statistical power. We also suggest a complementary analysis that recovers the sensory cue weights. Using both simulations and empirical data, we show that the proposed methods can accurately estimate sensory precision and cue weightings in the presence of central tendency biases. We conclude that central tendency biases should be (and can easily be) accounted for to consistently capture Bayesian cue combination in continuous response data.

Bayesian transfer in a complex spatial localization task

Prior knowledge can help observers in various situations. Adults can simultaneously learn two location priors and integrate these with sensory information to locate hidden objects. Importantly, observers weight prior and sensory (likelihood) information differently depending on their respective reliabilities, in line with principles of Bayesian inference. Yet, there is limited evidence that observers actually perform Bayesian inference, rather than a heuristic, such as forming a look-up table. To distinguish these possibilities, we ask whether previously learned priors will be immediately integrated with a new, untrained likelihood. If observers use Bayesian principles, they should immediately put less weight on the new, less reliable, likelihood ("Bayesian transfer"). In an initial experiment, observers estimated the position of a hidden target, drawn from one of two distinct distributions, using sensory and prior information. The sensory cue consisted of dots drawn from a Gaussian distribution centered on the true location with either low, medium, or high variance; the latter introduced after block three of five to test for evidence of Bayesian transfer. Observers did not weight the cue (relative to the prior) significantly less in the high compared to medium variance condition, counter to Bayesian predictions. However, when explicitly informed of the different prior variabilities, observers placed less weight on the new high variance likelihood ("Bayesian transfer"), yet, substantially diverged from ideal. Much of this divergence can be captured by a model that weights sensory information, according only to internal noise in using the cue. These results emphasize the limits of Bayesian models in complex tasks.

The Difficulty of Effectively Using Allocentric Prior Information in a Spatial Recall Task

Prior information represents the long-term statistical structure of an environment. For example, colds develop more often than throat cancer, making the former a more likely diagnosis for a sore throat. There is ample evidence for effective use of prior information during a variety of perceptual tasks, including the ability to recall locations using an egocentric (self-based) frame. However, it is not yet known if people can use prior information effectively when using an allocentric (world-based) frame. Forty-eight adults were shown sixty sets of three target locations in a sparse virtual environment with three beacons. The targets were drawn from one of four prior distributions. They were then asked to point to the targets after a delay and a change in perspective. While searches were biased towards the beacons, we did not find any evidence that participants successfully exploited the prior distributions of targets. These results suggest that allocentric reasoning does not conform to normative Bayesian models: we saw no evidence for use of priors in our cognitively-complex (allocentric) task, unlike in previous, simpler (egocentric) recall tasks. It is possible that this reflects the high biological cost of processing precise allocentric information.

Optimal, resource-rational or sub-optimal? Insights from cognitive development

We agree with the authors regarding the utility of viewing cognition as resulting from an optimal use of limited resources. Here, we advocate for extending this approach to the study of cognitive development, which we feel provides particularly powerful insight into the debate between bounded optimality and true sub-optimality, precisely because young children have limited computational and cognitive resources.

Young children combine sensory cues with learned information in a statistically efficient manner: But task complexity matters

Human adults are adept at mitigating the influence of sensory uncertainty on task performance by integrating sensory cues with learned prior information, in a Bayes-optimal fashion. Previous research has shown that young children and infants are sensitive to environmental regularities, and that the ability to learn and use such regularities is involved in the development of several cognitive abilities. However, it has also been reported that children younger than 8 do not combine simultaneously available sensory cues in a Bayes-optimal fashion. Thus, it remains unclear whether, and by what age, children can combine sensory cues with learned regularities in an adult manner. Here, we examine the performance of 6- to 7-year-old children when tasked with localizing a 'hidden' target by combining uncertain sensory information with prior information learned over repeated exposure to the task. We demonstrate that 6- to 7-year-olds learn task-relevant statistics at a rate on par with adults, and like adults, are capable of integrating learned regularities with sensory information in a statistically efficient manner. We also show that variables such as task complexity can influence young children's behavior to a greater extent than that of adults, leading their behavior to look sub-optimal. Our findings have important implications for how we should interpret failures in young children's ability to carry out sophisticated computations. These 'failures' need not be attributed to deficits in the fundamental computational capacity available to children early in development, but rather to ancillary immaturities in general cognitive abilities that mask the operation of these computations in specific situations.

The integration of probabilistic information during sensorimotor estimation is unimpaired in children with Cerebral Palsy

Background

It is important to understand the motor deficits of children with Cerebral Palsy (CP). Our understanding of this motor disorder can be enriched by computational models of motor control. One crucial stage in generating movement involves combining uncertain information from different sources, and deficits in this process could contribute to reduced motor function in children with CP. Healthy adults can integrate previously-learned information (prior) with incoming sensory information (likelihood) in a close-to-optimal way when estimating object location, consistent with the use of Bayesian statistics. However, there are few studies investigating how children with CP perform sensorimotor integration. We compare sensorimotor estimation in children with CP and age-matched controls using a model-based analysis to understand the process.

Methods and findings

We examined Bayesian sensorimotor integration in children with CP, aged between 5 and 12 years old, with Gross Motor Function Classification System (GMFCS) levels 1–3 and compared their estimation behavior with age-matched typically-developing (TD) children. We used a simple sensorimotor estimation task which requires participants to combine probabilistic information from different sources: a likelihood distribution (current sensory information) with a prior distribution (learned target information). In order to examine sensorimotor integration, we quantified how participants weighed statistical information from the two sources (prior and likelihood) and compared this to the statistical optimal weighting. We found that the weighing of statistical information in children with CP was as statistically efficient as that of TD children.

Conclusions

We conclude that Bayesian sensorimotor integration is not impaired in children with CP and therefore, does not contribute to their motor deficits. Future research has the potential to enrich our understanding of motor disorders by investigating the stages of motor processing set out by computational models. Therapeutic interventions should exploit the ability of children with CP to use statistical information.