You will be presented with the abstract, introduction, and discussion section from a biomedical research article. Your task is to create a summary that a layperson can understand, capturing the essence of the research article. Keep essential scientific terms, but ensure that the language remains clear and the concepts are explained in an uncomplicated manner.

Title: A New Perceptual Bias Reveals Suboptimal Population Decoding of Sensory Responses}
Article:
Abstract:
Several studies have reported optimal population decoding of sensory responses in two-alternative visual discrimination tasks. Such decoding involves integrating noisy neural responses into a more reliable representation of the likelihood that the stimuli under consideration evoked the observed responses. Importantly, an ideal observer must be able to evaluate likelihood with high precision and only consider the likelihood of the two relevant stimuli involved in the discrimination task. We report a new perceptual bias suggesting that observers read out the likelihood representation with remarkably low precision when discriminating grating spatial frequencies. Using spectrally filtered noise, we induced an asymmetry in the likelihood function of spatial frequency. This manipulation mainly affects the likelihood of spatial frequencies that are irrelevant to the task at hand. Nevertheless, we find a significant shift in perceived grating frequency, indicating that observers evaluate likelihoods of a broad range of irrelevant frequencies and discard prior knowledge of stimulus alternatives when performing two-alternative discrimination.
Introduction:
Perceptual decisions in a wide range of visual tasks ultimately rely on information encoded in neural responses in primary visual cortex( V1). However, this information may not be readily available to higher levels of the visual system because it is distributed across entire populations of neurons. Moreover, each neuron's reliability is limited by intrinsic response variability and its relevance strongly depends on the perceptual task in which the organism is engaged. To form accurate perceptual judgements, the brain thus needs to pool sensory responses efficiently, decoding the population response into a reliable decision variable. A wide range of psychophysical and physiological studies have investigated population decoding efficiency in simple visual tasks such as two-alternative detection and discrimination[1]. Results are not unambiguous: some studies suggest that the visual system uses a flexible precision pooling scheme in which the contribution of sensory responses to perceptual decisions depends on their reliability and relevance to the task at hand[2]–[7]. However, other studies[8]–[11] do not report such optimal decoding but rather suggest a crude, unselective pooling scheme in which the decision pool includes sensitive as well as many insensitive neurons. It is not clear why results differ across studies, which illustrates that neural decision making is, as yet, not fully understood. A crucial issue concerns the neural implementation of optimal population decoding. Formally, optimal decoding requires to evaluate neural responses probabilistically by computing the( log) likelihood function. This function captures the likelihood that specific stimuli gave rise to the observed population response. Theoretical work has shown that, under certain conditions, the necessary part of the log likelihood function can be obtained through simple linear combination of neural responses[12],[13]. However, computing the likelihood function only solves part of the decoding problem. Subsequently, the likelihood function has to be read out and linked to a decision variable[1]. In two-alternative discrimination tasks, only two stimulus alternatives need to be considered. An optimal decoder aiming to maximize accuracy therefore calculates a ratio of likelihoods by reading out the likelihood function precisely at two specific locations that correspond to the two possible stimulus alternatives. Likewise, in a detection task in which the quantity of the stimulus to be detected is known, such a decoder only considers the likelihood of the relevant stimulus quantity being present or absent. Formally, retrieving the likelihoods of two discrete stimulus values corresponds to integrating the likelihood function with appropriately placed and infinitely narrow read-out functions. While the use of a likelihood ratio decision variable has been demonstrated in various perceptual tasks[12],[14]–[16], it remains unclear to what extent the likelihood ratio can be computed with arbitrary high precision. A failure to sample the likelihood representation with high precision may account for the suboptimal unselective pooling reported previously. Here, we estimate the width of the likelihood read-out functions involved in two-alternative pattern detection and discrimination by modeling a new perceptual bias. We measured grating detectability and discriminability in the presence of filtered visual noise and found that filtered noise backgrounds dramatically alter the perception of grating spatial frequency. Embedding a grating in low-pass filtered noise causes the perceived spatial frequency of the grating to decrease, while high-pass filtered noise increases perceived grating spatial frequency. A population code model is proposed, consisting of a physiologically inspired V1 encoding front-end followed by a decoding stage. By simultaneously modeling grating detectability and discriminability, we were able to estimate both the amount of sensory information encoded in the V1 population response as well as the extent to which this information is used to maximize performance. While filtered visual noise induces an asymmetry in the likelihood function, an ideal observer only evaluates the likelihood of exactly the two possible stimuli and is thus not affected by this asymmetry. Therefore, the observed bias indicates severely suboptimal decoding which we assign to an imprecise read-out of the likelihood function. Only when read-out functions as broad as 4 octaves are assumed, the model accounts for all behavioural measurements. These findings suggest that observers failed to sample the likelihood function at the appropriate locations with arbitrary high precision and consequently, that precision pooling was not adopted in our tasks.
Discussion:
In the present study, we report a new perceptual bias. Filtered visual noise significantly alters the perception of two known gratings in a two-alternative spatial frequency discrimination task, shifting perceived spatial frequency to lower and higher frequencies in respectively low-pass and high-pass filtered noise conditions. The fact that we observed such a strong bias is not self-evident. Observers received extensive training prior to the start of the experiments and auditory feedback was provided after each trial. Furthermore, we informed observers of the veridical grating spatial frequencies via noise-free grating templates presented at the beginning of each trial block. It should be noted that the bias cannot be attributed to merely a low signal-to-noise ratio, preventing observers from detecting the gratings when embedded in visual noise. Gratings were presented at relatively high contrasts in the discrimination experiment, corresponding to the 84%-correct detection thresholds measured in broadband noise. Moreover, the fact that we measured high overall performance and correspondingly steep psychometric functions in the discrimination task indicates that observers base their decisions-at least partially- on the veridical grating spatial frequency. We propose a population code model, consisting of a physiologically inspired encoding front-end followed by a simple linear decoder. The best-fitting model accurately predicts the perceptual bias in the discrimination task while simultaneously capturing contrast detection performance in the absence of visual noise, in broadband noise as well as in filtered notched noise using a single set of parameters. Although few constraints were imposed, the estimates of the encoding stage parameters lie close to values reported in macaque or cat V1 single-cell recording studies. Ideal observer analysis revealed that a considerable amount of spatial frequency information is available in the encoding stage, even in the presence of filtered visual noise. Furthermore, using this information to achieve unbiased spatial frequency discrimination does not require complex decoding. A biologically plausible linear decoder[12], only requiring knowledge of V1 spatial frequency tuning but adopting narrow read-out functions to transform the likelihood function into a likelihood ratio decision variable, can achieve unbiased discrimination performance. In principle, however, a model implementing optimal read-out functions can account for the bias in the discrimination task, provided that the amount of information assumed to be available in the encoding stage is limited. The perceptual bias is thus a hallmark of suboptimal spatial frequency processing, which can be due to either inefficiencies in the encoding or decoding stage. However, grating detectability tightly constrains the amount of information available in the encoding stage, which allowed us to attribute the perceptual bias to suboptimal decoding involving broad read-out functions. While our unified suboptimal likelihood read-out scheme for contrast detection and spatial frequency discrimination accounts for all behavioural measurements, our data are not inconsistent with optimal read-out in the contrast detection task. However, previous studies[34] comparing human to ideal contrast detection performance have reported low detection efficiencies, which may be consistent with suboptimal likelihood read-out. Furthermore, it seems unlikely that observers, while able to read out the likelihood function optimally in the detection task, would not manage to do so in the discrimination task. One possibility is that observers do not use a likelihood ratio to discriminate between spatial frequencies. For instance, observers may estimate grating spatial frequency and indicate which of two gratings yields the largest estimate. Previous studies[35],[36] have proposed maximum-likelihood, maximum-a-posteriori( MAP) or minimum mean squared error( MMSE) decoding to estimate unknown stimulus quantities from the population response. In our task, however, maximum-likelihood decoding will yield unbiased estimates of grating frequency in the presence of filtered noise. While filtered noise induces an asymmetry in the likelihood function, the location of its peak remains largely unchanged( Figure 4). The MAP and MMSE decoders would estimate grating spatial frequency based on respectively the maximum and the mean of the posterior probability function. The posterior is obtained by integrating the likelihood function with a prior probability function. In a two-alternative discrimination task, only two grating spatial frequencies are a-priori likely to occur. Therefore, the prior probability of these specific frequencies equals 0. 5 while the prior probability of other, irrelevant frequencies equals zero. Integrating the likelihood function with such an optimal prior to obtain the posterior is equivalent to reading out the likelihood function using infinitely-small and appropriately-placed read-out functions. Consequently, decoders operating on the posterior are equivalent to our decoder computing a likelihood ratio decision variable with high precision and fail to predict the perceptual bias( see supporting text S1. 4). An interesting hypothesis is that observers do not use a prior that is optimal to the task at hand, but instead rely on a general prior based on natural scene statistics[36]. As the spatial frequency spectrum of natural scenes can be characterised by a 1/f relationship between amplitude and spatial frequency[37], this prior would presumably be broadband and skewed towards low spatial frequencies. A MAP or MMSE estimator incorporating such a prior might also predict a noise-induced perceptual bias. This bias, however, will be asymmetric as likelihoods of low spatial frequencies are preferentially weighted when obtaining the posterior. More specifically, low-pass filtered noise is expected to induce a stronger bias compared to high-pass noise. Our data provide no consistent evidence for such an asymmetry( see supporting text S2). To read out the likelihood function with high precision, the visual system requires a-priori knowledge of the grating spatial frequencies presented on each trial in the discrimination experiment. In other words, the brain has to be able to represent appropriate, narrow signal templates. A theoretical issue concerns whether and how such templates can be reliably implemented in populations of noisy and broadly-tuned neurons. Recurrent network models have been proposed, capable of removing noise from the population response and representing arbitrarily small templates with high accuracy[38],[39]. Our results indicate that observers did not have access to such accurate templates and may have been uncertain about grating spatial frequency. Signal uncertainty has been studied extensively in psychophysical detection tasks[19],[40] but not in the context of neural population decoding[41]. Our model differs from traditional psychophysical models of early visual encoding of gratings embedded in external noise[42], as these models typically assume that external noise only affects the variability of sensory responses without changing the average response( see supporting text S4). Physiological evidence, however, suggests that response variability is proportional to response mean, even in the presence of early additive noise[43]. Furthermore, in our discrimination experiment, changes in sensory variability alone may affect the slope of the psychometric functions but cannot account for systematic shifts in their position[36]. Moreover, similar physiologically inspired population code models have been successfully used to relate single-cell response characteristics to human psychophysical grating detectability and discriminability[29],[44]. Various studies have measured psychophysical two-alternative detection and discrimination performance while simultaneously determining the amount of sensory information encoded by early visual brain areas. A common finding, consistent with our results, is that simple decoding schemes, while straightforward to implement and achieving near-optimal performance, consistently overestimate empirical performance[8]–[11]. An important question that remains to be answered is how these results can be reconciled with studies reporting near-optimal population decoding and precision pooling in two-alternative discrimination tasks. The answer may lie in the complexity and predictability of stimuli used in different tasks. For instance, Purushotaman and Bradley[7] report precision pooling in a fine orientation discrimination task using highly-coherent and thus highly-predictable random dot stimuli. Shadlen et al.[11] and Cohen and Newsome[9], reporting a lack of precision pooling, used coarse discrimination tasks in which the average coherence of the random dot stimuli was considerably lower. We also used highly-stochastic broadband stimuli in our experiments, which might have prevented the formation of small-band signal templates. Perceptual biases are usually interpreted as a hallmark of optimal statistical inference[36]. Here, we developed a novel paradigm to obtain a set of findings that challenge this view. Although we focused on grating detection and discrimination, the utility of our approach is not limited to the domain of pattern vision. Future studies may investigate whether a similar bias can be found in other tasks such as fine motion orientation discrimination, often used to demonstrate optimal population decoding. A crucial question for future research will be to identify determinants that explain the large variations in sensory decoding efficiency across different stimulus domains and tasks.
An attractive view on human information processing proposes that inference problems are dealt with in a statistically optimal fashion . This hypothesis can explain aspects of perception , movement planning , cognition and decision making . In the present study , I use a new psychophysical paradigm that reveals surprisingly suboptimal perceptual decision making . Observers discriminate between two sinusoidal gratings of a different spatial frequency . Making use of visual noise , I induce an asymmetry in neural population responses to the gratings and find this asymmetry to effectively bias perceptual decision making . A simple ideal observer model , uninformed about the presence of visual noise but only considering the two grating spatial frequencies relevant to the task at hand , manages to avoid such a bias . I conclude that observers are limited in their ability to make use of prior knowledge of relevant visual features when performing this task . These results are in line with a growing number of findings suggesting that near-optimal decoders , although straightforward to implement and achieving near-maximal performance , consistently overestimate empirical performance in simple perceptual tasks .