To study the neural code for uncertainty, we capitalize on a well-studied behavioral bias called serial dependence (Cicchini et al., 2014; Fischer and Whitney, 2014; Liberman et al., 2014): when a stimulus is embedded in a sequence, human observers tend to judge it as being more similar to previously seen stimuli than it really is (but see Gibson and Radner, 1937; Chopin and Mamassian, 2012; Fritsche et al., 2017). Serial dependence is particularly well suited to the issue at hand because it appears to reflect a statistically advantageous sensory integration strategy (Cicchini et al., 2014; Fischer and Whitney, 2014). That is, considering that the natural environment is largely stable across time (Dong and Atick, 1995), the statistically ideal observer integrates past and present sensory inputs, weighting each by its associated uncertainty. This integration process not only results in more accurate behavior, but also biases behavioral estimates toward previously seen stimuli. Critically, for the ideal observer, the magnitude of the biasing effect depends on the degree of sensory uncertainty. This, then, yields a straightforward prediction that we leverage in the present study: if the decoded probability distributions reflect the uncertainty that is used in decisions (as hypothesized by probabilistic theories of neural coding), then decoded uncertainty should be directly linked to the magnitude of the serial dependence bias observed in human behavior.
To test for serial dependence in behavior, we compared the orientation reported on the current trial with that of the preceding trial. This comparison revealed that behavioral estimates were biased toward the orientation of the previous stimulus (cluster-based permutation test: p = 0.017; Fig. 6a,b), as predicted by the naturalistic observer model and observed in previous studies (e.g., Fischer and Whitney, 2014; Fritsche et al., 2017). To further quantify the effect, the naturalistic observer model was fit to participant behavior (see Materials and Methods). The model explained substantial and significant variance, suggesting that it captured relevant aspects of human behavior (R2 = 0.86, p = 0.02; parameter estimates: psame^ = 0.64, ulow^=uhigh^ = 4.4, width (SD) and kurtosis of central peak in transition model: 16.9 and 2.6, respectively). These results were similar when serial dependence biases were computed with respect to the reported, rather than the presented, orientation on the preceding trial, with a reliable bias over the same range of orientation differences (cluster-based permutation test: p = 0.002) that was well captured by the naturalistic observer model (R2 = 0.82, permutation test: p = 0.03). This suggests that human observers capitalize on the stability of the natural environment, by integrating current with previous sensory observations.
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To test the degree to which knowledge of natural temporal statistics is necessary to capture the behavioral effect, we next compared human behavior against an observer model that operated under the naive assumption that consecutive sensory observations always arise from a common source. Given this assumption, the optimal integration strategy is to simply average uncertainty-weighted sensory observations over time, with no regard to their orientation difference (as implemented by the temporally misinformed observer model). Human observers appear to compute such linear averages in many other sensory integration contexts (Ernst and Banks, 2002; Knill and Saunders, 2003; Alais and Burr, 2004). Interestingly, the temporally misinformed observer model failed to appropriately capture the shape of the serial dependence curve (R2 = 0.02, p = 0.41; Fig. 6b): while this model predicts a stronger bias the larger is the orientation difference between current and previous observations, serial dependence effects in participant behavior reached a maximum at relatively small orientation differences, a pattern that was well captured by the naturalistic observer model (see above). This suggests that human observers do not merely average sensory observations, but rather use an internal model of natural temporal statistics to determine how successive sensory inputs are best combined.
Earlier work on the cortical code for uncertainty (van Bergen et al., 2015) relied on a poorly understood behavioral bias with ill-defined links to uncertainty, leaving room for alternative explanations. This earlier work focused on a repulsive bias away from the cardinal axes; however, it is currently unclear how this cardinal repulsion bias might benefit the observer as an inference or decision strategy. In contrast, the serial dependence effect studied here better lends itself for an explanation based on normative principles, given the availability of real-world videos to characterize the temporal statistics of the natural environment. The here-discussed model implements a Bayesian recursive estimation strategy, whereby sensory estimates are continuously updated based on both knowledge of natural temporal orientation statistics and an uncertainty-weighted combination of current and previous observations to make the best possible decisions. The close match between model and human behavior suggests that serial dependence in perception (Fischer and Whitney, 2014) can be understood in relation to the features of such a recursive estimation process, and provides strong support for the hypothesis that the imprecision in a cortical stimulus representation reflects Bayesian uncertainty or probability.
Our findings suggest that human observers use knowledge of natural temporal statistics to determine whether or not previous sensory observations should be integrated, or rather segregated, in the current decision. Such an ideal serial integration process predicts biases toward recently seen stimuli when the difference between successive stimuli is relatively small, much like we observed in participant behavior. Interestingly, for larger changes in orientation (orientation angles > 60), we additionally observed a tentative repulsive bias away from the previous stimulus, although this effect was only marginally significant. Such a repulsive effect at extreme stimulus differences has been reported by a few previous behavioral studies on serial dependence (Bliss et al., 2017; Fritsche et al., 2017), although not by others (Fischer and Whitney, 2014; St. John-Saaltink et al., 2016), and appears to reflect a different neural process that operates in parallel with the attractive bias considered here (Fischer and Whitney, 2014; Schwiedrzik et al., 2014; Fritsche et al., 2017; Kiyonaga et al., 2017). For example, whereas the attractive effect transfers across retinotopic locations, the repulsive effect is spatially specific, suggesting that it arises due to a relatively low-level process akin to sensory adaptation (Fischer and Whitney, 2014; Fritsche et al., 2017). Moreover, attractive and repulsive biases evolve in different directions during working memory maintenance (Bliss et al., 2017; Fritsche et al., 2017), and appear to map onto distinct cortical networks (Schwiedrzik et al., 2014). While the current study focuses on attractive effects in behavior, the model does not preclude any additional influences on serial decisions, which may, for instance, work toward suppressing redundant information or detecting change in the environment (Schwiedrzik et al., 2014). It will be interesting for future research to disentangle this interplay between positive and negative serial dependencies in perceptual decisions.
Our work is related to previous studies on predictions in perception. Several studies examined the behavioral and neural correlates of temporally constant perceptual priors (or expectations) in speed, direction of motion, or orientation perception (Weiss et al., 2002; Stocker and Simoncelli, 2006; Girshick et al., 2011; Kok et al., 2013; Vintch and Gardner, 2014). Our work differs in that we focus on the temporal predictability of sensory inputs from one moment to the next. Others have suggested that serial dependence effects in perception might reflect an advantageous sensory integration strategy used by the brain to improve behavior (Cicchini et al., 2014, 2017, 2018; Fischer and Whitney, 2014). Very few of these studies, however, have cast this notion in an explicit normative framework. One notable exception (Cicchini et al., 2014) proposed a Kalman filter-like model that based its predictions on not only previous sensory inputs, but also their associated uncertainty. We extend this work by incorporating an explicit model of real-world temporal statistics in perceptual predictions, and use the framework to investigate how uncertainty is represented in visual cortex. Our findings indicate that human observers temporally combine sensory inputs in a statistically advantageous fashion by relying on the precision of internal stimulus knowledge. More fundamentally, our results advance understanding of how the nervous system represents uncertainty by showing that the fidelity of a cortical stimulus representation is directly linked to the uncertainty that observers appear to use in their decisions.
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