Authors: Caroline Bévalot, Florent Meyniel
Categories: Article, Computational models, Human behaviour
Source: Communications Psychology
The brain constantly uses prior knowledge of the statistics of its environment to shape perception. These statistics are often implicit (not directly observable) and learned incrementally from observation, but they can also be explicitly communicated to the observer, especially in humans. Here, we show that priors are used differently in human perceptual inference depending on whether they are explicit or implicit in the environment. Bayesian modeling of learning and perception revealed that the weight of the sensory likelihood in perceptual decisions was highly correlated across participants between tasks with implicit and explicit priors, and slightly stronger in the implicit task. By contrast, the weight of priors was much less correlated across tasks, and it was markedly smaller for explicit priors. The model comparison also showed that different computations underpinned perceptual decisions depending on the origin of the priors. This dissociation may resolve previously conflicting results about the appropriate use of priors in human perception.
**Subject ** Human behaviour, Computational models
The use of prior knowledge reflecting the statistics of the environment is ubiquitous in cognition. In perception, studies over more than a century^1,2^ have shown that the brain uses prior knowledge to compensate for the frequent poverty and ambiguity of the data provided by the sensory organs. These priors shape perceptions^3^, but also decisions based on the prospect of some reward^4,5^, expectations of future events^6,7^, language acquisition and processing^8,9^, and more abstract forms of reasoning^10,11^.
Humans can make more or less appropriate use of these priors when they combine them with the data immediately available to assess different hypotheses. In Bayesian inference, different hypotheses are compared by multiplying the prior probability of each hypothesis, and the probability of the data given each hypothesis (the latter quantity is term likelihood). In perception, the combination of sensory likelihood and priors controls a trade-off between information that is available locally in time and space (the sensory likelihood), and information provided by a global context (the prior)^12,13^. To illustrate, on a road they travel frequently, drivers may rely on previous encounters with wildlife (this is the global context) to identify a deer crossing when they only see a faint silhouette ahead. If the prior is too strong, drivers may have the illusion that a deer is present when it is not there; if the prior is too weak, they may fail to detect it in time when it is there. In the general population, the weight of priors is sometimes reported to be just right on average^14–17^, but also sometimes too weak^18,19^ or too strong^20,21^.
An understanding of the strikingly different weights that participants reportedly assign to priors in different studies is still lacking. One possibility is that the origin of priors may partly explain these differences^22,23^. Here, we explored a distinction between explicit priors, which are directly observable in the environment and in that sense explicitly communicated to the observer, and implicit priors, which are latent properties of the environment, i.e. not directly observable, and that must be learned based on experience^24,25^. As we aim to study how different experimental paradigms might affect the use of priors, the explicit/implicit distinction we make is a property of the environment with respect to an observer (whether a given feature of the environment is directly observable or latent, respectively) and not a property of an observer (e.g. whether they process information consciously or not). Interestingly, explicit priors are particularly common in humans^26^. To illustrate, unlike local drivers, tourists cannot use previous encounters with animals to infer the likely presence of wildlife (which is an implicit prior following our distinction), but they can be informed about it by road signs or by chatting with local drivers (which are explicit priors).
There are well-known examples in which the weight of priors is different depending on their implicit/explicit origin. In the reward-based decision-making literature, this difference is known as the “experience-description gap”^27–30^ (experience/description corresponding to the implicit/explicit distinction). The comparison of different experimental fields also provides suggestive and indirect evidence that the implicit/explicit distinction may correspond to a difference in the weight of priors. In perception and sensorimotor control, priors are often learned implicitly during the course of a task^14,31–33^ or during development and evolution^15,34^; in this case, the use of priors often seems appropriate. By contrast, the format of information is often purely explicit in reasoning tasks, and in this case, the use of priors is often reported to be more inadequate^10,19,35^.
Here, we tested within the same field, namely visual perception, whether decisions are influenced differently by priors depending on their implicit/explicit origin. Previous studies in perception have yielded conflicting results when either implicit or explicit priors were used (see review in Ref. ^22^). These conflicts could be due to the implicit/explicit origin of priors, but the evidence remains inconclusive because this difference has been confounded by different tasks and participants across studies. We propose to help resolve these conflicts by characterizing the use of explicit and implicit priors within the same perceptual decision-making task and group of participants.
To anticipate our results, we found differences in perceptual decisions between explicit and implicit priors. In principle, such differences can arise from different uses of the same prior value, or from a different prior value itself. Unlike explicit priors, implicit priors are, by definition, not directly observable by participants and the experimenter. The experimenter might infer that participants weigh explicit and implicit priors differently, whereas in fact the weight is the same, and the value of the participant’s implicit prior differs from the experimenter’s expectation^22^. Therefore, we set out to disentangle the weight of implicit priors at the perceptual decision stage from their learning. To this end, we modeled both learning and decision as Bayesian inference^13^, and we used this overarching framework to compare the weights of implicit and explicit priors in perceptual decisions.
No preregistration was conducted for the study.
The study was approved by the local Ethics Committee (CER Paris Saclay, n°222) and participants gave their informed written consent before participating. Participants were compensated for their time. 279 participants (136 female and 143 male) aged between 19 and 52 (mean = 31; SD = 8) were recruited online and (Prolific.co) and 277 completed the two tasks. Data on sex relied on self-report of sex assigned at birth excluded participants based on catch trials presenting strong and congruent sensory evidence and prior values (both with p(house)>0.85 or p(face)>0.85). Participants whose proportion of aberrant answers on catch trials exceeded 2 standard deviations of the group-mean were excluded, as they indicate clear non-compliance with the task. The final sample size was 277-55 = 222 participants.
The tasks were run on Gorilla^TM^. The experiment was composed of two tasks (with explicit and then implicit priors). They contained respectively 300 trials and around 600 trials (mean = 597, SD = 15; variability arises from sampling the length of each stable period, see below). Each task was divided into three parts separated by self-paced breaks.
Stimuli were noisy, gray-scaled, morphed images of faces and houses. Noise was first added on images with the GNU image. Morphed images were created in the Fourier space, by computing a weighted average of the phase values of each pair of face and house images, and using the mean amplitudes of all images (all images therefore have the same frequency spectrum). The level of perceptual evidence in favor of the house/face category was estimated empirically for each image as the proportion of house/face responses in a categorization task performed by a group of 47 typical human observers who did not participate in the main experiment, see Supplementary Methods.
Each trial of the main experiment consisted in the categorization of an image presented for 150 ms. Participants reported their responses on a keyboard with the keys ‘e’ and ‘p’ for face and house (counterbalanced across participants), within a response window of 2000 ms. In the explicit task, each image was preceded by a cue consisting of a set of pictograms indicating the prior probability of the house/face category, presented for 1500 ms. In the implicit task, the latent prior value was stable in periods of 40 trials (±4) separated by unsignaled change point. The possible values of this prior probability of seeing a house were 0.1, 0.3, 0.5, 0.7 and 0.09. In both tasks and on each trial, the latent category was sampled according to its prior probability, and an image corresponding to this category was sampled pseudo-randomly. To make the detection of a change point easier in the implicit task, three images with strong likelihood (p(house)>0.85 or <0.15) were presented among the first four images after each change point. In the task with explicit priors, participants were prompted to report the prior value corresponding to each pictogram at the end of the task on a quasi-continuous rating scale. In the task with implicit priors, participants were periodically (every 14 trials) asked to report the current (implicit) prior value. In supplementary information, we provide the instruction slides containing the cover story that we used to gamify the task and make it intuitive.
Both tasks are to infer, on each trial k, whether the latent category ck is a house (denoted H) or a face (F) based on the noisy image Ik and some prior about the category. We focus first on the explicit task, in which the prior value does not depend on previous images, but only on the cue. Formally, this inference amounts to estimating the posterior probability p(ck=H∣Ik), which is done optimally with Bayes
where pck=H is the prior probability of the latent category being a house on trial k, which we note θk for brevity below (note that pck=F=1−θk); and p(Ik∣c=H) is the sensory likelihood about the house category based on image Ik only. We introduce the notation xk=p(Ik∣ck=H)p(Ik∣ck=H)+p(Ik∣ck=F) for the normalized sensory likelihood, and rewrite Equation (1) more concisely
The equation is even simpler when using the log-odd transformation ℓ(x)=logx1−x:
The (normalized) sensory evidence xk corresponding to each image was estimated empirically in an independent group of participants (see Supplementary Methods).
The prior θk was equal to its explicit value in the explicit task. To analyze the implicit task, we used in different analyses either its generative value or its value learned based on previous images by the BAYES-OPTIMAL model or the BAYES-FIT-ALL model.
The BAYES-OPTIMAL observer learns the prior θ by updating optimally its posterior distribution after every image in the sequence (it starts with a uniform distribution before the first image). The generative process of the sequence has an interesting property (known as the Markov property): if the previous prior value θk−1 is given, then the previous observations I1,...,Ik−1(denoted I1:k−1 below) are not informative about the current prior value θk. This is because here, θk will be equal to θk−1 if no change point occurs (which happens with prior probability ν, called volatility) and different otherwise; and this potential change does not depend on I1:k−1. This Markov property makes it possible to cast the updating process as the forward pass of a hidden Markov chain^6,24^, resulting in the following iterative equation for learning the prior θ:
where pIk∣θk is the likelihood of the current image given some prior value θk; which is obtained by marginalizing over the unknown latent
We computed the integral in Equation 4 numerically by discretization on a grid. Note that Equation 4 returns the inferred prior value after having observed Ik. In Equation 2, the prior that is used to infer the category of image Ik is the prior estimated before seeing Ik; it is obtained by marginalizing over the values of θk−1 given the previous observations I1:k−1:
where E denotes the expectation and θ0 is the distribution from which new values of θ are sampled in case a change point occurs.
This model differs from the BAYES-OPTIMAL with 6 free parameters that are fit to the choices of each participant. At the learning stage (Equation 4), the volatility parameter is a free parameter because the value assumed by participants may differ from the generative value. This BAYES-FIT-ALL model also allows for distortions of the likelihood function pIk∣θk that can exacerbate it, dampen it, or bias it. We considered a distortion that is affine in log-odd^36^, hence yielding two additional free parameters. At the decision stage, the BAYES-FIT-ALL model has three free parameters because it considers participant-specific weights on the likelihood wDL and prior wDP terms in Eq. 3 and an additive bias term δD (in the BAYES-OPTIMAL model, wDP=wDL=1 and δD=0). The resulting modified Eq. 3 can be fit to each participant’s choices with logistic
This model uses the prior values θk of the BAYES-OPTIMAL model and differs in the perception the heuristic log-odd posterior (and thus, choice probability) is simply a linear combination of the prior and sensory
The free parameters of the BAYES-FIT-ALL model were fitted to the choices of each participant by minimizing the negative log-likelihood of the participant’s choices (Equation 7). We used a Nelder-Mead algorithm implemented in Scipy’s optimize module^37^, and we took the best fit after 50 random initializations of the parameter search to avoid local minima.
We checked the recoverability and the identifiability of parameters by applying the same fitting procedure to simulated participant choices with known parameters (Supplementary Fig. 1, 2).
Depending on the task and analysis, the priors could be the explicit ones, the BAYES-OPTIMAL ones or the BAYES-FIT-ALL ones. We estimated the weights of those priors (and the sensory likelihood and bias) in each participant with logistic regression (implemented in scikit-learn with the default Ridge penalty λ=1) in all cases for consistency. In the specific case of BAYES-FIT-ALL priors, those weights can also be estimated with the Nelder-Mead algorithm; parameter estimates were highly correlated with the logistic estimates.
We studied how priors were updated after a change point, in participants’ choices and in an ideal observer’s choices (simulated with the BAYES-OPTIMAL model) by computing several logistic regressions, one per trial number i relative to the change point, estimated on choices from all participants together (in order to have reliable parameter estimates). For example, the data point on trial i = 2 is the result of a logistic regression considering the choices made two trials after a change point in all participants (thus including nchange points × nparticipants trials). For each logistic regression, we used three the values of the sensory likelihood on each trial, the values of the generative prior before the change point and the values of the generative prior after the change point.
We compared models using their mean cross-validated log likelihood (cvLL) given each participant’s choices (Supplementary Fig. 3). Cross-validation penalizes models for over-fitting^38^, which is critical here since different models have different numbers of free parameters. We used a three-fold cross-validation for each task, using as folds the task sessions (i.e. sequences of images that were separated by short breaks during each task). The reported cvLL is the mean log-likelihood of choices on the left-out fold (the one not used to fit the model).
We also studied the correlation across participants in model predictive accuracy between, both within and between tasks, for the BAYES-FIT-DECISION and the HEURISTIC models separately. The correlation between tasks corresponds to the correlation (across participants) of the predictive accuracy of a given model between the two tasks. The correlation within tasks corresponds to the mean of the correlation (across participants) of the predictive accuracy of a given model between sessions of the same task. We bootstrapped these correlations and tested, for each model, whether the between-task correlation was significantly different from the within-task correlation.
Wilcoxon tests were used as data were not normally distributed.
Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.
We designed a set of two tasks to compare perceptual inference in the presence of explicit and implicit priors (depending on whether prior information is directly observable or latent in the task) (Fig. 1A). The participant’s task was identical in both categorize as house or face each noisy morphed image presented in a sequence. For each image, the likelihood of the category corresponds to the probability (for a human observer) that this image is the result of taking a picture of a house (rather than a face). This likelihood was estimated for each image in an independent task (see Methods), and pseudo-randomly changed across trials. On a given trial, the image category was sampled with probability 0.1, 0.3, 0.5, 0.7 or 0.9 to be a house, called generative prior hereafter. In the first task, priors about the category were provided explicitly before each image in the form of pictograms. Participants were instructed that the relative size of the house and face pictograms denoted the prior value (see supplementary methods - task instructions). Participants’ reports of the prior values corresponding to each pictogram tightly correlated with their true values (Supplementary Fig. 3, mean ρ = 0.76, Wilcoxon < 3 10^-35^, 95% CI = [0.71, 0.82], Cohen’s d = 1.98, t = 29.55, s.e.m = 0.03, df = 221), demonstrating a good understanding of the pictograms. In the second task, such explicit cues were not provided, but participants were instructed that the latent prior was constant in uncued blocks of trials, making it possible for them to learn the prior value (Fig. 1B). Occasional reports of the latent prior value tightly correlated with the generative values (mean ρ = 0.50, Wilcoxon < 3 10^-32^, 95% CI= [0.45, 0.54], Cohen’s d = 1.65, t = 24.59, s.e.m = 0.02, df = 221). To make sure that priors were strictly explicit in the first task and not implicitly informed by past images, the image categories (and priors) were randomly changed across trials (Fig. 1B). Therefore the key difference between the two tasks is the type of whether they are explicitly or implicitly conveyed by the task structure.
Fig. 1 Both explicit and implicit priors influence perception.A. Task: participants categorized each noisy image as face or house. The sensory likelihood conveyed by each image was measured in an independent group of participants. Priors correspond to the prior probability of the latent category (face or house) on each trial. In the explicit task, priors changed from trial-to-trial and were communicated explicitly as the relative size of pictograms presented before each image (and reminded to participants at the response stage). In the implicit task, priors were not communicated but they remained constant within uncued blocks of trials, making it possible to learn their value from the sequence of images. Participants were occasionally asked to report the prior value. B Sequence of generative prior values used in the explicit and the implicit task for an example participant. In the explicit task, the prior changes independently from trial to trial. In the implicit task, the prior is piecewise constant for 40 ± 4 trials. In both tasks, the sequence is split in three sessions separated by short breaks. C Average proportion of answers (plotted in log-odds) sorted by bins of sensory likelihood and generative prior values. Error bars correspond to 95% CIs.
To characterize computationally perceptual inference in these two tasks, we used a Bayesian observer model (Fig. 2A). At the decision stage, Bayesian inference prescribes that the posterior probability of the latent category given the image should be the product of the prior and the likelihood normalized by the image probability. This relationship is advantageously simpler when expressed in log-odds: the posterior log-odds is the sum of the prior log-odds and likelihood log-odds (see Methods, Eq. 3). Participant responses showed clear effects of the generative priors and the sensory likelihood in both tasks (Fig. 1C). To quantify those effects, we estimated a logistic regression of each participant’s choices using the log-odds of generative priors and of sensory likelihood as predictors (as in Bayesian inference). The prior and sensory likelihood both influenced participants’ choices significantly (in the explicit task, mean weight=0.81, Wilcoxon <7 10^-38^, Cohen’s d = 0.97, 95% CI = [0.68, 0.93], s.e.m.=0.06, t = 14.51; mean weight=0.67, Wilcoxon<7 10^-38^, Cohen’s d = 2.00, 95% CI = [0.62, 0.72], s.e.m.=0.02, t = 29.85; in the implicit task, mean weight = 0.43, Wilcoxon <7 10^-38^, Cohen’s d = 2.02, 95% CI = [0.39, 0.46], s.e.m. = 0.01, t = 30.08; mean weight=0.81, Wilcoxon <4 10^-38^, Cohen’s d = 2.32, 95% CI = [0.76, 0.86], s.e.m.=0.02, t = 34.53; tests against 0, df = 221).
Fig. 2 Bayesian modeling of learning and choice.A Schematic of the information flow in the Bayesian model representing the free parameters for learning and decision-making. Choices follow probabilistically a combination of the prior and sensory likelihood (with a bias δ
D, and weighting factors wDPand wDL, respectively). The learned prior value θ is updated based on the sensory likelihood (with a bias δL, and weighting factor wLL) by assuming a volatility level (i.e. change point probability) ν. B List of models and their free parameters. C Logistic regression of the weights of the generative priors and sensory likelihood onto choices, locked onto change points in the implicit task, in participants and in an ideal observer (choices simulated with the BAYES-OPTIMAL model). Learning results in a change in the weights of given to generative priors before and after the change point, as the model’s prior and the participants’ prior progressively align with the new generative prior. Note that even an ideal observer needs several trials to learn the new prior value after a change point. Error bars correspond to 95% CI.
Data analysis based on generative prior values is relevant when they are communicated explicitly, but questionable when they remain implicit. To illustrate, it is impossible to know the new generative prior value when it has just changed in the implicit task. Therefore, a model for learning the prior based on previous images in the implicit task would be valuable to compare the two tasks. Bayesian inference can again be used to this end, by inverting the generative process of the sequence of images (see Methods). Such inference (corresponding to the BAYES-OPTIMAL model hereafter) defines a benchmark for the learning of priors, and for the use of prior and likelihood in the perception decision. The BAYES-OPTIMAL model illustrates that generative prior values can only provide a limited account of behavior in the implicit task. A trial-by-trial logistic regression analysis locked on change points in generative prior values (with the log-odds of the previous and new generative prior and likelihood as predictors) showed that simulated choices of the BAYES-OPTIMAL model are not influenced by the new generative prior value immediately after a change point. Instead, the effect of the new generative prior gradually builds up as the learned prior is being updated. Those dynamics are a signature of prior learning, and they are clearly visible in participants too (Fig. 2C; see also Supplementary Fig. 4).
Human participants may depart from the BAYES-OPTIMAL model in different ways (Fig. 2A, B). At the perceptual decision stage, they may over or underweight the prior and the sensory likelihood or have responses biases. Figure 1C already reveals such differences. At the learning stage, participants may assume that the generative priors change more or less often than they actually do (Nassar et al., 2012), or have an exacerbated, dampened or biased use of the sensory likelihood. We designed a parameterized version of the Bayesian observer (the BAYES-FIT-ALL model) to characterize those departures from the BAYES-OPTIMAL model. We verified the recoverability of parameter estimates (see Supplementary Fig. 1) and the identifiability of these two models (Supplementary Fig. 5) and fitted the model to the choices of each participant separately in the two tasks (see Methods; note that in the explicit task, both models use the generative priors that are communicated explicitly). We used the mean cross-validated log likelihood of choices (cvLL) as a predictive accuracy metric to compare models with different degrees of freedom (Supplementary Fig. 6). The (parameter-free) BAYES-OPTIMAL model captured participants’ behavior better than chance cvLLchance = log(0.5) = −0.69) in the task with explicit priors (cvLL = −0.49, difference from Wilcoxon<5 10^-28^, Cohen’s d = 1.12, 95% CI = [0.15, 0.20], s.e.m = 0.01, t = 16.63, df = 221) and in the task with implicit priors (cvLL = −0.47, difference from Wilcoxon<1 10^-31^, Cohen’s d = 1.33, 95% CI = [0.17, 0.22], s.e.m = 0.01, t = 19.80, df = 221). As expected based on previous studies (Wilson & Collins, 2019), by taking into account participant-specific aspects of perceptual inference the BAYES-FIT-ALL model better accounted for the participants’ choices in the explicit task (cvLL = −0.43, difference from BAYES-OPTIMAL: Wilcoxon<2 10^-23^, Cohen’s d = 0.69, 95% CI = [0.06, 0.10], s.e.m = 0.01, t = 10.28, df = 221) and in the implicit task (cvLL = −0.42, difference from BAYES-OPTIMAL: Wilcoxon<9 10^-31^, Cohen’s d = 0.85, 95% CI = [0.05, 0.07], s.e.m = 0.01, t = 12.67, df = 221, see also Supplementary Fig. 4 compared to Fig. 2C).
Some deviations from the BAYES-OPTIMAL model may be more critical than others to account for the participant’s choices. We tested simpler versions of the BAYES-FIT-ALL model, fixing some learning parameters to their optimal values and fitting the perceptual decision parameters. The model with optimal learning parameters (thereafter BAYES-FIT-DECISION) performed slightly better than models that also included free parameters at the learning stage (Supplementary Fig. 6), indicating that deviations in the perceptual decision parameters are more critical than deviations in the learning parameters. To be conservative, in the main text below we report results based on the BAYES-FIT-ALL model that estimates each participant’s perceptual decision parameters while taking into account their specific learning parameters, and we report similar conclusions with alternative analyses in Supplementary Fig. 7.
We compared choices in the two tasks using logistic regressions with the (log-odds of the) posterior probability about the image category computed by the BAYES-FIT-ALL model (thereby taking into account participant-specific parameters in both perceptual decision and learning). Participants’ choices followed this posterior more when priors were implicit than when they were explicit (Fig. 3A, mean inter-task difference = −0.23, Wilcoxon p < 1 10^-23^, Cohen’s d = −0.84, 95% CI = [−0.28, −0.19], s.e.m.=0.02, tvalue = −12.46, df=221). This difference could be driven by choices being more influenced by the sensory likelihood or priors (or both) in the case of implicit priors. Another logistic regression model including both the (log-odds of the) likelihood and the prior (instead of the posterior) revealed that participants’s choices were more influenced by both the prior (mean inter-task difference = −0.42, Wilcoxon p < 3 10^-09^, Cohen’s d = −0.33, 95% CI = [−0.61, −0.23], s.e.m.=0.08, tvalue = −4.97, df=221) and the likelihood (mean inter-task difference = −0.22, Wilcoxon p < 6 10^-23^, Cohen’s d = −0.80, 95% CI = [−0.26, −0.18], s.e.m. = 0.02, tvalue = −11.91, df = 221) when priors are implicit (also see Supplementary Fig. 8). The difference was slightly more pronounced for the prior than the likelihood (mean difference of difference=0.20, Wilcoxon p = 0.003, Cohen’s d = 0.14, 95% CI = [−0.01, 0.41], s.e.m. = 0.09, t = 2.13, df = 221, also see Supplementary Fig. 8). Interestingly, the standard error of the mean of the paired difference was 4 times larger for the prior than the likelihood, indicating that the weight of the likelihood was more conserved across tasks than the weight of the prior. To further characterize this dissociation, we compared the correlations of weights across participants between the two tasks and found a strong correlation for the likelihood (spearman rho = 0.72, p < 8 10^-37^, 95% CI = [0.65, 0.78], slope = 0.75, t = 15.40, df = 220 ; Fig. 3E) and only a weak correlation for the prior (spearman rho = 0.14, p = 0.03, 95% CI = [0.01, 0.27], slope = 0.09, t = 2.13, df = 220 ; Fig. 3D; significance of the p < 0.0001 bootstrap; in a supplementary analysis we rule out that the weak correlation in the case of priors could arise from noise in parameter estimates, see Supplementary Fig. 9).
Fig. 3 Dissociation between contexts in the use of priors, rather likelihood.A–C Between-task comparison of the weights of the BAYES-FIT-ALL posterior probability of the category (A), the prior (B), and the sensory likelihood (C) onto participants’ choices (one line is one participant). Building on Equation (7) in the Methods, we ran a logistic regression to compute the weights given to priors (B) and sensory likelihood (C). We also ran a separate logistic regression to compute the weight given to posteriors (A). Note that the task-difference is larger for priors than for the sensory likelihood. Weights were estimated in a logistic regression with the log-odds predictor values, so that the optimal weight is 1 in A–C (see Eq. 3 in Methods). Small correlation of prior weights (D) and strong correlation of sensory likelihood weights (E) between tasks (one dot is one participant, the black line is the identity) **p < 0.005 ; ***p < 0.0005.
The fact that the weights of the prior are much less correlated between tasks than the weights of the likelihood was robust across the same dissociation was found when using the generative priors, and the optimally-estimated priors (BAYES-OPTIMAL), instead of the priors based on participant-specific learning parameters (BAYES-FIT-ALL), see Supplementary Fig. 7.
However, a concern the dissociation could be due to the inability of these models to capture the priors used by participants in the implicit task. To rule out this possibility, we asked participants, occasionally during the task, to report the value of the current prior on a scale (see Methods). Their reports corresponded remarkably well to the BAYES-FIT-ALL priors at the participant-level (the correlation was significant at p < 0.05 in 90% of participants) and the group-level (Fig. 4A; mean ρ = 0.53, Wilcoxon p < 8 10^-31^, Cohen’s d = 1.39, 95% CI = [0.47, 0.59], s.e.m.=0.03, t = 20.67, df = 220).
Fig. 4 Similar dissociation with a model-free estimation of priors.A Prior values reported by participants correlated tightly with the implicit prior values estimated by the BAYES-FIT-ALL model (s.e.m. shown). B Logistic regression weights of priors on the choices that immediately followed each report (one line is one participant). Note that the BAYES-FIT-ALL prior better explains the participant’s choices. C Absence of correlation (p > 0.3) between the weights of reported priors in the implicit task and the weights of priors in the explicit task (one dot is one participant). ***p < 0.0005
In fact, the BAYES-FIT-ALL prior proved superior to the reported prior to predict the participants’ choice when tested on the first trial after the report (Fig. 4B, mean difference = −0.15, Wilcoxon p < 9 10^−9^, Cohen’s d = −0.33, 95% CI = [−0.23, −0.08], s.e.m. = 0.03, t = −4.96, df = 221). The weight of the reported prior in the case of implicit task was also largely uncorrelated to the weight of the prior in the case of explicit task (Fig. 4C, spearman correlation rho = 0.07, p = 0.30, 95% CI = [−0.06, 0.20], slope=0.04, t = 1.04, df = 220) replicating the result obtained with model-based priors.
So far, we have characterized, within the same model, a dissociation in the weights of priors depending on their type. We now explore another potential facet of this the use of different computations with explicit and implicit priors. The lower weights of the posterior probability of the image category computed with the Bayesian model and the lower weights of the components of this posterior (prior and likelihood) when priors are explicit could suggest a reduced adherence to Bayesian principles in this case. To test this hypothesis, we considered a HEURISTIC a model that combined linearly the prior and likelihood (instead of the non-linear Bayesian combination, which is linear only in log-odds we verified model identifiability, see Supplementary Fig. 10). We compared this heuristic model to the BAYES-FIT-DECISION both models use the BAYES-OPTIMAL prior and differ only in the way this prior is combined with the sensory likelihood.
In the case of implicit priors, the best model was the BAYES-FIT-DECISION (Fig. 5A, difference in cvLL=0.00041, Wilcoxon p = 0.25, Cohen’s d = 0.06, 95% CI = [−0.00061, 0.00142], s.e.m. = 0.00045, t = 0.91, df = 221). In the case of explicit priors, the best model was the HEURISTIC one (difference in cvLL = −0.0024, Wilcoxon p = 0.00045, Cohen’s d = −0.12, 95% CI = [−0.0054, 0.0006], s.e.m. = 0.0013, t = -1.82, df = 221), indicating that different computations underlie perceptual inference in the two tasks.
Fig. 5 Different computations in perceptual inference depending on the prior type.A Predictive accuracy of the BAYES-FIT-DECISION model, relative to the heuristic model (median of participants’ paired difference; predictive accuracy is defined as mean cross-validated log-likelihood of choices), error bars correspond to 95% CI. See Figure S4 for the model recovery analysis. B Correlation of predictive accuracy was estimated within tasks (between sessions) and between tasks for each model (BAYES-FIT-DECISION and HEURISTIC). Bars and error bars indicate the mean and 95 CI of the bootstrapped estimation. C Correlation of the relative predictive accuracy across tasks (BAYES-FIT-DECISION minus HEURISTIC; one dot is one participant). **p < 0.005, ***p < 0.0005
In order to further test whether computations are different depending on the prior type, we estimated the correlation across participants in model predictive accuracy, within each task and between the two tasks (see Methods). If computations are participant-specific and independent of the prior type, we expect similar between- and within-task correlations; by contrast, if computations depend on the prior type, we expect a larger correlation within tasks than between tasks. Within-task and between-task correlations were markedly different, for the BAYES-FIT-DECISION model (between-task correlation ρ = 0.32, p < 1 10^-6^, 95% CI of the bootstrapped mean correlation = [0.18, 0.46], slope = 0.20, t = 5.03 and within-task correlation (mean across pairs of sessions) ρ = 0.59, p < 4 10^-13^ in each pair of sessions, 95% CI of the bootstrapped mean correlation = [0.53, 0.64], slope = 0.47, t = 11.14 and 95% CI of the bootstrapped difference in mean correlation between or within-task = [0.12, 0.42], df = 220 for correlations). The same was true for the HEURISTIC model (between-task ρ = 0.32, p < 2 10^-6^, 95% CI of the bootstrapped mean correlation = [0.17, 0.45], slope = 0.20, t = 4.92 and within-task (mean across pairs of sessions) ρ = 0.59, p < 4 10^-13^ in each pair of sessions, 95% CI of the bootstrapped mean correlation = [0.53, 0.65], slope = 0.49, t = 11.25; and 95% CI of the bootstrapped difference in mean correlation between or within-task = [0.13, 0.43],df = 220 for correlations), see Fig. 5B. Note that smaller between-task correlations could be partly driven by some participants being better in one task than the other (which would be reflected for each model by a corresponding difference in cvLL between tasks and not, or less so, within-tasks). We thus tested whether the paired difference in cvLL between models (which reflects the preference for a type of computation) was correlated between tasks. We found only a small correlation (spearman ρ = 0.126, p = 0.060, df = 220, Fig. 5C).
Together these results indicate that different computations underpin perceptual inference in the explicit and implicit tasks.
We used the framework of Bayesian inference to compare the use of explicit and implicit priors in perceptual decision-making. We found three main differences. First, the weights of explicit priors were smaller (and further from the optimal weight) than those of implicit priors. Second, the weights of priors were hardly correlated across tasks and individuals. In contrast, likelihood weights were more similar on average and highly correlated across tasks. Third, perceptual decisions were supported by different the prior-likelihood combination was closer to Bayesian integration when priors were implicit, and closer to a simpler heuristic when they were explicit.
Our finding that perceptual decisions are more optimal when priors are implicit (rather than explicit) is consistent with previous findings. Studies in which participants are presented with explicit information have often emphasized that their behavior deviates from optimality (e.g. probability judgments or value-based decisions^19,20,39,40^. In contrast, behavior has been reported to be close to the optimum when information is more implicit and dominated by low-level processing (e.g., in perception^12,15,17,34^ and sensorimotor control^32,41^. However, comparisons with the optimum in these studies remain mostly qualitative, and their conclusions may reflect the perspective of the authors. Quantifying this optimality would be useful to compare different studies using the same metric. Unfortunately, direct and quantitative comparisons of decisions based on implicit and explicit priors are rare^42,43^.
Our estimate of prior and likelihood weights has the advantage of being quantitative. It is also absolute rather than simply relative. Absolute quantification is possible here because our task involves categorical choices (see Eq. 3). It is not possible in tasks involving continuous percepts and Gaussian distributions (a common experimental choice). The mean percept resulting from a Gaussian prior and a Gaussian likelihood is in principle the average of their means weighted by their relative precisions. Since the weighting is relative in this case, the effects of a weaker (i.e., more imprecise) prior and a stronger (i.e., more precise) likelihood are indistinguishable^44^. Note that when categorical percepts are used (which allows estimation of absolute weights), sometimes only the relative prior-likelihood weight is estimated due to specific modeling choices^45,46^.
Differences between tasks can be quantified within the same model, but computations may in fact differ profoundly between tasks. The difference in computations that we found for perceptual decisions based on implicit and explicit priors is reminiscent of a similar difference reported for value-based decisions^30^. Specifically, we found that the prior-likelihood integration was more Bayesian with implicit priors. This conclusion is based on the contrast between the Bayesian computation and a linear approximation. We emphasize that this comparison is relative; quantifying the extent to which a computation is Bayesian would require more model comparisons^47,48^. For example, models of circular prior-likelihood integration have been proposed by others^35,42^.
Our characterization of the differences between the use of explicit and implicit priors is at the computational level. It raises interesting possibilities in terms of their neurobiological implementation. For example, the difference in their use could arise from the fact that the neural representations of explicit and implicit priors are different. In value-based decision-making, the neural correlates of explicit and implicit prior values were measured with functional MRI and found to be indeed anatomically distinct^27^.
Another, non-mutually exclusive possibility is that the prior-likelihood integration recruits different brain circuits depending on the format of the priors. When priors are implicit, this integration could be handled by the interaction of statistical learning, and perceptual decision-making systems^49,50^. Such integration may operate beyond the scope of consciousness, as often reported in statistical learning^51^. In contrast, when priors are explicit, a symbolic or semantic understanding is required. Therefore, the integration of explicit priors with likelihood may recruit sensory areas, associative areas such as the parietal cortex, and hubs such as the temporal cortex or the prefrontal cortex associated with semantic knowledge or conscious access^52,53^. Thus, prior-likelihood integration may rely on different levels of processing when priors are implicit or explicit, recruiting lower or higher levels of the cortical hierarchy, respectively. Anecdotally, but in line with this explanation (and the assumption that higher-level processing is more effortful^54^), 20 pilot participants in the laboratory reported that the explicit task was harder. Such a difference in processing levels could explain the more Bayesian integration observed with implicit priors, as lower-level processes have been hypothesized to be more Bayesian^55–57^. The processing of explicit and implicit priors at different levels of the brain hierarchy and the more approximate computations subtending the use of explicit priors compared to implicit prior could explain why the lower weight of explicit priors in participants’ choices compared to implicit priors.
Another explanation of this difference, perhaps rooted in evolution^58^, is the social dimension of explicit priors. Contrary to implicit priors which must be learned from the environment, explicit priors are often communicated by another person. Other processes such as trust, theory of mind, judgment of expertise might intervene in the decision function^26,59^.
Our results contribute to the understanding of the basic principles of perceptual decision-making in the general population. They are also relevant to the study of disorders. Perception has been extensively studied in psychiatry because the representation of priors and likelihoods, and their integration, have been hypothesized to be altered, particularly in autism^60^ and schizophrenia^61^. Empirical evidence remains mixed. In the case of autism, it has been suggested that the nature of prior (implicit/explicit) should be taken into account, as alterations appear to be more pronounced for implicit than for explicit priors^22^. In the case of schizophrenia, experiments have used priors that are either explicit^35,62,63^ or implicit^33,64,65^. Evidence for altered prior-likelihood combination is also mixed in schizophrenia^66^. For example, the weight of priors in the beads task has been reported to be abnormally strong in patients when priors are explicit^63^ and abnormally weak when they are implicit^64^. Our results in the general population showed that the weights of explicit and implicit priors are essentially unrelated, so it is expected that the alteration of the prior weights observed in one group of patients may not generalize across prior types.
We now turn to some of the limitations and open questions of our study. One weakness is that the order of the tasks was fixed across participants, always starting with explicit priors. However, the order of the task seems unlikely to have influenced the main results. The larger prior weight in the second task could in principle be due to a gradual improvement with task exposure, but the evolution of the effects during the task actually rules out this possibility (Supplementary Fig. 2). Furthermore, the task order cannot explain the negligible correlation of prior weights between tasks. A second limitation is that better communication of explicit priors could have led to larger prior weights in perceptual decisions. To mitigate this concern, we used ratings to verify that participants correctly understood the pictograms we used to communicate priors. However, this may not be sufficient, as the format of probabilistic information is known to influence the success of its use, particularly whether it adheres to Bayesian principles in reasoning tasks^67^. Third, our results leave open the stage at which implicit and explicit priors shape perceptual they may bias the incoming sensory evidence^68^ or the motor response^69^. This issue should be addressed in future studies. A fourth limitation is that our tasks do not enable us to study the extent to which participants were aware of the prior value during their decisions. Our goal was to understand whether the use of priors was comparable depending on their origins in the environment (which we implemented in two different tasks) rather than exploring the conscious/unconscious processing of priors (See Supplementary Fig. 11). We acknowledge that such a difference in prior processing could be a psychological and mechanistic explanation for the different use of priors we found in the two tasks and that it should be investigated in future research.
Our results suggest that explicitly or implicitly acquired priors are used differently in perceptual decisions. As a consequence, inferences made with explicit or implicit priors should not be grouped indiscriminately, and the relevant literature should be reviewed with this distinction in mind.
This work has been funded by the “Fondation pour la Recherche Médicale” and the Inserm. F.M. is supported by the European Research Council (ERC grant #94105). The funders had no role in study design, data collection, and analysis, the decision to publish or preparation of the manuscript. We thank Thomas Mauras for sharing his stimuli.
C.B. and F.M.: design of the study, data analysis and writing. F.M.: design of computational models. C.B.: data collection.
Communications psychology thanks Tim Rohe and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editors: Eva Pool and Marike Schiffer. A peer review file is available.
The raw data are available on OSF : https://osf.io/2hp8q/.
The code to reproduce the results are 10.5281/zenodo.13740001.
The authors declare no competing interests.
Caroline Bévalot, Email: bevalot.caroline@gmail.com.
Florent Meyniel, Email: florent.meyniel@cea.fr.
The online version contains supplementary material available at 10.1038/s44271-024-00162-w.
The raw data are available on OSF : https://osf.io/2hp8q/.
The code to reproduce the results are 10.5281/zenodo.13740001.