A common computational and neural anomaly across mouse models of autism

Abstract

Computational psychiatry studies suggest that individuals with autism spectrum disorder (ASD) inflexibly update their expectations. Here we leveraged high-yield rodent psychophysics, extensive behavioral modeling and brain-wide single-cell extracellular recordings to assess whether mice with different genetic perturbations associated with ASD show this same computational anomaly, and if so, what neurophysiological features are shared across genotypes. Mice harboring mutations in Fmr1, Cntnap2 or Shank3B show a blunted update of priors during decision-making. Compared with mice that flexibly updated their priors, inflexible updating of priors was associated with a shift in the weighting of prior encoding from sensory to frontal cortices. Furthermore, frontal areas in mouse models of ASD showed more units encoding deviations from the animals’ long-run prior, and sensory responses did not differentiate between expected and unexpected observations. These findings suggest that distinct genetic instantiations of ASD may yield common neurophysiological and behavioral phenotypes.

Autism spectrum disorder (ASD) is a neurodevelopmental condition characterized by abundant heterogeneity, both at biological (for example, genetics and neurochemistry^1–4) and behavioral scales (for example, anomalies across social, communicative, perceptual and motor domains^5–7). This diversity hinders our ability to understand and develop therapeutic support for the condition.

To address the phenotypic heterogeneity, computational psychiatry^8–17 has cast ASD in terms of probabilistic inference¹⁸ and suggested that individuals within the spectrum (1) have attenuated expectations¹⁹ (2) inflexibly weight predictions relative to sensory observations²⁰ and/or (3) overestimate the volatility of their sensory environment and are thus less surprised by statistically unlikely events²¹. Each of these computational accounts suggests that the learning of context-dependent statistical regularities (that is, ‘contextual priors’²²) is different (for example, slow^23,24) in people with ASD. This convergence on a putative computational deficit in humans with ASD represents an opportunity to now account for biological heterogeneity.

We attempt to bridge the gap between computational accounts of ASD and its neurobiological and genetic instantiation. Namely, we hypothesized that if a single computation (for example, aberrant prior updating) may account for a myriad of behavioral symptoms in ASD^19–24, then the distinct genetic makeups of the condition may similarly (1) all express this computational deficit and (2) share a common underlying neurophysiological profile. We test this hypothesis across three monogenetic mouse models of ASD (Fmr1 (ref. ²⁵), Cntnap2 (ref. ²⁶) and Shank3b (ref. ²⁷)) by leveraging a standardized high-yield visual detection task requiring the use of priors²⁸, behavioral modeling of online adaptation to changes in statistical regularities^29,30, and large-scale neurophysiological recordings³¹.

Results demonstrate that all three mouse models of ASD underused adaptive statistical regularities during decision-making. Compared to wild-type mice, these animals showed a blunted update of their priors^23,24 and were not surprised by statistically unlikely events²¹. Brain-wide extracellular recordings showed that the relative weighting of prior encoding, at the unit level and population level, shifted from sensory cortex (in wild-type mice) to frontal cortex (FC; in the three mouse models of ASD). Furthermore, we observed a preponderance of units coding for deviations from the animals’ long-run prior (prior mean) and a lack of sensory-driven prediction errors in frontal cortices of the mouse models of ASD. The degree to which sensory-driven prediction errors (that is, a ‘surprise’ signal) were absent in frontal cortices correlated with computational anomalies and reflected the degree of unit- and population-level encoding of the prior. Together, these results suggest that both global and local neural imbalances engender the inflexible updating of Bayesian priors in ASD. Globally, there is a shift in prior encoding from sensory to frontal areas. Locally, within frontal areas (that is, anterior cingulate cortex (ACA) and secondary motor cortex (MOs)), there is a suppression of statistically surprising sensory observations and an outsized influence of signals coding for the prior mean.

More broadly, the results demonstrate a common computational and neural anomaly across mouse models of ASD, suggesting that distinct genetic instantiations of the condition may converge onto common behavioral and neurophysiological phenotypes.

Results

Reduced use of statistical regularities in ASD mouse models

Wild-type mice (C57BL/6J; $n=15$) and three genetic mouse models of $\text{ASD}—{Fmr\mathit{1}}^{-/y}(n=19)$, ${Cntnap\mathit{2}}^{\mathit{lacZ/+}}(n=21)$ and ${Shank\mathit{3}b}^{+/-}(n=20)$—were first trained on a prior-independent, two-alternative forced-choice visual detection task. We leveraged the standardized task and protocols from the International Brain Laboratory²⁸ (Fig. 1a). Briefly, a grating of varying contrast was presented with equal probability to the left or right of a head-fixed mouse. The animal then selected a choice (that is, left or right) by turning a steering wheel coupled to the grating location. If the mouse brought the grating to the center of its visual field, it was rewarded. Instead, if the animal moved the grating by an equivalent distance in the other direction (that is, off-screen), it was penalized by a timeout (Fig. 1b; Methods).

Fig. 1 |. Reduced usage of statistical regularities in mouse models of ASD.

a, Rendering of the standardized behavioral apparatus allowing for the study of visually guided decisions in rodents. b, Schematic representation of the task. c, Performance of control (C57BL6) and mouse models of ASD (Fmr1, green; Cntnap2, yellow and Shank3, brown) on ‘easy’ trials (that is, 50% and 100% contrast) as a function of session number. Animals were considered trained when they performed at or above 80% (black dashed line) on ‘easy’ trials (moving average over three sessions). d, Psychometric functions describing the fraction of rightward choices as a function of contrast and animal genotype. Negative contrasts denote stimuli on the left. Thin and transparent lines are individual animals, while thicker and opaque lines are averages. These psychometric curves are derived by combining all sessions after animals were considered proficient (average number of trials per animal, $n=1250.9$). e, Schematic representation illustrating the ‘biased’ version of the task. The firThe verticalst 90 trials are ‘unbiased’ in that gratings appear with equal probability on the left and right (50:50). Subsequently, blocks of varying length (range = 20–100 trials, decaying exponentially such that the hazard rate was approximately constant) show gratings predominantly on the left or right (80:20 versus 20:80, respectively, in purple and gold). f, Change in the fraction of rightward responses as a function of block (rightward–leftward, fitted curves as in d), contrast and animal genotype (average number of trials per animal, $n=5645.0$). Vertical axis ($y$) in the rightmost panel is compressed to show difference between wild-type animals (black) and mouse models of ASD (colored). IR, infrared.

Mice of all genotypes learned this task (learned/total; C57BL6—15/15, Fmr1—17/19, Cntnap2—19/21 and Shank3—18/20; ${\chi }^2$ test, $P=0.90$). Furthermore, provided that an animal became proficient at the task, it did so in an equal number of sessions (Fig. 1c; mean ± s.e.m.; C57BL—12.9 ± 2.2, Fmr1—16.8 ± 2.2, Cntnap2—13.8 ± 2.4 and Shank3—12.8 ± 1.4) regardless of genotype ($P=0.52$). At asymptotic behavior, psychometric performance on this prior-independent task was equal across genotypes (Fig. 1d; overall mean ± s.e.m.; bias, −1.97 ± 0.94; threshold, 14.6 ± 1.13; lapses, 0.06 ± 0.005; all $P>0.53$), indicating that mouse models of ASD detect visual stimuli equally well to their control counterparts.

Following proficiency on the visual detection task, we introduced a dynamic prior. Sessions started with an unbiased block of trials (50:50 probability of stimuli being on the left or right) and then alternated between gratings being more frequent on the left (right) visual field (80:20 versus 20:80 probability; Fig. 1e). The change in block (for example, from leftward to rightward) was unsignaled and thus had to be inferred from the stream of stimuli. Moreover, 0% contrast trials were rewarded according to the prior, and thus optimal performance on the task required that animals incorporate knowledge of the prior in making decisions.

To quantify the impact of this prior, we fit psychometric curves to responses during leftward- and rightward-biased blocks (equation (1) in Methods; see Extended Data Fig. 1 for example animals). Then, we subtract these curves (see ref. 28 for a similar approach). As expected, the prior was most informative when sensory evidence was weak, resulting in the largest difference between left- and right-prior blocks being at zero contrast (peak at 0.33% contrast, no difference across genotypes; $P=0.28$; Fig. 1f). Most strikingly, the impact of the prior was greater in the control animals (differences in fraction ‘rightward’ responses at contrast = 0, 0.27 ± 0.005) than in the mouse models of ASD (Fig. 1f; Fmr1—0.24 ± 0.004, Cntnap2—0.20 ± 0.003 and Shank3—0.21 ± 0.005; one-way analysis of variance (ANOVA), $P=0.05$). This same conclusion held true when we simply contrasted the fraction of ‘rightward’ choices as a function of contrast and block (Extended Data Fig. 2a; one-way ANOVA, $P<0.05$ with C57BL6 greater than all mouse models of ASD at contrasts = −12.5, 0, 6.25 and 12.5; Bonferroni-corrected). Furthermore, we confirmed that our sample of C57BL6 animals ($n=15$) used their priors to a similar extent than a much larger sample of wild-type animals performing the same task (Extended Data Fig. 2b; International Brain Laboratory (IBL) dataset, $n=137$, ANOVA, all $P>0.32$), although they had experienced a different behavioral shaping regime (Methods).

The observation that genetic mouse models of ASD underused statistical regularities in their environment was corroborated via pupillometry demonstrating a surprise signal during the presentation of statistically unlikely events (for example, high contrast on the right during a leftward block) in wild-type animals but not models of ASD (Extended Data Fig. 3).

Together, these results mimic findings (but do not directly ‘translate’ them, as different tasks were used) from the human literature. Indeed, the results demonstrate an attenuated use of priors^23,24 and the lack of a surprise signal (at least insofar as indexed via pupillometry; see refs. ^32–34 for a similar approach) during the presentation of statistically unlikely events in mouse models of ASD. This was a generalized finding, being true for all mouse models of ASD tested.

Blunted accumulation of sensory history in ASD mouse models

Next, we aimed at understanding the strategies used by different animals to update their priors and to estimate the ‘subjective’ (versus ‘objective’ or experimenter-imposed) prior used by each animal on each trial. To do so, we derived a set of models (principled and heuristic) and contrasted their performance in explaining animal behavior.

We fit a total of ten models, comprising variations (for example, assumptions over symmetry of the prior; Methods) over four broad classes.

First, we simply fit psychometric curves (Fig. 2a, top row) for each of the three blocks (50:50, 80:20 and 20:80). This effort does not postulate any particular strategy animals may have used in solving the task but serves as a benchmark in accounting for observed responses.

Fig. 2 |. Blunted accumulation of recent sensory history in mouse models of ASD.

a, Difference in cross-validated log likelihoods (that is, ‘badness’ of fit) relative to the best model (‘exp. bias’, highlighted in red). Lower is better. Description of each model in the ‘Main’. See Supplementary Fig. 2 for a different visualization of this same data, showing each individual animal. See Supplementary Fig. 3 for parameter estimates from the c.p. free run model, demonstrating that while it was a comparable fit to the exp. bias model for C57BL6 and Fmr1 animals, its resulting parameters suggest animals did not infer the presence of experimental blocks. Color scheme for genotypes follows that of Fig. 1. Error bars are ±1 s.e.m. across animals, with the smallest $n=15\text{mice}$. b, Fraction of rightward choices as a function of block (80:20 leftward in purple, 50:50 unbiased in black and 20:80 rightward in gold) for four example animals; one per genotype. Circles are data, and lines are fits from the exp. bias model. c, Example fits of the exp. bias model (lines) when plotting data as a function of trials to and since block change (in this case, from 80:20 to 20:80). As expected, behavior change is most notable for 0 contrast trials (colored). The rest of contrasts are grouped, with the color gradient (from dark to light blue) following the spectrum from strong evidence for left targets to right targets. d, Visualization of the average exponential decay (top) and $\beta$ hyper-priors (bottom) dictating the exp. bias model for wild-type (black) and mouse models of ASD (colored). The hyper-priors being taller and narrower in ASD result in a diminished change in the subjective prior with changing environmental statistics. PDF, probability density function. e, Illustration of an experimental sequence of trials; the experimentally imposed probability that the stimuli will be on the left (black step functions), what an optimal observer would be able to infer (gray) and the best estimates of subjective priors for the average control animal (top; black jagged line), as well as the average Fmr1 (top; green), Cntnap2 (middle; yellow) and Shank3 (bottom; brown) animal. f, Subjective prior before and after block changes in the wild-type (black) and mouse models of ASD (colored). Estimates are baseline-corrected averages across animals and all transitions. Error bars represent ±1 s.e.m. C.p., change point.

Second, we build a Bayesian decision-maker (Methods), but directly provide this model with the true prior probability of observing gratings on the left versus right (omniscient model; Fig. 2a, second row) or allow for a single fixed prior (fixed model; Fig. 2a, third row). These variants establish model performance when the prior remains fixed to the experimentally imposed value, or does not vary dynamically before model evaluation.

Third, we use the same decision-maker as above but also use multiple variants of a Bayesian online change-point (c.p.) detection algorithm (c.p. models^29,30; Fig. 2a, fourth to eighth rows) to estimate the prior. The algorithm is ‘online’ in that it only uses observations until the current trial and is built iteratively. These models explicitly hypothesize that animals have an understanding of the task structure. For example, there are blocks of trials wherein stimulus presentation is biased toward the left or right, or these trial sequences have a minimum and maximum run length. The exact parameters estimated may deviate from those imposed experimentally.

Finally, we built a heuristic model (exponential weighting models (exp. models); Fig. 2a, ninth and tenth rows) wherein animals do not know about block structures but track statistical regularities by computing an exponentially weighted average (favoring the most recent stimuli) of their recent sensory past. In a second variant of this exponential weighting model (Fig. 2a, tenth row—exp. bias model in red), animals also have a prior over counts (that is, ‘pseudocounts’ or ‘hyper-prior’) that may bias their weighted average and change the relative weighting between observed sensory history and observation independent a priori counts. The ‘pseudocounts’ are formally instantiated as the $\alpha$ and $\beta$ parameters of a $\beta$ distribution, where the larger their sum ($\alpha +\beta$; assuming they are approximately balanced), the narrower the hyper-prior and thus the greater its influence in estimating where the next target is likely to appear (left versus right; see Supplementary Note for further detail).

Model comparison (Fig. 2a; cross-validated log-likelihood) favored the biased exponential weighted average model (‘exp. bias model’; ANOVA, $P=1.46\times {10}^{-13}$), and this was true across all genotypes (interaction term, $P=0.88$; see Supplementary Fig. 1 for model and parameter recovery simulations). This demonstrates that we can estimate an animal’s task strategies (that is, psychometric fits did not account best for responses; see Fig. 2b for fits from the preferred model). It also suggests that the animals did keep track of the statistical regularity embedded in the sequence of grating presentations (that is, fixed model was not favored; Fig. 2c), but did so via heuristics as opposed to developing a full generative understanding of the task. Finally, it suggests that the different genotypes did not use categorically different strategies, which allows for contrasting recovered model parameters, as well as estimating ‘subjective’ priors on a trial-by-trial basis.

From the biased exponential weighted average model (exp. bias model), we may estimate a time (in fact, ‘trial’) constant over which animals accumulate evidence in estimating the probability that the following stimuli will be presented on the left (versus right). We may also estimate a ‘pseudocount’ prior, putatively biasing the count and rendering its update less dependent on observations (versus a higher-order prior). These are illustrated in Fig. 2d and show that while the trial constant was not significantly different across the wild-type and mouse models of ASD (top; one-way ANOVA, $P=0.15$; half-width ~5 trials), the hyper-priors (or ‘pseudocounts’) exerted a greater influence in all mouse models of ASD relative to the control (bottom; one-way ANOVA contrasting the sum $\alpha +\beta$ across the four genotypes; $P=0.04$). This accounts for the reduced change in choices across blocks in the mouse models of ASD (Figs. 1 and 2b,c). Furthermore, when applying these parameters to a sequence of trials, we can see that the subjective priors (even for the control animal) are far from the extremes imposed experimentally (0.2–0.8; Fig. 2e), and this effect is exacerbated in mouse models of ASD (Fig. 2f; $P<0.003$).

Large-scale neurophysiological survey across ASD models

Having established that multiple mouse models of ASD exhibited a similar computational anomaly in inflexibly updating their priors (Fig. 1) and intimated a putative computational strategy (Fig. 2), we were next interested in establishing its neural underpinning. Namely, the fact that multiple genotypes displayed the same deficit allows us to attempt distilling causal contributions to prior coding and updating, as well as its putative dysfunction in models of ASD; that is, what neural features are common across all mouse models of ASD and different from the control?

Answering this question requires a neural survey on the scale of the whole brain^35–37. In turn, we used Neuropixel probes³¹ (NP1.0, 323 insertions) to record from a total of 53,219 units across 150 brain regions (Fig. 3a; see Methods and ref. 38 for further detail; see Supplementary Fig. 4 for histology). To reliably compare neural features across genotypes, we need a population of units within a defined anatomical region for all animal types. Thus, we set a threshold of a minimum of 40 units per area and genotype (twice the criteria from ref. 36). This reduced the dataset to 39,393 units across 36 brain regions (Fig. 3b; abbreviations follow the Allen Common Coordinate Framework (CCF)³⁹).

Fig. 3 |. A large-scale neurophysiological survey across mouse models of ASD.

a, Reconstruction of probe locations for the different genotypes (C57BL6, black; Fmr1, green; Cntnap2, yellow and Shank3, brown). b, Number of units recorded per area ($y$ axis; subset shown) and genotype. Bars are filled and opaque if all genotypes had at least 40 units in that area, filled and transparent if the given genotype had 40+ units but others did not and empty if less than 40. c, Raster plot (top) and PSTH (bottom) to stimulus onset for example units in VISp. Raster is sorted by contrast (positive values indicating gratings presented on the right; recordings on the left hemisphere; a). d, Similar to c but showing responses in anterior cingulate area, dorsal part (ACAd). e, Raster and PSTH to stimulus onset, but sorted as a function of choice. Areas are marked on the top left of raster plots. f, Similar to c–e, but sorted by alignment to feedback onset and sorted as a function of correct and incorrect responses. g, Example spike counts (normalized; colored by genotype) before stimulus onset (−300 to −50 ms) as a function of trial number (x axis). Also plotted are the experimentally imposed prior and the subjective estimate of the prior for the given animal per session. Right, we highlight example periods where the firing rate changes during changes in the subjective prior and stable experimental prior in gray color.

Raster plots (Fig. 3c–f, top) and peri-stimulus time histograms (PSTHs; Fig. 3c–f, bottom) demonstrated standard features of neural responses in all genotypes. Namely, visual evoked responses occurred at earlier latencies and were more robust with increasing contrast (Fig. 3c). These responses were distributed, often contralateral in the primary visual areas (VISp; Fig. 3c; examples shown) and regularly bilateral and at larger latencies elsewhere (for example, ACAd; Fig. 3d). Units across many regions^35,36 appeared to correlate with the choice of the animal (Fig. 3e; examples in CP, MOs, cornu ammonis area 1 (CA1) and triangular nucleus of septum (TRS) shown). Similarly, responses to feedback (for example, incorrect response) were also distributed and could be expressed as an increase (Fig. 3f, first and third columns) or decrease (Fig. 3f, second and fourth columns) of firing rates. The responses to feedback were overall no different across the wild-type and mouse models of ASD (see Extended Data Fig. 4 for both behavioral and neural quantification). For a full characterization of these phenomena, readers are referred to previous reports using very similar³⁵ or identical³⁶ protocols. Instead, here we focus on coding of the subjective prior, as estimated by a biased exponential weighting of recent sensory history and on differentiating factors between wild-type mice and mouse models of ASD.

We computed spike counts within a window preceding trial onset (−300 to −50 ms) and plotted these on a trial-by-trial fashion, jointly with the experimentally imposed prior and our behavioral estimate (Fig. 2; exp. bias model) of this prior. This suggested the presence of a subset of units (Fig. 3g; four shown—one per genotype) whose prestimulus firing rates covaried with block. Interestingly, close inspection showed periods where prestimulus firing rates changed as the subjective estimate of the prior changed, even when the experimentally imposed prior remained constant (for example, in Fig. 3g, Shank3 example is in brown and periods are highlighted in gray). This motivates a quantitative detailing of neural responses to the subjective prior. We first take a big-picture approach by examining population-level encoding (Fig. 4) and then examine unit responses and neural tuning (Figs. 5 and 6).

Fig. 4 |. Population encoding of subjective prior shifts from visual to FC in mouse models of ASD.

a, Four example dPCA sessions, one per genotype. Analysis was conducted to separate quintiles of the subjective prior and left versus right decision. Top row shows a ‘condition-independent’ subspace capturing the stimulus-evoked response (only left decision—solid lines—shown for clarity). Middle row shows the decision subspace appropriately separating left (solid line) and right (dashed line) choices. Bottom row shows the subjective prior subspace. Of note, the quintiles of the subjective prior are differentiated before the stimulus is presented (x axis = 0). b, Categorization of brain regions into ‘macro-areas’ for statistical power and coarse summary (see Supplementary Table 1 for further detail on the categorization). c, Variance explained by the subjective prior subspace as a function of ‘macro-area’ and mouse genotype (C57BL6, black; Fmr1, green; Cntnap2, yellow and Shank3, brown). Error bars represent ±1 s.e.m. with the smallest $n=13$ (macro-area–genotype pair). See Supplementary Fig. 5 for an alternative illustration showing all sessions. STR, striatum.

Fig. 5 |. Unit encoding of subjective prior shifts from visual and frontal cortices in mouse models of ASD.

a, Schematic representation of the pGAM encoding model. b, Example units showing the empirical PSTH (black, $x$ axis is time), the reconstructed average from the pGAM (red) and the (exponentiated) visual stimulus kernel (blue). The latter is the contribution to the observed response that the encoding model ascribes (factorized) to visual stimulus presentation. c, Example tuning function to the subjective prior. Follows the format from b, with the difference that the $x$ axis is not time anymore, but the value taken by the subjective prior. The $x$ axis is normalized such that the lowest value taken during a recording (y axis in Fig. 2b) takes a value of 0 and the maximum takes a value of 1. By definition, therefore, 0.5 corresponds to the average subjective prior of the animal. d, Fraction of units significantly tuned ( $P<0.001$) to the subjective prior as a function of brain region (vertical; see Allen CCF for acronyms) and genotype (C57BL6, black; Fmr1, green; Cntnap2, yellow and Shank3, brown). e, Follows the convention from d, showing the informativeness of tuning functions (measured in MI). Error bars are ±1 s.e.m, with the smallest $n=40$ neurons. ProS, prosubiculum; SUB, subiculum; LD, lateral dorsal nucleus; LGd, lateral geniculate nucleus, dorsal part; PO, posterior thalamic nuclear group; CP, caudoputamen; LS, lateral septal nucleus; MRN, median raphe nucleus; PRT, pretectal region; SF, subfornical organ.

Fig. 6 |. Outsized coding of deviations from long-run prior across mouse models of ASD.

a, Two-dimensional t-SNE of tuning functions to the subjective prior as a function of brain area (colors). Inset shows the average and s.e.m. silhouette values (that is, relative distance of points to others within and across clusters) as a function of a number of clusters. A high silhouette value indicates that points within a cluster are well matched to their own cluster and poorly matched to other clusters. b, Examples (thin and transparent) and average (dark and opaque) tuning functions to the subjective prior as a function of cluster (one through four). c, Left, fraction of the units tuned to the subjective prior that belong to each of the four clusters (shown in b) as a function of genotype (rows; C57BL6, Fmr1, Cntnap2 and Shank3, respectively). Right, fraction of units increasing their firing rate with decreasing (left—red) versus increasing (left—blue) value of the subjective prior (gray), and fraction of units increasing their firing rate with increasing (left—green) versus decreasing (left—purple) distance from the long-run prior (that is, normalized subjective prior = 0.5). d, Fraction of cluster 1/cluster 2 (gray in c) as a function of genotype (colors) and macro-brain area. Acronyms follow the convention from Fig. 4. e, As d, showing the fraction of cluster 3/cluster 4. The dashed line shows a fraction = 1.

Population prior encoding shifts from the visual and frontal cortices in ASD models

We examined low-dimensional population-level encoding via demixed principal component analysis (dPCA⁴⁰). This method is conceptually similar to PCA, but keeps the learned components interpretable vis-à-vis task features (for example, decision or prior; Fig. 4a). In the current dataset, dPCA explained 86.1% of the variance explained by PCA over the first ten principal components (PCs). The PC space explained 96.3% of total variance over the first ten PCs (Extended Data Fig. 5). The dPCA analysis was performed on individually CCF-defined regions (Figs. 3b and 4a, example sessions), yet to derive a coarse-level picture and for statistical power, we subsequently coalesced regions into ‘macro-areas’ (Fig. 4b and Supplementary Table 1; see ref. 41 for a similar approach).

This analysis demonstrated that information regarding the subjective prior (as derived from the exp. bias model) was present throughout the brain and spanning all levels of the neural hierarchy (Fig. 4c; see ref. 37 for a similar finding). The total variance explained by subjective prior subspaces was 28.3% ± 0.4%, and this value was not different across genotypes (one-way ANOVA, $P=0.29$). The subjective prior accounted for about two-thirds (68.0%) of the variance explained by evoked visual responses (41.3% ± 0.5%) and for three times as much as decision subspaces (8.65% ± 0.1%). When splitting by brain area, we did observe differences across genotypes (ANOVA interaction term, $P=0.039$), which was driven by (1) an increased population-level encoding of the subjective prior in frontal areas (FC—ACAd, anterior cingulate area, ventral part (ACAv), and MOs) of mouse models of ASD (variance explained; Fmr1, 31.8% ± 1.95%; Cntnap2, 32.0% ± 3.13% and Shank3, 31.5% ± 2.14%) relative to the wild type (26.1% ± 1.94% and all $P<0.05$; Figs. 4c), and (2) more prominent encoding of the prior in visual areas of the wild-type animal (34.3% ± 3.40%) relative to mouse models of ASD (Fmr1, 28.7% ± 1.79%; Cntnap2, 27.5% ± 3.73% and Shank3, 24.6% ± 1.75%; significant for wild type versus Shank3, $P=0.02$, and showing trends for Cntnap2 and Fmr1, $P=0.10$ and $P=0.11$, respectively).

These results suggest that while a multitude of neural regions may show responses reflecting the subjective prior of animals³⁷, the differentiating factor between animals updating their priors stereotypically versus only modestly (mouse models of ASD) is a graded shift in the prior encoding from visual to frontal (for example, ACAd, ACAv and MOs) cortices. This analysis, however, is only coarse-level and could be driven by covariates (for example, correlation between prior and choice). Thus, we next examined unit properties with an encoding model disentangling the contributions of covariates.

Unit prior encoding shifts from the visual and frontal cortices in ASD models

Spike trains were fit to a Poisson generalized additive model (pGAM)⁴², with predictors including the timing and contrast of gratings, choice (left or right) and feedback (correct or incorrect). We also include the choice and feedback on the previous trial, as well as the first ten PCs of video body-part tracking data, and the experimental (20:80, 50:50 and 80:20) and subjective (exp. bias model) prior (Fig. 5a, left column). The inclusion of both the experimental prior and the immediately precedent choice/feedback ensures that units labeled as encoding for the subjective prior do not simply reflect stimulus statistics or the immediately previous choices/feedback but, in fact, reflect a (weighted and biased) accumulated sensory history (that is, the exp. bias model; ‘Behavioral modeling’). Finally, the model attempts to also account for elements of internal neural dynamics by allowing unit-to-unit couplings and spike history (Fig. 5a, right column; see refs. ^43–45 for a similar approach; see Extended Data Fig. 6 for characterization of the stability of coupling filters as a function of block and genotype). Beyond capturing arbitrary nonlinearities and handling colinear predictors⁴⁶, the specific pGAM we fit⁴² infers marginal confidence bounds for the contribution of each feature and thus allows identifying the minimal subset of factors that significantly ( $P<0.001$) impact neural responses without computationally costly model selection procedures. We achieve a goodness-of-fit ($\text{pseudo-}{R}^2=0.0745$) on par with state-of-the-art machine learning techniques⁴⁷ while reducing our encoding models by an order of magnitude (see Extended Data Figs. 7 and 8 for further model performance quantification and Fig. 5b and the Supplementary Note for pGAM estimated visual responses).

The subjective prior was encoded in units throughout the brain (examples shown in Fig. 5c), in fractions (averaged across genotypes) ranging from 0.14 (triangular nucleus of septum) to 0.36 (anterior cingulate area (ACA); $\alpha$ set at 0.001 and thus well below these fractions; Fig. 5d). Separating by brain area and genotype, we observed that, akin to the population-level results, the subjective prior was more frequently coded in frontal areas (FC) in mouse models of ASD relative to the control (coalescing ACAd, ACAv and MOs; ${\chi }^2$ test = 30.67, $P={10}^{-5}$; when taking the areas independently, $P<3.5\times {10}^{-4}$ for ACAv and MOs, and $P=0.10$ for ACAd; all mouse models of ASD > wild type in each frontal area, except for Shank3 in ACAd). Concurring with the population-level results, the subjective prior was less frequently coded in the visual cortex in mouse models of ASD relative to the control ($P={10}^{-5}$; independently, all mouse models of ASD < wild type, all $P<2.0\times {10}^{-4}$). We also estimated the informativeness (Methods) of each of these tuning functions (Fig. 5e; a continuous variable as opposed to the binary tuned versus not tuned). Results showed greater mutual information (MI) in mouse models of ASD than in the wild type in each of the frontal areas (all $P<3.8\times {10}^{-3}$) and reduced MI relative to the control in visual cortex ($P=3.04\times {10}^{-4}$; Fig. 5e and Supplementary Fig. 6). Other areas (most prominently CA3) showed differences in frequency ($P=0.004$) and informativeness ($P=8.14\times {10}^{-16}$) of tuning in mouse model of ASD relative to the control, but these differences were either (1) not consistent within neighboring regions/established circuits (for example, CA1 versus CA3 or dentate gyrus (DG); Figs. 5d,e), (2) not true across measures (for example, medial geniculate nucleus fraction tuned (MG FT) versus MI, respectively; Fig. 5d,e) or (3) not observed across all mouse models of ASD tested (for example, LS or primary motor cortex (MOp)).

Outsized coding of deviations from long-run prior across ASD models

Next, we sought to move beyond the summary characterization of frequency (Fig. 5d) or informativeness (Fig. 5e) of neural responses vis-à-vis the subjective prior and, instead, examine the underlying shape of these tuning functions. We retained the top 10k tuning functions by MI with the subjective prior and performed $K$-means clustering⁴⁸ while allowing the number of clusters to vary from two to ten. We also projected the subjective prior kernels (blue in Fig. 5c) onto a two-dimensional (2D) t-distributed stochastic neighbor embedding (t-SNE; Fig. 6a (ref. ⁴⁹)) for visualization. The tuning functions were best described as pertaining to four clusters (Fig. 6a, inset shows silhouette values quantifying separateness of clusters). Cluster 1 (Fig. 6b, first row) was units whose responses monotonically decreased as the subjective prior increased from its lowest value (normalized value of 0, $P_{\text{left}}$ low). These are units that fired when the subjective prior indicated a high probability that the next stimulus would be presented on the right. Cluster 2 (Fig. 6b, second row) was the mirror image of cluster 1, with neural responses monotonically increasing from $P_{\text{left}}$ low to $P_{\text{left}}$ high. Both these clusters code for the current value of the subjective prior. In contrast, cluster 3 (Fig. 6b, third row) was comprised of units whose firing rate was minimal at a normalized subjective prior of 0.5 and fired more at both high and low values of the subjective prior. That is, these units were driven by deviations from the animal’s particular prior mean, the long-run prior of each animal (that is, the mean along the $y$ axis in Fig. 2e). Finally, cluster 4 (Fig. 6b, fourth row) was the inverse of cluster 3, with units firing most readily when the animal’s current expectation (that is, subjective prior) was most similar to its long-run mean. Clusters 3 and 4 code for the absolute value of the difference between the session-average subjective prior (that is, the prior mean) and the current, or instantaneous, trial subjective prior.

Units of all cluster types were present in each brain area (Fig. 6a). Thus, we examined the fraction of each cluster type throughout the brain of wild-type and mouse models of ASD. These were not equally distributed across all genotypes (${\chi }^2$ test = 50.38, $P<{10}^{-5}$). Instead, cluster 3 was overrepresented in the Cntnap2 ($P=0.002$) and Shank3 ($P=0.008$) animals, and cluster 4 was underrepresented in Fmr1 ($P=0.04$; Fig. 6c). Clusters were uniformly represented in the wild type ($P=0.21$). Given that clusters 1 and 2 (coding for subjective prior value) and clusters 3 and 4 (coding for absolute difference from the long-run prior) were mirror images of each other, we computed the relative fraction of these cluster types. This analysis showed an approximately equal fraction of units increasing or decreasing their firing rate with the value of the subjective prior (Fig. 6c, right, gray). Instead, Fmr1, Cntnap2 and Shank3 animals had, respectively, a 33%, 45% and 46% increase in units, increasing their firing rates as the subjective prior took on values further from their long-run prior (Fig. 6c, right, colored). This was not true of the wild-type animals, with an equal number of units increasing (cluster 3) and decreasing (cluster 4) their firing rate with deviations from their long-run prior.

When splitting across ‘macro-areas’ (Supplementary Table 1), it remained true that across genotypes and areas, a similar fraction of units either increased or decreased their firing rate with the value of the subjective prior (Fig. 6d; ${\chi }^2$ test, all $P>0.13$). That is, across areas, wild-type and mouse models of ASD coded similarly for the instantaneous value of their prior. Instead, the outsized population of units coding for deviations from the prior mean in ASD (Fig. 6c) seemed to be driven by FC (${\chi }^2$ test = 113.14, $P<{10}^{-5}$) and, to a lesser extent, by the hippocampal formation (${\chi }^2$ test = 17.40, $P=5.85\times {10}^{-4}$; Fig. 6e).

These results demonstrate both global and local differences in unit coding of the prior across animals flexibly and inflexibly updating their expectations. Globally, mouse models of ASD more heavily rely on frontal cortices, and less so on visual cortices, to encode their priors. Locally, the tuning functions in FC demonstrate a selective preponderance of units increasing their firing rates with deviations from the long-run prior of the animals.

Lack of prediction errors in FC in ASD models

The updating of priors should be driven by the observation of statistically unlikely events. Thus, we examined how the encoding of gratings was modulated by their statistical likelihood. To do so, we fit the pGAMs⁴² separately for each experimental block (80:20 and 20:80) and compute MI at each contrast. We observe that when most stimuli were presented on the left/right hemifield, the encoding of stimuli (as indexed by MI) presented on the opposite side was strengthened (Fig. 7; all brain areas and genotypes combined, $P=1.27\times {10}^{-43}$; 20:80 > 80:20 for negative contrasts and 20:80 < 80:20 for positive contrasts). This is in line with the theoretical framework of predictive coding⁵⁰.

Fig. 7 |.

Lack of sensory-driven prediction errors in FC of mouse models of ASD. MI ($y$ axis) as a function of grating contrast (y axis; negative contrasts are gratings presented on the left hemifield), experimental block (leftward bias block in purple, 80:20), macro-area (columns) and genotype (rows). Error bars are ±1 s.e.m, with the smallest $n=40\text{neurons}$.

We observed abundant variability when separating across ‘macro-areas’ (Supplementary Table 1) and genotypes. For instance, the Cntnap2 animals (Fig. 7, third row) showed a widespread lack of sensory prediction errors (for example, hippocampal areas (HIP), midbrain (MB), somatosensory and motor (SM), ANOVA interaction term; all $P>0.11$), which was not evident in the other genetic models of ASD (HIP, MB and SM in Fmr1 and Shank3; all $P<0.05$). Similarly, across a number of brain regions (for example, thalamus (TH) and visual areas (VIS)), we observed the presence of sensory-driven prediction errors in control animals and not in a subset of the mouse models of ASD (for example, TH in Cntnap2 and VIS in Shank3). Most strikingly, it was only in frontal cortices where we observed a differential coding of expected and unexpected stimuli in control animals (ANOVA interaction term, $P<0.001$) and the lack thereof across all mouse models of ASD (all $P>0.61$; Fig. 7, first column). This lack of sensory-driven prediction errors in FC of mouse models of ASD is also observable in grand-average PSTHs (Extended Data Fig. 9). The difference in observed sensory prediction errors across wild-type and mouse models of ASD was not driven by a differential sampling of cortical layers across genotypes (Extended Data Fig. 10 and Supplementary Note).

Frontal surprise responses reflect reduced prior encoding

Finally, we attempt to explain how the neural observations (Figs. 3–7) relate to behavior and the computational anomalies (Figs. 1 and 2) observed in ASD (that is, a narrower ‘hyper-prior’ leading to ‘conservatism’ wherein priors are updated slowly), as well as how the different neural effects may relate to one another. It must be noted, this attempt is correlational by necessity.

The computational anomaly is best captured by the sum of $\alpha$ and $\beta$ parameters dictating the shape of the $\beta$ distribution hyper-prior. Thus, we build a multiple linear regression (tenfold cross-validation) of the form $y~\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{p}\mathrm{t}+{\beta }_1{x}_1+{\beta }_2{x}_2\dots {\beta }_n{x}_n$, where $y$ is the sum of $\alpha$ and $\beta$. These parameters were estimated separately for each of the 297 sessions comprising the physiology dataset (each animal was recorded on multiple successive days). The regressors used were (1) the variance explained by the subjective prior dPCA subspace (Fig. 4), (2) the fraction of neurons tuned to the subjective prior and (3) their informativeness regarding the prior (Fig. 5) and (4) the magnitude of a neural ‘surprise’ response (that is, sensory prediction error; Fig. 7; area shown in gray in FC for C57BL6 animals). The relative fraction of units coding for deviations from the long-run prior (Fig. 6e) was not used because of the difficulty in estimating these fractions on a session-by-session basis. The brain regions included were the frontal and visual ‘macro-areas’ (FC and VIS), given the results above (Figs. 3–7), as well as CA3 and MOp, as these areas also showed strong unit effects (Figs. 5d,e and 6e, ‘HIP’). Overall, the regression based on neural features was a good predictor of the computational parameters ($R^2=0.34$, $F$ statistic versus constant model—2.86, $P=0.035$), and examination of individual coefficients revealed that the sole significant single coefficient was the ‘surprise’ signal (that is, sensory prediction error) in FC (Fig. 8a; $P<0.05$, $t$ statistic = 3.49). The estimated coefficient for the surprise (${\beta }_{\text{surprise}}$) in FC was negative (Fig. 8a, left, dashed gray line = 0), indicating that the smaller the magnitude of prediction errors observed in FC, the sharper the animal’s hyper-prior (that is, $\alpha +\beta$ in the behavioral model). In contrast, the rest of the coefficients in FC were positive.

Fig. 8 |. FC surprise responses reflect the computational anomaly and reduced prior encoding.

a, Regression coefficients (left) and P values (right) associated with coefficients from a multiple regression of the form $y~\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{p}\mathrm{t}+{\beta }_1{x}_1+{\beta }_2{x}_2\dots {\beta }_n{x}_n$, where $y$ is the sum of the parameters dictating the shape of the hyperprior $\beta$ distribution (that is, sum of $\alpha +\beta$), which leads mouse models of ASD toward ‘conservatism’, and the $x$’s are shown along the rows and columns of b. The only significant coefficient ( $P<0.05$) was the degree of surprise responses (that is, sensory prediction error) in FC. This coefficient was negative (that is, less FC surprise correlates with more conservatism), while the rest of the coefficients in FC were positive. b, Correlation matrix between the coefficient inputs in a. $R$ values are plotted color coded as a function of whether correlations were positive (red) or negative (blue). Asterisks indicate $P$ values < 0.05 with Bonferroni correction. The matrix is symmetrical vis-à-vis the diagonal, and thus asterisks are only marked on the lower half. For visualization, each area (CA, MOp, FC and VIS) is highlighted in a black box, and correlations within area with the magnitude of surprise responses are highlighted in green.

Examination of the correlations between neural characteristics showed a number of noteworthy features (in Fig. 8b, asterisks show $P<0.05$ with Bonferroni correction, only shown on the lower half of the symmetrical correlation matrix). First, they were more prominent within (14 significant correlations of 24 possible, or 58.3%) than across area (15/96, or 15.6%) correlations. The correlations that did exist across areas were between FC and CA3 (negative) and MOp (positive), as well as between MOp and VIS (mixed). Interestingly, despite the findings showing a gradation in prior encoding from VIS to FC as prior updating becomes more inflexible (Figs. 4 and 5), FC and VIS did not show direct correlations. Instead, the general pattern suggests positive correlations between FC/MOp, which are then negatively correlated with neural observations in CA3/HIP and VIS (‘Discussion’).

Within areas (Fig. 8b, black boxes), there was almost always (dPCA and fraction tuned in MOp being the only exception) a positive correlation between the variance explained by dPCA, the fraction of neurons tuned to and the informativeness of these tuning functions, vis-à-vis the subjective prior. The degree to which a given area showed a surprise signal (that is, a sensory prediction error; Fig. 7) was only correlated with other neural features in FC (Fig. 8b, green boxes). Namely, the more ‘surprise’ in FC, the less variance was explained by the dPCA subjective prior subspace, the fewer units were tuned to this variable in FC and the less informative these tuning functions were (Fig. 8a, left). The fact that the surprise signal in FC (but not other areas) accounts for the other neural features seemingly explains why it is most strongly correlated with the behavioral/computational parameters (Fig. 8a).

Discussion

We examine the behavioral, computational and neural underpinnings of prior updating in wild-type and three different monogenic mouse models of ASD (Fmr1, Cntnap2 and Shank3).

Behaviorally, the results show that mice of genotypes linked to ASD underused the statistical regularities present in their environment. These animals were also less surprised—as indexed by pupil diameter—during the presentation of statistically unlikely events. These results are largely consistent with human reports suggesting that prior experience has a reduced role in perception in autistic individuals¹⁹, that autistic individuals have inflexible predictions/prediction errors²⁰, that they show a slow update of priors^23,24 and/or demonstrate a reduced surprise when expectations are violated²¹ (but see also refs. ^14,51–53 for exemplar contradictory results from the human literature). The results are also conceptually consistent with hierarchical Bayesian accounts of autism (for example, refs. ^11,13,54), wherein the establishing and updating of priors is a key step in any inference process (that is, by Bayes’ rule). The results are not consistent with accounts suggesting that the computational anomaly in ASD is an increased precision of likelihoods⁵⁵, as we observe no difference in grating detection performance across genotypes when no prior was present (Fig. 1d; see also ref. 12).

Computationally, the results suggest that the animals did not learn a ‘generative model’ of the task in which, for instance, the location of targets changes within blocks of a minimum length. Instead, the modeling results suggest that the animals generally performed a weighted and biased average of recent sensory observations. Animals that inflexibly updated their expectations had a stronger (observation independent) hyper-prior over the predicted target locations. This leads to a blunted update of (observation-dependent) priors. These results are consistent with previous modeling efforts studying prior updating in humans³⁰ (also demonstrating a weighted and biased averaging). However, other models are in principle possible and should be explored in future work. For instance, ref. 37 argues that rodents accumulate past actions, as opposed to past sensory observations. These two models (that is, accumulating past sensory observations versus past actions) are indistinguishable if animals were to perform the task with 100% accuracy—in that case, the stimuli would perfectly predict actions. Thus, the trials differentiating these two models (that is, ‘action-prior’³⁷ and ‘sensory-prior’) are those in which the animals make mistakes. Interestingly, prior work has shown that mice fluctuate between ‘engaged states’, where stimuli largely dictate actions, and ‘disengaged states’, where animals repeatedly select an action regardless of task demands^56,57. It is thus possible that the ‘action-prior’ model³⁷ is accounting for these task-independent periods, and it is possible that animals may use different strategies to update priors in engaged and disengaged states. Another possible computational model for future study is the hierarchical Gaussian filter^58,59. This model has been successfully applied in determining how individuals with ASD respond to environmental change²¹ (that is, they overestimate volatility and thus are less surprised when their expectations are violated). However, the hierarchical Gaussian filter has been applied to associative learning paradigms (for example, a cue probabilistically predicts a target), which does not apply here—there was no cue. It also assumes a hierarchy, with animals learning the dynamics associated with a context. According to the modeling results, by and large, the animals here did not learn that there were distinct contexts. Finally, simulations demonstrate that explicit inferences over volatility (a higher-order context) are not needed in explaining human behavior in volatile environments. In fact, models positing an explicit representation of volatility perform worse than models simply accounting for low-level uncertainty⁶⁰.

Neurally, we show that encoding of priors shifts from sensory cortices (in wild-type mice) to frontal cortices (in ASD model mice) as priors become less flexible. We also observed local changes with frontal cortices (ACAd, ACAv and MOs). Namely, while mouse models of ASD did not differ from the wild type regarding their coding of the instantaneous prior, they did show an outsized presence of units coding for deviations from the animals’ long-run prior (see ref. 61 for a similar distinction between ‘immediate’ and ‘second-order’ priors and for evidence showing that the orbitofrontal cortex encodes the latter). Finally, we demonstrate that neural responses to unexpected observations—precisely those that should lead to an update of our internal models—were augmented relative to expected stimuli in frontal cortices of wild-type animals, but not in mouse models of ASD. The degree to which frontal areas showed sensory prediction errors was inversely correlated with the degree to which FC units and populations encoded the prior and most strongly predicted the behavioral/computational deficits shown in ASD. These results are reminiscent of blood oxygen level-dependent correlates in humans¹⁵ demonstrating that neurotypical and autistic individuals showed strong differences in the blood oxygen level-dependent activity that prediction errors drove in the anterior cingulate cortex. Similarly, in rodents, prediction error signals in the anterior cingulate cortex drive task-switching⁶², and it is well-established that ACA/MOs project to VISp, with the higher-order areas modulating the sensory area, in particular as a function of the predictability of visual stimuli^63–66. The ACA is also a major cortical input to the locus coeruleus⁶⁷, which is heavily implicated in driving sensory prediction errors^68,69.

The hippocampus and MOp also showed some strong effects (for example, Figs. 5 and 6, particularly for HIP), although these were less consistent across analyses, levels of description and genotypes. Nevertheless, the presence of (arguably more subtle) effects in the hippocampus—and in particular its apparent antithesis with FC (that is, Fig. 8b)—may be an important feature of neural function. Indeed, recent work⁷⁰ has demonstrated that the hippocampus is key in supporting hidden state inference. By and large, the mice in the current task did not appear to perform hidden state inference (that is, deducing a context), but, in principle, it is possible they did so intermittently (for example, within ‘engaged’ states but not ‘disengaged’ ones). This could be reflected in the effects observed in the hippocampus. Similarly, EEG work in humans suggests that prior expectations may alter both sensory encoding and motor preparation⁷¹, and thus it is possible that multiple processes—sensory and motor—are involved, with the latter being reflected in MOp.

The neural results also bring to light important aspects in which computational theories of ASD (which have lacked the neural resolution we have here) ought to be revised. Namely, the inflexible predictions account of autism²⁰ suggests a ‘high and inflexible’ weight attributed to prediction errors in ASD. Our results demonstrate not the inflexible nature of these prediction errors, but their total absence in frontal cortices in mouse models of the disorder. Furthermore, we observed a preponderance of units coding for deviations from the prior mean in mouse models of ASD. To the best of our knowledge, these units—not coding for the immediate prior, but for its deviance from the prior mean—are not part of current neuroscience or computational psychiatry theory and ought to be incorporated into accounts of prior updating and its anomaly in ASD. Fittingly, the anterior cingulate—where we observe an abundance of these units—is well-established as an error monitoring node⁷² and is causally involved in engendering prediction errors in lower-level sensory areas (for example, primary visual cortex^73,74).

In future work, it will be important to simultaneously record from ACAd/ACAv/MOs and visual cortices to further understand the relationship between units coding for deviations from the animals’ long-run prior and prediction errors in both frontal and sensory cortices (for example, via wide-field imaging). The analyses between FC and VIS in the current work failed to show a meaningful direct correlation, but the recording strategy here was not designed to specifically record from this pair. We did, however, observe positive correlations between the neural effects in FC/MOp, which in turn were negatively correlated with neural observations in HIP/VIS, potentially reflecting different computational approaches (for example, context-based versus not)—a speculation that awaits future work. Similarly, in future work, it will be interesting to discretize behavior into periods defined by different task strategies or internal states and examine how accumulation not only of sensory history but also of action history³⁷ may influence prior updating in each of these periods (for example, engaged or disengaged⁵⁶) and across genotypes.

In conclusion, we uncover a common computational and neural anomaly across distinct genetic mouse models of autism. The computational deficit is broadly aligned with recent behavioral findings from human computational psychiatry^21,23,24 and thus supposes a potential translational opportunity to further understand the neurobiology of autism. The results demonstrate a degree of biological degeneracy⁷⁵ wherein different genetic perturbations may lead to similar neurophysiological consequences, both at a brain-wide scale and within local populations in FC.

Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41593-025-01965-8.

Methods

Animals

Experiments were performed in a total of 75 male and female mice of mixed genetic background (C57BL/6J), between 10 (headbar implantation and initial training) and 29 weeks of age (max number of sessions across all animals = 97). On average, animals were 22.2 weeks old during neurophysiological recordings. In addition to wild-type control animals ($n=15$), three different monogenetic mouse models of ASD were used. Fmr1 KO²⁵ (males are ${Fmr\mathit{1}}^{-/y}$ and females are ${Fmr\mathit{1}}^{-/-}$; no sex difference, $n=19$; Jackson Laboratory (JAX), 003025) mice have a neomycin resistance cassette replacing exon 5 of the fragile X mental retardation syndrome 1. ${Cntnap\mathit{2}}^{\mathit{tlacz/tlacz}}(n=21$; JAX, 028635) mice²⁶ have a dysfunctional contactin-associated protein-like 2 gene by replacement of the exon 1 on the Cntnap2 gene. ${Shank\mathit{3}b}^{+/-}(n=20$; JAX, 017688) mice²⁷ have a neocasette replacing the PDZ domain (exons 13–16) on the Shank3 gene, resulting in altered expression of the synaptic scaffolding protein expressed in the postsynaptic density of excitatory synapses. These animals were used as they are well-established models of ASD (refs. ^75,76; relevance to humans⁷⁷) and have previously been used in attempts to establish commonalities across mouse models of ASD^78–81. The Fmr1 KO animal demonstrates anomalies in networks thought to underpin social behavioral, reduced vocalization, repetitive behaviors and cognitive anomalies^82,83. The Cntnap2 animal has shown social deficits, as well as cognitive and motor anomalies^26,84, and more recently repetitive behaviors⁸⁵. Finally, the Shank3B animal has shown deficits across networks, including all the abovementioned domains^27,86. Notably, all three of these animals are visually similar to wild-type animals, sharing a mixed genetic background. The latter point is important given that behavioral training and testing were conducted by a hypothesis-naive (blinded) experimenter (J.B.). Male and female mice of the same genotype were first analyzed separately to assess potential sex-related differences in behaviors. Given no differences were observed, male and female mice of the same genotype were grouped together for final analyses. No statistical methods were used to predetermine sample sizes, but our sample sizes are similar to those reported in previous publications^28,35,38. All procedures performed in this study were approved by the Institutional Animal Care and Use Committee at New York University (protocol 18–1868).

Surgeries

Each animal had two surgeries. A first one to secure a headbar on their skull, allowing for head fixation, and a second one to perform craniotomies, allowing for neurophysiological probe insertions.

For headbar implants, mice (~12 weeks old) were initially anesthetized by placing them in an induction box at 3–5% isoflurane. They were then fixed in a stereotaxic frame and maintained anesthetized at 1–1.5% isoflurane. Under a microscope (Leica, M60), the dorsal surface of the skull was cleared of skin and periosteum, bregma and lambda were marked, the lateral and middle tendons were removed using fine forceps and the headbar was placed and cemented on a leveled skull. A small amount of cyanoacrylate (VetBond; World Precision Instruments) was applied to the edges of the skin wound to seal it off and avoid future infections. Finally, the exposed skull was covered with clear UV-curing optical glue (Norland Optical Adhesives 81; Norland Products).

On the first day of neural recordings, up to four microcraniotomies were made, either with a dental drill or a biopsy punch. A gold pin touching the brain was implanted for referencing. The induction procedures followed that of the headbar implants, and craniotomies were performed at −2.7 mm mediolateral (ML)/−3.5 mm anteroposterior (AP), −1.76 mm ML/−2.00 mm AP, −0.40 mm ML/−1.06 mm AP and −0.80 mm ML/0.50 mm AP (negative ML values indicating the left hemisphere and negative AP values indicating posterior to Bregma). Craniotomies were covered with a low-viscosity silicon sealant (Kwik-Cast; World Precision Instruments) to prevent drying. Animals were given at least 4 h of recovery before neural recordings.

Behavioral procedures

Following headbar implantation, animals were given at least 3 days of recovery. Then, they were handled for at least 15 min d⁻¹ for 2 days. On the second day, the mouse was allowed to explore the behavioral rig for 10 min. The following 3 days (20, 40 and 60 min, respectively), the mice were head-fixed and passively presented with full-contrast (100%) Gabors (vertical orientation, 1/10th of a cycle per visual degree masked by a Gaussian window of 7°). The wheel used to make responses was locked. The gratings appeared on either the left or right visual field (35° eccentricity and 0° elevation) for an average of 10 s. The Gabor then moves to the center of the visual field (0° eccentricity) for 1 s. The animal was given a reward (3 μl, 10% sucrose) 500 ms after the presentation of the Gabor in the center.

Active training began on the 4th day of head fixation. The wheel was unlocked and in closed-loop with the Gabor. Gabors were presented, given that the animal did not move the wheel (<2°) during a quiescence period (exponential distribution, 200–500 ms range, 350 ms average). Initially, Gabors of either 100% or 50% contrast were presented (left or right, equal probability, presentation order randomized). A tone (100 ms duration, 10 ms ramp, 5 kHz) was played at Gabor onset. If the mouse moved the Gabor to the center of the screen within 60 s of presentation, it was rewarded (3 μl, 10% sucrose). If it moved the Gabor in the opposite direction by a similar displacement (35°), the trial was considered incorrect. If it did not respond within 60 s, the trial was timed out. In either of the latter two cases, a noise burst was played for 500 ms. At the onset of this active phase of training, the Gabor moved eight visual degrees per millimeter of movement at the wheel surface. If the mouse completed at least 200 correct trials within a session (typically ~45 min), the gain of the wheel for all future sessions was halved, remaining at four visual degrees per 1 mm of movement at the surface of the wheel. Similarly, if a mouse completed 200 trials in the previous session, the reward volume was lowered by 0.1 μl until a floor of 1.5 μl was reached.

Behavioral training on this unbiased version of the task (that is, probability of left versus right visual stimuli = 50:50) had six phases. First, only 100% and 50% Gabors were presented. If the animal performed above 80% correctly, it moved to phase 2, where a 25% contrast Gabor was added to the set. Similarly, if the animal performed above 80% correctly in phase 2, it moved to phase 3. In this phase, 12.5% contrast Gabors were added to the mix. To progress to phase 4, animals had to complete 200 trials within a session, regardless of performance. In phase 5, the 0% contrast was added. If animals completed 200 trials within a session, regardless of performance, they advanced to phase 6. In this last phase, the 50% contrast was dropped. The mice were considered to be trained on this unbiased visual detection task if they were in phase 6 and completed at least 200 trials, performing above 80% correct for 100% contrast trials for three consecutive sessions. Furthermore, their psychometric estimates for the combined last 3 days were required to meet the following criteria: bias below 16, threshold below 19 and lapses (high and low) below 0.2. Gabor contrast and location were randomized. If animals did not learn this task within 40 sessions, they were considered untrainable. A small minority of animals were trained for over 40 sessions due to long breaks (2+ weeks) in training at an early stage.

Animals who successfully trained on the unbiased version of the task were moved to a ‘biased’ version of the task, wherein animals must use a dynamically updating strategy before reaching optimal performance. Namely, each session started with 90 trials where the Gabors appeared with equal probability on the left and right visual fields. The side (and thus correct response) for 0% contrast Gabors was chosen randomly. After these initial 90 trials, stimuli were presented in blocks. In one block, Gabors are presented on the left with probability 80% (right, 20%). In the other block type, Gabors are presented on the left with a probability of 20% (that is, 20:80). In a given session, there was an equal probability that the first biased block was ‘leftward’ or ‘rightward’. Gabors of 0% contrast are rewarded according to the prior. The number of trials for each biased block is drawn from an exponential distribution with a mean of 60, a minimum of 20 and a maximum of 100 trials. This yields an almost flat hazard rate (corrupted by the clipping of a maximum trial number). The change in blocks is not signaled. Critically, animals performed 15 sessions of this biased task before being moved to physiology. There was no performance requirement, which distinguishes this from the broader IBL dataset^36,38.

Neural recordings

Neural recordings were performed with Neuropixels 1.0 (ref. ³¹; Interuniversity Microelectronics Centre (IMEC)) on the acquisition configuration (AP—30 kHz, gain = 500; LFP—250 Hz, gain = 250), recording from the bottom 384 sites of a 1-cm shank. Probes were mounted on a steel rod, which was in turn held by a micromanipulator (uMP-4; Sensapex). Probes had a soldered connection to short the external reference to ground, and this latter one was connected to a gold pin fixed on the skull and in contact with the brain. Silicone artificial dura repair compound (Dura-Gel; Cambridge NeuroTech) was placed over the craniotomies during recordings. Before insertion, probes were labeled for subsequent histological reconstruction (see below). On most recording days, we inserted two probes—one per craniotomy. The probes were lowered into position at ~10 μm s⁻¹. Electrodes were allowed to settle for ~10 min before starting the recording. Data were acquired via a PXIe (PXI-1000; National Instruments) using SpikeGLX (Janelia Research Campus) and stored on a PC and cloud for subsequent analyses. At most, over four consecutive days, we performed eight insertions in each animal—two per craniotomy (four craniotomies), one medially and one laterally at a 15° angle from vertical. In between recording days, we covered craniotomies and exposed skulls with silicon sealant (Kwik-Cast; World Precision Instruments).

Probe labeling

For histological reconstruction, we labeled the probes with CM-Dil (Thermo Fisher Scientific, V22888) immediately before insertion. Neuropixels were secured onto a micromanipulator and lowered under a microscope (Leica, M60) onto a coverslip or parafilm containing the dye (1 μl). The tips of the probes were maintained in CM-Dil until the dye dried out (~20 s).

Histology and probe reconstruction

We followed the procedures standardized by the International Brain Laboratory³⁸. Namely, mice were given a terminal dose of pentobarbital within the peritoneal cavity. Then, phosphate buffered saline was followed by a 4% formaldehyde solution (Thermo Fisher Scientific, 28908) in 0.1 M phosphate buffer (pH 7.4) and was perfused through the left ventricle. The brain was subsequently dissected and postfixed in formaldehyde for a minimum of 24 h at room temperature. The tissue was then washed and stored for up to ~6 weeks in phosphate buffered saline at 4 °C. The brains were then embedded in a 5% agarose gel block and imaged via serial section two-photon microscopy (whole brain coronal image stacks acquired at a resolution of 4.4 × 4.4 × 25.0 μm) under control of custom software (BakingTray). Image tiles were then assembled into 2D planes (StitchIt), downsampled to 25 μm isotropic voxels and registered to the adult mouse Allen CCF using BrainRegister, an elastix-based registration pipeline with parameters optimized for mouse brain registration. Next, we reconstructed the location of probes by manually tracing the fluorescent dye on CCF-aligned coronal and sagittal images using a Python-based image viewer (Lasagna) equipped with a plugin tailored for this task. Finally, we manually aligned electrophysiological and anatomical landmarks along the probe trajectory using a custom tool (see ref. 38 and associated protocols for further detail).

Spike sorting and curation

Data were spike sorted with Kilosort 2 (KS2 (refs. ^87,88)) and/or a custom Python version of the algorithm. Entire sessions were then inspected by constructing ‘drift maps’ (channel × time, spikes as dots). If significant drift was evident, the session was rejected. Data were then manually curated via visual inspection (for example, waveforms and auto-correlograms) with the Phy graphical user interface. Units were included in the analyzed dataset if (1) their average firing rate was over 0.5 Hz, (2) the automated labeling of units by KS2 indicated the unit as ‘good’ (that is, single cell), (3) during manual curation the unit was not labeled as ‘noise’ and (4) it had a presence ratio (1 minus the fraction of 1-min bins with no spikes) above 0.9. Throughout the report, we refer to the clusters satisfying these criteria as ‘units’, given the possibility that a subset of these clusters were multiunit, even if labeled as single units by KS2.

Video recordings and pupil tracking during neurophysiology

We briefly describe the video analysis pipeline, which is fully detailed elsewhere⁸⁹. We recorded videos (CM3-U3–13Y3M-CS, Point Gray) of the animals performing the task from the following three cameras/angles: top, right and left (Extended Data Fig. 3a shows the left camera). In the current analysis, we used the left (60 Hz, 1,280 × 1,024) and right (150 Hz, 640 × 512) cameras, with the latter being flipped and spatially upsampled to resemble the left camera. We detect four regions of interest (ROI) on each frame (Extended Data Fig. 3a, inset, red rectangles), crop these and apply a separate neural network to each ROI to track features of interest. In addition to other body parts, we tracked the top, bottom, left and right corners of the pupil via DeepLabCut. Pupil tracking was not reliable in a number of sessions, likely due to the camera positions being optimized for simultaneous paw and tongue tracking rather than for pupil tracking. Thus, we performed pupillometry analyses only on the subset of sessions ($n=58$ sessions) with reliable pupil diameter estimation. In each session, we dropped frames with a likelihood <0.9 and smoothed the pupil diameter estimation. We then averaged pupil diameters across the left and right cameras and subsequently across animals within a given genotype. We consider pupil responses to differentiate 80:20 and 20:80 blocks if $P<0.05$ for at least ten consecutive samples^90,91.

Modeling and analysis

Data exclusion criteria.

Individual mice were removed from behavioral analyses within the ‘biased blocks’ (that is, where the probability of the grating alternated between being 80% left versus 80% right hemifield) if they did not reach proficiency (80% correct on 100% contrast stimuli) in the ‘unbiased’ version of the task. This resulted in 8% of animals being removed from the behavioral results report below. Neurons were not analyzed if they were localized to a brain region with less than 40 units per area in any of the four genotypes tested. No other data were excluded.

Behavioral analyses.

Training times (Fig. 1c) were determined as the number of sessions $t$ (typically five sessions per week) for an animal to reach 80% correct on trials with contrast 100% or 50% (easy trials). To account for infrequent and sudden drops in performance (likely driven by stress caused during head fixation), the fraction of correct trials on ‘easy trials’ as a function of session was computed within a moving average of three sessions (window centered on session $t$). Psychometric curves (Fig. 1d) were fit by a parametric error function (equation (1); ref. 36) with the following four free parameters: bias ($\mu$), threshold ($\sigma$) and lapse rates for stimuli presented on the left and right (respectively, $\gamma$ and $\lambda$). These functions fit the data well ($R^2—0.99\pm 9.18\times {10}^{-4}$) and equally across genotypes ($P=0.91$). For visualization (Fig. 1f), we construct an average psychometric curve by prior across all animals of a given genotype, and then these are subtracted. For all statistical tests, whether behavioral, modeling or neural (below), data met the assumptions of the statistical tests used.

$$P=\gamma +(1-\gamma -\lambda )\mathrm{e}\mathrm{r}\mathrm{f}\left(\frac{c-\mu }{\sigma }\right)/2.$$ (1)

Behavioral modeling.

We build an ideal observer that has access to a noisy representation of the current stimulus (stimulus $s$, noisy measurement $x$) and the unbiased history of category labels ($C_{1:t}$) experienced up to the present moment. We can assume an unbiased history of category labels given that animals are given feedback on each trial. The observer does not have access to the entire sequence of stimuli presented in a session, but only until trial $t$. Furthermore, we aim to build an iterative formalism, which allows the observer to perform online inference in a tractable manner (that is, tracking sufficient statistics and performing a simple operation at each new observation). The observer model can be decoupled into the following two components: a prior-tracking model computing an a priori probability of observing a given stimulus (for example, left) given previous observations ($C_{1:t-1}$) and a perceptual decision-making model at trial $t$. We detail each of these in turn.

Prior tracking.

Online c.p. detection.

The Bayesian c.p. detection model, which estimates the posterior distribution over the current run length ($r_t$, that is, number of trials since the last change in block) and category probabilities (that is, left or right) based on the data observed so far (category labels until trial $t,C_{1:t}$; refs. ^29,30). The predicted probability that the next trial presented will be on the left is as follows:

$$P\left(C_{t+1}=L\mid C_{1:t}\right)=\sum _{r_t}\sum _{{\xi }_t}P\left(C_{t+1}=L,r_t,{\xi }_t,\mid ,C_{1:t}\right),$$ (2)

where ${\xi }_t$ is the state of the previous block (${\xi }_t\in S_{\pi }$, with $S_{\pi }=\left\{\mathrm{0.2,0.5,0.8}\right\}$). This predictive distribution over future categories may be decomposed as follows:

$$P\left(C_{t+1}=L\mid C_{1:t}\right)=\sum _{r_t}\sum _{{\xi }_t}P\left(C_{t+1}=L\mid r_t,{\xi }_t,C_t^{(r)}\right)\times P\left(r_t,{\xi }_t\mid C_{1:t}\right),$$ (3)

with $C_t^{(r)}$ being the category labels associated with the run length $r_t$, and the second term of equation (3) being the run length and block posterior. Via iterative expansion, we can write

$$\begin{gathered} P\left(r_t,{\xi }_t,C_{1:t}\right)=\sum _{r_{t-1}} \sum _{{\xi }_{t-1}} \left(P\left(r_t,{\xi }_t\mid r_{t-1},{\xi }_{t-1},C_t^{(r)}\right)\right. \\ \left.\times P\left(C_t\mid r_{t-1},{\xi }_{t-1},C_{t-1}^{(r)}\right)\times P\left(r_{t-1},{\xi }_{t-1},C_{1:t-1}\right)\right) \end{gathered}$$ (4)

Of note, equation (4) is recursive (last term being the joint distribution from the previous iteration) and affords computing $P\left(r_t,{\xi }_t\mid C_{1:t}\right)$, given that,

$$P\left(r_t,{\xi }_t\mid C_{1:t}\right)=\frac{P\left(r_t,{\xi }_t,C_{1:t}\right)}{P\left(C_{1:t}\right)}.$$ (5)

The second term in equation (4) (and the first of equation (3)) may be computed as follows:

$$P\left(C_t\mid r_{t-1},{\xi }_{t-1},C_{t-1}^{(r)}\right)=\sum _{{\pi }_{t-1}}P\left(C_t\mid {\pi }_{t-1}\right)\times P\left({\pi }_{t-1}\mid r_{t-1},{\xi }_{t-1},C_{t-1}^{(r)}\right).$$ (6)

In turn,

$$P\left({\pi }_{t-1}\mid r_{t-1},{\xi }_{t-1},C_{t-1}^{(r)}\right)\propto P\left({\pi }_{t-1}\mid {\xi }_{t-1}\right)\times P\left(C_{t-1}^{(r)}\mid r_{t-1},{\pi }_{t-1}\right),$$ (7)

which are, respectively, the transition probability between blocks in the task (which is experimentally imposed) and the sequence likelihood. By definition, the transition matrix between blocks is

$$P\left({\pi }_{t-1}\mid {\xi }_{t-1}\right)=\left(\begin{array}{ccc}0& 0& 1\\ \frac{1}{2}& 0& \frac{1}{2}\\ 1& 0& 0\end{array}\right)\begin{array}{rr}& {\xi }_{t-1}=0.2\\ & {\xi }_{t-1}=0.5\\ & {\xi }_{t-1}=0.8\end{array},$$ (8)

and the sequence likelihood is

$$P\left(C_{t-1}^{(r)}\mid r_{t-1},{\pi }_{t-1}\right)\propto {\pi }_{t-1}^{\left|C_{t-1}^{(r)}=L\right|}{\left(1-{\pi }_{t-1}\right)}^{\left|C_{t-1}^{(r)}=R\right|}.$$ (9)

Returning to equation (6), we thus have

$$P\left(C_t\mid r_{t-1},{\xi }_{t-1},C_{t-1}^{(r)}\right)\propto \sum _{{\pi }_{t-1}}P\left(C_t\mid {\pi }_{t-1}\right)\times P\left({\pi }_{t-1}\mid {\xi }_{t-1}\right)\times P\left(C_{t-1}^{(r)}\mid r_{t-1},{\pi }_{t-1}\right),$$ (10)

Finally, returning to equation (4), we are missing the first term. We can write

$$P\left(r_t,{\xi }_t\mid r_{t-1},{\xi }_{t-1},C_t^{(r)}\right)=P\left({\xi }_t\mid r_t,r_{t-1},{\xi }_{t-1},C_t^{(r)}\right)\times P\left(r_t\mid r_{t-1}\right),$$ (11)

where the terms are, respectively, the previous-block update and the run-length update. Both of these are again experimentally imposed and defined as follows:

$$P\left({\xi }_t\mid r_t,r_{t-1},{\xi }_{t-1},C_t,C_{t-1}^{(r)}\right)=\left\{\begin{array}{ll}\left.P\left({\pi }_{t-1}={\xi }_t\right)r_{t-1},{\xi }_{t-1},C_t,C_{t-1}^{(r)}\right)& \text{if}{r}_t=0\\ \delta \left({\xi }_t-{\xi }_{t-1}\right)& \text{otherwise}\end{array}\right.$$ (12)

and

$$P\left(r_t\mid r_{t-1}\right)=\left\{\begin{array}{cc}H\left(r_{t-1}+1\right)\hfill & \text{if}{r}_t=0\\ 1-H\left(r_{t-1}+1\right)\hfill & \text{if}{r}_t=r_{t-1}+1\\ 0& \text{otherwise}\end{array}\right.$$ (13)

where $H$ is the hazard function, the instantaneous probability on each trial that there is a c.p. Namely,

$$H\left(n\right)=\frac{P_{\text{length}}\left(n\right)}{\sum _{n^{\prime }=n}^{\mathrm{\infty }} P_{\text{length}}\left(n^{\prime }\right)}.$$ (14)

In the particular case of this experiment, where block lengths are drawn from a truncated decaying exponential with time constant 60 and minimum and maximum blocks, respectively, of 20 and 100 trials, we have

$$P_{\text{length}}(n)\propto e^{-\frac{n}{60}}\cdot (20\le n\le 100).$$ (15)

This hazard rate is approximately constant until $n$ becomes large (~80 trials).

Exponential weighting.

The exponential-averaging model, which postulates that animals do not explicitly know about the task structure (for example, possessing blocks wherein stimuli presentation is biased on one side). Instead, it computes a smooth estimate of category probability by taking a weighted average of previously experienced category labels, giving more weight to recently experienced labels:

$$P\left(C_{t+1}=L\mid C_{1:t}\right)={\alpha }_{\mathrm{e}\mathrm{x}\mathrm{p}}{C}_t+\left(1-{\alpha }_{\mathrm{e}\mathrm{x}\mathrm{p}}\right)P\left(C_t=L\right).$$ (16)

The time constant of memory decay for this model is as follows:

$$\tau =\frac{-1}{\mathrm{l}\mathrm{o}\mathrm{g}\left(1-{\alpha }_{\mathrm{e}\mathrm{x}\mathrm{p}}\right)}.$$ (17)

We account for potential conservatism⁹² in a biased version of this exponential weighting model; the exponential weighted average model with bias (‘exp. bias model’, best model in the ‘Main’). In the latter, the estimates from equation (16) are biased by adding ‘pseudocounts’ to the observations of ‘left’ and ‘right’ in past trials (this is a hyper-prior applied in the computation of the prior based on sensory observations). This is equivalent to placing a $\beta$ distribution hyper-prior with parameters $\alpha$ and $\beta$ on the estimated probability from equation (16). A very similar model has been previously used³⁰ (see ExpBias model in ref. 30) and deemed the best model in accounting for how human observers update their expectations. Our implementation is more general than the previous (where there was a $w$ parameter weighting a prior that was fixed at 0.5) in that the $\beta$ distribution can be unbalanced ($\alpha >>\beta$ or $\alpha <<\beta$) and thus yield to distributions peaking near 0 or 1, and thus not leading to conservatism, but the opposite. We call this model the ‘exp. bias model’ because it is an exponentially weighted averaging model, which is biased by a hyper-prior (which takes the form of a $\beta$ distribution).

Perceptual decision-making model.

The stimulus, $s$, on each trial is drawn from a set of contrasts (−1, −0.25, −0.125, −0.0625, 0, 0.0625, 0.125, 0.25, 1), where negative values indicate stimuli presented on the left visual field. The observer does not have direct access to these stimuli, but only to a noisy measurement, $x$. We assume,

$$x\sim n\left(x;\mu (s),{\sigma }^2(s)\right),$$ (18)

where $n$ defines a Gaussian distribution, and $\mu$ and ${\sigma }^2$ are, respectively, means and variances that depend on the stimuli presented, $s$. The ratio of posterior probabilities that a stimulus was presented on the left and right, or the decision variable, is

$$d(x)=\mathrm{l}\mathrm{o}\mathrm{g}\left(\frac{P(L)}{1-P(L)}\frac{P(x,\mid ,L)}{P(x,\mid ,R)}\right)=\mathrm{l}\mathrm{o}\mathrm{g}\left(\frac{P(L)}{1-P(L)}\frac{\sum _{s<0} P\left(x,\mid ,\mu (s),{\sigma }^2(s)\right)}{\sum _{s>0} P\left(x,\mid ,\mu (s),{\sigma }^2(s)\right)}\right),$$ (19)

where $P(L)$ is computed according to the prior-tracking model of choice (above), and we assume that a response ‘left’ is made if $d(x)>0$, and ‘right’ otherwise. Finally, in the case the animals do not lapse, we can write,

$$P\left(\text{choice}\text{left}∣s\right)=\int \left(d\left(x\right)>0\right)n\left(x;\mu \left(s\right),{\sigma }^2\left(s\right)\right)dx.$$ (20)

Or if the observer has an unbiased, nonzero lapse rate, we can write,

$$P\left(\text{choice}\text{left}∣s,\text{lapse}\right)=\frac{\lambda }{2}+\left(1-\lambda \right)\int \left(d\left(x\right)>0\right)n\left(x;\mu \left(s\right),{\sigma }^2\left(s\right)\right)dx,$$ (21)

where $\lambda$ is the probability that the mouse responds randomly.

Model fitting and comparison.

We fit ten models (Fig. 2a) to the responses of each subject. The psychometric model is descriptive, not attempting to explain internal representation. It has four free parameters (as in equation (1)) and is fit separately to the three different blocks (50:50, 80:20 and 20:80), thus resulting in a total of 12 parameters. The omniscient and fixed models possess the perceptual decision-making model but do not compute the prior, $P(L)$. Instead, the omniscient model has direct access to the true value (0.2, 0.5 or 0.8), and the fixed model uses a single $P(L)$ value throughout the session. Next, the c.p. models (five in total, see below) use variants of the Bayes optimal online c.p. detection model for estimating the prior and the perceptual decision-making model for making a choice. The c.p. model has a potential of four free parameters. The a priori block probabilities ${\xi }_t$ experimentally belong to the set $S_{\pi }=\left\{\mathrm{0.2,0.5,0.8}\right\}$. In model fitting, we set $S_{\pi }=\left\{P_{\text{low}},0.5,P_{\text{high}}\right\}$. Similarly, the run lengths are experimentally defined by a time constant $\tau =60$ and a minimum length $r_{\text{min}}=20$ (equation (15)). In the c.p. model, the four parameters ($P_{\text{low}},P_{\text{high}},\tau$ and $r_{\text{min}}$) are set to the experimentally imposed values. In c.p. free sym, we set $\tau$ and $r_{\text{min}}$ to their experimental values, and $P_{\text{low}}$ and $P_{\text{high}}$ have to be symmetric (that is, adding to 1). In c.p. free, we allow $P_{\text{low}}$ and $P_{\text{high}}$ to vary independently. c.p. free sym run is as c.p. free sym but also allows $\tau$ and $r_{\text{min}}$ to take on any value. c.p. free run is as the c.p. free model but allows $\tau$ and $r_{\text{min}}$ to take on any value. Finally, the exponential weighting models (two in total, see below) use exponential averaging for estimating the prior and the same perceptual decision-making model as the rest. In the no-bias variant of the model (exp. no bias), the free parameter is ${\alpha }_{\text{exp}}$, dictating the shape of the time constant of memory decay. In the biased version of the model (exp. bias), there are additionally the parameters $\alpha$ and $\beta$ dictating the shape of the $\beta$ distribution acting as pseudocounts.

We fit the above-described models by minimizing the negative log-likelihood of the data using Bayesian adaptive direct search⁹³ and taking the best result of 20 optimization runs with randomized starting points. Furthermore, we cross-validate log likelihoods (Fig. 2a) by splitting training and testing data according to odd and even sessions.

Neural analyses.

dPCA.

We used dPCA⁴⁰ to examine interpretable neural manifolds. This technique (see ref. 40 for details) requires convolved firing rates (as opposed to spike trains) and a given set of experimental conditions (that is, not a continuous value). Thus, we convolved spike trains (1 ms bins) with a causal Gaussian kernel (s.d. = 10 ms), epoched each trial from 500 ms before stimulus onset to 1,500 ms after stimulus onset, and averaged according to choice (left or right) and subjective prior. The latter, being a continuous variable, was binned in quintiles (five levels of equal number of trials). The resulting matrix used in the dPCA was $n$ (units) × $P$ (five quintiles of the prior) × $D$ (two choices) × $T$ (time). While the analyses are conducted on individual CCF-defined regions, in the ‘Main’, we amalgamate results across ‘macro-areas’ (Supplementary Table 1) for statistical power and deriving a coarse-level summary. We included in the analysis sessions with at least ten simultaneous units within a given CCF-defined region³⁹. Including sessions/areas with more than ten units simultaneously recorded results in a better estimate of the underlying latent dynamics, but did not statistically change the fraction of variance explained by the different subspaces.

pGAM.

To estimate tuning functions and their statistical contribution to a unit’s overall response, we fit a pGAM⁴². The pGAM defines a nonlinear mapping between spike counts of a unit $y_t\in n_0$ and a set of continuous covariates ${\mathit{x}}_j$, as well as discrete events ${\mathit{z}}_k$. In this case, the continuous covariates included were both the experimentally imposed prior (for example, 80:20 or 20:80 probability of stimuli being on the left) and the ‘subjective’ prior estimated via behavioral model fitting (exp. bias model). Furthermore, to account for idiosyncratic body movements, we also included the first ten PCs of video recordings. These PCs accounted for 79.16% of the variance in video data. As discrete events, we included visual contrasts (−100%, −25%, −12.5%, −6.25%, 0%, 6.25%, 12.5%, 25% and 100%) at stimulus onset, as well choice and feedback (at their respective times), both for the current trial as well as for the previous one. The previous choice and feedback were modeled as accounting for sustained responses (as opposed to evoked) even before trial onset. Finally, above and beyond the experimental variables, we also accounted for elements of internal neural dynamics by including the concurrent firing of simultaneously recorded units in the same region, $y_t$ Together, a unit’s log-firing rate is modeled as a linear combination of arbitrary nonlinear functions (B-splines) of the covariates,

$$\mathrm{l}\mathrm{o}\mathrm{g}\mu =\sum _j{f}_j\left(x_j\right)+\sum _k{f}_k\times z_k+\sum _t{h}_t\times y_t+C,$$ (22)

where $\times$ is the convolution operator, and the spike counts are generated as Poisson random variables with the rate specified by equation (22). Input-specific nonlinearities $f(\cdot )$ were expressed in terms of flexible B-splines, $f(\cdot )\approx \mathit{\beta }\cdot \mathit{b}(\cdot )$. Similarly, $h_t$ are smooth causal filters (also learned) capturing the directional coupling between units, including an autoregressive component that accounts for refractory periods of units. Covariates and spike counts were discretized in 5-ms bins. The estimated kernels ($f$ and $h$ ) were associated with a smoothness-enforcing penalization term controlled by a scale parameter ${\lambda }_f$,

$$\mathrm{P}\mathrm{E}\mathrm{N}\left(f,{\lambda }_f\right)=-\frac{1}{2}{\lambda }_f{\beta }^T{S}_f\beta ,S_f=\int b^{\prime \prime }\cdot b^{\prime \prime }\mathrm{d}x.$$ (23)

The larger ${\lambda }_f$, the smoother the model. These penalization terms can be interpreted as Gaussian priors over model parameters. The resulting log-likelihood of the model takes the form,

$$ℒ(y)=\mathrm{l}\mathrm{o}\mathrm{g}P(y,\mid ,x,z,\beta )+\sum _f\mathrm{P}\mathrm{E}\mathrm{N}\left(f,{\lambda }_f\right),$$ (24)

with $y\in {\mathbb{R}}^T$ being the spike counts of the unit, $x\in {\mathbb{R}}^{J\times T}$ being the continuous task variables, $z\in {\mathbb{R}}^{K\times T}$ being the discrete task events, $T$ being the time points, $\beta$ being the collection of all B-spline coefficients, and being $P(\cdot )$ the Poisson likelihood. Both parameters $\beta$ and the hyperparameters $\lambda$ are learned from the data by an iterative optimization procedure that switches between maximizing equation (24) and minimizing a cross-validation score as a function of hyperparameters (see ref. 42 for further details). We used 11 nodes ($\beta s$) per fitted covariable (19 experimental + a variable number of simultaneously recorded units), resulting in the average full encoding model having 590.33 parameters. Notably, the probabilistic interpretation of the penalization terms allowed us to compute a posterior distribution for the model parameters. In turn, this allows us to derive confidence intervals with desirable frequentist coverage properties and implement a statistical test for inclusion of a minimal subset of task variables explaining most of the variance. In other words, it allows fitting an encoding model and performing implicit model selection within our large neurophysiological dataset (see refs. ^45,94 for a similar approach and additional model validations). The average reduced model had 61.25 parameters (10.3% of the full model) with no detriment to its ability to account for spiking activity (all $P>0.36$; Supplementary Fig. 3).

The encoding model fit quality was assessed via $\text{pseudo-}{R}^2$ on a subset of held-out test trials (20% of the total trials). $\text{Pseudo-}{R}^2$ is a goodness-of-fit measure that is suitable for models with Poisson observation noise⁹⁵. The score is computed as follows:

$$\text{pseudo}-R^2=1-\frac{ℒ(y)-ℒ(\hat{y})}{ℒ(y)-ℒ(\bar{y})},$$ (25)

with $ℒ(y)$ being the likelihood of the true spike counts, $ℒ(\hat{y})$ being the likelihood of the pGAM prediction and $ℒ(\bar{y})$ being the likelihood of a Poisson null model (mean rate). $\text{Pseudo-}{R}^2$ is 0 when the pGAM fits are no more likely than the null model, 1 when it perfectly matches the data and can be negative when overfitting occurs (for test-set data, 0.5% of the recorded units). Empirically, the $\text{pseudo-}{R}^2$ is a stringent metric and ranges in values that are substantially lower than the standard $R^2$ when both are applicable⁹⁶. Our average score of 0.0745 is two to four times better than standard GLM performance⁴⁷. The $R^2$ of trial-averaged firing rates to variables deemed to significantly contribute to spike trains was on average 0.82. For analyses downstream of the pGAM, we include units with a minimum $\text{pseudo-}{R}^2$ of 0.01, deem variables as significantly contributing to spike trains at $\alpha <0.001$ and include regions in the analysis if at least 40 units per area were properly fit, in each of the genotypes (Figs. 5 and 6c–e) or across genotypes (Fig. 6a,b). For Fig. 7, we fit separate pGAMs for each biased block (80:20 and 20:80) and remove the experimental prior as a covariate. This allowed us to estimate responses to each contrast for each of the experimental priors.

We compute the MI between an experimental variable and the observed spiking activity, where $y_t$ are the spike counts at time $t$, and $y_t\mid \beta ,X_t\sim \mathrm{P}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{s}\mathrm{o}\mathrm{n}\left(X_t,\beta \right)$, where $X_t$ is the stimulus matrix at time $t$. We know that $\beta \mid X\sim 𝒩(\hat{\beta },\mathrm{\Sigma })$. We select one stimulus dimension, $x_j=X_{:j}$ and discretize it into $n$ values, $x_j\in \{x_j^1\dots x_j^n\}$. We approximate the input distribution using a binomial $P(x_j^k)=p_k$, where $p_k$ is the empirically observed frequency of the stimulus. For each time point we computed,

$$\begin{gathered} E\left(y_t\mid X\right)=E_{\beta \mid X}\left(E\left(y_t\mid X,\beta \right)\right) \\ =E_{\beta \mid X}\left(\mathrm{e}\mathrm{x}\mathrm{p}\left(X_t\beta \right)\right) \\ ={\mu }_t+{\sigma }_t^2/2, \end{gathered}$$ (26)

where ${\mu }_t=X_t\hat{\beta }$ and ${\sigma }_t^2=X_t{X}_t^T$. We approximate the conditional entropy $H(y\mid x_j^k)$ as the entropy of a Poisson variable with mean equal to $\frac{1}{T}{\mathrm{\Sigma }}_{t}E\left(y_t\mid X\right)$, where the sum is taken over the $T$ time points in which $x_{jt}=x_j^k$. We also approximate the entropy of spikes $H(y)$ as the entropy of a Poisson with mean the average firing rate of the unit. MI was computed as follows:

$$\begin{gathered} I\left(x_j,y\right)=H(y)-H\left(y_t,\mid ,x_j\right) \\ =H(y)-\sum _k p_{k}H\left(y_t,\mid ,x_j^k\right). \end{gathered}$$ (27)

Extended Data

Extended Data Fig. 1 |. Example psychometric fits during biased sessions.

Psychometric fits to the fraction of ‘rightward’ responses as a function of contrast (x axis) and experimental block (colors; dark color indicated a left-biased block). Four example animals (columns) are shown for each of the 4 genotypes (rows). Circles are the observed fraction of responses, and curves are fits.

Extended Data Fig. 2 |. Influence of prior on decision-making in the absence of psychometric fitting.

a, Change in fraction ‘rightward’ choice as a function of block and contrast. Wild-type animals (C57BL6, n = 15) changed their choice as a function of block more than all mouse models of ASD (Fmr1, n = 19, green; Cntnap2, n = 21, yellow; Shank3, n = 20, brown) when the grating contrast was low (−12.5, 0, 6.25 and 12.5). Please note each animal was recorded for approximately 4 sessions (mean = 3.97) and on average performed 661 trials/session, thus resulting in ~2,600 trials/animal, 40k trials in the genotype with the smallest number of animals (C57BL6) and a total dataset of almost 200k trials. Error bars are ±1s.e.m. across animals. b, Comparison of current dataset to a publicly released²⁸ dataset of wild-type animals performing the same task (IBL, n = 137, orange). The wild-type animals in our cohort were no different from the larger sample. Error bars are ±1s.e.m. across animals. Of note, all animals in the current dataset (a) were trained in the same manner. Most notably, there was no requirement for showing a change in responses as a function of the prior to be moved to physiology recordings. Animals simply performed 10–15 sessions of ‘biased blocks’ before being moved to physiology. In contrast, the IBL dataset²⁸ is fabricated to show choice differences across blocks, as there was a requirement on this criterion (5% bias, see appendix 1 in ref. 28) to move animals from training to physiology recording.

Extended Data Fig. 3 |. Lack of surprise during the presentation of statistically unlikely events in mouse models of ASD.

a, Video recordings and schematic showing pupil tracking. b, Grand-average pupil diameter as a function of time since stimulus presentation. c, Pupil diameter as a function of experimental block (80:20 in purple and 20:80 in gold), genotype (rows; C57BL6, Fmr1, Cntnap2 and Shank3, respectively) and contrasts (columns). In control animals (C57BL6), we observe that at −100% (p < 0.05, 1.79 s post-stimulus onset), −25% (1.31 s post-stimulus onset) and 100% (1.23 s post-stimulus onset) contrasts, the late latency (that is, surprise-driven) pupil diameter was modulated by sensory history. Notably, dilation was greater when statistically unlikely events were presented (that is, high contrast on the right visual field under the left prior or high contrast on the left visual field during the right prior) and did not occur when sensory observations were uncertain (low contrast). The prior-dependent pupil dilation indicating surprise was not present in any of the mouse models of ASD (second and third row, all p > 0.16), with exception for a single contrast (−25%, p < 0.05, 1.46 post-stimulus onset) in the Shank3 animals (bottom row, second column). Shaded area is ±1s.e.m.

Extended Data Fig. 4 |. Impact of feedback on behavior and neural responses.

It is possible that the reduced use of priors in mouse models of ASD was due to reduced perceptual error monitoring and the incorporation of feedback in guiding subsequent behavior. To test for this possibility, we examine the impact of feedback on behavior and physiology and whether this differed across genotypes. a, For behavior, we examined how responses on the current trial (y axis) varied as a function of current contrast (y axis), previous contrast (x axis) and whether the previous response was correct (top) or incorrect (bottom). We subtracted the average psychometric curve (computed from all trials) from each psychometric curve computed conditional on the specifics of the previous trial (that is, ‘update matrices’). As expected, after a correct trial, the updating was minimal when the current choice was easy, regardless of the difficulty of the previous choice. Instead, after a correct trial, the amount of updating was large if the current and previous choices were both difficult (that is, low contrast). In other words, when sensory evidence was weak, the previous reward influenced choices more so if the reward was earned on a difficult trial. The opposite was true on trials following incorrect choices (bottom), where animals tended to switch responses, particularly if the trial had been easy. b, This tendency to incorporate feedback into behavior was no different across genotypes. To quantify this, we build a linear classifier (SVM) trained to classify animals into their correct genotype according to update matrices (separately for trials following correct and incorrect responses). The confusion matrices from this classifier showed poor performance (chance = 25.37% given the uneven number of animals per genotype), with animals not being more likely to be classified in their appropriate category than chance (both p > 0.19). c, Grand-average peri-event time histogram (PETH) for feedback-responding units across all brain areas. While numerically the response to feedback was larger in C57BL6 animals, this was not statistically significant (one-way ANOVA, p = 0.09). d, We examine responses to feedback with more granularity by examining the mutual information afforded by units in specific brain regions according to the pGAM. This analysis showed a number of areas (all p < 0.05), where the Shank3 animal more vigorously differentiated between correct and incorrect feedback (MRN, PO, PRT, RSPv and SUB), but none in which the C57BL6 animal was different from all mouse models of ASD. Error bars are ±1s.e.m. with the smallest n = 40 neurons.

Extended Data Fig. 5 |. Variance explained by PCA and dPCA as a function of number of dimensions.

The variance explained by PCA (black) and dPCA (red) monotonically increased with the number of dimensions included. Including 10 dimensions (which the Main analyses do), PCA explained nearly all variance in neural responses (96.3%). Thin, transparent lines in the background are individual sessions. In the Main, dPCA variance explained is expressed as a fraction of PCA variance explained, as this latter one can vary considerably by brain region, and thus the variance that PCA can explain is used as a normalizing factor across brain areas.

Extended Data Fig. 6 |. Stability of coupling filters across experimental blocks.

a, We compute the Pearson correlation coefficient (r) between coupling filters across a given pair of units estimated by the pGAM in leftward (80:20) and rightward-biased (20:80) experimental blocks (over 640k pairs in total). These showed a strong degree of stability (r ~0.70) and no difference across genotypes (one-way ANOVA, p = 0.79; error bars are ±1s.e.m. with the smallest n = 111,639 pairs of neurons). When separating into macro-areas (b), we observed more remapping of noise correlations in STR than the rest of areas (p < 0.05; c), but no systematic effect wherein all mouse models of ASD differed from the control. Error bars are ±1s.e.m. with the smallest n = 339 pairs of neurons.

Extended Data Fig. 7 |. Performance of the encoding model (pGAM).

We fit a coupled model (that is, with neural responses of one unit putatively impacting the firing of another) to account not solely for task-driven responses but also for internal neural dynamics. a, Comparison of $\text{pseudo-}{\mathrm{R}}^2$ for the coupled model (y axis) and an uncoupled model (x axis). Transparent dots are sessions (colored according to genotype), and opaque dots are averaged across sessions. Error bars are s.e.m. In all genotypes, the coupled model accounts better for spike trains (all p < 0.003). To assess performance of the variable selection procedure, we contrast $\text{pseudo-}{\mathrm{R}}^2$ of the models allowing for coupling, in full ($\mathrm{x}$ axis, average of 590.33 parameters) and when reduced to the variables deemed to significantly account for spiking activity ($\mathrm{y}$ axis, average of 61.25 parameters, $\alpha$ set at 0.001). b, The full and reduced models accounted for an equal portion of the variance (all p > 0.36), while the latter had a tenth of the number of parameters/retained variables.

Extended Data Fig. 8 |. Responses to contralateral and ipsilateral high contrast gratings predicted by the pGAM.

a, Evoked firing rates to high contrast gratings. As previously demonstrated (ref. ³⁵), primary visual cortex (VISp) is particularly tuned to contralateral stimuli, while the rest of regions respond fairly equally across hemi-fields. b, Difference in the mutual information between neural responses evoked by contralateral and ipsilateral grating presentation. Error bars are ±1 s.e.m. with the smallest n = 40 neurons.

Extended Data Fig. 9 |. Peri-stimulus time histograms (PSTH) across frontal cortices as a function of sensory history.

In control animals (C57BL7, top row), neural responses were stronger to unexpected stimuli—for instance, a grating on the left hemifield (negative contrasts) under a rightward-biased block (gold color). This effect, consistent with predictive coding, was absent in Fmr1 (second row, green), Cntnap2 (third row, yellow) and Shank3 (brown) animals.

Extended Data Fig. 10 |. Sensory prediction errors as a function of cortical layer.

Sensory prediction errors are typically considered to be most common in superficial cortical layers, while silicon probes oversample deeper cortical layers. Thus, in addition to acknowledging that the method used here may not be the best suited to examine cortical sensory prediction errors, it is also possible that differences across genotypes may have arisen from a differential sampling of cortical regions. To examine this possibility, we first examined the fraction of neurons across cortical layers in each of the genotypes. a, Across the cortex as a whole, most neurons were recorded in L5 (${\chi }^2$ test, p < 0.001), followed by an approximately equal number of neurons in L2/L3 and L6 (${\chi }^2$ test contrasting L2/L3 and L6, p > 0.19). There was a nominal number of neurons in L1 and L4. This pattern was true across all genotypes (${\chi }^2$ test, p = 0.79). b, Same analysis and illustration as in a, while restricting the analysis to frontal cortical areas ACAd, ACAv and MOs. Again, there was no difference in layer sampling across genotypes (${\chi }^2$ test, p = 0.68). c, Same analyses as in b, while restricting analysis to visual cortices (VISp, VISa and VISam). There was no difference in layer sampling across genotypes (${\chi }^2$ test, p = 0.41). d, We questioned how the presence of sensory prediction errors varied across layers in FC. Unfortunately, this analysis was not possible in L1 and L4, given their very small sample sizes. Across the rest of layers (L2/L3, L5 and L6), we observe the same effect reported in the Main; presence of sensory prediction errors in C57BL7 but not mouse models of ASD (ANOVA interaction term, p < 0.001; error bars are ±1s.e.m. with the smallest n = 40 neurons). e, Prediction errors were observed in all genotypes in L2/L3 (ANOVA interaction term, p = 0.198) and not in L5 or L6 (ANOVA interaction prior block × contrast; both p > 0.71; error bars are ±1s.e.m. with the smallest n = 40 neurons).

Supplementary Material

Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41593-025-01965-8.

The International Brain Laboratory

Dora Angelaki^7,8, Julius Benson⁷, Daniel Birman⁹, Niccolo Bonacchi¹⁰, Matteo Carandini¹¹, Joana A. Catarino¹⁰, Gaelle A. Chapuis¹², Anne K. Churchland¹³, Yang Dan¹⁴, Felicia Davatolhagh¹³, Peter Dayan¹⁵, Eric EJ DeWitt¹⁰, Tatiana A. Engel¹⁶, Mayo Faulkner¹⁰, Ila Rani Fiete¹⁷, Laura Freitas-Silva¹⁰, Berk Gercek¹², Kenneth D. Harris¹¹, Michael Hausser¹¹, Sonja B. Hofer¹⁸, Fei Hu¹⁴, Julia M. Huntenburg¹⁰, Anup Khanal¹³, Christopher Krasniak¹⁹, Zachary F. Mainen¹⁰, Guido T. Meijer¹⁰, Nathaniel J. Miska¹⁸, Thomas D. Mrsic-Flogel¹⁸, Jean-Paul Noel^1,2,3,4, Alejandro Pan-Vazquez¹⁶, Liam Paninski²⁰, Alexandre Pouget¹², Cyrille Rossant¹¹, Noam Roth⁹, Michael Schartner¹⁰, Karolina Z. Socha¹¹, Nicholas A. Steinmetz⁹, Karel Svoboda²¹, Anne E. Urai²², Miles J. Wells¹¹, Steven Jon West¹⁸, Matthew R. Whiteway²⁰, Olivier Winter¹⁰ & Ilana B. Witten¹⁶

⁹University of Washington, Seattle, WA, USA. ¹⁰Champalimaud Foundation, Lisbon, Portugal. ¹¹University College London, London, UK. ¹²University of Geneva, Geneva, Switzerland. ¹³University of California, Los Angeles, Los Angeles, CA, USA. ¹⁴University of California, Berkeley, Berkeley, CA, USA. ¹⁵Max Planck Institute, University of Tubingen, Tubingen, Germany. ¹⁶Princeton University, Princeton, NJ, USA. ¹⁷Massachusetts Institute of Technology, Boston, MA, USA. ¹⁸Sainsbury Wellcome Center, London, UK. ¹⁹Cold Spring Harbor Laboratory, Laurel Hollow, NY, USA. ²⁰Columbia University, New York City, NY, USA. ²¹Allen Institute for Neural Dynamics, Seattle, WA, USA. ²²Leiden University, Leiden, the Netherlands.

Data availability

Raw data can be accessed following the instructions given at https://osf.io/fap2s. Summary data to reproduce the figures are available at https://osf.io/fap2s/.

Code availability

Code to reproduce the figures is available at https://osf.io/fap2s/. Code to fit behavioral models is available at https://github.com/int-brain-lab/ibl-changepoint. Code to fit encoding models is available at https://github.com/BalzaniEdoardo/PGAM.