A theory of autism bridging across levels of description

Abstract

Autism impacts a wide range of behaviors and neural functions. As such, theories of ASD are numerous and span different levels of description, from neurocognitive to molecular. We propose how existent behavioral, computational, algorithmic, and neural accounts of ASD may relate to one another. Specifically, we argue that ASD may be casted as a disorder of causal inference (computational level). This computation relies on marginalization, which is thought to be subserved by divisive normalization (algorithmic level). In turn, divisive normalization may be impaired by excitatory-to-inhibitory imbalances (neural implementation level). We also discuss ASD within similar frameworks, those of predictive coding and circular inference. Together, we hope to motivate work unifying across the different accounts of ASD.

In need of a new kind of theory of ASD

Autism spectrum disorder (ASD) is a heterogeneous neurodevelopmental condition of unknown etiology. It impacts a wide range of functions, from social and communicative faculties [1], to motor behaviors [2], and sensory processing [3]. Similarly, a wide range of genetic [4] and environmental [5] factors have been linked to the disorder. As such, there are a great number of theories of ASD, and these are as diverse as the condition itself. Some emphasize psychological descriptions (e.g., weak central coherence (see Glossary) [6], theory of mind [7]), or focus on brain-wide [8] or micro-circuit [9] connectivity patterns, while yet others highlight particular neuro-transmitters [10] or genetic mutations [11-13]. Many of these theories are well supported by empirical results, and yet we do not understand the root cause, or causes, of ASD.

We argue that a new kind of theory is needed. One that bridges across levels of description. Computational models are well suited to this task because they allow complex phenomena to be distilled into a set of precisely defined equations and parameters. Further, the latter may then be searched for in neural activity. In turn, in recent years we have seen a flurry of formal proposals [14-20], most commonly within the framework of the Bayesian brain and addressing mechanisms of perception. A mathematical formulation, however, is only the first step. Next, we need to specify how neurons, synapses, proteins, and genes may support this computation, both in neurotypical brains and in those of individuals with ASD. Here, we sketch a working hypothesis, starting from computation and bridging to algorithm and neural instantiation. Although many of the details are still missing, this highlights the need for a cross-disciplinary framework guiding new, theoretically-motivated experiments.

Behavior and computation: causal inference

ASD phenotypes are varied and impact a wide range of functions. In perception, for instance, anomalies have been reported across vision [21], audition [22], touch [23], and olfaction [24], among other sensory modalities. Likewise, reports have highlighted differences in both low-level encoding [25], as well as in the higher-level interpretation of sensory evidence, or semantic understanding [26]. It follows that if there is a single computation that has gone awry in ASD, this ought to be a canonical one – a modular computation that can be widely applied across behavioral challenges, brain regions, and even animal species. In our opinion, a strong candidate for such a computation is causal inference [27, 28].

Causal inference is the ubiquitous and flexible process of attributing observations to (hidden) cause(s) [28]. Some refer to this process as structure learning; the process of deducing which hidden environmental structure may have generated observed signals. In perception, for example, we do not have direct access to environmental objects and events, nor to their causal relationship (the “generative model” producing environmental signals). Instead, our biological sensors process only a limited set of available inputs. These are stochastic and may be ambiguous. Thus, in building internal models of the external environmental, we must first ascribe observations to their likely underlying environmental cause, or causes. That is, we must deduce the set of causal relations within a hypothesized generative model linking observations and hidden (or latent) causes (Fig. 1). For instance, an auditory and a visual cue may relate to a single object (e.g., a heard and seen cab), or could indicate two separate ones (e.g., a seen cab and another heard-yet-unseen cab; Fig. 1A, see caption and Box 1 for mathematical formalism). Thus, to behave adaptively, we first have to form a hypothesis specifying the probability associated with potential world states. Then, these hypotheses are weighted according to their relative evidence in generating a percept taking into account all possible worlds. This is a process of marginalization, where we remove a variable (in this case the hypothesized world states) by summing over all possible values this variable could take (note, this process of marginalization may be implicit, for instance in the use of mixture priors [30, 31]). Importantly, this process of causal inference is not only true in perception, but also in cognition and action. For example, in reasoning we may attempt to deduce the causal structure between a set of factors (e.g., age, sex, contact with a virus) and an outcome (e.g., disease), or during motor behaviors we may attempt to classify sensory input as consequences of our actions or as emanating from the external environment.

Figure 1. Bridging across computational, algorithmic, and neural accounts of ASD.

A. Causal inference. A generative model for the example where sounds and sights pertain to a single source (C = 1) or multiple sources (C = 2). Left panel: visual (X_v, yellow) and auditory (X_A, blue) signals pertain to a single source (i.e., green = yellow + blue). Right panel: visual (X_v, yellow) and auditory (X_A, blue) signals pertain to separate sources. Observers first infer the likely causal structure (Box 1, Eq. 1), and then weigh these interpretations in perceiving (Box 1, Eqs. 2-4). B. Divisive normalization. Responses of single neurons (output) are divided by the sum of activity from a normalization pool. C. Predictive coding. In cortical circuits there are likely at least two flavors of prediction error neurons; those indicating the unexpected presence (Type 1) or absence (Type 2) of a signal. This implies a critical role for inhibitory interneurons (orange) in the schematized circuit. Further, a gating or modulatory mechanism dictates when errors might indicate a true change in the environment or not. We propose this mechanism may be driven by causal inference, attributing deviations from an expectation to either “noise” (expected fluctuations) or a true change in the environment (unexpected fluctuations), and instantiated via divisive normalization.

Box 1. Mathematical formalism of causal inference.

Let’s take the example of inferring the location of an object (or objects) in the environment given two cues, an auditory $(a)$ and visual $(v)$ one. In probabilistic terms, to infer the causal structure given sensory observations, we apply Bayes’ rule,

$$p(C\mid X_a,X_V)=\frac{p(X_a,X_V\mid C)p(C)}{p(X_a,X_V)}$$ (Eq. 1)

where $p(C)$ is the prior probability of assuming that signals belong to either a single or multiple sources (i.e., cabs), and $p(X_a,X_V)$ is chosen such that $p(C=1\mid X_a,X_V)$ and $p(C=2\mid X_a,X_V)$ sum to 1 (in this case where the graphical model assumes $C=1$ and $C=2$ represent the totality of all possibilities, Fig. 1A). $p(C=1)$ is typically referred to as “p-common”, the prior probability of combining cues. Then, assuming a particular cost function (i.e., what type of error we would like to minimize), we may estimate the visual source as a weighted sum of the estimates under different possible causal structures,

$${\widehat{S}}_v=p(C=1\mid X_a,X_V){\widehat{S}}_{v,c=1}+(1-p(C=1\mid X_a,X_V)){\widehat{S}}_{v,c=2}$$ (Eq. 2)

where ${\widehat{S}}_{v,c=1}$ is the estimate given we assume auditory and visual cues pertain to the same cab. The optimal (i.e., reliability-weighted [29]) solution with Gaussian likelihoods is,

$${\widehat{S}}_{v,c=1}=\frac{\frac{x_v}{{\sigma }_v^2}+\frac{x_a}{{\sigma }_a^2}+\frac{{\mu }_v}{{\sigma }_p^2}}{\frac{1}{{\sigma }_v^2}+\frac{1}{{\sigma }_a^2}+\frac{1}{{\sigma }_p^2}}$$ (Eq. 3).

${\widehat{S}}_{v,c=2}$ is the visual estimate independent of auditory signals,

$${\widehat{S}}_{v,c=2}=\frac{\frac{x_v}{{\sigma }_v^2}+\frac{{\mu }_v}{{\sigma }_p^2}}{\frac{1}{{\sigma }_v^2}+\frac{1}{{\sigma }_p^2}}$$ (Eq. 4).

The details specifying the rest of parameters (e.g., ${\mu }_v$, ${\sigma }_p^2$, ${\sigma }_v^2$, ${\sigma }_a^2$) and analytical forms for the full equation are described elsewhere [27], and depend on the generative model of the specific problem at hand (c.f. Figure 2 in [28] for depiction of a number of different generative models). It is important to note, however, that causal inference is the general operation of weighting different world-views according to their inferred probabilities. Namely, a critical step in this computation is summing out the different interpretations and the parameters within these interpretations (Eq. 2). A component ingredient of causal inference is the optimal combination of cues (Eq. 3, [29]), provided that these were inferred to relate to the same source.

In perception, the tell-tale sign of causal inference is a stereotyped pattern of behavior wherein independent sources may bias perception of one another when they are weakly (dis)similar, but not when they are very distinct [27, 28]. For example, when trying to localize a cab, if auditory and visual signals originate from vastly distinct locations, these ought to be treated independently, and thus not bias the localization of one another. However, if a visible cab and a honking-yet-unseen cab are near one another, we may deduce an incorrect set of causal relations (i.e., internal model) in attributing both visual and auditory signals to a single cab. In this scenario, we would misuse both auditory and visual cues to estimate the location of our (e.g., visual) source of interest, yielding perceptual biases. This pattern of behavior, with (attractive) biases being expressed exclusively when distinct cues have relatively similar features has been observed across a wide array of tasks, including but not limited to spatial localization [27, 32, 33], orientation judgments [34], rate detection [35], speech intelligibility [36], weight [37] and body [38-40] perception, motor learning [41], heading estimation [42], and spatial navigation [43].

The suggestion that causal inference is impaired in ASD was supported first by tangential evidence, and more recently by a larger scale, multi-experiment approach combined with formal model fitting. The early hints came from studies in binocular rivalry demonstrating that individuals with ASD altered between ambiguous percepts at a slower rate than their neurotypical counterparts [44]. That is, the set of causal relations hypothesized to link observed photons and their underlying generative images is less flexible in individuals with ASD (see [45] for a related interpretation of bistable perception based on circular inference). Secondly, there is a vast literature demonstrating that individuals with ASD will claim that audio-visual cues were presented synchronously at larger asynchronies than control subjects ([46], see [47] for a meta-analysis of 53 of such studies). Leveraging speech stimuli, researchers [48] applied a causal inference model [36] to simultaneity judgments from neurotypical controls and individuals with ASD. Findings suggested that individuals with ASD had a greater a priori probability of combining audio and visual cues, regardless of whether these signals ought to or not be integrated. This is typically referred to as a heightened “p-common” (i.e., an a priori probability of combining cues).

More recently, a large-scale study (five psychophysical studies including over 90 adolescents) was conducted to directly test whether individuals with ASD showed impairments in causal inference [49]. The researchers measured (1) unisensory auditory and visual localization thresholds, (2) Bayes optimal cues combination not requiring the deduction of causal relations [29], (3) explicit causal inference, as well as implicit causal inference across (4) audio-visual and (5) visual-visual pairings. That is, this study tested low-level sensory encoding, multisensory integration (i.e., optimal cue combination), and causal inference within a single cohort and stimulus set. All data was used to create a single model fit per participant, which demonstrated no impairment in sensory processing or cue combination in ASD, but did show a larger (implicit) “p-common” in these individuals relative to their neurotypical counterparts. Namely, even at very large audio-visual or visual-visual disparities (the former in spatial location, the latter in velocity of motion) individuals with ASD behaved as if always (maladaptively) combining cues. Together, these results explain why individuals with ASD have been widely reported to show anomalous multisensory behavior [46, 47, 50]. It is not due to an impairment in the process of multisensory integration itself, which is in line with statistical optimality [29] in both controls and individuals with ASD [49, 51], but because of a more general anomaly in establishing and updating an internal model specifying when cues ought to or not be combined. The observation that causal inference is impaired in ASD, but optimal cue combination [29] is not [49, 51], provides an important clue to a potential algorithmic deficit that may exist in ASD.

Algorithm: marginalization and divisive normalization

Bayesian cue combination [29] specifies howto combine signals in a statistically optimal manner, provided that these belong to the same source (see Box 1). That is, it is a sub-component of the larger causal inference scheme. This process of cue combination is not impaired in ASD [49, 51]. From the standpoint of mathematical operations, a major differentiator between cue combination (intact in ASD) and causal inference (impaired in ASD) is the presence of marginalization in the latter but not the former. Interestingly, theoretical work [52] showed that biologically-plausible neural networks (e.g., those associated with constant fano factors as in linear probabilistic population codes [53]) perform marginalization via a neural computation known as divisive normalization [54]. The implication is that causal inference may rely on divisive normalization, and thus this is a neural operation that may have gone awry in ASD.

Divisive normalization is a critical operation allowing neurons to adapt their dynamic range according to context, and thus combat saturation. This is accomplished by computing a ratio between the response of an individual neuron and the summed activity of a pool of neurons (Fig. 1B, [54, 55]). Importantly, this form of gain control effectively modulates synaptic weights and is considered a canonical neural computation [55] in that it has been described across primary [54] and extrastriate [56] visual cortex, auditory cortex [57], the superior colliculus [58], and the antenna lobe of fruit flies [59], among other. It is thought to be involved in contrast- and pattern-invariant visual representations [55, 60], as well as in concentration-invariant odorant encoding in the olfactory system [59]. Namely, just as causal inference is a canonical behavioral computation, divisive normalization is a canonical neural computation.

In line with the argument that marginalization through divisive normalization may have gone awry in ASD, in silico simulations [61] showed that alterations in divisive normalization could account for diverse phenomena present in the condition, such as alterations in visuo-spatial suppression [62, 63], or greater tunnel vision by surround suppression [64, 65] (see [21] and [66] respectively for a classic and recent review on sensory perception in ASD, including the highlighting of numerous conflicting results). This modeling work [61] argued that differences in divisive normalization could also putatively account for enhanced local (vs. global [67]) and simple (vs. complex [68]) processing in ASD, as well as for deficits in social cognition [69], altered visual search [70], and increased variance [71, 72] and size of receptive fields [73] in ASD. However, subsequent reports examining cross-orientation suppression [74] and adaptation to gaze direction [75], processes thought to rely on divisive normalization, showed no difference between controls and individuals with ASD.

To summarize, divisive normalization is a canonical neural computation [53] that may subserve causal inference ([52], see also [76, 77]) and accounts for a variety of the peculiarities present in ASD [61], but not all [74, 75]. The likely resolution to the latter observation is that “vanilla” divisive normalization models are imperfect. Fittingly, recent work [78] examined whether a standard divisive normalization model could account for neural responses in V1 as macaques viewed natural images (as opposed to the better-studied yet less ecologically relevant Gabors). The authors reported that variability in V1 spiking activity was not well explained by existing descriptions of surround suppression through divisive normalization. Instead, they were better predicted by a model wherein divisive normalization was gated by a probabilistic inference regarding the homogeneity of images. In short, according to this model [78], divisive normalization should or is only applied when neurons and their normalization pools encode a single object. Put differently, in the augmented divisive normalization model [78], causal inference gates divisive normalization (see [74] for an earlier account arguing that this augmented divisive normalization model may better explain disparities between ASD and neurotypical perception than the standard model [61]).

Neural Instantiation: E/I balance

So far, we have argued that anomalies in perception-driven behavior in ASD may emanate from abnormalities in causal inference [48, 49] and that this computation is subserved algorithmically by a process of marginalization. Further, we have suggested that marginalization relies on divisive normalization [52, 54, 55]. Consistent with this, we have seen that idiosyncrasies in divisive normalization may partially account for phenotypes observed in ASD [61], and that authors have argued for a strong relation between divisive normalization and causal inference (either the latter being subserved by the former [52, 76, 77], or the latter gating the former [78]). In this section, we briefly discuss neural instantiation.

There is a strong and previously discussed (e.g., [61]) relation between divisive normalization and the well-known hypothesis that ASD symptomatology arises from a heightened excitatory-to-inhibitory ratio (E/I balance, [79]). This hypothesis explains the frequent comorbidity between autism and seizures [80], and has been supported by observations indicating increased glutamatergic and decreased GABAergic activity, as well as a decrease in the number of GABA receptors [81] in ASD. Similarly, many of the genes associated with ASD – and as a consequence many of the developed mouse models of the disorder [82, 83] – relate to glutamate or GABA signaling. Studies leveraging magnetic resonance spectroscopy have also indicated disruptions in GABA concentration in visual [84], auditory [84], and somatosensory [85] cortices of humans with ASD. In fact, GABA concentrations seemingly correlate with ASD symptomatology severity [86], even though there is not always a categorical difference in GABA concentration between neurotypical and atypical groups [86], putatively due to homeostatic compensatory mechanisms [83].

Relating back to divisive normalization, one could of course conjecture that alterations in the genetic and neurochemical makeup of the brains of individuals with ASD may impact the machinery necessary for divisive normalization. The inverse relation may also be true, with the inability for gain-modulation through divisive normalization leading to, for example, increased seizures [80] and alterations in the amplitude of neural responses [72] and size of receptive fields [73]. We are agnostic as to whether molecular (e.g., availability of GABA) or circuit (e.g., gain-modulation via divisive normalization) level mechanisms are “primary” in ASD, with the condition potentially being expressed due to several different biological root causes (i.e., an equifinal entity). Instead, we aim to highlight that a computational deficit in causal inference [27, 28, 48, 49] – which implies (non-linear) inference over putative generative structures in addition to (linear) combination of Bayesian likelihoods and priors within a given structure – naturally suggests impairments in divisive normalization [61] and E/I balance [71].

Multi-level models: predictive coding and circular inference

The framework we have described has the advantage of neatly dissociating between computational, algorithmic, and biological levels of analysis. As such, it may be useful in making predictions at each level of analysis (e.g., computational prediction of the current account: no deficit in ASD in combining priors and likelihoods within static generative structures, but in adaptively updating inferred generative structures [87]; biological prediction: changing interpretations of a given sensory milieu should be accompanied by changing functional connectivity within normalization pools, and maladaptively so in ASD). However, the distinction between levels of analysis may be more useful to researchers than a reality of brain function (e.g., there is no computational level in the brain). In turn, it is important to highlight largely compatible models that apply across levels of description, such as predictive coding [88] and notions of circular inference [89] (see Box 2 for further comparison between our account and predictive coding theories of ASD).

Box 2. Bayesian brain hypotheses of ASD.

The initial “Bayesian brain” account of ASD stated that individuals with the condition underutilized their expectations, or Bayesian priors [14]. This account has been challenged by empirical work (e.g., [17, 51, 99], see [87] for a review) but did lead to a more subtle formulation; that individuals with ASD have “high, inflexible precision of prediction errors (HIPPEA)” [15]. This latter account has received support [16, 100], but has also made predictions that have not been borne out in empirical findings. For instance, a biological implementation of HIPPEA would involve the inappropriate cancelation of prediction errors leading to circular inference [89, 98] wherein bottom-up signals reverberate and are misinterpreted as predictions. A recent study [101], however, did not find increased circular inference in ASD (although this work awaits replication due to a limited range in ASD or ASD-like phenotypes and the fact that it was not conducted in a controlled environment). Similarly, HIPPEA [15] states that “optimal [multisensory] integration will not take place, because all cues, even redundant or very uncertain ones, will be weighed equally”. This prediction has been falsified across visual-vestibular [51], audio-visual [49], and visual-visual [49] pairings, where individuals with ASD combine cues in a statistically optimal manner, akin to their neurotypical counterparts. This is true even when cue reliability changes on a trial-by-trial basis [49], and thus demands appropriate reliability-based weighting.

We consider the causal inference account proposed here to be an evolution of rather than a departure from HIPPEA [15]. Indeed, these models have more in common than in difference (see e.g., [102]). As HIPPEA, we consider the defining characteristic of ASD pathology to be the inability to flexibly adjust to context. However, we consider this to be true only when the adjustment of inferred causal structures (“what observation relates to what latent cause”) is needed. This is seemingly congruent with the observation that updating of contextual (i.e., experiment-specific) but not structural (i.e., true in the external world) priors is impaired in ASD [87]. In particular, the causal inference account would not predict a heightened weight of prediction errors, as during bottom-up circular inference [101], or impaired optimal cue combination.

It is true that two studies fitting formal causal inference models to ASD data [48, 49] demonstrated a heightened “p-common”. However, we do not consider a heightened “p-common” as the defining characteristic, but simply the inflexible adjustment of inferred causal structures, as demonstrated by studies in binocular rivalry [44, 103-108].

ASD has been described as a disorder of prediction [15, 16, 90], and just as causal inference and divisive normalization may respectively be canonical computations at a behavioral and algorithmic level, predictive coding has been described as a basic computational and neural motif [91]. In short, in predictive coding perception is as much “top-down” as it is “bottom-up”. Instead of neural codes becoming increasingly complex as one ascends the neural hierarchy (i.e., a representational framework), in predictive coding neural nodes compare their inputs to their expectations, as inherited from “top-down” signals. Then, the difference between these, the prediction errors, are sent downstream and become the input to the next node in the neuraxis. Within this framework, the inhibition of neural responses that occurs as stimuli extend into surround fields ([92], algorithmically explained by divisive normalization [61] and anomalous in ASD [62]) is the consequence of stimuli at a given location acting as a prediction for stimuli in neighboring regions [91]. Thus, within this framework, differences in surround suppression in ASD [62] are due to deficits in making adaptive predictions.

To instantiate the framework of predictive coding, neural networks necessitate a micro-circuit to maintain an internal model giving rise to predictions, as well as a comparator micro-circuit computing the prediction error between bottom-up inputs and top-down predictions. In cortical nodes where neurons do not have high intrinsic firing rates (in contrast to subcortical areas), neurons may be able to signal the presence of an unexpected input via an increase in firing rate, but they would not be able to signal the absence of an expected input (putatively requiring a decrease in firing rate). Thus, it is likely that two types of prediction error neurons exist [91], either increasing their firing according to a difference between input and prediction (Type 1; Input - Prediction) or the difference between prediction and input (Type 2; Prediction – Input). This could be accomplished by a circuit akin to that depicted in Figure 1C, which emphasizes the critical need for inhibitory interneurons (i.e., E/I Balance). This critical need is similarly emphasized in quantitative simulations [89] demonstrating that the absence of proper inhibitory loops subtracting predictions and prediction errors results in pathological circular belief propagation wherein predictions (priors) or prediction errors (likelihoods) reverberate throughout the circuit and end up exerting undue influence (i.e., as in the heightened precision account of ASD [15, 92], see Box 2 for further discussion contrasting causal inference and the heightened precision of prediction errors accounts of ASD).

A second critical element of the predictive coding circuitry ought to be a gating or modulatory signal ([16, 91, 93], Fig. 1C), given that not all errors (or surprises) are created equally. Some should be expected given contextual cues (as when stimuli are noisy), while others should not. Only “unexpected uncertainty” should result in a changed internal model, as these likely reflect a change in the external environment [94, 95]. Just as dopaminergic signals are thought to adjust learning rates in reward prediction errors [96], some [16, 93] have suggested that neuromodulators (particularly acetylcholine and norepinephrine) fine-tune the precision, and thus weight, attributed to predictions and prediction errors. And it is precisely this context-dependent modulation that is hypothesized to be aberrant in ASD [15, 16, 92], and which potentially leads to the slow updating of internal models, including their associated expectations, or priors [16, 18, 19, 97]. Here, we speculate that divisive normalization may be a circuit-level mechanism to regulate the precision of prediction errors and that this mechanism may be selectively involved in computations leading to an inference over generative structure(s), or structure learning [78]. Nonetheless, broadly our account based on causal inference is largely compatible with the inflexible precision of prediction errors account [15, 16, 92] (see Box 2) – which may render the process of structure learning an optimization rather than an inference problem. In our opinion, however, the current account more naturally links to existent theories based on divisive normalization [61] and E/I balance [79].

Concluding remarks

In summary, we have sketched a roadmap from behavior and causal inference to marginalization, divisive normalization, and E/I imbalance. We also discussed predictive coding and its similarities and dissimilarities with the current account (see Box 2). Prior work has suggested that individuals with ASD show impairments in each of these elements (causal inference [48, 49], divisive normalization [55, 61], predictive coding [15, 16], context-dependent uncertainty partitioning [16, 94], E/I balance [79]). Similarly, prior work has made the association between some of these elements (see [15, 61, 74, 89]). Our contribution here is in highlighting the relationship between each of these individual elements, and in arguing that these may not be different theories or accounts of the disorder, but all part of a unified one bridging across levels of description. Further, unlike prior work, we emphasize deficits in the flexible updating of inferred generative structures – the process of causal inference [27, 28, 48, 49] – as key in ASD pathology. In our opinion, this view most naturally relates to impairments in marginalization, divisive normalization, and E/I imbalances. But it is certainly not incompatible nor contradictory with previous predictive coding [15] and circular inference [89, 98] accounts of ASD and psychopathology more generally. Of course, much work remains to be done (see Outstanding Questions), both from a basic science and clinical perspective (see Box 3 for speculation on how our framework may relate to ASD symptomatology). Although direct evidence for certain aspects of our proposal are limited at present, the strength of the current framework is that it naturally ties in previous, more established accounts (particularly the association between causal inference and divisive normalization). We hope this big-picture perspective will help design future theory-motivated experiments, and ultimately impact positively the lives of those with the condition.

Outstanding Questions.

1. Would individuals with ASD show anomalies in causal inference within naturalistic contexts? Causal inference has been well studied in laboratory tasks requiring binary choices and discretizing action and perception. However, we do not know how this translates to more natural contexts with continuous-time and active sensing.

2. How is causal inference computed by neurons and neural ensembles? There seems to be a strong association between causal inference and divisive normalization, but the exact relation is unknown. The relation currently rests on the observation that algorithmically causal inference necessitates marginalization, which can be implemented via divisive normalization.

3. Can “augmented” divisive normalization models account for recent empirical observations within the cognitive neuroscience study of ASD? How does divisive normalization relate to hypo- and hyper-sensitivity to sensory stimuli (see Box 3)?

4. What animal models and what behavioral protocols would be most effective in querying predictive coding in ASD from a systems neuroscience perspective? Dissection of the neural circuit supporting predictive coding is occuring at the level of systems neuroscience, while theories of predictive coding in ASD exist at the levels of psychology and cognitive neuroscience.

5. Can we assume that cost functions are similar across individuals with ASD and their neurotypical counterparts? Most reports fitting Bayesian models to the study of ASD assume a given cost function (e.g., maximizing reward rate), but these are subjective and difficult to establish. For instance, the subjective cost associated with performing actions may be different across ASD and neurotypical individuals.

6. Would manipulations of E/I balance and divisive normalization selectively impair causal inference without impairing optimal cue combination?

Box 3. Relation to ASD symptomatology.

ASD is clinically characterized by socio-communicative impairments, restrictive and repetitive behaviors, and perceptual anomalies including hyper- and hypo-sensitivity to sensory stimulation [1]. How does an account based on links between causal inference, marginalization, divisive normalization, and E/I balance relate to this symptomatology?

We can only speculate, given that few studies have formally tested causal inference within an ASD population, and none has meticulously characterized the symptomatology of the tested cohort. Given this caveat, we consider the key behavioral deficit in ASD to be the inability to update internal models linking observations to hidden causes -- e.g., flexibly deciding whether multisensory cues relate to the same objects and thus ought to be integrated, or not. This includes the inflexible updating of expectations [15, 18, 19]. Accordingly, anomalies in perception are due to a mismatch between the true and inferred generative structures yielding sensory signals. Hyper- and hypo-sensitivity may also emanate from deficits in contextualization, where a given stimulus may appear disproportionality intense/dull depending on context. In this line, some [66] have recently argued that disturbances in divisive normalization and E/I balance may explain the striking finding that perception in ASD does not adhere to Weber’s law [109] (i.e., is not properly contextualized).

Repetitive behaviors, insistence on sameness, and stereotypy could result from attempts to align incoming sensory evidence with the inflexible expectations of what that sensory input ought to be. In fact, recent work demonstrates that individuals with ASD will take overt compensatory measures [49] when faced with ambiguous generative structures.

As others before us (e.g., [15, 21]), we consider that socio-communicative impairments may be scaffolded on perceptual deficits and/or be particularly complex scenarios where latent structures are intricate and continuously changing, thus readily highlighting the computational deficits present in ASD.

Highlights.

1. Autism is a pervasive condition broadly afflicting perceptual, cognitive, social, and motor function.

2. There are a large number of theories of ASD and these span the gamut in terms of levels of description: behavioral, algorithmic, neural instantiation.

3. Here we attempt to close the gap between different theories (causal inference, marginalization, divisive normalization, E/I balance, and predictive coding) and levels of description.

Glossary

Bayesian brain

The assumption that the brain can be modeled as performing Bayesian computations and thus inverting generative models via Bayes’ rule and representing information in probabilistic terms.

Divisive normalization

Neural operation wherein responses are the ratio between an excitatory driven and a normalization signal.

Dynamic range

Within the context of spiking activity, the range (defined over the state space of the stimuli) over which a change in stimuli will lead to a change in neural activity

Fano factor

Variance-to-mean ratio of spike counts, usually within a particular time-window. Used to measure the variability of spike trains.

Gain control

Mechanism that allows for a change in gain that multiplies or divides the amplitude or strength of (neural) responses to a given input.

Localization thresholds

Minimal detectable spatial separation between cues, or between a cue and a reference point (measured in degrees, for example).

Magnetic resonance spectroscopy

Non-invasive technique allowing for the detection and quantification of tissue metabolites.

Marginalization

Mathematical term referring to summing over all possible values of one variable to determine the “marginal” contribution of another.

Mixture priors

A prior distribution that is a mixture of two or more probability distributions.

P-common

The prior probability that there is a single cause versus two causes.

Probabilistic population codes

Encoding-decoding framework wherein neural populations represent probability distributions over the stimulus.

Saturation

Within the context of spiking activity, the level at which neurons cannot increase their firing rate.

Surround suppression

The phenomenon where the relative firing of a neuron decreases when a stimulus is enlarged (usually beyond the size of the neuron’s receptive field).

Weak central coherence

A theory suggesting that individuals with ASD fail to see the big picture.