Functional connectivity and glutamate levels of the medial prefrontal cortex in schizotypy are related to sensory amplification in a probabilistic reasoning task.

The circular inference (CI) computational model assumes a corruption of sensory data by prior information and vice versa, leading at the extremes to 'see what we expect' (through prior amplification) and/or to 'expect what we see' (through sensory amplification). Although a CI mechanism has been reported in a schizophrenia population, it has not been investigated in individuals experiencing psychosis-like experiences, such as people with high schizotypy traits. Furthermore, the neurobiological basis of CI, such as the link between hierarchical amplifications, excitatory neurotransmission, and resting state functional connectivity (RSFC), remains untested. The participants included in the present study consisted of a subsample of those recruited in a study previously published by our group, Kozhuharova et al. (2021b). We included 36 participants with High (n=18) and Low (n=18) levels of schizotypy who completed a probabilistic reasoning task (the Fisher task) for which individual confidence levels were obtained and fitted to the CI model. Participants also underwent a 1H-Magnetic Resonance Spectroscopy (MRS) scan to measure medial prefrontal cortex (mPFC) glutamate metabolite levels, and a functional Magnetic Resonance Imaging (fMRI) scan to measure RSFC of the medial prefrontal cortex (mPFC). People with high levels of schizotypy exhibited changes in CI parameters, altered cortical excitatory neurotransmission and RSFC that were all associated with sensory amplification. Our findings capture a multimodal signature of CI that is observable in people early in the psychosis spectrum.

Efficient and robust coding in heterogeneous recurrent networks.

Cortical networks show a large heterogeneity of neuronal properties. However, traditional coding models have focused on homogeneous populations of excitatory and inhibitory neurons. Here, we analytically derive a class of recurrent networks of spiking neurons that close to optimally track a continuously varying input online, based on two assumptions: 1) every spike is decoded linearly and 2) the network aims to reduce the mean-squared error between the input and the estimate. From this we derive a class of predictive coding networks, that unifies encoding and decoding and in which we can investigate the difference between homogeneous networks and heterogeneous networks, in which each neurons represents different features and has different spike-generating properties. We find that in this framework, 'type 1' and 'type 2' neurons arise naturally and networks consisting of a heterogeneous population of different neuron types are both more efficient and more robust against correlated noise. We make two experimental predictions: 1) we predict that integrators show strong correlations with other integrators and resonators are correlated with resonators, whereas the correlations are much weaker between neurons with different coding properties and 2) that 'type 2' neurons are more coherent with the overall network activity than 'type 1' neurons.

No increased circular inference in adults with high levels of autistic traits or autism.

Autism spectrum disorders have been proposed to arise from impairments in the probabilistic integration of prior knowledge with sensory inputs. Circular inference is one such possible impairment, in which excitation-to-inhibition imbalances in the cerebral cortex cause the reverberation and amplification of prior beliefs and sensory information. Recent empirical work has associated circular inference with the clinical dimensions of schizophrenia. Inhibition impairments have also been observed in autism, suggesting that signal reverberation might be present in that condition as well. In this study, we collected data from 21 participants with self-reported diagnoses of autism spectrum disorders and 155 participants with a broad range of autistic traits in an online probabilistic decision-making task (the fisher task). We used previously established Bayesian models to investigate possible associations between autistic traits or autism and circular inference. There was no correlation between prior or likelihood reverberation and autistic traits across the whole sample. Similarly, no differences in any of the circular inference model parameters were found between autistic participants and those with no diagnosis. Furthermore, participants incorporated information from both priors and likelihoods in their decisions, with no relationship between their weights and psychiatric traits, contrary to what common theories for both autism and schizophrenia would suggest. These findings suggest that there is no increased signal reverberation in autism, despite the known presence of excitation-to-inhibition imbalances. They can be used to further contrast and refine the Bayesian theories of schizophrenia and autism, revealing a divergence in the computational mechanisms underlying the two conditions.

A functional theory of bistable perception based on dynamical circular inference.

When we face ambiguous images, the brain cannot commit to a single percept; instead, it switches between mutually exclusive interpretations every few seconds, a phenomenon known as bistable perception. While neuromechanistic models, e.g., adapting neural populations with lateral inhibition, may account for the dynamics of bistability, a larger question remains unresolved: how this phenomenon informs us on generic perceptual processes in less artificial contexts. Here, we propose that bistable perception is due to our prior beliefs being reverberated in the cortical hierarchy and corrupting the sensory evidence, a phenomenon known as "circular inference". Such circularity could occur in a hierarchical brain where sensory responses trigger activity in higher-level areas but are also modulated by feedback projections from these same areas. We show that in the face of ambiguous sensory stimuli, circular inference can change the dynamics of the perceptual system and turn what should be an integrator of inputs into a bistable attractor switching between two highly trusted interpretations. The model captures various aspects of bistability, including Levelt's laws and the stabilizing effects of intermittent presentation of the stimulus. Since it is related to the generic perceptual inference and belief updating mechanisms, this approach can be used to predict the tendency of individuals to form aberrant beliefs from their bistable perception behavior. Overall, we suggest that feedforward/feedback information loops in hierarchical neural networks, a phenomenon that could lead to psychotic symptoms when overly strong, could also underlie perception in nonclinical populations.

Learning to represent signals spike by spike.

Networks based on coordinated spike coding can encode information with high efficiency in the spike trains of individual neurons. These networks exhibit single-neuron variability and tuning curves as typically observed in cortex, but paradoxically coincide with a precise, non-redundant spike-based population code. However, it has remained unclear whether the specific synaptic connectivities required in these networks can be learnt with local learning rules. Here, we show how to learn the required architecture. Using coding efficiency as an objective, we derive spike-timing-dependent learning rules for a recurrent neural network, and we provide exact solutions for the networks' convergence to an optimal state. As a result, we deduce an entire network from its input distribution and a firing cost. After learning, basic biophysical quantities such as voltages, firing thresholds, excitation, inhibition, or spikes acquire precise functional interpretations.

Circular inference in bistable perception.

When facing ambiguous images, the brain switches between mutually exclusive interpretations, a phenomenon known as bistable perception. Despite years of research, a consensus on whether bistability is driven primarily by bottom-up or top-down mechanisms has not been achieved. Here, we adopted a Bayesian approach to reconcile these two theories. Fifty-five healthy participants were exposed to an adaptation of the Necker cube paradigm, in which we manipulated sensory evidence and prior knowledge. Manipulations of both sensory evidence and priors significantly affected the way participants perceived the Necker cube. However, we observed an interaction between the effect of the cue and the effect of the instructions, a finding that is incompatible with Bayes-optimal integration. In contrast, the data were well predicted by a circular inference model. In this model, ambiguous sensory evidence is systematically biased in the direction of current expectations, ultimately resulting in a bistable percept.

Computational Account of Spontaneous Activity as a Signature of Predictive Coding.

Spontaneous activity is commonly observed in a variety of cortical states. Experimental evidence suggested that neural assemblies undergo slow oscillations with Up ad Down states even when the network is isolated from the rest of the brain. Here we show that these spontaneous events can be generated by the recurrent connections within the network and understood as signatures of neural circuits that are correcting their internal representation. A noiseless spiking neural network can represent its input signals most accurately when excitatory and inhibitory currents are as strong and as tightly balanced as possible. However, in the presence of realistic neural noise and synaptic delays, this may result in prohibitively large spike counts. An optimal working regime can be found by considering terms that control firing rates in the objective function from which the network is derived and then minimizing simultaneously the coding error and the cost of neural activity. In biological terms, this is equivalent to tuning neural thresholds and after-spike hyperpolarization. In suboptimal working regimes, we observe spontaneous activity even in the absence of feed-forward inputs. In an all-to-all randomly connected network, the entire population is involved in Up states. In spatially organized networks with local connectivity, Up states spread through local connections between neurons of similar selectivity and take the form of a traveling wave. Up states are observed for a wide range of parameters and have similar statistical properties in both active and quiescent state. In the optimal working regime, Up states are vanishing, leaving place to asynchronous activity, suggesting that this working regime is a signature of maximally efficient coding. Although they result in a massive increase in the firing activity, the read-out of spontaneous Up states is in fact orthogonal to the stimulus representation, therefore interfering minimally with the network function.

Sensory noise predicts divisive reshaping of receptive fields.

In order to respond reliably to specific features of their environment, sensory neurons need to integrate multiple incoming noisy signals. Crucially, they also need to compete for the interpretation of those signals with other neurons representing similar features. The form that this competition should take depends critically on the noise corrupting these signals. In this study we show that for the type of noise commonly observed in sensory systems, whose variance scales with the mean signal, sensory neurons should selectively divide their input signals by their predictions, suppressing ambiguous cues while amplifying others. Any change in the stimulus context alters which inputs are suppressed, leading to a deep dynamic reshaping of neural receptive fields going far beyond simple surround suppression. Paradoxically, these highly variable receptive fields go alongside and are in fact required for an invariant representation of external sensory features. In addition to offering a normative account of context-dependent changes in sensory responses, perceptual inference in the presence of signal-dependent noise accounts for ubiquitous features of sensory neurons such as divisive normalization, gain control and contrast dependent temporal dynamics.

Predictive Ensemble Decoding of Acoustical Features Explains Context-Dependent Receptive Fields.

A primary goal of auditory neuroscience is to identify the sound features extracted and represented by auditory neurons. Linear encoding models, which describe neural responses as a function of the stimulus, have been primarily used for this purpose. Here, we provide theoretical arguments and experimental evidence in support of an alternative approach, based on decoding the stimulus from the neural response. We used a Bayesian normative approach to predict the responses of neurons detecting relevant auditory features, despite ambiguities and noise. We compared the model predictions to recordings from the primary auditory cortex of ferrets and found that: (1) the decoding filters of auditory neurons resemble the filters learned from the statistics of speech sounds; (2) the decoding model captures the dynamics of responses better than a linear encoding model of similar complexity; and (3) the decoding model accounts for the accuracy with which the stimulus is represented in neural activity, whereas linear encoding model performs very poorly. Most importantly, our model predicts that neuronal responses are fundamentally shaped by "explaining away," a divisive competition between alternative interpretations of the auditory scene. SIGNIFICANCE STATEMENT: Neural responses in the auditory cortex are dynamic, nonlinear, and hard to predict. Traditionally, encoding models have been used to describe neural responses as a function of the stimulus. However, in addition to external stimulation, neural activity is strongly modulated by the responses of other neurons in the network. We hypothesized that auditory neurons aim to collectively decode their stimulus. In particular, a stimulus feature that is decoded (or explained away) by one neuron is not explained by another. We demonstrated that this novel Bayesian decoding model is better at capturing the dynamic responses of cortical neurons in ferrets. Whereas the linear encoding model poorly reflects selectivity of neurons, the decoding model can account for the strong nonlinearities observed in neural data.

Constructing Precisely Computing Networks with Biophysical Spiking Neurons.

While spike timing has been shown to carry detailed stimulus information at the sensory periphery, its possible role in network computation is less clear. Most models of computation by neural networks are based on population firing rates. In equivalent spiking implementations, firing is assumed to be random such that averaging across populations of neurons recovers the rate-based approach. Recently, however, Denéve and colleagues have suggested that the spiking behavior of neurons may be fundamental to how neuronal networks compute, with precise spike timing determined by each neuron's contribution to producing the desired output (Boerlin and Denéve, 2011; Boerlin et al., 2013). By postulating that each neuron fires to reduce the error in the network's output, it was demonstrated that linear computations can be performed by networks of integrate-and-fire neurons that communicate through instantaneous synapses. This left open, however, the possibility that realistic networks, with conductance-based neurons with subthreshold nonlinearity and the slower timescales of biophysical synapses, may not fit into this framework. Here, we show how the spike-based approach can be extended to biophysically plausible networks. We then show that our network reproduces a number of key features of cortical networks including irregular and Poisson-like spike times and a tight balance between excitation and inhibition. Lastly, we discuss how the behavior of our model scales with network size or with the number of neurons "recorded" from a larger computing network. These results significantly increase the biological plausibility of the spike-based approach to network computation. SIGNIFICANCE STATEMENT: We derive a network of neurons with standard spike-generating currents and synapses with realistic timescales that computes based upon the principle that the precise timing of each spike is important for the computation. We then show that our network reproduces a number of key features of cortical networks including irregular, Poisson-like spike times, and a tight balance between excitation and inhibition. These results significantly increase the biological plausibility of the spike-based approach to network computation, and uncover how several components of biological networks may work together to efficiently carry out computation.

Predictive coding of dynamical variables in balanced spiking networks.

Two observations about the cortex have puzzled neuroscientists for a long time. First, neural responses are highly variable. Second, the level of excitation and inhibition received by each neuron is tightly balanced at all times. Here, we demonstrate that both properties are necessary consequences of neural networks that represent information efficiently in their spikes. We illustrate this insight with spiking networks that represent dynamical variables. Our approach is based on two assumptions: We assume that information about dynamical variables can be read out linearly from neural spike trains, and we assume that neurons only fire a spike if that improves the representation of the dynamical variables. Based on these assumptions, we derive a network of leaky integrate-and-fire neurons that is able to implement arbitrary linear dynamical systems. We show that the membrane voltage of the neurons is equivalent to a prediction error about a common population-level signal. Among other things, our approach allows us to construct an integrator network of spiking neurons that is robust against many perturbations. Most importantly, neural variability in our networks cannot be equated to noise. Despite exhibiting the same single unit properties as widely used population code models (e.g. tuning curves, Poisson distributed spike trains), balanced networks are orders of magnitudes more reliable. Our approach suggests that spikes do matter when considering how the brain computes, and that the reliability of cortical representations could have been strongly underestimated.

Circular inferences in schizophrenia.

A considerable number of recent experimental and computational studies suggest that subtle impairments of excitatory to inhibitory balance or regulation are involved in many neurological and psychiatric conditions. The current paper aims to relate, specifically and quantitatively, excitatory to inhibitory imbalance with psychotic symptoms in schizophrenia. Considering that the brain constructs hierarchical causal models of the external world, we show that the failure to maintain the excitatory to inhibitory balance results in hallucinations as well as in the formation and subsequent consolidation of delusional beliefs. Indeed, the consequence of excitatory to inhibitory imbalance in a hierarchical neural network is equated to a pathological form of causal inference called 'circular belief propagation'. In circular belief propagation, bottom-up sensory information and top-down predictions are reverberated, i.e. prior beliefs are misinterpreted as sensory observations and vice versa. As a result, these predictions are counted multiple times. Circular inference explains the emergence of erroneous percepts, the patient's overconfidence when facing probabilistic choices, the learning of 'unshakable' causal relationships between unrelated events and a paradoxical immunity to perceptual illusions, which are all known to be associated with schizophrenia.

Conspiracy beliefs and perceptual inference in times of political uncertainty.

Sociopolitical crises causing uncertainty have accumulated in recent years, providing fertile ground for the emergence of conspiracy ideations. Computational models constitute valuable tools for understanding the mechanisms at play in the formation and rigidification of these unshakeable beliefs. Here, the Circular Inference model was used to capture associations between changes in perceptual inference and the dynamics of conspiracy ideations in times of uncertainty. A bistable perception task and conspiracy belief assessment focused on major sociopolitical events were administered to large populations from three polarized countries. We show that when uncertainty peaks, an overweighting of sensory information is associated with conspiracy ideations. Progressively, this exploration strategy gives way to an exploitation strategy in which increased adherence to conspiracy theories is associated with the amplification of prior information. Overall, the Circular Inference model sheds new light on the possible mechanisms underlying the progressive strengthening of conspiracy theories when individuals face highly uncertain situations.

Perceptual inference predicts contextual modulations of sensory responses.

Sensory receptive fields (RFs) vary as a function of stimulus properties and measurement methods. Previous stimuli or surrounding stimuli facilitate, suppress, or change the selectivity of sensory neurons' responses. Here, we propose that these spatiotemporal contextual dependencies are signatures of efficient perceptual inference and can be explained by a single neural mechanism, input targeted divisive inhibition. To respond both selectively and reliably, sensory neurons should behave as active predictors rather than passive filters. In particular, they should remove input they can predict ("explain away") from the synaptic inputs to all other neurons. This implies that RFs are constantly and dynamically reshaped by the spatial and temporal context, while the true selectivity of sensory neurons resides in their "predictive field." This approach motivates a reinvestigation of sensory representations and particularly the role and specificity of surround suppression and adaptation in sensory areas.

Optimal and suboptimal use of postsaccadic vision in sequences of saccades.

Saccades are imprecise, due to sensory and motor noise. To avoid an accumulation of errors during sequences of saccades, a prediction derived from the efference copy can be combined with the reafferent visual feedback to adjust the following eye movement. By varying the information quantity of the visual feedback, we investigated how the reliability of the visual information affects the postsaccadic update in humans. Two elements of the visual scene were manipulated, the saccade target or the background, presented either together or in isolation. We determined the weight of the postsaccadic visual information by measuring the effect of intrasaccadic visual shifts on the following saccade. We confirmed that the weight of visual information evolves with information quantity as predicted for a statistically optimal system. In particular, we found that the visual background alone can guide the postsaccadic update, and that information from target and background are optimally combined. Moreover, these visual weights are adjusted dynamically and on a trial-to-trial basis to the level of visual noise determined by target eccentricity and reaction time. In contrast, we uncovered a dissociation between the visual signals used to update the next planned saccade (main saccade) and those used to generate an involuntary corrective saccade. The latter was exclusively based on visual information about the target, and discarded all information about the background: a suboptimal use of visual evidence.

Spike-based population coding and working memory.

Compelling behavioral evidence suggests that humans can make optimal decisions despite the uncertainty inherent in perceptual or motor tasks. A key question in neuroscience is how populations of spiking neurons can implement such probabilistic computations. In this article, we develop a comprehensive framework for optimal, spike-based sensory integration and working memory in a dynamic environment. We propose that probability distributions are inferred spike-per-spike in recurrently connected networks of integrate-and-fire neurons. As a result, these networks can combine sensory cues optimally, track the state of a time-varying stimulus and memorize accumulated evidence over periods much longer than the time constant of single neurons. Importantly, we propose that population responses and persistent working memory states represent entire probability distributions and not only single stimulus values. These memories are reflected by sustained, asynchronous patterns of activity which make relevant information available to downstream neurons within their short time window of integration. Model neurons act as predictive encoders, only firing spikes which account for new information that has not yet been signaled. Thus, spike times signal deterministically a prediction error, contrary to rate codes in which spike times are considered to be random samples of an underlying firing rate. As a consequence of this coding scheme, a multitude of spike patterns can reliably encode the same information. This results in weakly correlated, Poisson-like spike trains that are sensitive to initial conditions but robust to even high levels of external neural noise. This spike train variability reproduces the one observed in cortical sensory spike trains, but cannot be equated to noise. On the contrary, it is a consequence of optimal spike-based inference. In contrast, we show that rate-based models perform poorly when implemented with stochastically spiking neurons.

From hallucinations to synaesthesia: A circular inference account of unimodal and multimodal erroneous percepts in clinical and drug-induced psychosis.

Psychedelics distort perception and induce visual and multimodal hallucinations as well as synaesthesia. This is in contradiction with the high prevalence of distressing voices in schizophrenia. Here we introduce a unifying account of unimodal and multimodal erroneous percepts based on circular inference. We show that amplification of top-down predictions (descending loops) leads to an excessive reliance on priors and aberrant levels of integration of the sensory representations, resulting in crossmodal percepts and stronger illusions. By contrast, amplification of bottom-up information (ascending loops) results in overinterpretation of unreliable sensory inputs and high levels of segregation between sensory modalities, bringing about unimodal hallucinations and reduced vulnerability to illusions. We delineate a canonical microcircuit in which layer-specific inhibition controls the propagation of information across hierarchical levels: inhibitory interneurons in the deep layers exert control over priors, removing descending loops. Conversely, inhibition in the supragranular layers counterbalances the effects of the ascending loops. Overall, we put forward a multiscale and transnosographic account of erroneous percepts with important theoretical, conceptual and clinical implications.

Circular inference predicts nonuniform overactivation and dysconnectivity in brain-wide connectomes.

Schizophrenia is a severe mental disorder whose neural basis remains difficult to ascertain. Among the available pathophysiological theories, recent work has pointed towards subtle perturbations in the excitation-inhibition (E/I) balance within different neural circuits. Computational approaches have suggested interesting mechanisms that can account for both E/I imbalances and psychotic symptoms. Based on hierarchical neural networks propagating information through a message-passing algorithm, it was hypothesized that changes in the E/I ratio could cause a "circular belief propagation" in which bottom-up and top-down information reverberate. This circular inference (CI) was proposed to account for the clinical features of schizophrenia. Under this assumption, this paper examined the impact of CI on network dynamics in light of brain imaging findings related to psychosis. Using brain-inspired graphical models, we show that CI causes overconfidence and overactivation most specifically at the level of connector hubs (e.g., nodes with many connections allowing integration across networks). By also measuring functional connectivity in these graphs, we provide evidence that CI is able to predict specific changes in modularity known to be associated with schizophrenia. Altogether, these findings suggest that the CI framework may facilitate behavioral and neural research on the multifaceted nature of psychosis.

Predictive learning as a network mechanism for extracting low-dimensional latent space representations.

Artificial neural networks have recently achieved many successes in solving sequential processing and planning tasks. Their success is often ascribed to the emergence of the task's low-dimensional latent structure in the network activity - i.e., in the learned neural representations. Here, we investigate the hypothesis that a means for generating representations with easily accessed low-dimensional latent structure, possibly reflecting an underlying semantic organization, is through learning to predict observations about the world. Specifically, we ask whether and when network mechanisms for sensory prediction coincide with those for extracting the underlying latent variables. Using a recurrent neural network model trained to predict a sequence of observations we show that network dynamics exhibit low-dimensional but nonlinearly transformed representations of sensory inputs that map the latent structure of the sensory environment. We quantify these results using nonlinear measures of intrinsic dimensionality and linear decodability of latent variables, and provide mathematical arguments for why such useful predictive representations emerge. We focus throughout on how our results can aid the analysis and interpretation of experimental data.

Optimal sensorimotor control in eye movement sequences.

Fast and accurate motor behavior requires combining noisy and delayed sensory information with knowledge of self-generated body motion; much evidence indicates that humans do this in a near-optimal manner during arm movements. However, it is unclear whether this principle applies to eye movements. We measured the relative contributions of visual sensory feedback and the motor efference copy (and/or proprioceptive feedback) when humans perform two saccades in rapid succession, the first saccade to a visual target and the second to a memorized target. Unbeknownst to the subject, we introduced an artificial motor error by randomly "jumping" the visual target during the first saccade. The correction of the memory-guided saccade allowed us to measure the relative contributions of visual feedback and efferent copy (and/or proprioceptive feedback) to motor-plan updating. In a control experiment, we extinguished the target during the saccade rather than changing its location to measure the relative contribution of motor noise and target localization error to saccade variability without any visual feedback. The motor noise contribution increased with saccade amplitude, but remained <30% of the total variability. Subjects adjusted the gain of their visual feedback for different saccade amplitudes as a function of its reliability. Even during trials where subjects performed a corrective saccade to compensate for the target-jump, the correction by the visual feedback, while stronger, remained far below 100%. In all conditions, an optimal controller predicted the visual feedback gain well, suggesting that humans combine optimally their efferent copy and sensory feedback when performing eye movements.