Stimulus-dependent variability and noise correlations in cortical MT neurons

Recurrent network dynamics reconciles visual motion segmentation and integration

In sensory systems, a range of computational rules are presumed to be implemented by neuronal subpopulations with different tuning functions. For instance, in primate cortical area MT, different classes of direction-selective cells have been identified and related either to motion integration, segmentation or transparency. Still, how such different tuning properties are constructed is unclear. The dominant theoretical viewpoint based on a linear-nonlinear feed-forward cascade does not account for their complex temporal dynamics and their versatility when facing different input statistics. Here, we demonstrate that a recurrent network model of visual motion processing can reconcile these different properties. Using a ring network, we show how excitatory and inhibitory interactions can implement different computational rules such as vector averaging, winner-take-all or superposition. The model also captures ordered temporal transitions between these behaviors. In particular, depending on the inhibition regime the network can switch from motion integration to segmentation, thus being able to compute either a single pattern motion or to superpose multiple inputs as in motion transparency. We thus demonstrate that recurrent architectures can adaptively give rise to different cortical computational regimes depending upon the input statistics, from sensory flow integration to segmentation.

The modulation of EEG variability between internally- and externally-driven cognitive states varies with maturation and task performance

Increasing evidence suggests that brain signal variability is an important measure of brain function reflecting information processing capacity and functional integrity. In this study, we examined how maturation from childhood to adulthood affects the magnitude and spatial extent of state-to-state transitions in brain signal variability, and how this relates to cognitive performance. We looked at variability changes between resting-state and task (a symbol-matching task with three levels of difficulty), and within trial (fixation, post-stimulus, and post-response). We calculated variability with multiscale entropy (MSE), and additionally examined spectral power density (SPD) from electroencephalography (EEG) in children aged 8–14, and in adults aged 18–33. Our results suggest that maturation is characterized by increased local information processing (higher MSE at fine temporal scales) and decreased long-range interactions with other neural populations (lower MSE at coarse temporal scales). Children show MSE changes that are similar in magnitude, but greater in spatial extent when transitioning between internally- and externally-driven brain states. Additionally, we found that in children, greater changes in task difficulty were associated with greater magnitude of modulation in MSE. Our results suggest that the interplay between maturational and state-to-state changes in brain signal variability manifest across different spatial and temporal scales, and influence information processing capacity in the brain.

Adaptation in the visual cortex: a case for probing neuronal populations with natural stimuli

The perception of, and neural responses to, sensory stimuli in the present are influenced by what has been observed in the past—a phenomenon known as adaptation. We focus on adaptation in visual cortical neurons as a paradigmatic example. We review recent work that represents two shifts in the way we study adaptation, namely (i) going beyond single neurons to study adaptation in populations of neurons and (ii) going beyond simple stimuli to study adaptation to natural stimuli. We suggest that efforts in these two directions, through a closer integration of experimental and modeling approaches, will enable a more complete understanding of cortical processing in natural environments.

Distinct Correlation Structure Supporting a Rate-Code for Sound Localization in the Owl's Auditory Forebrain

While a topographic map of auditory space exists in the vertebrate midbrain, it is absent in the forebrain. Yet, both brain regions are implicated in sound localization. The heterogeneous spatial tuning of adjacent sites in the forebrain compared to the midbrain reflects different underlying circuitries, which is expected to affect the correlation structure, i.e., signal (similarity of tuning) and noise (trial-by-trial variability) correlations. Recent studies have drawn attention to the impact of response correlations on the information readout from a neural population. We thus analyzed the correlation structure in midbrain and forebrain regions of the barn owl’s auditory system. Tetrodes were used to record in the midbrain and two forebrain regions, Field L and the downstream auditory arcopallium (AAr), in anesthetized owls. Nearby neurons in the midbrain showed high signal and noise correlations (R_NCs), consistent with shared inputs. As previously reported, Field L was arranged in random clusters of similarly tuned neurons. Interestingly, AAr neurons displayed homogeneous monotonic azimuth tuning, while response variability of nearby neurons was significantly less correlated than the midbrain. Using a decoding approach, we demonstrate that low R_NC in AAr restricts the potentially detrimental effect it can have on information, assuming a rate code proposed for mammalian sound localization. This study harnesses the power of correlation structure analysis to investigate the coding of auditory space. Our findings demonstrate distinct correlation structures in the auditory midbrain and forebrain, which would be beneficial for a rate-code framework for sound localization in the nontopographic forebrain representation of auditory space.

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.

The Influence of Mexican Hat Recurrent Connectivity on Noise Correlations and Stimulus Encoding

Noise correlations are a common feature of neural responses and have been observed in many cortical areas across different species. These correlations can influence information processing by enhancing or diminishing the quality of the neural code, but the origin of these correlations is still a matter of controversy. In this computational study we explore the hypothesis that noise correlations are the result of local recurrent excitatory and inhibitory connections. We simulated two-dimensional networks of adaptive spiking neurons with local connection patterns following Gaussian kernels. Noise correlations decay with distance between neurons but are only observed if the range of excitatory connections is smaller than the range of inhibitory connections (“Mexican hat” connectivity) and if the connection strengths are sufficiently strong. These correlations arise from a moving blob-like structure of evoked activity, which is absent if inhibitory interactions have a smaller range (“inverse Mexican hat” connectivity). Spatially structured external inputs fixate these blobs to certain locations and thus effectively reduce noise correlations. We further investigated the influence of these network configurations on stimulus encoding. On the one hand, the observed correlations diminish information about a stimulus encoded by a network. On the other hand, correlated activity allows for more precise encoding of stimulus information if the decoder has only access to a limited amount of neurons.

Stimulus background influences phase invariant coding by correlated neural activity

Previously we reported that correlations between the activities of peripheral afferents mediate a phase invariant representation of natural communication stimuli that is refined across successive processing stages thereby leading to perception and behavior in the weakly electric fish Apteronotus leptorhynchus (Metzen et al., 2016). Here, we explore how phase invariant coding and perception of natural communication stimuli are affected by changes in the sinusoidal background over which they occur. We found that increasing background frequency led to phase locking, which decreased both detectability and phase invariant coding. Correlated afferent activity was a much better predictor of behavior as assessed from both invariance and detectability than single neuron activity. Thus, our results provide not only further evidence that correlated activity likely determines perception of natural communication signals, but also a novel explanation as to why these preferentially occur on top of low frequency as well as low-intensity sinusoidal backgrounds.

Neural Computations in a Dynamical System with Multiple Time Scales

Neural systems display rich short-term dynamics at various levels, e.g., spike-frequency adaptation (SFA) at the single-neuron level, and short-term facilitation (STF) and depression (STD) at the synapse level. These dynamical features typically cover a broad range of time scales and exhibit large diversity in different brain regions. It remains unclear what is the computational benefit for the brain to have such variability in short-term dynamics. In this study, we propose that the brain can exploit such dynamical features to implement multiple seemingly contradictory computations in a single neural circuit. To demonstrate this idea, we use continuous attractor neural network (CANN) as a working model and include STF, SFA and STD with increasing time constants in its dynamics. Three computational tasks are considered, which are persistent activity, adaptation, and anticipative tracking. These tasks require conflicting neural mechanisms, and hence cannot be implemented by a single dynamical feature or any combination with similar time constants. However, with properly coordinated STF, SFA and STD, we show that the network is able to implement the three computational tasks concurrently. We hope this study will shed light on the understanding of how the brain orchestrates its rich dynamics at various levels to realize diverse cognitive functions.

Dynamics of Population Activity in Rat Sensory Cortex: Network Correlations Predict Anatomical Arrangement and Information Content

To study the spatiotemporal dynamics of neural activity in a cortical population, we implanted a 10 × 10 microelectrode array in the vibrissal cortex of urethane-anesthetized rats. We recorded spontaneous neuronal activity as well as activity evoked in response to sustained and brief sensory stimulation. To quantify the temporal dynamics of activity, we computed the probability distribution function (PDF) of spiking on one electrode given the observation of a spike on another. The spike-triggered PDFs quantified the strength, temporal delay, and temporal precision of correlated activity across electrodes. Nearby cells showed higher levels of correlation at short delays, whereas distant cells showed lower levels of correlation, which tended to occur at longer delays. We found that functional space built based on the strength of pairwise correlations predicted the anatomical arrangement of electrodes. Moreover, the correlation profile of electrode pairs during spontaneous activity predicted the "signal" and "noise" correlations during sensory stimulation. Finally, mutual information analyses revealed that neurons with stronger correlations to the network during spontaneous activity, conveyed higher information about the sensory stimuli in their evoked response. Given the 400-μm-distance between adjacent electrodes, our functional quantifications unravel the spatiotemporal dynamics of activity among nearby and distant cortical columns.

Direction-Selective Circuits Shape Noise to Ensure a Precise Population Code

Neural responses are noisy, and circuit structure can correlate this noise across neurons. Theoretical studies show that noise correlations can have diverse effects on population coding, but these studies rarely explore stimulus dependence of noise correlations. Here, we show that noise correlations in responses of ON-OFF direction-selective retinal ganglion cells are strongly stimulus dependent, and we uncover the circuit mechanisms producing this stimulus dependence. A population model based on these mechanistic studies shows that stimulus-dependent noise correlations improve the encoding of motion direction 2-fold compared to independent noise. This work demonstrates a mechanism by which a neural circuit effectively shapes its signal and noise in concert, minimizing corruption of signal by noise. Finally, we generalize our findings beyond direction coding in the retina and show that stimulus-dependent correlations will generally enhance information coding in populations of diversely tuned neurons.

Decentralized Multisensory Information Integration in Neural Systems

How multiple sensory cues are integrated in neural circuitry remains a challenge. The common hypothesis is that information integration might be accomplished in a dedicated multisensory integration area receiving feedforward inputs from the modalities. However, recent experimental evidence suggests that it is not a single multisensory brain area, but rather many multisensory brain areas that are simultaneously involved in the integration of information. Why many mutually connected areas should be needed for information integration is puzzling. Here, we investigated theoretically how information integration could be achieved in a distributed fashion within a network of interconnected multisensory areas. Using biologically realistic neural network models, we developed a decentralized information integration system that comprises multiple interconnected integration areas. Studying an example of combining visual and vestibular cues to infer heading direction, we show that such a decentralized system is in good agreement with anatomical evidence and experimental observations. In particular, we show that this decentralized system can integrate information optimally. The decentralized system predicts that optimally integrated information should emerge locally from the dynamics of the communication between brain areas and sheds new light on the interpretation of the connectivity between multisensory brain areas.

SIGNIFICANCE STATEMENT

To extract information reliably from ambiguous environments, the brain integrates multiple sensory cues, which provide different aspects of information about the same entity of interest. Here, we propose a decentralized architecture for multisensory integration. In such a system, no processor is in the center of the network topology and information integration is achieved in a distributed manner through reciprocally connected local processors. Through studying the inference of heading direction with visual and vestibular cues, we show that the decentralized system can integrate information optimally, with the reciprocal connections between processers determining the extent of cue integration. Our model reproduces known multisensory integration behaviors observed in experiments and sheds new light on our understanding of how information is integrated in the brain.

Neural correlations enable invariant coding and perception of natural stimuli in weakly electric fish

Neural representations of behaviorally relevant stimulus features displaying invariance with respect to different contexts are essential for perception. However, the mechanisms mediating their emergence and subsequent refinement remain poorly understood in general. Here, we demonstrate that correlated neural activity allows for the emergence of an invariant representation of natural communication stimuli that is further refined across successive stages of processing in the weakly electric fish Apteronotus leptorhynchus. Importantly, different patterns of input resulting from the same natural communication stimulus occurring in different contexts all gave rise to similar behavioral responses. Our results thus reveal how a generic neural circuit performs an elegant computation that mediates the emergence and refinement of an invariant neural representation of natural stimuli that most likely constitutes a neural correlate of perception.

DOI:http://dx.doi.org/10.7554/eLife.12993.001

We can effortlessly recognize an object – a car, for example – in many different contexts such as when seen from behind, under different lighting levels or even from different viewpoints. This phenomenon is known as perceptual invariance: objects are correctly recognized, despite variations in exactly what is seen (or otherwise sensed). However, it is still not clear how the brain processes perceptual information to recognize the same object under a wide variety of contexts.

Some fish, such as the brown ghost knifefish, produce a weak electric signal that they can alter to communicate with other members of their species. A communication call may be produced in a variety of contexts that alter which aspects of the signal nearby fish detect. Despite this, fish tend to respond to a given communication call in the same way regardless of its context; this suggests that these fish also have perceptual invariance.

The communication calls of weakly electric fish can be easily mimicked in a laboratory and produce reliable behavioral responses, which makes these fish a good model for understanding how perceptual invariance might be coded in the brain. Therefore, Metzen et al. recorded the activity of the receptor neurons that first respond to communication calls in weakly electric fish. The results revealed that a given communication signal made the firing patterns of all receptor neurons in the fish’s brain more similar to each other, regardless of the signal’s context. This occurs despite the changes in context causing single receptor neurons to respond in different ways. At each stage of the process by which information is transmitted from the receptor neurons to neurons deeper in the brain, the similarity in the neurons’ firing patterns is refined, thereby giving rise to perceptual invariance.

While perceptual invariance to a given object in different contexts is desirable, it is also important to be able to distinguish between different objects. This implies that neurons should respond similarly to stimuli associated with the same object and differently to stimuli associated with different objects. Further studies are now needed to confirm whether this is the case.

DOI:http://dx.doi.org/10.7554/eLife.12993.002

Continuous Attractor Neural Networks: Candidate of a Canonical Model for Neural Information Representation

Owing to its many computationally desirable properties, the model of continuous attractor neural networks (CANNs) has been successfully applied to describe the encoding of simple continuous features in neural systems, such as orientation, moving direction, head direction, and spatial location of objects. Recent experimental and computational studies revealed that complex features of external inputs may also be encoded by low-dimensional CANNs embedded in the high-dimensional space of neural population activity. The new experimental data also confirmed the existence of the M-shaped correlation between neuronal responses, which is a correlation structure associated with the unique dynamics of CANNs. This body of evidence, which is reviewed in this report, suggests that CANNs may serve as a canonical model for neural information representation.

Testing the odds of inherent vs. observed overdispersion in neural spike counts

The repeated presentation of an identical visual stimulus in the receptive field of a neuron may evoke different spiking patterns at each trial. Probabilistic methods are essential to understand the functional role of this variance within the neural activity. In that case, a Poisson process is the most common model of trial-to-trial variability. For a Poisson process, the variance of the spike count is constrained to be equal to the mean, irrespective of the duration of measurements. Numerous studies have shown that this relationship does not generally hold. Specifically, a majority of electrophysiological recordings show an "overdispersion" effect: responses that exhibit more intertrial variability than expected from a Poisson process alone. A model that is particularly well suited to quantify overdispersion is the Negative-Binomial distribution model. This model is well-studied and widely used but has only recently been applied to neuroscience. In this article, we address three main issues. First, we describe how the Negative-Binomial distribution provides a model apt to account for overdispersed spike counts. Second, we quantify the significance of this model for any neurophysiological data by proposing a statistical test, which quantifies the odds that overdispersion could be due to the limited number of repetitions (trials). We apply this test to three neurophysiological data sets along the visual pathway. Finally, we compare the performance of this model to the Poisson model on a population decoding task. We show that the decoding accuracy is improved when accounting for overdispersion, especially under the hypothesis of tuned overdispersion.

Where's the Noise? Key Features of Spontaneous Activity and Neural Variability Arise through Learning in a Deterministic Network

Even in the absence of sensory stimulation the brain is spontaneously active. This background “noise” seems to be the dominant cause of the notoriously high trial-to-trial variability of neural recordings. Recent experimental observations have extended our knowledge of trial-to-trial variability and spontaneous activity in several directions: 1. Trial-to-trial variability systematically decreases following the onset of a sensory stimulus or the start of a motor act. 2. Spontaneous activity states in sensory cortex outline the region of evoked sensory responses. 3. Across development, spontaneous activity aligns itself with typical evoked activity patterns. 4. The spontaneous brain activity prior to the presentation of an ambiguous stimulus predicts how the stimulus will be interpreted. At present it is unclear how these observations relate to each other and how they arise in cortical circuits. Here we demonstrate that all of these phenomena can be accounted for by a deterministic self-organizing recurrent neural network model (SORN), which learns a predictive model of its sensory environment. The SORN comprises recurrently coupled populations of excitatory and inhibitory threshold units and learns via a combination of spike-timing dependent plasticity (STDP) and homeostatic plasticity mechanisms. Similar to balanced network architectures, units in the network show irregular activity and variable responses to inputs. Additionally, however, the SORN exhibits sequence learning abilities matching recent findings from visual cortex and the network’s spontaneous activity reproduces the experimental findings mentioned above. Intriguingly, the network’s behaviour is reminiscent of sampling-based probabilistic inference, suggesting that correlates of sampling-based inference can develop from the interaction of STDP and homeostasis in deterministic networks. We conclude that key observations on spontaneous brain activity and the variability of neural responses can be accounted for by a simple deterministic recurrent neural network which learns a predictive model of its sensory environment via a combination of generic neural plasticity mechanisms.

Neural recordings seem very noisy. If the exact same stimulus is shown to an animal multiple times, the neural response will vary substantially. In fact, the activity of a single neuron shows many features of a random process. Furthermore, the spontaneous activity occurring in the absence of any sensory stimulus, which is usually considered a kind of background noise, often has a magnitude comparable to the activity evoked by stimulus presentation and interacts with sensory inputs in interesting ways. Here we show that the key features of neural variability and spontaneous activity can all be accounted for by a simple and completely deterministic neural network learning a predictive model of its sensory inputs. The network’s deterministic dynamics give rise to structured but variable responses matching key experimental findings obtained in different mammalian species with different recording techniques. Our results suggest that the notorious variability of neural recordings and the complex features of spontaneous brain activity could reflect the dynamics of a largely deterministic but highly adaptive network learning a predictive model of its sensory environment.

Origin of information-limiting noise correlations

The ability to discriminate between similar sensory stimuli relies on the amount of information encoded in sensory neuronal populations. Such information can be substantially reduced by correlated trial-to-trial variability. Noise correlations have been measured across a wide range of areas in the brain, but their origin is still far from clear. Here we show analytically and with simulations that optimal computation on inputs with limited information creates patterns of noise correlations that account for a broad range of experimental observations while at same time causing information to saturate in large neural populations. With the example of a network of V1 neurons extracting orientation from a noisy image, we illustrate to our knowledge the first generative model of noise correlations that is consistent both with neurophysiology and with behavioral thresholds, without invoking suboptimal encoding or decoding or internal sources of variability such as stochastic network dynamics or cortical state fluctuations. We further show that when information is limited at the input, both suboptimal connectivity and internal fluctuations could similarly reduce the asymptotic information, but they have qualitatively different effects on correlations leading to specific experimental predictions. Our study indicates that noise at the sensory periphery could have a major effect on cortical representations in widely studied discrimination tasks. It also provides an analytical framework to understand the functional relevance of different sources of experimentally measured correlations.

Signal Integration in Human Visual Speed Perception

Object motion in natural scenes results in visual stimuli with a rich and broad spatiotemporal frequency spectrum. While the question of how the visual system detects and senses motion energies at different spatial and temporal frequencies has been fairly well studied, it is unclear how the visual system integrates this information to form coherent percepts of object motion. We applied a combination of tailored psychophysical experiments and predictive modeling to address this question with regard to perceived motion in a given direction (i.e., stimulus speed). We tested human subjects in a discrimination experiment using stimuli that selectively targeted four distinct spatiotemporally tuned channels with center frequencies consistent with a common speed. We first characterized subjects' responses to stimuli that targeted only individual channels. Based on these measurements, we then predicted subjects' psychometric functions for stimuli that targeted multiple channels simultaneously. Specifically, we compared predictions of three Bayesian observer models that either optimally integrated the information across all spatiotemporal channels, or only used information from the most reliable channel, or formed an average percept across channels. Only the model with optimal integration was successful in accounting for the data. Furthermore, the proposed channel model provides an intuitive explanation for the previously reported spatial frequency dependence of perceived speed of coherent object motion. Finally, our findings indicate that a prior expectation for slow speeds is added to the inference process only after the sensory information is combined and integrated.

Task-Driven Activity Reduces the Cortical Activity Space of the Brain: Experiment and Whole-Brain Modeling

How a stimulus or a task alters the spontaneous dynamics of the brain remains a fundamental open question in neuroscience. One of the most robust hallmarks of task/stimulus-driven brain dynamics is the decrease of variability with respect to the spontaneous level, an effect seen across multiple experimental conditions and in brain signals observed at different spatiotemporal scales. Recently, it was observed that the trial-to-trial variability and temporal variance of functional magnetic resonance imaging (fMRI) signals decrease in the task-driven activity. Here we examined the dynamics of a large-scale model of the human cortex to provide a mechanistic understanding of these observations. The model allows computing the statistics of synaptic activity in the spontaneous condition and in putative tasks determined by external inputs to a given subset of brain regions. We demonstrated that external inputs decrease the variance, increase the covariances, and decrease the autocovariance of synaptic activity as a consequence of single node and large-scale network dynamics. Altogether, these changes in network statistics imply a reduction of entropy, meaning that the spontaneous synaptic activity outlines a larger multidimensional activity space than does the task-driven activity. We tested this model’s prediction on fMRI signals from healthy humans acquired during rest and task conditions and found a significant decrease of entropy in the stimulus-driven activity. Altogether, our study proposes a mechanism for increasing the information capacity of brain networks by enlarging the volume of possible activity configurations at rest and reliably settling into a confined stimulus-driven state to allow better transmission of stimulus-related information.

Task- or stimulus-related changes of brain dynamics have been the subject of intense investigation during the last years. One of the most robust hallmarks of task/stimulus-driven brain dynamics, as measured using diverse recording techniques, is the decrease of variability with respect to the spontaneous level. This has led several researchers to focus on the second-order statistics of evoked activity and to study their functional consequences for information processing. In particular, it was observed that the trial-to-trial variability (related to variable responses to an identical stimulus from one presentation to the next) and the temporal variance of functional magnetic resonance imaging (fMRI) signals decrease in the task-driven activity. Here, we built a computational model of the whole brain to understand how local and large-scale brain dynamics contribute to these effects. The model allowed us to derive equations for the network statistics of both spontaneous and evoked activity. We observed that, as a consequence of single node and network dynamics, stimulus input impacts network statistics in such a way that the entropy of the stimulus-driven activity is lower than that during spontaneous activity. We confirmed this model prediction using empirical fMRI data and we further discuss its functional implications.

Nonlinear transfer of signal and noise correlations in cortical networks

Signal and noise correlations, a prominent feature of cortical activity, reflect the structure and function of networks during sensory processing. However, in addition to reflecting network properties, correlations are also shaped by intrinsic neuronal mechanisms. Here we show that spike threshold transforms correlations by creating nonlinear interactions between signal and noise inputs; even when input noise correlation is constant, spiking noise correlation varies with both the strength and correlation of signal inputs. We characterize these effects systematically in vitro in mice and demonstrate their impact on sensory processing in vivo in gerbils. We also find that the effects of nonlinear correlation transfer on cortical responses are stronger in the synchronized state than in the desynchronized state, and show that they can be reproduced and understood in a model with a simple threshold nonlinearity. Since these effects arise from an intrinsic neuronal property, they are likely to be present across sensory systems and, thus, our results are a critical step toward a general understanding of how correlated spiking relates to the structure and function of cortical networks.

The Nature of Shared Cortical Variability

Neuronal responses of sensory cortex are highly variable, and this variability is correlated across neurons. To assess how variability reflects factors shared across a neuronal population, we analyzed the activity of many simultaneously recorded neurons in visual cortex. We developed a simple model that comprises two sources of shared variability: a multiplicative gain, which uniformly scales each neuron’s sensory drive, and an additive offset, which affects different neurons to different degrees. This model captured the variability of spike counts and reproduced the dependence of pairwise correlations on neuronal tuning and stimulus orientation. The relative contributions of the additive and multiplicative fluctuations could vary over time and had marked impact on population coding. These observations indicate that shared variability of neuronal populations in sensory cortex can be largely explained by two factors that modulate the whole population.

•

Response variability in V1 neuronal populations is largely shared across neurons

•

Shared variability involves two factors: a multiplicative gain and an additive offset

•

These two factors predict sensory responses of large populations on single trials

•

They determine pairwise correlations and constrain information coding

Effects of attention and distractor contrast on the responses of middle temporal area neurons to transient motion direction changes

The ability of primates to detect transient changes in a visual scene can be influenced by the allocation of attention, as well as by the presence of distractors. We investigated the neural substrates of these effects by recording the responses of neurons in the middle temporal area (MT) of two monkeys while they detected a transient motion direction change in a moving target. We found that positioning a distractor near the target impaired the change-detection performance of the animals. This impairment monotonically decreased as the distractor's contrast decreased. A neural correlate of this effect was a decrease in the ability of MT neurons to signal the direction change (detection sensitivity or DS) when a distractor was near the target, both located inside the neuron's receptive field. Moreover, decreasing distractor contrast increased neuronal DS. On the other hand, directing attention away from the target decreased neuronal DS. At the level of individual neurons, we found a negative correlation between the degree of response normalization and the DS. Finally, the intensity of a neuron's response to the change was predictive of the animal's reaction time, suggesting that the activity of our recorded neurons was linked to the animal's detection performance. Our results suggest that the ability of an MT neuron to signal a transient direction change is regulated by the degree of inhibitory drive into the cell. The presence of distractors, their contrast and the allocation of attention influence such inhibitory drive, therefore modulating the ability of the neurons to signal transient changes in stimulus features and consequently behavioral performance.

Coding of envelopes by correlated but not single-neuron activity requires neural variability

Understanding how the brain processes sensory information is often complicated by the fact that neurons exhibit trial-to-trial variability in their responses to stimuli. Indeed, the role of variability in sensory coding is still highly debated. Here, we examined how variability influences neural responses to naturalistic stimuli consisting of a fast time-varying waveform (i.e., carrier or first order) whose amplitude (i.e., envelope or second order) varies more slowly. Recordings were made from fish electrosensory and monkey vestibular sensory neurons. In both systems, we show that correlated but not single-neuron activity can provide detailed information about second-order stimulus features. Using a simple mathematical model, we made the strong prediction that such correlation-based coding of envelopes requires neural variability. Strikingly, the performance of correlated activity at predicting the envelope was similarly optimally tuned to a nonzero level of variability in both systems, thereby confirming this prediction. Finally, we show that second-order sensory information can only be decoded if one takes into account joint statistics when combining neural activities. Our results thus show that correlated but not single-neural activity can transmit information about the envelope, that such transmission requires neural variability, and that this information can be decoded. We suggest that envelope coding by correlated activity is a general feature of sensory processing that will be found across species and systems.

Stochastic transitions into silence cause noise correlations in cortical circuits

The spiking activity of cortical neurons is highly variable. This variability is generally correlated among nearby neurons, an effect commonly interpreted to reflect the coactivation of neurons due to anatomically shared inputs. Recent findings, however, indicate that correlations can be dynamically modulated, suggesting that the underlying mechanisms are not well understood. Here, we investigate the hypothesis that correlations are dominated by neuronal coinactivation: the occurrence of brief silent periods during which all neurons in the local network stop firing. We recorded spiking activity from large populations of neurons in the auditory cortex of anesthetized rats across different brain states. During spontaneous activity, the reduction of correlation accompanying brain state desynchronization was largely explained by a decrease in the density of the silent periods. The presentation of a stimulus caused an initial drop of correlations followed by a rebound, a time course that was mimicked by the instantaneous silence density. We built a rate network model with fluctuation-driven transitions between a silent and an active attractor and assumed that neurons fired Poisson spike trains with a rate following the model dynamics. Variations of the network external input altered the transition rate into the silent attractor and reproduced the relation between correlation and silence density found in the data, both in spontaneous and evoked conditions. This suggests that the observed changes in correlation, occurring gradually with brain state variations or abruptly with sensory stimulation, are due to changes in the likeliness of the microcircuit to transiently cease firing.

Improved estimation and interpretation of correlations in neural circuits

Ambitious projects aim to record the activity of ever larger and denser neuronal populations in vivo. Correlations in neural activity measured in such recordings can reveal important aspects of neural circuit organization. However, estimating and interpreting large correlation matrices is statistically challenging. Estimation can be improved by regularization, i.e. by imposing a structure on the estimate. The amount of improvement depends on how closely the assumed structure represents dependencies in the data. Therefore, the selection of the most efficient correlation matrix estimator for a given neural circuit must be determined empirically. Importantly, the identity and structure of the most efficient estimator informs about the types of dominant dependencies governing the system. We sought statistically efficient estimators of neural correlation matrices in recordings from large, dense groups of cortical neurons. Using fast 3D random-access laser scanning microscopy of calcium signals, we recorded the activity of nearly every neuron in volumes 200 μm wide and 100 μm deep (150-350 cells) in mouse visual cortex. We hypothesized that in these densely sampled recordings, the correlation matrix should be best modeled as the combination of a sparse graph of pairwise partial correlations representing local interactions and a low-rank component representing common fluctuations and external inputs. Indeed, in cross-validation tests, the covariance matrix estimator with this structure consistently outperformed other regularized estimators. The sparse component of the estimate defined a graph of interactions. These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive 'excitatory' interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative 'inhibitory' interactions were less selective. Because of its superior performance, this 'sparse+latent' estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix.

Sensory integration dynamics in a hierarchical network explains choice probabilities in cortical area MT

Neuronal variability in sensory cortex predicts perceptual decisions. This relationship, termed choice probability (CP), can arise from sensory variability biasing behaviour and from top-down signals reflecting behaviour. To investigate the interaction of these mechanisms during the decision-making process, we use a hierarchical network model composed of reciprocally connected sensory and integration circuits. Consistent with monkey behaviour in a fixed-duration motion discrimination task, the model integrates sensory evidence transiently, giving rise to a decaying bottom-up CP component. However, the dynamics of the hierarchical loop recruits a concurrently rising top-down component, resulting in sustained CP. We compute the CP time-course of neurons in the medial temporal area (MT) and find an early transient component and a separate late contribution reflecting decision build-up. The stability of individual CPs and the dynamics of noise correlations further support this decomposition. Our model provides a unified understanding of the circuit dynamics linking neural and behavioural variability.

Information-limiting correlations

Computational strategies used by the brain strongly depend on the amount of information that can be stored in population activity, which in turn strongly depends on the pattern of noise correlations. In vivo, noise correlations tend to be positive and proportional to the similarity in tuning properties. Such correlations are thought to limit information, which has led to the suggestion that decorrelation increases information. In contrast, we found, analytically and numerically, that decorrelation does not imply an increase in information. Instead, the only information-limiting correlations are what we refer to as differential correlations: correlations proportional to the product of the derivatives of the tuning curves. Unfortunately, differential correlations are likely to be very small and buried under correlations that do not limit information, making them particularly difficult to detect. We found, however, that the effect of differential correlations on information can be detected with relatively simple decoders.

Balanced neural architecture and the idling brain

A signature feature of cortical spike trains is their trial-to-trial variability. This variability is large in the spontaneous state and is reduced when cortex is driven by a stimulus or task. Models of recurrent cortical networks with unstructured, yet balanced, excitation and inhibition generate variability consistent with evoked conditions. However, these models produce spike trains which lack the long timescale fluctuations and large variability exhibited during spontaneous cortical dynamics. We propose that global network architectures which support a large number of stable states (attractor networks) allow balanced networks to capture key features of neural variability in both spontaneous and evoked conditions. We illustrate this using balanced spiking networks with clustered assembly, feedforward chain, and ring structures. By assuming that global network structure is related to stimulus preference, we show that signal correlations are related to the magnitude of correlations in the spontaneous state. Finally, we contrast the impact of stimulation on the trial-to-trial variability in attractor networks with that of strongly coupled spiking networks with chaotic firing rate instabilities, recently investigated by Ostojic (2014). We find that only attractor networks replicate an experimentally observed stimulus-induced quenching of trial-to-trial variability. In total, the comparison of the trial-variable dynamics of single neurons or neuron pairs during spontaneous and evoked activity can be a window into the global structure of balanced cortical networks.

Bump attractor dynamics in prefrontal cortex explains behavioral precision in spatial working memory

Prefrontal persistent activity during the delay of spatial working memory tasks is thought to maintain spatial location in memory. A 'bump attractor' computational model can account for this physiology and its relationship to behavior. However, direct experimental evidence linking parameters of prefrontal firing to the memory report in individual trials is lacking, and, to date, no demonstration exists that bump attractor dynamics underlies spatial working memory. We analyzed monkey data and found model-derived predictive relationships between the variability of prefrontal activity in the delay and the fine details of recalled spatial location, as evident in trial-to-trial imprecise oculomotor responses. Our results support a diffusing bump representation for spatial working memory instantiated in persistent prefrontal activity. These findings reinforce persistent activity as a basis for spatial working memory, provide evidence for a continuous prefrontal representation of memorized space and offer experimental support for bump attractor dynamics mediating cognitive tasks in the cortex.