Relating Divisive Normalization to Neuronal Response Variability

Adult neurogenesis improves spatial information encoding in the mouse hippocampus

Adult neurogenesis is a unique form of neuronal plasticity in which newly generated neurons are integrated into the adult dentate gyrus in a process that is modulated by environmental stimuli. Adult-born neurons can contribute to spatial memory, but it is unknown whether they alter neural representations of space in the hippocampus. Using in vivo two-photon calcium imaging, we find that male and female mice previously housed in an enriched environment, which triggers an increase in neurogenesis, have increased spatial information encoding in the dentate gyrus. Ablating adult neurogenesis blocks the effect of enrichment and lowers spatial information, as does the chemogenetic silencing of adult-born neurons. Both ablating neurogenesis and silencing adult-born neurons decreases the calcium activity of dentate gyrus neurons, resulting in a decreased amplitude of place-specific responses. These findings are in contrast with previous studies that suggested a predominantly inhibitory action for adult-born neurons. We propose that adult neurogenesis improves representations of space by increasing the gain of dentate gyrus neurons and thereby improving their ability to tune to spatial features. This mechanism may mediate the beneficial effects of environmental enrichment on spatial learning and memory.

Signal switching may enhance processing power of the brain

Our ability to perceive multiple objects is mysterious. Sensory neurons are broadly tuned, producing potential overlap in the populations of neurons activated by each object in a scene. This overlap raises questions about how distinct information is retained about each item. We present a novel signal switching theory of neural representation, which posits that neural signals may interleave representations of individual items across time. Evidence for this theory comes from new statistical tools that overcome the limitations inherent to standard time-and-trial-pooled assessments of neural signals. Our theory has implications for diverse domains of neuroscience, including attention, figure binding/scene segregation, oscillations, and divisive normalization. The general concept of switching between functions could also lend explanatory power to theories of grounded cognition.

Origins of noise in both improving and degrading decision making

Noise is a fundamental problem for information processing in neural systems. In decision-making, noise is assumed to have a primary role in errors and stochastic choice behavior. However, little is known about how noise arising from different sources contributes to value coding and choice behaviors, especially when it interacts with neural computation. Here we examine how noise arising early versus late in the choice process differentially impacts context-dependent choice behavior. We found in model simulations that early and late noise predict opposing context effects: under early noise, contextual information enhances choice accuracy; while under late noise, context degrades choice accuracy. Furthermore, we verified these opposing predictions in experimental human choice behavior. Manipulating early and late noise - by inducing uncertainty in option values and controlling time pressure - produced dissociable positive and negative context effects. These findings reconcile controversial experimental findings in the literature reporting either context-driven impairments or improvements in choice performance, suggesting a unified mechanism for context-dependent choice. More broadly, these findings highlight how different sources of noise can interact with neural computations to differentially modulate behavior.

Significance

The current study addresses the role of noise origin in decision-making, reconciling controversies around how decision-making is impacted by context. We demonstrate that different types of noise - either arising early during evaluation or late during option comparison - leads to distinct results: with early noise, context enhances choice accuracy, while with late noise, context impairs it. Understanding these dynamics offers potential strategies for improving decision-making in noisy environments and refining existing neural computation models. Overall, our findings advance our understanding of how neural systems handle noise in essential cognitive tasks, suggest a beneficial role for contextual modulation under certain conditions, and highlight the profound implications of noise structure in decision-making.

How does V1 population activity inform perceptual certainty?

Neural population activity in sensory cortex informs our perceptual interpretation of the environment. Oftentimes, this population activity will support multiple alternative interpretations. The larger the spread of probability over different alternatives, the more uncertain the selected perceptual interpretation. We test the hypothesis that the reliability of perceptual interpretations can be revealed through simple transformations of sensory population activity. We recorded V1 population activity in fixating macaques while presenting oriented stimuli under different levels of nuisance variability and signal strength. We developed a decoding procedure to infer from V1 activity the most likely stimulus orientation as well as the certainty of this estimate. Our analysis shows that response magnitude, response dispersion, and variability in response gain all offer useful proxies for orientation certainty. Of these three metrics, the last one has the strongest association with the decoder's uncertainty estimates. These results clarify that the nature of neural population activity in sensory cortex provides downstream circuits with multiple options to assess the reliability of perceptual interpretations.

Response sub-additivity and variability quenching in visual cortex

Sub-additivity and variability are ubiquitous response motifs in the primary visual cortex (V1). Response sub-additivity enables the construction of useful interpretations of the visual environment, whereas response variability indicates the factors that limit the precision with which the brain can do this. There is increasing evidence that experimental manipulations that elicit response sub-additivity often also quench response variability. Here, we provide an overview of these phenomena and suggest that they may have common origins. We discuss empirical findings and recent model-based insights into the functional operations, computational objectives and circuit mechanisms underlying V1 activity. These different modelling approaches all predict that response sub-additivity and variability quenching often co-occur. The phenomenology of these two response motifs, as well as many of the insights obtained about them in V1, generalize to other cortical areas. Thus, the connection between response sub-additivity and variability quenching may be a canonical motif across the cortex.

A dynamic attractor network model of memory formation, reinforcement and forgetting

Empirical evidence shows that memories that are frequently revisited are easy to recall, and that familiar items involve larger hippocampal representations than less familiar ones. In line with these observations, here we develop a modelling approach to provide a mechanistic understanding of how hippocampal neural assemblies evolve differently, depending on the frequency of presentation of the stimuli. For this, we added an online Hebbian learning rule, background firing activity, neural adaptation and heterosynaptic plasticity to a rate attractor network model, thus creating dynamic memory representations that can persist, increase or fade according to the frequency of presentation of the corresponding memory patterns. Specifically, we show that a dynamic interplay between Hebbian learning and background firing activity can explain the relationship between the memory assembly sizes and their frequency of stimulation. Frequently stimulated assemblies increase their size independently from each other (i.e. creating orthogonal representations that do not share neurons, thus avoiding interference). Importantly, connections between neurons of assemblies that are not further stimulated become labile so that these neurons can be recruited by other assemblies, providing a neuronal mechanism of forgetting.

Modeling the diverse effects of divisive normalization on noise correlations

Divisive normalization, a prominent descriptive model of neural activity, is employed by theories of neural coding across many different brain areas. Yet, the relationship between normalization and the statistics of neural responses beyond single neurons remains largely unexplored. Here we focus on noise correlations, a widely studied pairwise statistic, because its stimulus and state dependence plays a central role in neural coding. Existing models of covariability typically ignore normalization despite empirical evidence suggesting it affects correlation structure in neural populations. We therefore propose a pairwise stochastic divisive normalization model that accounts for the effects of normalization and other factors on covariability. We first show that normalization modulates noise correlations in qualitatively different ways depending on whether normalization is shared between neurons, and we discuss how to infer when normalization signals are shared. We then apply our model to calcium imaging data from mouse primary visual cortex (V1), and find that it accurately fits the data, often outperforming a popular alternative model of correlations. Our analysis indicates that normalization signals are often shared between V1 neurons in this dataset. Our model will enable quantifying the relation between normalization and covariability in a broad range of neural systems, which could provide new constraints on circuit mechanisms of normalization and their role in information transmission and representation.

Unsupervised approach to decomposing neural tuning variability

Neural representation is often described by the tuning curves of individual neurons with respect to certain stimulus variables. Despite this tradition, it has become increasingly clear that neural tuning can vary substantially in accordance with a collection of internal and external factors. A challenge we are facing is the lack of appropriate methods to accurately capture the moment-to-moment tuning variability directly from the noisy neural responses. Here we introduce an unsupervised statistical approach, Poisson functional principal component analysis (Pf-PCA), which identifies different sources of systematic tuning fluctuations, moreover encompassing several current models (e.g.,multiplicative gain models) as special cases. Applying this method to neural data recorded from macaque primary visual cortex- a paradigmatic case for which the tuning curve approach has been scientifically essential- we discovered a simple relationship governing the variability of orientation tuning, which unifies different types of gain changes proposed previously. By decomposing the neural tuning variability into interpretable components, our method enables discovery of unexpected structure of the neural code, capturing the influence of the external stimulus drive and internal states simultaneously.

Size tuning of neural response variability in laminar circuits of macaque primary visual cortex

A defining feature of the cortex is its laminar organization, which is likely critical for cortical information processing. For example, visual stimuli of different size evoke distinct patterns of laminar activity. Visual information processing is also influenced by the response variability of individual neurons and the degree to which this variability is correlated among neurons. To elucidate laminar processing, we studied how neural response variability across the layers of macaque primary visual cortex is modulated by visual stimulus size. Our laminar recordings revealed that single neuron response variability and the shared variability among neurons are tuned for stimulus size, and this size-tuning is layer-dependent. In all layers, stimulation of the receptive field (RF) reduced single neuron variability, and the shared variability among neurons, relative to their pre-stimulus values. As the stimulus was enlarged beyond the RF, both single neuron and shared variability increased in supragranular layers, but either did not change or decreased in other layers. Surprisingly, we also found that small visual stimuli could increase variability relative to baseline values. Our results suggest multiple circuits and mechanisms as the source of variability in different layers and call for the development of new models of neural response variability.

Coordinated multiplexing of information about separate objects in visual cortex

Sensory receptive fields are large enough that they can contain more than one perceptible stimulus. How, then, can the brain encode information about each of the stimuli that may be present at a given moment? We recently showed that when more than one stimulus is present, single neurons can fluctuate between coding one vs. the other(s) across some time period, suggesting a form of neural multiplexing of different stimuli (Caruso et al., 2018). Here, we investigate (a) whether such coding fluctuations occur in early visual cortical areas; (b) how coding fluctuations are coordinated across the neural population; and (c) how coordinated coding fluctuations depend on the parsing of stimuli into separate vs. fused objects. We found coding fluctuations do occur in macaque V1 but only when the two stimuli form separate objects. Such separate objects evoked a novel pattern of V1 spike count ('noise') correlations involving distinct distributions of positive and negative values. This bimodal correlation pattern was most pronounced among pairs of neurons showing the strongest evidence for coding fluctuations or multiplexing. Whether a given pair of neurons exhibited positive or negative correlations depended on whether the two neurons both responded better to the same object or had different object preferences. Distinct distributions of spike count correlations based on stimulus preferences were also seen in V4 for separate objects but not when two stimuli fused to form one object. These findings suggest multiple objects evoke different response dynamics than those evoked by single stimuli, lending support to the multiplexing hypothesis and suggesting a means by which information about multiple objects can be preserved despite the apparent coarseness of sensory coding.

Divisive normalization is an efficient code for multivariate Pareto-distributed environments

Divisive normalization is a canonical computation in the brain, observed across neural systems, that is often considered to be an implementation of the efficient coding principle. We provide a theoretical result that makes the conditions under which divisive normalization is an efficient code analytically precise: We show that, in a low-noise regime, encoding an n-dimensional stimulus via divisive normalization is efficient if and only if its prevalence in the environment is described by a multivariate Pareto distribution. We generalize this multivariate analog of histogram equalization to allow for arbitrary metabolic costs of the representation, and show how different assumptions on costs are associated with different shapes of the distributions that divisive normalization efficiently encodes. Our result suggests that divisive normalization may have evolved to efficiently represent stimuli with Pareto distributions. We demonstrate that this efficiently encoded distribution is consistent with stylized features of naturalistic stimulus distributions such as their characteristic conditional variance dependence, and we provide empirical evidence suggesting that it may capture the statistics of filter responses to naturalistic images. Our theoretical finding also yields empirically testable predictions across sensory domains on how the divisive normalization parameters should be tuned to features of the input distribution.

Explaining Orientation Adaptation in V1 by Updating the State of a Spatial Model

In this work, we extend an influential statistical model based on the spatial classical receptive field (CRF) and non-classical receptive field (nCRF) interactions (Coen-Cagli et al., 2012) to explain the typical orientation adaptation effects observed in V1. If we assume that the temporal adaptation modifies the “state” of the model, the spatial statistical model can explain all of the orientation adaptation effects in the context of neuronal output using small and large grating observed in neurophysiological experiments in V1. The “state” of the model represents the internal parameters such as the prior and the covariance trained on a mixed dataset that totally determine the response of the model. These two parameters, respectively, reflect the probability of the orientation component and the connectivity among neurons between CRF and nCRF. Specifically, we have two key findings: First, neural adapted results using a small grating that just covers the CRF can be predicted by the change of the prior of our model. Second, the change of the prior can also predict most of the observed results using a large grating that covers both CRF and nCRF of a neuron. However, the prediction of the novel attractive adaptation using large grating covering both CRF and nCRF also necessitates the involvement of a connectivity change of the center-surround RFs. In addition, our paper contributes a new prior-based winner-take-all (WTA) working mechanism derived from the statistical-based model to explain why and how all of these orientation adaptation effects can be predicted by relying on this spatial model without modifying its structure, a novel application of the spatial model. The research results show that adaptation may link time and space by changing the “state” of the neural system according to a specific adaptor. Furthermore, different forms of stimulus used for adaptation can cause various adaptation effects, such as an a priori shift or a connectivity change, depending on the specific stimulus size.

Divisive normalization unifies disparate response signatures throughout the human visual hierarchy

A canonical neural computation is a mathematical operation applied by the brain in a wide variety of contexts and capable of explaining and unifying seemingly unrelated neural and perceptual phenomena. Here, we use a combination of state-of-the-art experiments (ultra-high-field functional MRI) and mathematical methods (population receptive field [pRF] modeling) to uniquely demonstrate the role of divisive normalization (DN) as the canonical neural computation underlying visuospatial responses throughout the human visual hierarchy. The DN pRF model provides a tool to investigate and interpret the computational processes underlying neural responses in human and animal recordings, but also in clinical and cognitive dimensions.

Neural processing is hypothesized to apply the same mathematical operations in a variety of contexts, implementing so-called canonical neural computations. Divisive normalization (DN) is considered a prime candidate for a canonical computation. Here, we propose a population receptive field (pRF) model based on DN and evaluate it using ultra-high-field functional MRI (fMRI). The DN model parsimoniously captures seemingly disparate response signatures with a single computation, superseding existing pRF models in both performance and biological plausibility. We observe systematic variations in specific DN model parameters across the visual hierarchy and show how they relate to differences in response modulation and visuospatial information integration. The DN model delivers a unifying framework for visuospatial responses throughout the human visual hierarchy and provides insights into its underlying information-encoding computations. These findings extend the role of DN as a canonical computation to neuronal populations throughout the human visual hierarchy.

Heterogeneous side effects of cortical inactivation in behaving animals

Cortical inactivation represents a key causal manipulation allowing the study of cortical circuits and their impact on behavior. A key assumption in inactivation studies is that the neurons in the target area become silent while the surrounding cortical tissue is only negligibly impacted. However, individual neurons are embedded in complex local circuits composed of excitatory and inhibitory cells with connections extending hundreds of microns. This raises the possibility that silencing one part of the network could induce complex, unpredictable activity changes in neurons outside the targeted inactivation zone. These off-target side effects can potentially complicate interpretations of inactivation manipulations, especially when they are related to changes in behavior. Here, we demonstrate that optogenetic inactivation of glutamatergic neurons in the superficial layers of monkey primary visual cortex (V1) induces robust suppression at the light-targeted site, but destabilizes stimulus responses in the neighboring, untargeted network. We identified four types of stimulus-evoked neuronal responses within a cortical column, ranging from full suppression to facilitation, and a mixture of both. Mixed responses were most prominent in middle and deep cortical layers. These results demonstrate that response modulation driven by lateral network connectivity is diversely implemented throughout a cortical column. Importantly, consistent behavioral changes induced by optogenetic inactivation were only achieved when cumulative network activity was homogeneously suppressed. Therefore, careful consideration of the full range of network changes outside the inactivated cortical region is required, as heterogeneous side effects can confound interpretation of inactivation experiments.

Neuronal variability reflects probabilistic inference tuned to natural image statistics

Neuronal activity in sensory cortex fluctuates over time and across repetitions of the same input. This variability is often considered detrimental to neural coding. The theory of neural sampling proposes instead that variability encodes the uncertainty of perceptual inferences. In primary visual cortex (V1), modulation of variability by sensory and non-sensory factors supports this view. However, it is unknown whether V1 variability reflects the statistical structure of visual inputs, as would be required for inferences correctly tuned to the statistics of the natural environment. Here we combine analysis of image statistics and recordings in macaque V1 to show that probabilistic inference tuned to natural image statistics explains the widely observed dependence between spike count variance and mean, and the modulation of V1 activity and variability by spatial context in images. Our results show that the properties of a basic aspect of cortical responses-their variability-can be explained by a probabilistic representation tuned to naturalistic inputs.

Individuals with autism spectrum disorder have altered visual encoding capacity

Perceptual anomalies in individuals with autism spectrum disorder (ASD) have been attributed to an imbalance in weighting incoming sensory evidence with prior knowledge when interpreting sensory information. Here, we show that sensory encoding and how it adapts to changing stimulus statistics during feedback also characteristically differs between neurotypical and ASD groups. In a visual orientation estimation task, we extracted the accuracy of sensory encoding from psychophysical data by using an information theoretic measure. Initially, sensory representations in both groups reflected the statistics of visual orientations in natural scenes, but encoding capacity was overall lower in the ASD group. Exposure to an artificial (i.e., uniform) distribution of visual orientations coupled with performance feedback altered the sensory representations of the neurotypical group toward the novel experimental statistics, while also increasing their total encoding capacity. In contrast, neither total encoding capacity nor its allocation significantly changed in the ASD group. Across both groups, the degree of adaptation was correlated with participants’ initial encoding capacity. These findings highlight substantial deficits in sensory encoding—independent from and potentially in addition to deficits in decoding—in individuals with ASD.

It is increasingly recognized that individuals with Autism Spectrum Disorder (ASD) show anomalies in perception, and these have been recently attributed to altered decoding (i.e. interpretation of sensory signals). This study reveals that independent of these changes, individuals with ASD show upstream deficits in sensory encoding (i.e., how samples are drawn from the environment).

Neuronal response variability as a product of divisive normalization; neurobiological implications at a macroscale level

The occurrence of neuronal spikes recorded directly from sensory cortex is highly irregular within and between presentations of an invariant stimulus. The traditional solution has been to average responses across many trials. However, with this approach, response variability is downplayed as noise, so it is assumed that statistically controlling it will reveal the brain’s true response to a stimulus. A mounting body of evidence suggests that this approach is inadequate. For example, experiments show that response variability itself varies as a function of stimulus dimensions like contrast and state dimensions like attention. In other words, response variability has structure, is therefore potentially informative and should be incorporated into models which try to explain neural encoding. In this article we provide commentary on a recently published study by Coen-Cagli and Solomon that incorporates spike variability in a quantitative model, by explaining it as a function of divisive normalization. We consider the potential role of neural oscillations in this process as a potential bridge between the current microscale findings and response variability at the mesoscale/macroscale level.

Representation of visual uncertainty through neural gain variability

Uncertainty is intrinsic to perception. Neural circuits which process sensory information must therefore also represent the reliability of this information. How they do so is a topic of debate. We propose a model of visual cortex in which average neural response strength encodes stimulus features, while cross-neuron variability in response gain encodes the uncertainty of these features. To test this model, we studied spiking activity of neurons in macaque V1 and V2 elicited by repeated presentations of stimuli whose uncertainty was manipulated in distinct ways. We show that gain variability of individual neurons is tuned to stimulus uncertainty, that this tuning is specific to the features encoded by these neurons and largely invariant to the source of uncertainty. We demonstrate that this behavior naturally arises from known gain-control mechanisms, and illustrate how downstream circuits can jointly decode stimulus features and their uncertainty from sensory population activity.

Increased variability but intact integration during visual navigation in Autism Spectrum Disorder

Autism Spectrum Disorder (ASD) is a common neurodevelopmental disturbance afflicting a variety of functions. The recent computational focus suggesting aberrant Bayesian inference in ASD has yielded promising but conflicting results in attempting to explain a wide variety of phenotypes by canonical computations. Here, we used a naturalistic visual path integration task that combines continuous action with active sensing and allows tracking of subjects' dynamic belief states. Both groups showed a previously documented bias pattern by overshooting the radial distance and angular eccentricity of targets. For both control and ASD groups, these errors were driven by misestimated velocity signals due to a nonuniform speed prior rather than imperfect integration. We tracked participants' beliefs and found no difference in the speed prior, but there was heightened variability in the ASD group. Both end point variance and trajectory irregularities correlated with ASD symptom severity. With feedback, variance was reduced, and ASD performance approached that of controls. These findings highlight the need for both more naturalistic tasks and a broader computational perspective to understand the ASD phenotype and pathology.