Robust information propagation through noisy neural circuits

Spiking networks that efficiently process dynamic sensory features explain receptor information mixing in somatosensory cortex

How do biological neural systems efficiently encode, transform and propagate information between the sensory periphery and the sensory cortex about sensory features evolving at different time scales? Are these computations efficient in normative information processing terms? While previous work has suggested that biologically plausible models of of such neural information processing may be implemented efficiently within a single processing layer, how such computations extend across several processing layers is less clear. Here, we model propagation of multiple time-varying sensory features across a sensory pathway, by extending the theory of efficient coding with spikes to efficient encoding, transformation and transmission of sensory signals. These computations are optimally realized by a multilayer spiking network with feedforward networks of spiking neurons (receptor layer) and recurrent excitatory-inhibitory networks of generalized leaky integrate-and-fire neurons (recurrent layers). Our model efficiently realizes a broad class of feature transformations, including positive and negative interaction across features, through specific and biologically plausible structures of feedforward connectivity. We find that mixing of sensory features in the activity of single neurons is beneficial because it lowers the metabolic cost at the network level. We apply the model to the somatosensory pathway by constraining it with parameters measured empirically and include in its last node, analogous to the primary somatosensory cortex (S1), two types of inhibitory neurons: parvalbumin-positive neurons realizing lateral inhibition, and somatostatin-positive neurons realizing winner-take-all inhibition. By implementing a negative interaction across stimulus features, this model captures several intriguing empirical observations from the somatosensory system of the mouse, including a decrease of sustained responses from subcortical networks to S1, a non-linear effect of the knock-out of receptor neuron types on the activity in S1, and amplification of weak signals from sensory neurons across the pathway.

Simultaneous, cortex-wide dynamics of up to 1 million neurons reveal unbounded scaling of dimensionality with neuron number

The brain's remarkable properties arise from the collective activity of millions of neurons. Widespread application of dimensionality reduction to multi-neuron recordings implies that neural dynamics can be approximated by low-dimensional "latent" signals reflecting neural computations. However, can such low-dimensional representations truly explain the vast range of brain activity, and if not, what is the appropriate resolution and scale of recording to capture them? Imaging neural activity at cellular resolution and near-simultaneously across the mouse cortex, we demonstrate an unbounded scaling of dimensionality with neuron number in populations up to 1 million neurons. Although half of the neural variance is contained within sixteen dimensions correlated with behavior, our discovered scaling of dimensionality corresponds to an ever-increasing number of neuronal ensembles without immediate behavioral or sensory correlates. The activity patterns underlying these higher dimensions are fine grained and cortex wide, highlighting that large-scale, cellular-resolution recording is required to uncover the full substrates of neuronal computations.

Whole-brain neural substrates of behavioral variability in the larval zebrafish

Animals engaged in naturalistic behavior can exhibit a large degree of behavioral variability even under sensory invariant conditions. Such behavioral variability can include not only variations of the same behavior, but also variability across qualitatively different behaviors driven by divergent cognitive states, such as fight-or-flight decisions. However, the neural circuit mechanisms that generate such divergent behaviors across trials are not well understood. To investigate this question, here we studied the visual-evoked responses of larval zebrafish to moving objects of various sizes, which we found exhibited highly variable and divergent responses across repetitions of the same stimulus. Given that the neuronal circuits underlying such behaviors span sensory, motor, and other brain areas, we built a novel Fourier light field microscope which enables high-resolution, whole-brain imaging of larval zebrafish during behavior. This enabled us to screen for neural loci which exhibited activity patterns correlated with behavioral variability. We found that despite the highly variable activity of single neurons, visual stimuli were robustly encoded at the population level, and the visual-encoding dimensions of neural activity did not explain behavioral variability. This robustness despite apparent single neuron variability was due to the multi-dimensional geometry of the neuronal population dynamics: almost all neural dimensions that were variable across individual trials, i.e. the "noise" modes, were orthogonal to those encoding for sensory information. Investigating this neuronal variability further, we identified two sparsely-distributed, brain-wide neuronal populations whose pre-motor activity predicted whether the larva would respond to a stimulus and, if so, which direction it would turn on a single-trial level. These populations predicted single-trial behavior seconds before stimulus onset, indicating they encoded time-varying internal modulating behavior, perhaps organizing behavior over longer timescales or enabling flexible behavior routines dependent on the animal's internal state. Our results provide the first whole-brain confirmation that sensory, motor, and internal variables are encoded in a highly mixed fashion throughout the brain and demonstrate that de-mixing each of these components at the neuronal population level is critical to understanding the mechanisms underlying the brain's remarkable flexibility and robustness.

Applications of information geometry to spiking neural network activity

The space of possible behaviors that complex biological systems may exhibit is unimaginably vast, and these systems often appear to be stochastic, whether due to variable noisy environmental inputs or intrinsically generated chaos. The brain is a prominent example of a biological system with complex behaviors. The number of possible patterns of spikes emitted by a local brain circuit is combinatorially large, although the brain may not make use of all of them. Understanding which of these possible patterns are actually used by the brain, and how those sets of patterns change as properties of neural circuitry change is a major goal in neuroscience. Recently, tools from information geometry have been used to study embeddings of probabilistic models onto a hierarchy of model manifolds that encode how model outputs change as a function of their parameters, giving a quantitative notion of "distances" between outputs. We apply this method to a network model of excitatory and inhibitory neural populations to understand how the competition between membrane and synaptic response timescales shapes the network's information geometry. The hyperbolic embedding allows us to identify the statistical parameters to which the model behavior is most sensitive, and demonstrate how the ranking of these coordinates changes with the balance of excitation and inhibition in the network.

Simultaneous, cortex-wide and cellular-resolution neuronal population dynamics reveal an unbounded scaling of dimensionality with neuron number

The brain's remarkable properties arise from collective activity of millions of neurons. Widespread application of dimensionality reduction to multi-neuron recordings implies that neural dynamics can be approximated by low-dimensional "latent" signals reflecting neural computations. However, what would be the biological utility of such a redundant and metabolically costly encoding scheme and what is the appropriate resolution and scale of neural recording to understand brain function? Imaging the activity of one million neurons at cellular resolution and near-simultaneously across mouse cortex, we demonstrate an unbounded scaling of dimensionality with neuron number. While half of the neural variance lies within sixteen behavior-related dimensions, we find this unbounded scaling of dimensionality to correspond to an ever-increasing number of internal variables without immediate behavioral correlates. The activity patterns underlying these higher dimensions are fine-grained and cortex-wide, highlighting that large-scale recording is required to uncover the full neural substrates of internal and potentially cognitive processes.

Propagation of activity through the cortical hierarchy and perception are determined by neural variability

Brains are composed of anatomically and functionally distinct regions performing specialized tasks, but regions do not operate in isolation. Orchestration of complex behaviors requires communication between brain regions, but how neural dynamics are organized to facilitate reliable transmission is not well understood. Here we studied this process directly by generating neural activity that propagates between brain regions and drives behavior, assessing how neural populations in sensory cortex cooperate to transmit information. We achieved this by imaging two densely interconnected regions-the primary and secondary somatosensory cortex (S1 and S2)-in mice while performing two-photon photostimulation of S1 neurons and assigning behavioral salience to the photostimulation. We found that the probability of perception is determined not only by the strength of the photostimulation but also by the variability of S1 neural activity. Therefore, maximizing the signal-to-noise ratio of the stimulus representation in cortex relative to the noise or variability is critical to facilitate activity propagation and perception.

Linear Classification of Neural Manifolds with Correlated Variability

Understanding how the statistical and geometric properties of neural activity relate to performance is a key problem in theoretical neuroscience and deep learning. Here, we calculate how correlations between object representations affect the capacity, a measure of linear separability. We show that for spherical object manifolds, introducing correlations between centroids effectively pushes the spheres closer together, while introducing correlations between the axes effectively shrinks their radii, revealing a duality between correlations and geometry with respect to the problem of classification. We then apply our results to accurately estimate the capacity of deep network data.

Information-Theoretic Approaches in EEG Correlates of Auditory Perceptual Awareness under Informational Masking

In informational masking paradigms, the successful segregation between the target and masker creates auditory perceptual awareness. The dynamics of the build-up of auditory perception is based on a set of interactions between bottom-up and top-down processes that generate neuronal modifications within the brain network activity. These neural changes are studied here using event-related potentials (ERPs), entropy, and integrated information, leading to several measures applied to electroencephalogram signals. The main findings show that the auditory perceptual awareness stimulated functional activation in the fronto-temporo-parietal brain network through (i) negative temporal and positive centro-parietal ERP components; (ii) an enhanced processing of multi-information in the temporal cortex; and (iii) an increase in informational content in the fronto-central cortex. These different results provide information-based experimental evidence about the functional activation of the fronto-temporo-parietal brain network during auditory perceptual awareness.

Signal denoising through topographic modularity of neural circuits

Information from the sensory periphery is conveyed to the cortex via structured projection pathways that spatially segregate stimulus features, providing a robust and efficient encoding strategy. Beyond sensory encoding, this prominent anatomical feature extends throughout the neocortex. However, the extent to which it influences cortical processing is unclear. In this study, we combine cortical circuit modeling with network theory to demonstrate that the sharpness of topographic projections acts as a bifurcation parameter, controlling the macroscopic dynamics and representational precision across a modular network. By shifting the balance of excitation and inhibition, topographic modularity gradually increases task performance and improves the signal-to-noise ratio across the system. We demonstrate that in biologically constrained networks, such a denoising behavior is contingent on recurrent inhibition. We show that this is a robust and generic structural feature that enables a broad range of behaviorally relevant operating regimes, and provide an in-depth theoretical analysis unraveling the dynamical principles underlying the mechanism.

Computational methods to study information processing in neural circuits

The brain is an information processing machine and thus naturally lends itself to be studied using computational tools based on the principles of information theory. For this reason, computational methods based on or inspired by information theory have been a cornerstone of practical and conceptual progress in neuroscience. In this Review, we address how concepts and computational tools related to information theory are spurring the development of principled theories of information processing in neural circuits and the development of influential mathematical methods for the analyses of neural population recordings. We review how these computational approaches reveal mechanisms of essential functions performed by neural circuits. These functions include efficiently encoding sensory information and facilitating the transmission of information to downstream brain areas to inform and guide behavior. Finally, we discuss how further progress and insights can be achieved, in particular by studying how competing requirements of neural encoding and readout may be optimally traded off to optimize neural information processing.

Learning shapes cortical dynamics to enhance integration of relevant sensory input

Adaptive sensory behavior is thought to depend on processing in recurrent cortical circuits, but how dynamics in these circuits shapes the integration and transmission of sensory information is not well understood. Here, we study neural coding in recurrently connected networks of neurons driven by sensory input. We show analytically how information available in the network output varies with the alignment between feedforward input and the integrating modes of the circuit dynamics. In light of this theory, we analyzed neural population activity in the visual cortex of mice that learned to discriminate visual features. We found that over learning, slow patterns of network dynamics realigned to better integrate input relevant to the discrimination task. This realignment of network dynamics could be explained by changes in excitatory-inhibitory connectivity among neurons tuned to relevant features. These results suggest that learning tunes the temporal dynamics of cortical circuits to optimally integrate relevant sensory input.

The structures and functions of correlations in neural population codes

The collective activity of a population of neurons, beyond the properties of individual cells, is crucial for many brain functions. A fundamental question is how activity correlations between neurons affect how neural populations process information. Over the past 30 years, major progress has been made on how the levels and structures of correlations shape the encoding of information in population codes. Correlations influence population coding through the organization of pairwise-activity correlations with respect to the similarity of tuning of individual neurons, by their stimulus modulation and by the presence of higher-order correlations. Recent work has shown that correlations also profoundly shape other important functions performed by neural populations, including generating codes across multiple timescales and facilitating information transmission to, and readout by, downstream brain areas to guide behaviour. Here, we review this recent work and discuss how the structures of correlations can have opposite effects on the different functions of neural populations, thus creating trade-offs and constraints for the structure-function relationships of population codes. Further, we present ideas on how to combine large-scale simultaneous recordings of neural populations, computational models, analyses of behaviour, optogenetics and anatomy to unravel how the structures of correlations might be optimized to serve multiple functions.

Internally generated population activity in cortical networks hinders information transmission

How neuronal variability affects sensory coding is a central question in systems neuroscience, often with complex and model-dependent answers. Many studies explore population models with a parametric structure for response tuning and variability, preventing an analysis of how synaptic circuitry establishes neural codes. We study stimulus coding in networks of spiking neuron models with spatially ordered excitatory and inhibitory connectivity. The wiring structure is capable of producing rich population-wide shared neuronal variability that agrees with many features of recorded cortical activity. While both the spatial scales of feedforward and recurrent projections strongly affect noise correlations, only recurrent projections, and in particular inhibitory projections, can introduce correlations that limit the stimulus information available to a decoder. Using a spatial neural field model, we relate the recurrent circuit conditions for information limiting noise correlations to how recurrent excitation and inhibition can form spatiotemporal patterns of population-wide activity.

Developmental and evolutionary constraints on olfactory circuit selection

SignificanceIn this work, we explore the hypothesis that biological neural networks optimize their architecture, through evolution, for learning. We study early olfactory circuits of mammals and insects, which have relatively similar structure but a huge diversity in size. We approximate these circuits as three-layer networks and estimate, analytically, the scaling of the optimal hidden-layer size with input-layer size. We find that both longevity and information in the genome constrain the hidden-layer size, so a range of allometric scalings is possible. However, the experimentally observed allometric scalings in mammals and insects are consistent with biologically plausible values. This analysis should pave the way for a deeper understanding of both biological and artificial networks.

Correlations enhance the behavioral readout of neural population activity in association cortex

Noise correlations (that is, trial-to-trial covariations in neural activity for a given stimulus) limit the stimulus information encoded by neural populations, leading to the widely held prediction that they impair perceptual discrimination behaviors. However, this prediction neglects the effects of correlations on information readout. We studied how correlations affect both encoding and readout of sensory information. We analyzed calcium imaging data from mouse posterior parietal cortex during two perceptual discrimination tasks. Correlations reduced the encoded stimulus information, but, seemingly paradoxically, were higher when mice made correct rather than incorrect choices. Single-trial behavioral choices depended not only on the stimulus information encoded by the whole population, but unexpectedly also on the consistency of information across neurons and time. Because correlations increased information consistency, they enhanced the conversion of sensory information into behavioral choices, overcoming their detrimental information-limiting effects. Thus, correlations in association cortex can benefit task performance even if they decrease sensory information.

Correlated structure of neuronal firing in macaque visual cortex limits information for binocular depth discrimination

Variability in cortical neural activity potentially limits sensory discriminations. Theoretical work shows that information required to discriminate two similar stimuli is limited by the correlation structure of cortical variability. We investigated these information-limiting correlations by recording simultaneously from visual cortical areas primary visual cortex (V1) and extrastriate area V4 in macaque monkeys performing a binocular, stereo depth discrimination task. Within both areas, noise correlations on a rapid temporal scale (20–30 ms) were stronger for neuron pairs with similar selectivity for binocular depth, meaning that these correlations potentially limit information for making the discrimination. Between-area correlations (V1 to V4) were different, being weaker for neuron pairs with similar tuning and having a slower temporal scale (100+ ms). Fluctuations in these information-limiting correlations just prior to the detection event were associated with changes in behavioral accuracy. Although these correlations limit the recovery of information about sensory targets, their impact may be curtailed by integrative processing of signals across multiple brain areas.

NEW & NOTEWORTHY Correlated noise reduces the stimulus information in visual cortical neurons during experimental performance of binocular depth discriminations. The temporal scale of these correlations is important. Rapid (20–30 ms) correlations reduce information within and between areas V1 and V4, whereas slow (>100 ms) correlations between areas do not. Separate cortical areas appear to act together to maintain signal fidelity. Rapid correlations reduce the neuronal signal difference between stimuli and adversely affect perceptual discrimination.

A network model of the barrel cortex combined with a differentiator detector reproduces features of the behavioral response to single-neuron stimulation

The stimulation of a single neuron in the rat somatosensory cortex can elicit a behavioral response. The probability of a behavioral response does not depend appreciably on the duration or intensity of a constant stimulation, whereas the response probability increases significantly upon injection of an irregular current. Biological mechanisms that can potentially suppress a constant input signal are present in the dynamics of both neurons and synapses and seem ideal candidates to explain these experimental findings. Here, we study a large network of integrate-and-fire neurons with several salient features of neuronal populations in the rat barrel cortex. The model includes cellular spike-frequency adaptation, experimentally constrained numbers and types of chemical synapses endowed with short-term plasticity, and gap junctions. Numerical simulations of this model indicate that cellular and synaptic adaptation mechanisms alone may not suffice to account for the experimental results if the local network activity is read out by an integrator. However, a circuit that approximates a differentiator can detect the single-cell stimulation with a reliability that barely depends on the length or intensity of the stimulus, but that increases when an irregular signal is used. This finding is in accordance with the experimental results obtained for the stimulation of a regularly-spiking excitatory cell.

It is widely assumed that only a large group of neurons can encode a stimulus or control behavior. This tenet of neuroscience has been challenged by experiments in which stimulating a single cortical neuron has had a measurable effect on an animal’s behavior. Recently, theoretical studies have explored how a single-neuron stimulation could be detected in a large recurrent network. However, these studies missed essential biological mechanisms of cortical networks and are unable to explain more recent experiments in the barrel cortex. Here, to describe the stimulated brain area, we propose and study a network model endowed with many important biological features of the barrel cortex. Importantly, we also investigate different readout mechanisms, i.e. ways in which the stimulation effects can propagate to other brain areas. We show that a readout network which tracks rapid variations in the local network activity is in agreement with the experiments. Our model demonstrates a possible mechanism for how the stimulation of a single neuron translates into a signal at the population level, which is taken as a proxy of the animal’s response. Our results illustrate the power of spiking neural networks to properly describe the effects of a single neuron’s activity.

Cyclic transitions between higher order motifs underlie sustained asynchronous spiking in sparse recurrent networks

A basic—yet nontrivial—function which neocortical circuitry must satisfy is the ability to maintain stable spiking activity over time. Stable neocortical activity is asynchronous, critical, and low rate, and these features of spiking dynamics contribute to efficient computation and optimal information propagation. However, it remains unclear how neocortex maintains this asynchronous spiking regime. Here we algorithmically construct spiking neural network models, each composed of 5000 neurons. Network construction synthesized topological statistics from neocortex with a set of objective functions identifying naturalistic low-rate, asynchronous, and critical activity. We find that simulations run on the same topology exhibit sustained asynchronous activity under certain sets of initial membrane voltages but truncated activity under others. Synchrony, rate, and criticality do not provide a full explanation of this dichotomy. Consequently, in order to achieve mechanistic understanding of sustained asynchronous activity, we summarized activity as functional graphs where edges between units are defined by pairwise spike dependencies. We then analyzed the intersection between functional edges and synaptic connectivity- i.e. recruitment networks. Higher-order patterns, such as triplet or triangle motifs, have been tied to cooperativity and integration. We find, over time in each sustained simulation, low-variance periodic transitions between isomorphic triangle motifs in the recruitment networks. We quantify the phenomenon as a Markov process and discover that if the network fails to engage this stereotyped regime of motif dominance “cycling”, spiking activity truncates early. Cycling of motif dominance generalized across manipulations of synaptic weights and topologies, demonstrating the robustness of this regime for maintenance of network activity. Our results point to the crucial role of excitatory higher-order patterns in sustaining asynchronous activity in sparse recurrent networks. They also provide a possible explanation why such connectivity and activity patterns have been prominently reported in neocortex.

Neocortical spiking activity tends to be low-rate and non-rhythmic, and to operate near the critical point of a phase transition. It remains unclear how this kind of spiking activity can be maintained within a neuronal network. Neurons are leaky and individual synaptic connections are sparse and weak, making the maintenance of an asynchronous regime a nontrivial problem. Higher order patterns involving more than two units abound in neocortex, and several lines of evidence suggest that they may be instrumental for brain function. For example, stable activity in vivo displays elevated clustering dominated by specific three-node (triplet) motifs. In this study we demonstrate a link between the maintenance of asynchronous activity and triplet motifs. We algorithmically build spiking neural network models to mimic the topology of neocortex and the spiking statistics that characterize wakefulness. We show that higher order coordination of synapses is always present during sustained asynchronous activity. Coordination takes the form of transitions in time between specific triangle motifs. These motifs summarize the way spikes traverse the underlying synaptic topology. The results of our model are consistent with numerous experimental observations, and their generalizability to other weakly and sparsely connected networks is predicted.

Heterogeneous Synaptic Weighting Improves Neural Coding in the Presence of Common Noise

Simultaneous recordings from the cortex have revealed that neural activity is highly variable and that some variability is shared across neurons in a population. Further experimental work has demonstrated that the shared component of a neuronal population's variability is typically comparable to or larger than its private component. Meanwhile, an abundance of theoretical work has assessed the impact that shared variability has on a population code. For example, shared input noise is understood to have a detrimental impact on a neural population's coding fidelity. However, other contributions to variability, such as common noise, can also play a role in shaping correlated variability. We present a network of linear-nonlinear neurons in which we introduce a common noise input to model-for instance, variability resulting from upstream action potentials that are irrelevant to the task at hand. We show that by applying a heterogeneous set of synaptic weights to the neural inputs carrying the common noise, the network can improve its coding ability as measured by both Fisher information and Shannon mutual information, even in cases where this results in amplification of the common noise. With a broad and heterogeneous distribution of synaptic weights, a population of neurons can remove the harmful effects imposed by afferents that are uninformative about a stimulus. We demonstrate that some nonlinear networks benefit from weight diversification up to a certain population size, above which the drawbacks from amplified noise dominate over the benefits of diversification. We further characterize these benefits in terms of the relative strength of shared and private variability sources. Finally, we studied the asymptotic behavior of the mutual information and Fisher information analytically in our various networks as a function of population size. We find some surprising qualitative changes in the asymptotic behavior as we make seemingly minor changes in the synaptic weight distributions.

Dendritic Spikes Expand the Range of Well Tolerated Population Noise Structures

The brain operates surprisingly well despite the noisy nature of individual neurons. The central mechanism for noise mitigation in the nervous system is thought to involve averaging over multiple noise-corrupted inputs. Subsequently, there has been considerable interest in identifying noise structures that can be integrated linearly in a way that preserves reliable signal encoding. By analyzing realistic synaptic integration in biophysically accurate neuronal models, I report a complementary denoising approach that is mediated by focal dendritic spikes. Dendritic spikes might seem to be unlikely candidates for noise reduction due to their miniscule integration compartments and poor averaging abilities. Nonetheless, the extra thresholding step introduced by dendritic spike generation increases neuronal tolerance for a broad category of noise structures, some of which cannot be resolved well with averaging. This property of active dendrites compensates for compartment size constraints and expands the repertoire of conditions that can be processed by neuronal populations.SIGNIFICANCE STATEMENT Noise, or random variability, is a prominent feature of the neuronal code and poses a fundamental challenge for information processing. To reconcile the surprisingly accurate output of the brain with the inherent noisiness of biological systems, previous work examined signal integration in idealized neurons. The notion that emerged from this body of work is that accurate signal representation relies largely on input averaging in neuronal dendrites. In contrast to the prevailing view, I show that denoising in simulated neurons with realistic morphology and biophysical properties follows a different strategy: dendritic spikes act as classifiers that assist in extracting information from a variety of noise structures that have been considered before to be particularly disruptive for reliable brain function.

Neuromodulation influences synchronization and intrinsic read-out

Background: The roles of neuromodulation in a neural network, such as in a cortical microcolumn, are still incompletely understood. Neuromodulation influences neural processing by presynaptic and postsynaptic regulation of synaptic efficacy. Neuromodulation also affects ion channels and intrinsic excitability.

Methods: Synaptic efficacy modulation is an effective way to rapidly alter network density and topology. We alter network topology and density to measure the effect on spike synchronization. We also operate with differently parameterized neuron models which alter the neuron's intrinsic excitability, i.e., activation function.

Results: We find that (a) fast synaptic efficacy modulation influences the amount of correlated spiking in a network. Also, (b) synchronization in a network influences the read-out of intrinsic properties. Highly synchronous input drives neurons, such that differences in intrinsic properties disappear, while asynchronous input lets intrinsic properties determine output behavior. Thus, altering network topology can alter the balance between intrinsically vs. synaptically driven network activity.

Conclusion: We conclude that neuromodulation may allow a network to shift between a more synchronized transmission mode and a more asynchronous intrinsic read-out mode. This has significant implications for our understanding of the flexibility of cortical computations.

Information spectra and optimal background states for dynamical networks

We consider the notion of stimulus representation over dynamic networks, wherein the network states encode information about the identify of an afferent input (i.e. stimulus). Our goal is to understand how the structure and temporal dynamics of networks support information processing. In particular, we conduct a theoretical study to reveal how the background or 'default' state of a network with linear dynamics allows it to best promote discrimination over a continuum of stimuli. Our principal contribution is the derivation of a matrix whose spectrum (eigenvalues) quantify the extent to which the state of a network encodes its inputs. This measure, based on the notion of a Fisher linear discriminant, is relativistic in the sense that it provides an information value quantifying the 'knowablility' of an input based on its projection onto the background state. We subsequently optimize the background state and highlight its relationship to underlying state noise covariance. This result demonstrates how the best idle state of a network may be informed by its structure and dynamics. Further, we relate the proposed information spectrum to the controllabilty gramian matrix, establishing a link between fundamental control-theoretic network analysis and information processing.

State dependence of stimulus-induced variability tuning in macaque MT

Behavioral states marked by varying levels of arousal and attention modulate some properties of cortical responses (e.g. average firing rates or pairwise correlations), yet it is not fully understood what drives these response changes and how they might affect downstream stimulus decoding. Here we show that changes in state modulate the tuning of response variance-to-mean ratios (Fano factors) in a fashion that is neither predicted by a Poisson spiking model nor changes in the mean firing rate, with a substantial effect on stimulus discriminability. We recorded motion-sensitive neurons in middle temporal cortex (MT) in two states: alert fixation and light, opioid anesthesia. Anesthesia tended to lower average spike counts, without decreasing trial-to-trial variability compared to the alert state. Under anesthesia, within-trial fluctuations in excitability were correlated over longer time scales compared to the alert state, creating supra-Poisson Fano factors. In contrast, alert-state MT neurons have higher mean firing rates and largely sub-Poisson variability that is stimulus-dependent and cannot be explained by firing rate differences alone. The absence of such stimulus-induced variability tuning in the anesthetized state suggests different sources of variability between states. A simple model explains state-dependent shifts in the distribution of observed Fano factors via a suppression in the variance of gain fluctuations in the alert state. A population model with stimulus-induced variability tuning and behaviorally constrained information-limiting correlations explores the potential enhancement in stimulus discriminability by the cortical population in the alert state.

The brain controls behavior fluidly in a wide variety of cognitive contexts that alter the precision of neural responses. We examine how neural variability changes versus the mean response as a function of the stimulus and the behavioral state. We show that this scaled variability can have qualitatively different stimulus tuning in different behavioral contexts. In alert primates, scaled variability is tuned to the direction of motion of a visual stimulus and decreases around the preferred direction of each neuron. Under anesthesia, neurons show flat scaled variability tuning and, overall, responses are significantly more variable. We develop a simple model that includes a parameter describing firing rate gain fluctuations that can explain these changes. Our results suggest that tuned decreases in scaled variability during wakefulness may be mediated by an active process that suppresses synchronization and makes information transmission more reliable.

Neuromodulation influences synchronization and intrinsic read-out

Background: The roles of neuromodulation in a neural network, such as in a cortical microcolumn, are still incompletely understood. Neuromodulation influences neural processing by presynaptic and postsynaptic regulation of synaptic efficacy. Neuromodulation also affects ion channels and intrinsic excitability. Methods: Synaptic efficacy modulation is an effective way to rapidly alter network density and topology. We alter network topology and density to measure the effect on spike synchronization. We also operate with differently parameterized neuron models which alter the neuron's intrinsic excitability, i.e., activation function. Results: We find that (a) fast synaptic efficacy modulation influences the amount of correlated spiking in a network. Also, (b) synchronization in a network influences the read-out of intrinsic properties. Highly synchronous input drives neurons, such that differences in intrinsic properties disappear, while asynchronous input lets intrinsic properties determine output behavior. Thus, altering network topology can alter the balance between intrinsically vs. synaptically driven network activity. Conclusion: We conclude that neuromodulation may allow a network to shift between a more synchronized transmission mode and a more asynchronous intrinsic read-out mode. This has significant implications for our understanding of the flexibility of cortical computations.

Inference in the Brain: Statistics Flowing in Redundant Population Codes

It is widely believed that the brain performs approximate probabilistic inference to estimate causal variables in the world from ambiguous sensory data. To understand these computations, we need to analyze how information is represented and transformed by the actions of nonlinear recurrent neural networks. We propose that these probabilistic computations function by a message-passing algorithm operating at the level of redundant neural populations. To explain this framework, we review its underlying concepts, including graphical models, sufficient statistics, and message-passing, and then describe how these concepts could be implemented by recurrently connected probabilistic population codes. The relevant information flow in these networks will be most interpretable at the population level, particularly for redundant neural codes. We therefore outline a general approach to identify the essential features of a neural message-passing algorithm. Finally, we argue that to reveal the most important aspects of these neural computations, we must study large-scale activity patterns during moderately complex, naturalistic behaviors.