Neural Population Coding Research Articles

Computational model of layer 2/3 in mouse primary visual cortex explains observed visuomotor mismatch response.

Activity in layer 2/3 of the mouse primary visual cortex has been shown to depend both on visual input and the mouse's locomotion. Moreover, this activity is altered by a mismatch between the observed visual flow and the predicted visual flow from locomotion. Here, I present a simple computational model that explains previously reported recordings from layer 2/3 neurons in mice. In my model, layer 2/3 encodes the velocity difference between the estimate from visual flow and the prediction from locomotion using a neural population code. Moreover, I describe a hypothesized mechanism for how the brain may carry out computations of variables encoded in population codes. This mechanism may point to a general principle for computing any mathematical function in the brain.

Continuous Rotation Group Equivariant Network Inspired by Neural Population Coding

Neural population coding can represent continuous information by neurons with a series of discrete preferred stimuli, and we find that the bell-shaped tuning curve plays an important role in this mechanism. Inspired by this, we incorporate a bell-shaped tuning curve into the discrete group convolution to achieve continuous group equivariance. Simply, we modulate group convolution kernels by Gauss functions to obtain bell-shaped tuning curves. Benefiting from the modulation, kernels also gain smooth gradients on geometric dimensions (e.g., location dimension and orientation dimension). It allows us to generate group convolution kernels from sparse weights with learnable geometric parameters, which can achieve both competitive performances and parameter efficiencies. Furthermore, we quantitatively prove that discrete group convolutions with proper tuning curves (bigger than 1x sampling step) can achieve continuous equivariance. Experimental results show that 1) our approach achieves very competitive performances on MNIST-rot with at least 75% fewer parameters compared with previous SOTA methods, which is efficient in parameter; 2) Especially with small sample sizes, our approach exhibits more pronounced performance improvements (up to 24%); 3) It also has excellent rotation generalization ability on various datasets such as MNIST, CIFAR, and ImageNet with both plain and ResNet architectures.

Efficient Decoding of Large-Scale Neural Population Responses With Gaussian-Process Multiclass Regression.

Neural decoding methods provide a powerful tool for quantifying the information content of neural population codes and the limits imposed by correlations in neural activity. However, standard decoding methods are prone to overfitting and scale poorly to high-dimensional settings. Here, we introduce a novel decoding method to overcome these limitations. Our approach, the gaussian process multiclass decoder (GPMD), is well suited to decoding a continuous low-dimensional variable from high-dimensional population activity and provides a platform for assessing the importance of correlations in neural population codes. The GPMD is a multinomial logistic regression model with a gaussian process prior over the decoding weights. The prior includes hyperparameters that govern the smoothness of each neuron's decoding weights, allowing automatic pruning of uninformative neurons during inference. We provide a variational inference method for fitting the GPMD to data, which scales to hundreds or thousands of neurons and performs well even in data sets with more neurons than trials. We apply the GPMD to recordings from primary visual cortex in three species: monkey, ferret, and mouse. Our decoder achieves state-of-the-art accuracy on all three data sets and substantially outperforms independent Bayesian decoding, showing that knowledge of the correlation structure is essential for optimal decoding in all three species.

Self-Organization of Nonlinearly Coupled Neural Fluctuations Into Synergistic Population Codes.

Neural activity in the brain exhibits correlated fluctuations that may strongly influence the properties of neural population coding. However, how such correlated neural fluctuations may arise from the intrinsic neural circuit dynamics and subsequently affect the computational properties of neural population activity remains poorly understood. The main difficulty lies in resolving the nonlinear coupling between correlated fluctuations with the overall dynamics of the system. In this study, we investigate the emergence of synergistic neural population codes from the intrinsic dynamics of correlated neural fluctuations in a neural circuit model capturing realistic nonlinear noise coupling of spiking neurons. We show that a rich repertoire of spatial correlation patterns naturally emerges in a bump attractor network and further reveals the dynamical regime under which the interplay between differential and noise correlations leads to synergistic codes. Moreover, we find that negative correlations may induce stable bound states between two bumps, a phenomenon previously unobserved in firing rate models. These noise-induced effects of bump attractors lead to a number of computational advantages including enhanced working memory capacity and efficient spatiotemporal multiplexing and can account for a range of cognitive and behavioral phenomena related to working memory. This study offers a dynamical approach to investigating realistic correlated neural fluctuations and insights to their roles in cortical computations.

A manifold neural population code for space in hippocampal coactivity dynamics independent of place fields

Hippocampus place cell discharge is temporally unreliable across seconds and days, and place fields are multimodal, suggesting an "ensemble cofiring" spatial coding hypothesis with manifold dynamics that does not require reliable spatial tuning, in contrast to hypotheses based on place field (spatial tuning) stability. We imaged mouse CA1 (cornu ammonis 1) ensembles in two environments across three weeks to evaluate these coding hypotheses. While place fields "remap," being more distinct between than within environments, coactivity relationships generally change less. Decoding location and environment from 1-s ensemble location-specific activity is effective and improves with experience. Decoding environment from cell-pair coactivity relationships is also effective and improves with experience, even after removing place tuning. Discriminating environments from 1-s ensemble coactivity relies crucially on the cells with the most anti-coactive cell-pair relationships because activity is internally organized on a low-dimensional manifold of non-linear coactivity relationships that intermittently reregisters to environments according to the anti-cofiring subpopulation activity.

Invited Session IV: Studies of the visual cortex with sub-millimeter resolution: Toward an all-optical bi-directional interrogation of topographic population codes in primate cortex.

The representation of visual stimuli in primate V1 is widely distributed and topographic. This raises the possibility that in some visual tasks, downstream areas that decode V1 signals in order to mediate perception could combine V1 signals at a relevant topographic scale-e.g., at the scale of orientation columns. If this were the case, then the fundamental unit of information would be individual columns rather than single neurons, and to account for the subject's behavior in a perceptual task, it would be necessary and sufficient to consider the summed activity of the thousands of neurons within each column. In this presentation I will discuss our initial attempts to test this topographic-code hypothesis using our optical-genetic toolbox for "reading" and "writing" neural population codes at the spatial scales of topographic maps in V1 of behaving macaques.

Rate-distortion theory of neural coding and its implications for working memory.

Rate-distortion theory provides a powerful framework for understanding the nature of human memory by formalizing the relationship between information rate (the average number of bits per stimulus transmitted across the memory channel) and distortion (the cost of memory errors). Here we show how this abstract computational-level framework can be realized by a model of neural population coding. The model reproduces key regularities of visual working memory, including some that were not previously explained by population coding models. We verify a novel prediction of the model by reanalyzing recordings of monkey prefrontal neurons during an oculomotor delayed response task.

Spike-frequency adaptation inhibits the pairwise spike correlation.

The spike train output correlation with pairwise neurons determines the neural population coding, which depends on the average firing rate of individual neurons. Spike frequency adaptation (SFA), which serves as an essential cellular encoding strategy, modulates the firing rates of individual neurons. However, the mechanism by which the SFA modulates the output correlation of the spike trains remains unclear. We introduce a pairwise neuron model that receives correlated inputs to generate spike trains, and the output correlation is qualified using Pearson correlation coefficient. The SFA is modeled using adaptation currents to examine its effect on the output correlation. Moreover, we use dynamic thresholds to explore the effect of SFA on output correlation. Furthermore, a simple phenomenological neuron model with a threshold-linear transfer function is utilized to confirm the effect of SFA on decreasing the output correlation. The results show that the adaptation currents decreased the output correlation by reducing the firing rate of a single neuron. At the onset of a correlated input, a transient process shows a decrease in interspike intervals (ISIs), resulting in a temporary increase in the correlation. When the adaptation current is sufficiently activated, the correlation reached a steady state, and the ISIs are maintained at higher values. The enhanced adaptation current achieved by increasing the adaptation conductance further reduces the pairwise correlation. While the time and slide windows influence the correlation, they make no difference in the effect of SFA on decreasing the output correlation. Moreover, SFA simulated by dynamic thresholds also decreases the output correlation. Furthermore, the simple phenomenological neuron model with a threshold-linear transfer function confirms the effect of SFA on decreasing the output correlation. The strength of the signal input and the slope of the linear component of the transfer function, the latter of which can be decreased by SFA, could together modulate the strength of the output correlation. Stronger SFA will decrease the slope and hence decrease the output correlation. The results reveal that the SFA reduces the output correlation with pairwise neurons in the network by reducing the firing rate of individual neurons. This study provides a link between cellular non-linear mechanisms and network coding strategies.

Artificial neural network modelling of the neural population code underlying mathematical operations

Mathematical operations have long been regarded as a sparse, symbolic process in neuroimaging studies. In contrast, advances in artificial neural networks (ANN) have enabled extracting distributed representations of mathematical operations. Recent neuroimaging studies have compared distributed representations of the visual, auditory and language domains in ANNs and biological neural networks (BNNs). However, such a relationship has not yet been examined in mathematics. Here we hypothesise that ANN-based distributed representations can explain brain activity patterns of symbolic mathematical operations. We used the fMRI data of a series of mathematical problems with nine different combinations of operators to construct voxel-wise encoding/decoding models using both sparse operator and latent ANN features. Representational similarity analysis demonstrated shared representations between ANN and BNN, an effect particularly evident in the intraparietal sulcus. Feature-brain similarity (FBS) analysis served to reconstruct a sparse representation of mathematical operations based on distributed ANN features in each cortical voxel. Such reconstruction was more efficient when using features from deeper ANN layers. Moreover, latent ANN features allowed the decoding of novel operators not used during model training from brain activity. The current study provides novel insights into the neural code underlying mathematical thought.

Optogenetics-Inspired Fluorescent Synaptic Devices with Nonvolatility

Given the synergy of optogenetics and bioimaging in neuroscience, it is possible for light to simultaneously modulate and visualize synaptic events of optoelectronic synaptic devices, which are building blocks of a neuromorphic computing system with optoelectronic integration. Here we demonstrate the realization of the simultaneous modulation and visualization of synaptic events by using optically stimulated synaptic devices based on the heterostructure of fluorescent silicon quantum dots (Si QDs) and monolayer molybdenum disulfide (MoS2). The charge-transfer-enabled photogating effect of the Si QDs/MoS2 heterostructure leads to the nonvolatility of the synaptic devices, which exhibit important synaptic functionalities and synchronous fluorescence upon optical stimulation. An array of the Si QDs/MoS2 optoelectronic synaptic devices is well-employed to mimic robust neural population coding. Defective devices in this array may be pinpointed by the absence of their fluorescence. This work has an important implication for the development of synaptic devices facilitating the system-level diagnosis and device-level positioning of a neuromorphic computing system.

Coordinated drift of receptive fields in Hebbian/anti-Hebbian network models during noisy representation learning.

Recent experiments have revealed that neural population codes in many brain areas continuously change even when animals have fully learned and stably perform their tasks. This representational 'drift' naturally leads to questions about its causes, dynamics and functions. Here we explore the hypothesis that neural representations optimize a representational objective with a degenerate solution space, and noisy synaptic updates drive the network to explore this (near-)optimal space causing representational drift. We illustrate this idea and explore its consequences in simple, biologically plausible Hebbian/anti-Hebbian network models of representation learning. We find that the drifting receptive fields of individual neurons can be characterized by a coordinated random walk, with effective diffusion constants depending on various parameters such as learning rate, noise amplitude and input statistics. Despite such drift, the representational similarity of population codes is stable over time. Our model recapitulates experimental observations in the hippocampus and posterior parietal cortex and makes testable predictions that can be probed in future experiments.

A multivariate comparison of electroencephalogram and functional magnetic resonance imaging to electrocorticogram using visual object representations in humans.

Today, most neurocognitive studies in humans employ the non-invasive neuroimaging techniques functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG). However, how the data provided by fMRI and EEG relate exactly to the underlying neural activity remains incompletely understood. Here, we aimed to understand the relation between EEG and fMRI data at the level of neural population codes using multivariate pattern analysis. In particular, we assessed whether this relation is affected when we change stimuli or introduce identity-preserving variations to them. For this, we recorded EEG and fMRI data separately from 21 healthy participants while participants viewed everyday objects in different viewing conditions, and then related the data to electrocorticogram (ECoG) data recorded for the same stimulus set from epileptic patients. The comparison of EEG and ECoG data showed that object category signals emerge swiftly in the visual system and can be detected by both EEG and ECoG at similar temporal delays after stimulus onset. The correlation between EEG and ECoG was reduced when object representations tolerant to changes in scale and orientation were considered. The comparison of fMRI and ECoG overall revealed a tighter relationship in occipital than in temporal regions, related to differences in fMRI signal-to-noise ratio. Together, our results reveal a complex relationship between fMRI, EEG, and ECoG signals at the level of population codes that critically depends on the time point after stimulus onset, the region investigated, and the visual contents used.

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.

Emergent reliability in sensory cortical coding and inter-area communication.

Reliable sensory discrimination must arise from high-fidelity neural representations and communication between brain areas. However, how neocortical sensory processing overcomes the substantialvariability of neuronal sensory responses remains undetermined1-6. Here we imaged neuronalactivity in eight neocortical areas concurrently and over five days in mice performing a visual discrimination task, yielding longitudinal recordings of more than 21,000 neurons. Analyses revealed a sequence of events across the neocortex starting from a resting state, to early stages of perception, and through the formation of a task response. At rest, the neocortex had one pattern of functional connections, identified through sets of areas that shared activity cofluctuations7,8. Within about 200 ms after the onset of the sensory stimulus, such connections rearranged, with different areas sharing cofluctuations and task-related information. During this short-lived state(approximately 300 ms duration), bothinter-area sensory data transmission and the redundancy of sensory encoding peaked, reflecting a transient increase in correlated fluctuations among task-related neurons. By around 0.5 s after stimulus onset, thevisual representation reached a more stable form, the structure of which was robust to the prominent, day-to-day variations in the responses of individual cells. About 1 s into stimulus presentation, a global fluctuation mode conveyed the upcoming response of the mouse to every area examined and was orthogonal to modes carrying sensory data. Overall, the neocortex supports sensory performance through brief elevations in sensory coding redundancynear the start of perception, neural populationcodes that are robust to cellular variability, and widespreadinter-area fluctuation modes that transmit sensory data and task responses in non-interfering channels.

Sequential and efficient neural-population coding of complex task information

Recent work has highlighted that many types of variables are represented in each neocortical area. How can these many neural representations be organized together without interference and coherently maintained/updated through time? We recorded from excitatory neural populations in posterior cortices as mice performed a complex, dynamic task involving multiple interrelated variables. The neural encoding implied that highly correlated task variables were represented by less-correlated neural population modes, while pairs of neurons exhibited a spectrum of signal correlations. This finding relates to principles of efficient coding, but notably utilizes neural population modes as the encoding unit and suggests partial whitening of task-specific information where different variables are represented with different signal-to-noise levels. Remarkably, this encoding function was multiplexed with sequential neural dynamics yet reliably followed changes in task-variable correlations throughout the trial. We suggest that neural circuits can implement time-dependent encodings in a simple way using random sequential dynamics as a temporal scaffold.

Demonstration of Stochastic Resonance, Population Coding, and Population Voting Using Artificial MoS2 Based Synapses.

Fast detection of weak signals at low energy expenditure is a challenging but inescapable task for the evolutionary success of animals that survive in resource constrained environments. This task is accomplished by the sensory nervous system by exploiting the synergy between three astounding neural phenomena, namely, stochastic resonance (SR), population coding (PC), and population voting (PV). In SR, the constructive role of synaptic noise is exploited for the detection of otherwise invisible signals. In PC, the redundancy in neural population is exploited to reduce the detection latency. Finally, PV ensures unambiguous signal detection even in the presence of excessive noise. Here we adopt a similar strategies and experimentally demonstrate how a population of stochastic artificial neurons based on monolayer MoS2 field effect transistors (FETs) can use an optimum amount of white Gaussian noise and population voting to detect invisible signals at a frugal energy expenditure (∼10s of nano-Joules). Our findings can aid remote sensing in the emerging era of the Internet of things (IoT) that thrive on energy efficiency.

Closing the gap between single-unit and neural population codes: Insights from deep learning in face recognition.

Single-unit responses and population codes differ in the “read-out” information they provide about high-level visual representations. Diverging local and global read-outs can be difficult to reconcile with in vivo methods. To bridge this gap, we studied the relationship between single-unit and ensemble codes for identity, gender, and viewpoint, using a deep convolutional neural network (DCNN) trained for face recognition. Analogous to the primate visual system, DCNNs develop representations that generalize over image variation, while retaining subject (e.g., gender) and image (e.g., viewpoint) information. At the unit level, we measured the number of single units needed to predict attributes (identity, gender, viewpoint) and the predictive value of individual units for each attribute. Identification was remarkably accurate using random samples of only 3% of the network's output units, and all units had substantial identity-predicting power. Cross-unit responses were minimally correlated, indicating that single units code non-redundant identity cues. Gender and viewpoint classification required large-scale pooling of units—individual units had weak predictive power. At the ensemble level, principal component analysis of face representations showed that identity, gender, and viewpoint separated into high-dimensional subspaces, ordered by explained variance. Unit-based directions in the representational space were compared with the directions associated with the attributes. Identity, gender, and viewpoint contributed to all individual unit responses, undercutting a neural tuning analogy. Instead, single-unit responses carry superimposed, distributed codes for face identity, gender, and viewpoint. This undermines confidence in the interpretation of neural representations from unit response profiles for both DCNNs and, by analogy, high-level vision.

The Geometry of Information Coding in Correlated Neural Populations.

Neurons in the brain represent information in their collective activity. The fidelity of this neural population code depends on whether and how variability in the response of one neuron is shared with other neurons. Two decades of studies have investigated the influence of these noise correlations on the properties of neural coding. We provide an overview of the theoretical developments on the topic. Using simple, qualitative, and general arguments, we discuss, categorize, and relate the various published results. We emphasize the relevance of the fine structure of noise correlation, and we present a new approach to the issue. Throughout this review, we emphasize a geometrical picture of how noise correlations impact the neural code.

What do leave-one-person-out pattern analyses really tell us about the neural representation of visual object symmetries?

A key challenge in human neuroscience is to gain information about neural population codes using indirect measures of neural activity. Recently, a multivariate pattern analysis method termed Leave-One-Person-Out (LOPO) has been used to support inferences regarding neural coding. Two key caveats, however, have been overlooked by users of this method: (1) its sensitivity to low-level feature imbalances across conditions (e.g. image contrast, luminance, and their variability over instances of each stimulus class), and (2) implausibility of the methods’ assumption that spatial normalization meaningfully aligns neural patterns of activation across subjects. Here, we show with simulations instantiating multilayered randomly connected feedforward networks that LOPO leads to erroneous conclusions when the methods’ assumptions are not met. In particular, low-level properties of the images chosen by an experimenter are shown to largely determine the observed pattern of results, and not the covariance structure of the underlying spatial patterns of activation. We further show how deceptively complex representational structures emerge due to specifics of the LOPO analysis scheme. Interestingly, simulations initially intended to study the general behavior of LOPO led to concrete predictions regarding the relative norms, means and variances of images from an image database recently used in multiple recent neuroimaging studies. Low-level feature imbalances of the precise form predicted by our model were confirmed by ensuig direct analyses of these images. We argue that under plausible assumptions regarding the fMRI measurement process, the observed confounds may account for recent putative evidence of mirror-symmetric tuning of neural populations in a human face-selective area. In sum, we conclude that (1) LOPO is particularly sensitive to low-level image feature imbalances across conditions, and (2) the method’s sound interpretation hinges on implausible assumptions. Our observations cast doubts on the validity of LOPO analyses to support inferences that require the detection of spatially structured brain patterns.

Precision multidimensional neural population code recovered from single intracellular recordings

Neurons in sensory cortices are more naturally and deeply integrated than any current neural population recording tools (e.g. electrode arrays, fluorescence imaging). Two concepts facilitate efforts to observe population neural code with single-cell recordings. First, even the highest quality single-cell recording studies find a fraction of the stimulus information in high-dimensional population recordings. Finding any of this missing information provides proof of principle. Second, neurons and neural populations are understood as coupled nonlinear differential equations. Therefore, fitted ordinary differential equations provide a basis for single-trial single-cell stimulus decoding. We obtained intracellular recordings of fluctuating transmembrane current and potential in mouse visual cortex during stimulation with drifting gratings. We use mean deflection from baseline when comparing to prior single-cell studies because action potentials are too sparse and the deflection response to drifting grating stimuli (e.g. tuning curves) are well studied. Equation-based decoders allowed more precise single-trial stimulus discrimination than tuning-curve-base decoders. Performance varied across recorded signal types in a manner consistent with population recording studies and both classification bases evinced distinct stimulus-evoked phases of population dynamics, providing further corroboration. Naturally and deeply integrated observations of population dynamics would be invaluable. We offer proof of principle and a versatile framework.