Neural Population Models Research Articles

A dynamic neural resource model bridges sensory and working memory

Probing memory of a complex visual image within a few hundred milliseconds after its disappearance reveals significantly greater fidelity of recall than if the probe is delayed by as little as a second. Classically interpreted, the former taps into a detailed but rapidly decaying visual sensory or ‘iconic’ memory (IM), while the latter relies on capacity-limited but comparatively stable visual working memory (VWM). While iconic decay and VWM capacity have been extensively studied independently, currently no single framework quantitatively accounts for the dynamics of memory fidelity over these time scales. Here, we extend a stationary neural population model of VWM with a temporal dimension, incorporating rapid sensory-driven accumulation of activity encoding each visual feature in memory, and a slower accumulation of internal error that causes memorized features to randomly drift over time. Instead of facilitating read-out from an independent sensory store, an early cue benefits recall by lifting the effective limit on VWM signal strength imposed when multiple items compete for representation, allowing memory for the cued item to be supplemented with information from the decaying sensory trace. Empirical measurements of human recall dynamics validate these predictions while excluding alternative model architectures. A key conclusion is that differences in capacity classically thought to distinguish IM and VWM are in fact contingent upon a single resource-limited WM store.

A dynamic neural resource model bridges sensory and working memory.

Probing memory of a complex visual image within a few hundred milliseconds after its disappearance reveals significantly greater fidelity of recall than if the probe is delayed by as little as a second. Classically interpreted, the former taps into a detailed but rapidly decaying visual sensory or 'iconic' memory (IM), while the latter relies on capacity-limited but comparatively stable visual working memory (VWM). While iconic decay and VWM capacity have been extensively studied independently, currently no single framework quantitatively accounts for the dynamics of memory fidelity over these time scales. Here, we extend a stationary neural population model of VWM with a temporal dimension, incorporating rapid sensory-driven accumulation of activity encoding each visual feature in memory, and a slower accumulation of internal error that causes memorized features to randomly drift over time. Instead of facilitating read-out from an independent sensory store, an early cue benefits recall by lifting the effective limit on VWM signal strength imposed when multiple items compete for representation, allowing memory for the cued item to be supplemented with information from the decaying sensory trace. Empirical measurements of human recall dynamics validate these predictions while excluding alternative model architectures. A key conclusion is that differences in capacity classically thought to distinguish IM and VWM are in fact contingent upon a single resource-limited WM store.

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.

Metabolic energetics underlying attractors in neural models.

Neural population modeling, including the role of neural attractors, is a promising tool for understanding many aspects of brain function. We propose a modeling framework to connect the abstract variables used in modeling to recent cellular-level estimates of the bioenergetic costs of different aspects of neural activity, measured in ATP consumed per second per neuron. Based on recent work, an empirical reference for brain ATP use for the awake resting brain was estimated as ∼2 × 109 ATP/s-neuron across several mammalian species. The energetics framework was applied to the Wilson-Cowan (WC) model of two interacting populations of neurons, one excitatory (E) and one inhibitory (I). Attractors were considered to exhibit steady-state behavior and limit cycle behavior, both of which end when the excitatory stimulus ends, and sustained activity that persists after the stimulus ends. The energy cost of limit cycles, with oscillations much faster than the average neuronal firing rate of the population, is tracked more closely with the firing rate than the limit cycle frequency. Self-sustained firing driven by recurrent excitation, though, involves higher firing rates and a higher energy cost. As an example of a simple network in which each node is a WC model, a combination of three nodes can serve as a flexible circuit element that turns on with an oscillating output when input passes a threshold and then persists after the input ends (an "on-switch"), with moderate overall ATP use. The proposed framework can serve as a guide for anchoring neural population models to plausible bioenergetics requirements.NEW & NOTEWORTHY This work bridges two approaches for understanding brain function: cellular-level studies of the metabolic energy costs of different aspects of neural activity and neural population modeling, including the role of neural attractors. The proposed modeling framework connects energetic costs, in ATP consumed per second per neuron, to the more abstract variables used in neural population modeling. In particular, this work anchors potential neural attractors to physiologically plausible bioenergetics requirements.

Interpersonal alignment of neural evidence accumulation to social exchange of confidence.

Private, subjective beliefs about uncertainty have been found to have idiosyncratic computational and neural substrates yet, humans share such beliefs seamlessly and cooperate successfully. Bringing together decision making under uncertainty and interpersonal alignment in communication, in a discovery plus pre-registered replication design, we examined the neuro-computational basis of the relationship between privately held and socially shared uncertainty. Examining confidence-speed-accuracy trade-off in uncertainty-ridden perceptual decisions under social vs isolated context, we found that shared (i.e. reported confidence) and subjective (inferred from pupillometry) uncertainty dynamically followed social information. An attractor neural network model incorporating social information as top-down additive input captured the observed behavior and demonstrated the emergence of social alignment in virtual dyadic simulations. Electroencephalography showed that social exchange of confidence modulated the neural signature of perceptual evidence accumulation in the central parietal cortex. Our findings offer a neural population model for interpersonal alignment of shared beliefs.

High-Density Exploration of Activity States in a Multi-Area Brain Model

To simulate whole brain dynamics with only a few equations, biophysical, mesoscopic models of local neuron populations can be connected using empirical tractography data. The development of mesoscopic mean-field models of neural populations, in particular, the Adaptive Exponential (AdEx mean-field model), has successfully summarized neuron-scale phenomena leading to the emergence of global brain dynamics associated with conscious (asynchronous and rapid dynamics) and unconscious (synchronized slow-waves, with Up-and-Down state dynamics) brain states, based on biophysical mechanisms operating at cellular scales (e.g. neuromodulatory regulation of spike-frequency adaptation during sleep-wake cycles or anesthetics). Using the Virtual Brain (TVB) environment to connect mean-field AdEx models, we have previously simulated the general properties of brain states, playing on spike-frequency adaptation, but have not yet performed detailed analyses of other parameters possibly also regulating transitions in brain-scale dynamics between different brain states. We performed a dense grid parameter exploration of the TVB-AdEx model, making use of High Performance Computing. We report a remarkable robustness of the effect of adaptation to induce synchronized slow-wave activity. Moreover, the occurrence of slow waves is often paralleled with a closer relation between functional and structural connectivity. We find that hyperpolarization can also generate unconscious-like synchronized Up and Down states, which may be a mechanism underlying the action of anesthetics. We conclude that the TVB-AdEx model reveals large-scale properties identified experimentally in sleep and anesthesia.

Expressive architectures enhance interpretability of dynamics-based neural population models.

Artificial neural networks that can recover latent dynamics from recorded neural activity may provide a powerful avenue for identifying and interpreting the dynamical motifs underlying biological computation. Given that neural variance alone does not uniquely determine a latent dynamical system, interpretable architectures should prioritize accurate and low-dimensional latent dynamics. In this work, we evaluated the performance of sequential autoencoders (SAEs) in recovering latent chaotic attractors from simulated neural datasets. We found that SAEs with widely-used recurrent neural network (RNN)-based dynamics were unable to infer accurate firing rates at the true latent state dimensionality, and that larger RNNs relied upon dynamical features not present in the data. On the other hand, SAEs with neural ordinary differential equation (NODE)-based dynamics inferred accurate rates at the true latent state dimensionality, while also recovering latent trajectories and fixed point structure. Ablations reveal that this is mainly because NODEs (1) allow use of higher-capacity multi-layer perceptrons (MLPs) to model the vector field and (2) predict the derivative rather than the next state. Decoupling the capacity of the dynamics model from its latent dimensionality enables NODEs to learn the requisite low-D dynamics where RNN cells fail. Additionally, the fact that the NODE predicts derivatives imposes a useful autoregressive prior on the latent states. The suboptimal interpretability of widely-used RNN-based dynamics may motivate substitution for alternative architectures, such as NODE, that enable learning of accurate dynamics in low-dimensional latent spaces.

Neural coding of dichotic pitches in auditory midbrain.

Dichotic pitches such as the Huggins pitch (HP) and the binaural edge pitch (BEP) are perceptual illusions whereby binaural noise that exhibits abrupt changes in interaural phase differences (IPDs) across frequency creates a tonelike pitch percept when presented to both ears, even though it does not produce a pitch when presented monaurally. At the perceptual and cortical levels, dichotic pitches behave as if an actual tone had been presented to the ears, yet investigations of neural correlates of dichotic pitch in single-unit responses at subcortical levels are lacking. We tested for cues to HP and BEP in the responses of binaural neurons in the auditory midbrain of anesthetized cats by varying the expected pitch frequency around each neuron's best frequency (BF). Neuronal firing rates showed specific features (peaks, troughs, or edges) when the pitch frequency crossed the BF, and the type of feature was consistent with a well-established model of binaural processing comprising frequency tuning, internal delays, and firing rates sensitive to interaural correlation. A Jeffress-like neural population model in which the behavior of individual neurons was governed by the cross-correlation model and the neurons were independently distributed along BF and best IPD predicted trends in human psychophysical HP detection but only when the model incorporated physiological BF and best IPD distributions. These results demonstrate the existence of a rate-place code for HP and BEP in the auditory midbrain and provide a firm physiological basis for models of dichotic pitches.NEW & NOTEWORTHY Dichotic pitches are perceptual illusions created centrally through binaural interactions that offer an opportunity to test theories of pitch and binaural hearing. Here we show that binaural neurons in auditory midbrain encode the frequency of two salient types of dichotic pitches via specific features in the pattern of firing rates along the tonotopic axis. This is the first combined single-unit and modeling study of responses of auditory neurons to stimuli evoking a dichotic pitch.

Next generation neural population models

Low-dimensional neural mass models are often invoked to model the coarse-grained activity of large populations of neurons and synapses and have been used to help understand the coordination of large scale brain rhythms. However, they are phenomenological in nature and, although motivated by neurobiological considerations, the absence of a direct link to an underlying biophysical reality is a weakness that means they may not be best suited to capturing some of the rich behaviors seen in real neuronal tissue. In this perspective article I discuss a simple spiking neuron network model that has recently been shown to admit to an exact mean-field description for synaptic interactions. This has many of the features of a neural mass model coupled to an additional dynamical equation that describes the evolution of population synchrony. Thisnext generationneural mass model is ideally suited to understanding the patterns of brain activity that are ubiquitously seen in neuroimaging recordings. Here I review the mean-field equations, the way in which population synchrony, firing rate, and average voltage are intertwined, together with their application in large scale brain modeling. As well as natural extensions of this new approach to modeling the dynamics of neuronal populations I discuss some of the open mathematical challenges in developing a statistical neurodynamics that can generalize the one discussed here.

Analysis of a Neural Population Model for Interaction of LFP and Individual Action Potential

The brain encodes various information through the interaction between macro‐scale phenomena such as Local Field Potential and micro‐scale phenomena such as individual neuron action potential time series. However, the interaction between micro‐ and macro‐scale phenomena that affects episodic memory remains unexplained. We propose a new mathematical framework to predict the parameter conditions under which theta phase precession occurs by constructing models that reproduce the micro‐ and macro‐scale phenomena separately and deriving their phase equations. It was found that phase locking or phase shift between the micro‐scale phase and the macro‐scale phase can reproduce different storage schemes. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Towards a mesoscale physical modeling framework for stereotactic-EEG recordings

Objective. Stereotactic-electroencephalography (SEEG) and scalp EEG recordings can be modeled using mesoscale neural mass population models (NMMs). However, the relationship between those mathematical models and the physics of the measurements is unclear. In addition, it is challenging to represent SEEG data by combining NMMs and volume conductor models due to the intermediate spatial scale represented by these measurements. Approach. We provide a framework combining the multi-compartmental modeling formalism and a detailed geometrical model to simulate the transmembrane currents that appear in layer 3, 5 and 6 pyramidal cells due to a synaptic input. With this approach, it is possible to realistically simulate the current source density (CSD) depth profile inside a cortical patch due to inputs localized into a single cortical layer and the induced voltage measured by two SEEG contacts using a volume conductor model. Based on this approach, we built a framework to connect the activity of a NMM with a volume conductor model and we simulated an example of SEEG signal as a proof of concept. Main results. CSD depends strongly on the distribution of the synaptic inputs onto the different cortical layers and the equivalent current dipole strengths display substantial differences (of up to a factor of four in magnitude in our example). Thus, the inputs coming from different neural populations do not contribute equally to the electrophysiological recordings. A direct consequence of this is that the raw output of NMMs is not a good proxy for electrical recordings. We also show that the simplest CSD model that can accurately reproduce SEEG measurements can be constructed from discrete monopolar sources (one per cortical layer). Significance. Our results highlight the importance of including a physical model in NMMs to represent measurements. We provide a framework connecting microscale neuron models with the neural mass formalism and with physical models of the measurement process that can improve the accuracy of predicted electrophysiological recordings.

Automated Tuning of Closed-loop Neuromodulation Control Systems using Bayesian Optimization.

Tuning the parameters of controllers to attain the best performance is a challenging task in designing effective closed-loop neuromodulation systems. In this paper, we present a distributed architecture for automated tuning and adaptation of closed-loop neuromodulation control systems. We use this approach for the automated parameter tuning of a Proportional-Integral (PI) neuromodulation controller using Bayesian optimization. We use a biophysically-grounded mean-field model of neural populations under electrical stimulation as a simulation environment for testing and prototyping the proposed framework and characterizing its performance. Our results demonstrate the feasibility of using Bayesian optimization for performance-based automated tuning of a PI controller in closed-loop set-point neuromodulation control tasks.

An interference model for visual working memory: Applications to the change detection task

Most studies of visual-working memory employ one of two experimental paradigms: change-detection or continuous-stimulus reproduction. In this study, we extended the Interference Model (IM; Oberauer & Lin, 2017), which was designed for continuous reproduction, to the single-probe change-detection task. In continuous reproduction, participants occasionally report the non-target items instead of the target. The presence of non-target response is predicted by the Interference Model, which relies in part on the interference of non-target items to explain the set-size effect. By presenting a probe matching a non-target item, we can investigate the amount of interference from non-target items in change detection. As predicted by the Interference Model, we observed poorer performance in rejecting a probe matching a non-target item compared to a new probe (i.e., a cost due to intrusions from non-targets). We fitted the IM along with the Variable Precision, the Slot-Averaging, and the Neural-Population model to the data from two change-detection experiments. The models were equipped with a Bayesian decision rule based on the one used in Keshvari, van den Berg, and Ma (2013). The Interference Model and the Neural-Population model successfully predicted the set-size effect and the non-target intrusion cost, whereas the Variable Precision (VP) and Slot-Averaging (SA) models failed to predict the intrusion cost at all. Even with additional assumptions enabling VP and SA to produce intrusion costs, the IM still performed better than the competing models quantitatively.

Mechanisms of feature binding in visual working memory are stable over long delays.

The ability to accurately retain the binding between the features of different objects is a critical element of visual working memory. The underlying mechanism can be elucidated by analyzing correlations of response errors in dual-report experiments, in which participants have to report two features of a single item from a previously viewed stimulus array. Results from separate previous studies using different cueing conditions have indicated that location takes a privileged role in mediating binding between other features, in that largely independent response errors have been observed when location was used as a cue, but errors were highly correlated when location was one of the reported features. Earlier results from change detection tasks likewise support such a special role of location, but they also suggest that this role is substantially reduced for longer retention intervals in favor of object-based representation. In the present study, we replicated the findings of previous dual-report tasks with different cueing conditions, using matched stimuli and procedures. Moreover, we show that the observed patterns of error correlations remain qualitatively unchanged with longer retention intervals. Fits with neural population models demonstrate that the behavioral results at long, as well as short, delays are best explained by memory representations in independent feature maps, in which an item's features are bound to each other only via their shared location.

Temporally precise population coding of dynamic sounds by auditory cortex.

Fluctuations in the amplitude envelope of complex sounds provide critical cues for hearing, particularly for speech and animal vocalizations. Responses to amplitude modulation (AM) in the ascending auditory pathway have chiefly been described for single neurons. How neural populations might collectively encode and represent information about AM remains poorly characterized, even in primary auditory cortex (A1). We modeled population responses to AM based on data recorded from A1 neurons in awake squirrel monkeys and evaluated how accurately single trial responses to modulation frequencies from 4 to 512 Hz could be decoded as functions of population size, composition, and correlation structure. We found that a population-based decoding model that simulated convergent, equally weighted inputs was highly accurate and remarkably robust to the inclusion of neurons that were individually poor decoders. By contrast, average rate codes based on convergence performed poorly; effective decoding using average rates was only possible when the responses of individual neurons were segregated, as in classical population decoding models using labeled lines. The relative effectiveness of dynamic rate coding in auditory cortex was explained by shared modulation phase preferences among cortical neurons, despite heterogeneity in rate-based modulation frequency tuning. Our results indicate significant population-based synchrony in primary auditory cortex and suggest that robust population coding of the sound envelope information present in animal vocalizations and speech can be reliably achieved even with indiscriminate pooling of cortical responses. These findings highlight the importance of firing rate dynamics in population-based sensory coding.NEW & NOTEWORTHY Fundamental questions remain about population coding in primary auditory cortex (A1). In particular, issues of spike timing in models of neural populations have been largely ignored. We find that spike-timing in response to sound envelope fluctuations is highly similar across neuron populations in A1. This property of shared envelope phase preference allows for a simple population model involving unweighted convergence of neuronal responses to classify amplitude modulation frequencies with high accuracy.

A state observer for the computational network model of neural populations.

A state observer plays a vital role in the design of state feedback neuromodulation schemes used to prevent and treat neurological or psychiatric disorders. This paper aims to design a state observer to reconstruct all unmeasured states of the computational network model of neural populations that replicates patterns seen on the electroencephalogram by using the model inputs and outputs, as the theoretical basis for designing state feedback neuromodulation clinical schemes. The feasibility problem of linear matrix inequality conditions, which is the most important one for observer design of the computational network model of neural populations, is solved by using the input-output stability theory and the Lurie system theory. The observer matrices of the designed observer are formed by the optimal solution of the linear matrix inequality conditions. An illustrative example shows that the observer can simultaneously reproduce internal state variables of normal and lesion populations of the computational network model of neural populations under the background of focal origin brain dysfunction, and the designed observer has certain robustness toward input uncertainty and measurement noise. To the best of our knowledge, no observers have previously been designed for the computational network model of neural populations. The design of state feedback neuromodulation schemes based on the computational network model of neural populations is a new direction in the field of computational neuroscience.

Global phase-amplitude description of oscillatory dynamics via the parameterization method.

In this paper, we use the parameterization method to provide a complete description of the dynamics of an n-dimensional oscillator beyond the classical phase reduction. The parameterization method allows us, via efficient algorithms, to obtain a parameterization of the attracting invariant manifold of the limit cycle in terms of the phase-amplitude variables. The method has several advantages. It provides analytically a Fourier-Taylor expansion of the parameterization up to any order, as well as a simplification of the dynamics that allows for a numerical globalization of the manifolds. Thus, one can obtain the local and global isochrons and isostables, including the slow attracting manifold, up to high accuracy, which offer a geometrical portrait of the oscillatory dynamics. Furthermore, it provides straightforwardly the infinitesimal phase and amplitude response functions, that is, the extended infinitesimal phase and amplitude response curves, which monitor the phase and amplitude shifts beyond the asymptotic state. Thus, the methodology presented yields an accurate description of the phase dynamics for perturbations not restricted to the limit cycle but to its attracting invariant manifold. Finally, we explore some strategies to reduce the dimension of the dynamics, including the reduction of the dynamics to the slow stable submanifold. We illustrate our methods by applying them to different three-dimensional single neuron and neural population models in neuroscience.

Dimensional reduction of emergent spatiotemporal cortical dynamics via a maximum entropy moment closure.

Modern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena.

Inferring a simple mechanism for alpha-blocking by fitting a neural population model to EEG spectra.

Alpha blocking, a phenomenon where the alpha rhythm is reduced by attention to a visual, auditory, tactile or cognitive stimulus, is one of the most prominent features of human electroencephalography (EEG) signals. Here we identify a simple physiological mechanism by which opening of the eyes causes attenuation of the alpha rhythm. We fit a neural population model to EEG spectra from 82 subjects, each showing a different degree of alpha blocking upon opening of their eyes. Though it has been notoriously difficult to estimate parameters by fitting such models, we show how, by regularizing the differences in parameter estimates between eyes-closed and eyes-open states, we can reduce the uncertainties in these differences without significantly compromising fit quality. From this emerges a parsimonious explanation for the spectral differences between states: Changes to just a single parameter, pei, corresponding to the strength of a tonic excitatory input to the inhibitory cortical population, are sufficient to explain the reduction in alpha rhythm upon opening of the eyes. We detect this by comparing the shift in each model parameter between eyes-closed and eyes-open states. Whereas changes in most parameters are weak or negligible and do not scale with the degree of alpha attenuation across subjects, the change in pei increases monotonically with the degree of alpha blocking observed. These results indicate that opening of the eyes reduces alpha activity by increasing external input to the inhibitory cortical population.

Biophysically grounded mean-field models of neural populations under electrical stimulation.

Electrical stimulation of neural systems is a key tool for understanding neural dynamics and ultimately for developing clinical treatments. Many applications of electrical stimulation affect large populations of neurons. However, computational models of large networks of spiking neurons are inherently hard to simulate and analyze. We evaluate a reduced mean-field model of excitatory and inhibitory adaptive exponential integrate-and-fire (AdEx) neurons which can be used to efficiently study the effects of electrical stimulation on large neural populations. The rich dynamical properties of this basic cortical model are described in detail and validated using large network simulations. Bifurcation diagrams reflecting the network's state reveal asynchronous up- and down-states, bistable regimes, and oscillatory regions corresponding to fast excitation-inhibition and slow excitation-adaptation feedback loops. The biophysical parameters of the AdEx neuron can be coupled to an electric field with realistic field strengths which then can be propagated up to the population description. We show how on the edge of bifurcation, direct electrical inputs cause network state transitions, such as turning on and off oscillations of the population rate. Oscillatory input can frequency-entrain and phase-lock endogenous oscillations. Relatively weak electric field strengths on the order of 1 V/m are able to produce these effects, indicating that field effects are strongly amplified in the network. The effects of time-varying external stimulation are well-predicted by the mean-field model, further underpinning the utility of low-dimensional neural mass models.