Neural network mechanisms underlying stimulus driven variability reduction

It is well established that the variability of the neural activity across trials, as measured by the Fano factor, is elevated. This fact poses limits on information encoding by the neural activity. However, a series of recent neurophysiological experiments have changed this traditional view. Single cell recordings across a variety of species, brain areas, brain states and stimulus conditions demonstrate a remarkable reduction of the neural variability when an external stimulation is applied and when attention is allocated towards a stimulus within a neuron's receptive field, suggesting an enhancement of information encoding. Using an heterogeneously connected neural network model whose dynamics exhibits multiple attractors, we demonstrate here how this variability reduction can arise from a network effect. In the spontaneous state, we show that the high degree of neural variability is mainly due to fluctuation-driven excursions from attractor to attractor. This occurs when, in the parameter space, the network working point is around the bifurcation allowing multistable attractors. The application of an external excitatory drive by stimulation or attention stabilizes one specific attractor, eliminating in this way the transitions between the different attractors and resulting in a net decrease in neural variability over trials. Importantly, non-responsive neurons also exhibit a reduction of variability. Finally, this reduced variability is found to arise from an increased regularity of the neural spike trains. In conclusion, these results suggest that the variability reduction under stimulation and attention is a property of neural circuits.     

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

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

Occipital Alpha Activity during Stimulus Processing Gates the Information Flow to Object-Selective Cortex

Given the limited processing capabilities of the sensory system, it is essential that attended information is gated to downstream areas, whereas unattended information is blocked. While it has been proposed that alpha band (8–13 Hz) activity serves to route information to downstream regions by inhibiting neuronal processing in task-irrelevant regions, this hypothesis remains untested. Here we investigate how neuronal oscillations detected by electroencephalography in visual areas during working memory encoding serve to gate information reflected in the simultaneously recorded blood-oxygenation-level-dependent (BOLD) signals recorded by functional magnetic resonance imaging in downstream ventral regions. We used a paradigm in which 16 participants were presented with faces and landscapes in the right and left hemifields; one hemifield was attended and the other unattended. We observed that decreased alpha power contralateral to the attended object predicted the BOLD signal representing the attended object in ventral object-selective regions. Furthermore, increased alpha power ipsilateral to the attended object predicted a decrease in the BOLD signal representing the unattended object. We also found that the BOLD signal in the dorsal attention network inversely correlated with visual alpha power. This is the first demonstration, to our knowledge, that oscillations in the alpha band are implicated in the gating of information from the visual cortex to the ventral stream, as reflected in the representationally specific BOLD signal. This link of sensory alpha to downstream activity provides a neurophysiological substrate for the mechanism of selective attention during stimulus processing, which not only boosts the attended information but also suppresses distraction. Although previous studies have shown a relation between the BOLD signal from the dorsal attention network and the alpha band at rest, we demonstrate such a relation during a visuospatial task, indicating that the dorsal attention network exercises top-down control of visual alpha activity.     

Gamma oscillations of spiking neural populations enhance signal discrimination

Selective attention is an important filter for complex environments where distractions compete with signals. Attention increases both the gamma-band power of cortical local field potentials and the spike-field coherence within the receptive field of an attended object. However, the mechanisms by which gamma-band activity enhances, if at all, the encoding of input signals are not well understood. We propose that gamma oscillations induce binomial-like spike-count statistics across noisy neural populations. Using simplified models of spiking neurons, we show how the discrimination of static signals based on the population spike-count response is improved with gamma induced binomial statistics. These results give an important mechanistic link between the neural correlates of attention and the discrimination tasks where attention is known to enhance performance. Further, they show how a rhythmicity of spike responses can enhance coding schemes that are not temporally sensitive.     

Predictive Coding of Dynamical Variables in Balanced Spiking Networks

Two observations about the cortex have puzzled neuroscientists for a long time. First, neural responses are highly variable. Second, the level of excitation and inhibition received by each neuron is tightly balanced at all times. Here, we demonstrate that both properties are necessary consequences of neural networks that represent information efficiently in their spikes. We illustrate this insight with spiking networks that represent dynamical variables. Our approach is based on two assumptions: We assume that information about dynamical variables can be read out linearly from neural spike trains, and we assume that neurons only fire a spike if that improves the representation of the dynamical variables. Based on these assumptions, we derive a network of leaky integrate-and-fire neurons that is able to implement arbitrary linear dynamical systems. We show that the membrane voltage of the neurons is equivalent to a prediction error about a common population-level signal. Among other things, our approach allows us to construct an integrator network of spiking neurons that is robust against many perturbations. Most importantly, neural variability in our networks cannot be equated to noise. Despite exhibiting the same single unit properties as widely used population code models (e.g. tuning curves, Poisson distributed spike trains), balanced networks are orders of magnitudes more reliable. Our approach suggests that spikes do matter when considering how the brain computes, and that the reliability of cortical representations could have been strongly underestimated.     

Balanced networks under spike-time dependent plasticity

The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory–inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How do the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a theory of spike–timing dependent plasticity in balanced networks. We show that balance can be attained and maintained under plasticity–induced weight changes. We find that correlations in the input mildly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input.     

Bistable,Irregular Firing and Population Oscillations in a Modular Attractor Memory Network

Attractor neural networks are thought to underlie working memory functions in the cerebral cortex. Several such models have been proposed that successfully reproduce firing properties of neurons recorded from monkeys performing working memory tasks. However, the regular temporal structure of spike trains in these models is often incompatible with experimental data. Here, we show that the in vivo observations of bistable activity with irregular firing at the single cell level can be achieved in a large-scale network model with a modular structure in terms of several connected hypercolumns. Despite high irregularity of individual spike trains, the model shows population oscillations in the beta and gamma band in ground and active states, respectively. Irregular firing typically emerges in a high-conductance regime of balanced excitation and inhibition. Population oscillations can produce such a regime, but in previous models only a non-coding ground state was oscillatory. Due to the modular structure of our network, the oscillatory and irregular firing was maintained also in the active state without fine-tuning. Our model provides a novel mechanistic view of how irregular firing emerges in cortical populations as they go from beta to gamma oscillations during memory retrieval.     

The information theory of developmental pruning: Optimizing global network architectures using local synaptic rules

During development, biological neural networks produce more synapses and neurons than needed. Many of these synapses and neurons are later removed in a process known as neural pruning. Why networks should initially be over-populated, and the processes that determine which synapses and neurons are ultimately pruned, remains unclear. We study the mechanisms and significance of neural pruning in model neural networks. In a deep Boltzmann machine model of sensory encoding, we find that (1) synaptic pruning is necessary to learn efficient network architectures that retain computationally-relevant connections, (2) pruning by synaptic weight alone does not optimize network size and (3) pruning based on a locally-available measure of importance based on Fisher information allows the network to identify structurally important vs. unimportant connections and neurons. This locally-available measure of importance has a biological interpretation in terms of the correlations between presynaptic and postsynaptic neurons, and implies an efficient activity-driven pruning rule. Overall, we show how local activity-dependent synaptic pruning can solve the global problem of optimizing a network architecture. We relate these findings to biology as follows: (I) Synaptic over-production is necessary for activity-dependent connectivity optimization. (II) In networks that have more neurons than needed, cells compete for activity, and only the most important and selective neurons are retained. (III) Cells may also be pruned due to a loss of synapses on their axons. This occurs when the information they convey is not relevant to the target population.     

Conditions for noise reduction and stable encoding of spatial structure by cortical neural networks

Cortical circuits have been proposed to encode information by forming stable spatially structured attractors. Experimentally in the primary somatosensory cortex of the monkey, temporally invariant stimuli lead to spatially structured activity patterns. The purpose of this work is to study a recurrent cortical neural network model with lateral inhibition and examine what effect additive random noise has on the networks' ability to form stable spatially structured representations of the stimulus pattern. We show numerically that this network performs edge enhancement and forms statistically stationary, spatially structured responses when the lateral inhibition is of moderate strength. We then derive analytical conditions on the connectivity matrix that ensure stochasticly stable encoding of the stimulus spatial structure by the network. For stimuli whose strength falls in the near linear region of the sigmoid, we are able to give explicit conditions on the eigenvalues of the connection matrix. Finally, we prove that a network with a connection matrix, where the total excitation and inhibition impinging upon a neural unit are nearly balanced, will yield stable spatial attractor responses. Received: 16 October 1998 / Accepted in revised form: 25 November 1999     

Criticality enhances the multilevel reliability of stimulus responses in cortical neural networks

Cortical neural networks exhibit high internal variability in spontaneous dynamic activities and they can robustly and reliably respond to external stimuli with multilevel features–from microscopic irregular spiking of neurons to macroscopic oscillatory local field potential. A comprehensive study integrating these multilevel features in spontaneous and stimulus–evoked dynamics with seemingly distinct mechanisms is still lacking. Here, we study the stimulus–response dynamics of biologically plausible excitation–inhibition (E–I) balanced networks. We confirm that networks around critical synchronous transition states can maintain strong internal variability but are sensitive to external stimuli. In this dynamical region, applying a stimulus to the network can reduce the trial-to-trial variability and shift the network oscillatory frequency while preserving the dynamical criticality. These multilevel features widely observed in different experiments cannot simultaneously occur in non-critical dynamical states. Furthermore, the dynamical mechanisms underlying these multilevel features are revealed using a semi-analytical mean-field theory that derives the macroscopic network field equations from the microscopic neuronal networks, enabling the analysis by nonlinear dynamics theory and linear noise approximation. The generic dynamical principle revealed here contributes to a more integrative understanding of neural systems and brain functions and incorporates multimodal and multilevel experimental observations. The E–I balanced neural network in combination with the effective mean-field theory can serve as a mechanistic modeling framework to study the multilevel neural dynamics underlying neural information and cognitive processes.     

On population encoding and decoding of auditory information for bat echolocation

In this article, we study the neural encoding of acoustic information for FM-bats (such as Eptesicus fuscus) in simulation. In echolocation research, the frequency–time sound representation as expressed by the spectrogram is often considered as input. The rationale behind this is that a similar representation is present in the cochlea, i.e. the receptor potential of the inner hair cells (IHC) along the length of the cochlea, and hence similar acoustic information is relayed to the brain. In this article, we study to what extent the latter assumption is true. The receptor potential is converted into neural activity of the synapting auditory nerve cells (ANC), and information might be lost in this conversion process. Especially for FM-bats, this information transmission is not trivial: in contrast to other mammals, they detect short transient signals, and consequently neural activity can only be integrated over very limited time intervals. To quantify the amount of information transmitted we design a neural network-based algorithm to reconstruct the IHC receptor potentials from the spiking activity of the synapting auditory neurons. Both the receptor potential and the resulting neural activity are simulated using Meddis’ peripheral model. Comparing the reconstruction to the IHC receptor potential, we quantify the information transmission of the bat hearing system and investigate how this depends on the intensity of the incoming signal, the distribution of auditory neurons, and previous masking stimulation (adaptation). In addition, we show how this approach allows to inspect which spectral features survive neural encoding and hence can be relevant for echolocation.     

Stimulus-dependent Maximum Entropy Models of Neural Population Codes

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME) model—a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population.     

End-to-end neural system identification with neural information flow

Neural information flow (NIF) provides a novel approach for system identification in neuroscience. It models the neural computations in multiple brain regions and can be trained end-to-end via stochastic gradient descent from noninvasive data. NIF models represent neural information processing via a network of coupled tensors, each encoding the representation of the sensory input contained in a brain region. The elements of these tensors can be interpreted as cortical columns whose activity encodes the presence of a specific feature in a spatiotemporal location. Each tensor is coupled to the measured data specific to a brain region via low-rank observation models that can be decomposed into the spatial, temporal and feature receptive fields of a localized neuronal population. Both these observation models and the convolutional weights defining the information processing within regions are learned end-to-end by predicting the neural signal during sensory stimulation. We trained a NIF model on the activity of early visual areas using a large-scale fMRI dataset recorded in a single participant. We show that we can recover plausible visual representations and population receptive fields that are consistent with empirical findings.     

Encoding brain network response to free viewing of videos

A challenging goal for cognitive neuroscience researchers is to determine how mental representations are mapped onto the patterns of neural activity. To address this problem, functional magnetic resonance imaging (fMRI) researchers have developed a large number of encoding and decoding methods. However, previous studies typically used rather limited stimuli representation, like semantic labels and Wavelet Gabor filters, and largely focused on voxel-based brain patterns. Here, we present a new fMRI encoding model to predict the human brain’s responses to free viewing of video clips which aims to deal with this limitation. In this model, we represent the stimuli using a variety of representative visual features in the computer vision community, which can describe the global color distribution, local shape and spatial information and motion information contained in videos, and apply the functional connectivity to model the brain’s activity pattern evoked by these video clips. Our experimental results demonstrate that brain network responses during free viewing of videos can be robustly and accurately predicted across subjects by using visual features. Our study suggests the feasibility of exploring cognitive neuroscience studies by computational image/video analysis and provides a novel concept of using the brain encoding as a test-bed for evaluating visual feature extraction.     

Neural pattern dynamics in an oscillator model of the thalamo-reticular system.

One of development issues for information processing with synchronous oscillations in the brain is how new information is coded and how a comparison with already existing information is performed. In the present work we study a simple neural network model of the thalamo-reticular system based on the Wilson-Cowan model of neuronal oscillatory behavior. Our results show that both cortical control over the thalamus and external sensory input are essential in coordinating and generating spatio-temporal patterns of synchronous activity. A main finding of the numerical simulations is that the network connectivity and the intrinsic oscillatory properties of the neurons result in distinct collective behaviors within the network. By varying the connectivity schemes comparable with lesionated or damaged brain regions our results are in good agreement with in vivo experimental results. Suppressing the sensory input results in temporal oscillatory activity in the beta and gamma range and a strong spatial dependence of the network activity.     

On how network architecture determines the dominant patterns of spontaneous neural activity

In the absence of sensory stimulation, neocortical circuits display complex patterns of neural activity. These patterns are thought to reflect relevant properties of the network, including anatomical features like its modularity. It is also assumed that the synaptic connections of the network constrain the repertoire of emergent, spontaneous patterns. Although the link between network architecture and network activity has been extensively investigated in the last few years from different perspectives, our understanding of the relationship between the network connectivity and the structure of its spontaneous activity is still incomplete. Using a general mathematical model of neural dynamics we have studied the link between spontaneous activity and the underlying network architecture. In particular, here we show mathematically how the synaptic connections between neurons determine the repertoire of spatial patterns displayed in the spontaneous activity. To test our theoretical result, we have also used the model to simulate spontaneous activity of a neural network, whose architecture is inspired by the patchy organization of horizontal connections between cortical columns in the neocortex of primates and other mammals. The dominant spatial patterns of the spontaneous activity, calculated as its principal components, coincide remarkably well with those patterns predicted from the network connectivity using our theory. The equivalence between the concept of dominant pattern and the concept of attractor of the network dynamics is also demonstrated. This in turn suggests new ways of investigating encoding and storage capabilities of neural networks.     

Spatial learning and action planning in a prefrontal cortical network model

The interplay between hippocampus and prefrontal cortex (PFC) is fundamental to spatial cognition. Complementing hippocampal place coding, prefrontal representations provide more abstract and hierarchically organized memories suitable for decision making. We model a prefrontal network mediating distributed information processing for spatial learning and action planning. Specific connectivity and synaptic adaptation principles shape the recurrent dynamics of the network arranged in cortical minicolumns. We show how the PFC columnar organization is suitable for learning sparse topological-metrical representations from redundant hippocampal inputs. The recurrent nature of the network supports multilevel spatial processing, allowing structural features of the environment to be encoded. An activation diffusion mechanism spreads the neural activity through the column population leading to trajectory planning. The model provides a functional framework for interpreting the activity of PFC neurons recorded during navigation tasks. We illustrate the link from single unit activity to behavioral responses. The results suggest plausible neural mechanisms subserving the cognitive "insight" capability originally attributed to rodents by Tolman & Honzik. Our time course analysis of neural responses shows how the interaction between hippocampus and PFC can yield the encoding of manifold information pertinent to spatial planning, including prospective coding and distance-to-goal correlates.     

Spatiotemporal burst coding for extracting features of spatiotemporally varying stimuli

Encoding features of spatiotemporally varying stimuli is quite important for understanding the neural mechanisms of various sensory coding. Temporal coding can encode features of time-varying stimulus, and population coding with temporal coding is adequate for encoding spatiotemporal correlation of stimulus features into spatiotemporal activity of neurons. However, little is known about how spatiotemporal features of stimulus are encoded by spatiotemporal property of neural activity. To address this issue, we propose here a population coding with burst spikes, called here spatiotemporal burst (STB) coding. In STB coding, the temporal variation of stimuli is encoded by the precise onset timing of burst spike, and the spatiotemporal correlation of stimuli is emphasized by one specific aspect of burst firing, or spike packet followed by silent interval. To show concretely the role of STB coding, we study the electrosensory system of a weakly electric fish. Weakly electric fish must perceive the information about an object nearby by analyzing spatiotemporal modulations of electric field around it. On the basis of well-characterized circuitry, we constructed a neural network model of the electrosensory system. Here we show that STB coding encodes well the information of object distance and size by extracting the spatiotemporal correlation of the distorted electric field. The burst activity of electrosensory neurons is also affected by feedback signals through synaptic plasticity. We show that the control of burst activity caused by the synaptic plasticity leads to extracting the stimulus features depending on the stimulus context. Our results suggest that sensory systems use burst spikes as a unit of sensory coding in order to extract spatiotemporal features of stimuli from spatially distributed stimuli.     

Increased activity in human visual cortex during directed attention in the absence of visual stimulation

When subjects direct attention to a particular location in a visual scene, responses in the visual cortex to stimuli presented at that location are enhanced, and the suppressive influences of nearby distractors are reduced. What is the top-down signal that modulates the response to an attended versus an unattended stimulus? Here, we demonstrate increased activity related to attention in the absence of visual stimulation in extrastriate cortex when subjects covertly directed attention to a peripheral location expecting the onset of visual stimuli. Frontal and parietal areas showed a stronger signal increase during this expectation than did visual areas. The increased activity in visual cortex in the absence of visual stimulation may reflect a top-down bias of neural signals in favor of the attended location, which derives from a fronto-parietal network.     

Transitions between asynchronous and synchronous states: a theory of correlations in small neural circuits

The study of correlations in neural circuits of different size, from the small size of cortical microcolumns to the large-scale organization of distributed networks studied with functional imaging, is a topic of central importance to systems neuroscience. However, a theory that explains how the parameters of mesoscopic networks composed of a few tens of neurons affect the underlying correlation structure is still missing. Here we consider a theory that can be applied to networks of arbitrary size with multiple populations of homogeneous fully-connected neurons, and we focus its analysis to a case of two populations of small size. We combine the analysis of local bifurcations of the dynamics of these networks with the analytical calculation of their cross-correlations. We study the correlation structure in different regimes, showing that a variation of the external stimuli causes the network to switch from asynchronous states, characterized by weak correlation and low variability, to synchronous states characterized by strong correlations and wide temporal fluctuations. We show that asynchronous states are generated by strong stimuli, while synchronous states occur through critical slowing down when the stimulus moves the network close to a local bifurcation. In particular, strongly positive correlations occur at the saddle-node and Andronov-Hopf bifurcations of the network, while strongly negative correlations occur when the network undergoes a spontaneous symmetry-breaking at the branching-point bifurcations. These results show how the correlation structure of firing-rate network models is strongly modulated by the external stimuli, even keeping the anatomical connections fixed. These results also suggest an effective mechanism through which biological networks may dynamically modulate the encoding and integration of sensory information.