Probabilistic inference offers a principled framework for understanding both behaviour and cortical computation. However, two basic and ubiquitous properties of cortical responses seem difficult to reconcile with probabilistic inference: neural activity displays prominent oscillations in response to constant input, and large transient changes in response to stimulus onset. Here we show that these dynamical behaviours may in fact be understood as hallmarks of the specific representation and algorithm that the cortex employs to perform probabilistic inference. We demonstrate that a particular family of probabilistic inference algorithms, Hamiltonian Monte Carlo (HMC), naturally maps onto the dynamics of excitatory-inhibitory neural networks. Specifically, we constructed a model of an excitatory-inhibitory circuit in primary visual cortex that performed HMC inference, and thus inherently gave rise to oscillations and transients. These oscillations were not mere epiphenomena but served an important functional role: speeding up inference by rapidly spanning a large volume of state space. Inference thus became an order of magnitude more efficient than in a non-oscillatory variant of the model. In addition, the network matched two specific properties of observed neural dynamics that would otherwise be difficult to account for in the context of probabilistic inference. First, the frequency of oscillations as well as the magnitude of transients increased with the contrast of the image stimulus. Second, excitation and inhibition were balanced, and inhibition lagged excitation. These results suggest a new functional role for the separation of cortical populations into excitatory and inhibitory neurons, and for the neural oscillations that emerge in such excitatory-inhibitory networks: enhancing the efficiency of cortical computations.
We develop an extension of the Ott-Antonsen method that allows obtaining the mean activity (spiking rate) of a population of excitable units. By means of the Ott-Antonsen method, equations for the dynamics of the order parameters of coupled excitatory and inhibitory populations of excitable units are obtained, and their mean activities are computed. Two different excitable systems are studied: Adler units and theta neurons. The resulting bifurcation diagrams are compared to those obtained from studying the phenomenological Wilson-Cowan model in some regions of the parameter space. Compatible b…
We developed a model of cortical computation that implements key features of cortical circuitry and is capable of describing propagation of neural signals between cortical locations in response to spatially distributed stimuli. The model is based on the canonical neural circuit that consists of excitatory and inhibitory cells interacting through reciprocal connections, with recurrent feedback. The canonical circuit is used as a node in a distributed network with nearest neighbor coupling between the nodes. We find that this system is characterized by intrinsic preference for spatial frequency.…
Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in networks of deterministic, but randomly connected rate units. How this type of intrinsi- cally generated fluctuations appears in more realistic networks of spiking neurons has been a long standing question. To ease the comparison between rate and spiking networks, recent works investigated the dynami- cal regimes of randomly-connected rate networks with segrega…
Synaptic delays modulate population phase and amplitude responses in oscillatory excitatory-inhibitory networks
Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院）；Institute for Research in Fundamental Sciences (IPM)（基本科学研究院）；Pasargad Institute for Advanced Innovative Solutions (PIAIS)（帕萨尔加德先进创新解决方案研究所）；The Zapata-Briceño Institute of Neuroscience（萨帕塔-布里斯尼奥神经科学研究所）
Neural coding is a key problem in neuroscience, which can promote people's understanding of the mechanism that brain processes information. Among the classical theories of neural coding, the population rate coding has been studied widely in many works. Most computational studies considered the neurons and the corresponding presynaptic synapses as pre-determined excitatory or inhibitory types. According to physiological evidence, however, that the real effect of a synapse is inhibitory or excitatory is determined by the type of the activated receptors. The co-release of excitatory and inhibitor…
We study the dynamics of networks with inhibitory and excitatory leaky-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a Heterogeneous Mean-Field approximation, that allows to keep track of the effects of structural disorder in the network. We describe the complex behavior of different classes of excitatory and inhibitory components, that give rise to a rich dynamical phase-diagram as a function of the fraction of inhibitory neurons. By the same mean field approach, we study and solve a global…
Maximum Entropy models can be inferred from large data-sets to uncover how collective dynamics emerge from local interactions. Here, such models are employed to investigate neurons recorded by multielectrode arrays in the human and monkey cortex. Taking advantage of the separation of excitatory and inhibitory neuron types, we construct a model including this distinction. This approach allows to shed light upon differences between excitatory and inhibitory activity across different brain states such as wakefulness and deep sleep, in agreement with previous findings. Additionally, Maximum Entrop…
It is widely appreciated that well-balanced excitation and inhibition are necessary for proper function in neural networks. However, in principle, such balance could be achieved by many possible configurations of excitatory and inhibitory strengths, and relative numbers of excitatory and inhibitory neurons. For instance, a given level of excitation could be balanced by either numerous inhibitory neurons with weak synapses, or few inhibitory neurons with strong synapses. Among the continuum of different but balanced configurations, why should any particular configuration be favored? Here we add…
Localized persistent cortical neural activity is a validated neural substrate of parametric working memory. Such activity `bumps' represent the continuous location of a cue over several seconds. Pyramidal (excitatory) and interneuronal (inhibitory) subpopulations exhibit tuned bumps of activity, linking neural dynamics to behavioral inaccuracies observed in memory recall. However, many bump attractor models collapse these subpopulations into a single joint excitatory/inhibitory (lateral inhibitory) population, and do not consider the role of interpopulation neural architecture and noise correl…
This paper introduces a rate-based nonlinear neural network in which excitatory (E) neurons receive feedforward excitation from sensory (S) neurons, and inhibit each other through disynaptic pathways mediated by inhibitory (I) interneurons. Correlation-based plasticity of disynaptic inhibition serves to incompletely decorrelate E neuron activity, pushing the E neurons to learn distinct sensory features. The plasticity equations additionally contain "extra" terms fostering competition between excitatory synapses converging onto the same postsynaptic neuron and inhibitory synapses diverging from…
Excitation-inhibition (E-I) balance is ubiquitously observed in the cortex. Recent studies suggest an intriguing link between balance on fast timescales, tight balance, and efficient information coding with spikes. We further this connection by taking a principled approach to optimal balanced networks of excitatory (E) and inhibitory (I) neurons. By deriving E-I spiking neural networks from greedy spike-based optimizations of constrained minimax objectives, we show that tight balance arises from correcting for deviations from the minimax optima. We predict specific neuron firing rates in the n…
The elapsed time model has been widely studied in the context of mathematical neuroscience with many open questions left. The model consists of an age-structured equation that describes the dynamics of interacting neurons structured by the elapsed time since their last discharge. Our interest lies in highly connected networks leading to strong nonlinearities where perturbation methods do not apply. To deal with this problem, we choose a particular case which can be reduced to delay equations. We prove a general convergence result to a stationary state in the inhibitory and the weakly excitator…
For studying how dynamical responses to external stimuli depend on the synaptic-coupling type, we consider two types of excitatory and inhibitory synchronization (i.e., synchronization via synaptic excitation and inhibition) in complex small-world networks of excitatory regular spiking (RS) pyramidal neurons and inhibitory fast spiking (FS) interneurons. For both cases of excitatory and inhibitory synchronization, effects of synaptic couplings on dynamical responses to external time-periodic stimuli $S(t)$ (applied to a fraction of neurons) are investigated by varying the driving amplitude $A$…
Collective oscillations and their suppression by external stimulation are analyzed in a large-scale neural network consisting of two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. In the limit of an infinite number of neurons, the microscopic model of this network can be reduced to an exact low-dimensional system of mean-field equations. Bifurcation analysis of these equations reveals three different dynamic modes in a free network: a stable resting state, a stable limit cycle, and bistability with a coexisting resting state and a limit cycle. We sho…
A companion paper introduces a nonlinear network with Hebbian excitatory (E) neurons that are reciprocally coupled with anti-Hebbian inhibitory (I) neurons and also receive Hebbian feedforward excitation from sensory (S) afferents. The present paper derives the network from two normative principles that are mathematically equivalent but conceptually different. The first principle formulates unsupervised learning as a constrained optimization problem: maximization of S-E correlations subject to a copositivity constraint on E-E correlations. A combination of Legendre and Lagrangian duality yield…
An inverse procedure is developed and tested to recover functional and structural information from global signals of brains activity. The method assumes a leaky-integrate and fire model with excitatory and inhibitory neurons, coupled via a directed network. Neurons are endowed with a heterogenous current value, which sets their associated dynamical regime. By making use of a heterogenous mean-field approximation, the method seeks to reconstructing from global activity patterns the distribution of in-coming degrees, for both excitatory and inhibitory neurons, as well as the distribution of the …
The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including, an intermediate phase, between quiescence and saturation, that exhibits the key features of "asynchronous states" in cortical networks. Remarkably, in the inhibition-dominated case, it exhibits an extremely-rich phase diagram, that captures a wealth of non-trivial features of spontaneous brain activity, such as collective excitability, hysteresis, tilted avalanche shapes,…
The construction of biologically plausible models of neural circuits is crucial for understanding the computational properties of the nervous system. Constructing functional networks composed of separate excitatory and inhibitory neurons obeying Dale's law presents a number of challenges. We show how a target-based approach, when combined with a fast online constrained optimization technique, is capable of building functional models of rate and spiking recurrent neural networks in which excitation and inhibition are balanced. Balanced networks can be trained to produce complicated temporal pat…
Sequential chaotic oscillations in excitatory-inhibitory threshold-linear networks
Division of Applied Mathematics, Brown University（布朗大学应用数学系）；Robert J. and Nancy D. Carney Institute for Brain Science, Brown University（布朗大学罗伯特·J和南希·D·卡尼脑科学研究所）
Research on network mechanisms and coding properties of grid cells assume that the firing rate of a grid cell in each of its fields is the same. Furthermore, proposed network models predict spatial regularities in the firing of inhibitory interneurons that are inconsistent with experimental data. In this paper, by analyzing the response of grid cells recorded from rats during free navigation, we first show that there are strong variations in the mean firing rate of the fields of individual grid cells and thus show that the data is inconsistent with the theoretical models that predict similar p…
In this work, we study the dynamic range of a neuronal network of excitable neurons with excitatory and inhibitory synapses. We obtain an analytical expression for the critical point as a function of the excitatory and inhibitory synaptic intensities. We also determine an analytical expression that gives the critical point value in which the maximal dynamic range occurs. Depending on the mean connection degree and coupl\-ing weights, the critical points can exhibit ceasing or ceaseless dynamics. However, the dynamic range is equal in both cases. We observe that the external stimulus mask some …
Local patterns of excitation and inhibition that can generate neural waves are studied as a computational mechanism underlying the organization of neuronal tunings. Sparse coding algorithms based on networks of excitatory and inhibitory neurons are proposed that exhibit topographic maps as the receptive fields are adapted to input stimuli. Motivated by a leaky integrate-and-fire model of neural waves, we propose an activation model that is more typical of artificial neural networks. Computational experiments with the activation model using both natural images and natural language text are pres…
A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust inter-nodes correlations, that persist at large large distances. Anti-phase synchrony at small frequencies is resolved on adjacent nodes and found to promote the spontaneous generation of long-ranged stochastic patterns, that invade the network as a whole. These patterns are lacking under the idealized deterministic scenario, and could provide novel hints on how living systems implement an…
The Network of Noisy Leaky Integrate and Fire (NNLIF) model describes the behavior of a neural network at mesoscopic level. It is one of the simplest self-contained mean-field models considered for that purpose. Even so, to study the mathematical properties of the model some simplifications were necessary Cáceres-Carrillo-Perthame(2011), Cáceres-Perthame(2014), Cáceres-Schneider(2017), which disregard crucial phenomena. In this work we deal with the general NNLIF model without simplifications. It involves a network with two populations (excitatory and inhibitory), with transmission delays betw…
We investigate the synchronization properties between two excitatory coupled neurons in the presence of an inhibitory loop mediated by an interneuron. Dynamical inhibition together with noise independently applied to each neuron provide phase diversity in the dynamics of the neuronal motif. We show that the interplay between the coupling strengths and external noise controls the phase relations between the neurons in a counter-intuitive way. For a master-slave configuration (unidirectional coupling) we find that the slave can anticipate the master, on average, if the slave is subject to the in…
Characterizing the relation between weight structure and input/output statistics is fundamental for understanding the computational capabilities of neural circuits. In this work, I study the problem of storing associations between analog signals in the presence of correlations, using methods from statistical mechanics. I characterize the typical learning performance in terms of the power spectrum of random input and output processes. I show that optimal synaptic weight configurations reach a capacity of 0.5 for any fraction of excitatory to inhibitory weights and have a peculiar synaptic distr…
Advances in neural recording methods enable sampling from populations of thousands of neurons during the performance of behavioral tasks, raising the question of how recorded activity relates to the theoretical models of computations underlying performance. In the context of decision making in rodents, patterns of functional connectivity between choice-selective cortical neurons, as well as broadly distributed choice information in both excitatory and inhibitory populations, were recently reported [1]. The straightforward interpretation of these data suggests a mechanism relying on specific pa…
The statistical analysis of the collective neural activity known as avalanches provides insight into the proper behavior of brains across many species. We consider a neural network model based on the work of Lombardi, Herrmann, De Arcangelis et al. that captures the relevant dynamics of neural avalanches, and we show how tuning the fraction of inhibitory neurons in this model alters the connectivity of the network over time, removes exponential cut-offs present in the distributions of avalanche strength and duration, and transitions the power spectral density of the network into an `epileptic'…
Phase- and amplitude-dependent control of synchronization in excitatory-inhibitory networks via pulsed stimulation
Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran（巴斯研究学院物理系）；School of Biological Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran（基础科学研究所生物科学学院）；Pasargad Institute for Advanced Innovative Solutions (PIAIS), Tehran, Iran（帕萨加德先进创新解决方案研究所）；The Zapata-Briceño Institute of Neuroscience, Madrid, Spain（萨帕塔-布里斯涅奥神经科学研究所）
A great deal of research has been devoted on the investigation of neural dynamics in various network topologies. However, only a few studies have focused on the influence of autapses, synapses from a neuron onto itself via closed loops, on neural synchronisation. Here, we build a random network with adaptive exponential integrate-and-fire neurons coupled with chemical synapses, equipped with autapses, to study the effect of the latter on synchronous behaviour. We consider time delay in the conductance of the pre-synaptic neuron for excitatory and inhibitory connections. Interestingly, in neura…
The interaction between excitation and inhibition is crucial for brain computation. To understand synaptic mechanisms underlying brain function, it is important to separate excitatory and inhibitory inputs to a target neuron. In the traditional method, after applying somatic current or voltage clamp, the excitatory and inhibitory conductances are determined from the synaptic current-voltage (I-V) relation --- the slope corresponds to the total conductance and the intercept corresponds to the reversal current. Because of the space clamp effect, the measured conductance in general deviates subst…
This article is devoted to the theoretical and numerical analysis of a network of excitatory and inhibitory neurons of Hodgkin-Huxley (HH) type, for which the topology is inspired by that of a single local layer of visual cortex V1. Our model is related to the recent CSY model and therefore differs from other classical models in the field. It combines a driven stochastic drive -- which may be interpreted as an ambient drive for each neuron -- with recurrent inputs resulting from the network activity. After a review of the dynamics of a single HH equation for both the deterministic and the stoc…
Role of chloride concentration in modulating seizure transitions in excitatory and inhibitory networks
School of physics and Electronic Engineering, Jiangsu University（江苏大学物理与电子工程学院）；School of Mathematical Sciences, Jiangsu University（江苏大学数学科学学院）；Teaching Department, Jiangsu University Jingjiang College（江苏大学京江学院教学部）
Rich, spontaneous brain activity has been observed across a range of different temporal and spatial scales. These dynamics are thought to be important t for efficient neural functioning. Experimental evidence suggests that these neural dynamics are maintained across a variety of different cognitive states, in response to alterations of the environment and to changes in brain configuration (e.g., across individuals, development and in many neurological disorders). This suggests that the brain has evolved mechanisms to stabilize dynamics and maintain them across a range of situations. Here, we e…
How can neural networks learn to efficiently represent complex and high-dimensional inputs via local plasticity mechanisms? Classical models of representation learning assume that input weights are learned via pairwise Hebbian-like plasticity. Here, we show that pairwise Hebbian-like plasticity only works under unrealistic requirements on neural dynamics and input statistics. To overcome these limitations, we derive from first principles a learning scheme based on voltage-dependent synaptic plasticity rules. Here, inhibition learns to locally balance excitatory input in individual dendritic co…
Firing Rate Models as Associative Memory: Excitatory-Inhibitory Balance for Robust Retrieval
Department of Information Engineering（信息工程系）；Università degli Studi di Padova（帕多瓦大学）；Center for Control, Dynamical Systems and Computation（控制、动态系统与计算中心）；University of California at Santa Barbara（加州大学圣巴巴拉分校）
Directed information transmission is paramount for many social, physical, and biological systems. For neural systems, scientists have studied this problem under the paradigm of feedforward networks for decades. In most models of feedforward networks, activity is exclusively driven by excitatory neurons and the wiring patterns between them, while inhibitory neurons play only a stabilizing role for the network dynamics. Motivated by recent experimental discoveries of hippocampal circuitry, cortical circuitry, and the diversity of inhibitory neurons throughout the brain, here we illustrate that o…
We consider clustered small-world networks with both inhibitory (I) and excitatory (E) populations. This I-E neuronal network has adaptive dynamic I to E and E to I interpopulation synaptic strengths, governed by interpopulation spike-timing-dependent plasticity (STDP). In previous works without STDPs, fast sparsely synchronized rhythms, related to diverse cognitive functions, were found to appear in a range of noise intensity $D$ for static synaptic strengths. By varying $D$, we investigate the effect of interpopulation STDPs on diverse population and individual properties of fast sparsely sy…
Many experiments have evidenced that electrical and chemical synapses -- hybrid synapses -- coexist in most organisms and brain structures. The role of electrical and chemical synapse connection in diversity of neural activity generation has been investigated separately in networks of varying complexities. Nevertheless, theoretical understanding of hybrid synapses in diverse dynamical states of neural networks for self-organization and robustness still has not been fully studied. Here, we present a model of neural network built with hybrid synapses to investigate the emergence of global and co…
