Neuronal networks provide living organisms with the ability to process information. They are also characterized by abundant recurrent connections, which give rise to strong feedback that dictates their dynamics and endows them with fading (short-term) memory. The role of recurrence in long-term memory, on the other hand, is still unclear. Here we use the neuronal network of the roundworm C. elegans to show that recurrent architectures in living organisms can exhibit long-term memory without relying on specific hard-wired modules. A genetic algorithm reveals that the experimentally observed dynamics of the worm's neuronal network exhibits maximal complexity (as measured by permutation entropy). In that complex regime, the response of the system to repeated presentations of a time-varying stimulus reveals a consistent behavior that can be interpreted as soft-wired long-term memory.
Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of the correlations in recurrent networks is not fully understood. Here, we develop a general theory for the emergence of correlated neuronal activity from the dynamics in strongly recurrent networks consisting of several populations of binary neurons. We apply this theory to the case in which the connectivity depends on the anatomical or functional distance be…
We here unify the field theoretical approach to neuronal networks with large deviations theory. For a prototypical random recurrent network model with continuous-valued units, we show that the effective action is identical to the rate function and derive the latter using field theory. This rate function takes the form of a Kullback-Leibler divergence which enables data-driven inference of model parameters and calculation of fluctuations beyond mean-field theory. Lastly, we expose a regime with fluctuation-induced transitions between mean-field solutions.
We propose a neuronal network model which undergoes a saddle-node bifurcation on an invariant circle as the mechanism of the transition from the interictal to the ictal (seizure) state. In the vicinity of this transition, the model captures important dynamical features of both interictal and ictal states. We study the nature of interictal spikes and early warnings of the transition predicted by this model. We further demonstrate that recurrent seizures emerge due to the interaction between two networks.
We use a biophysical model of a local neuronal circuit to study the implications of synaptic plasticity for the detection of weak sensory stimuli. Networks with fast plastic coupling show behavior consistent with stochastic resonance. Addition of an additional slow coupling that accounts for the asynchronous release of neurotransmitter results in qualitatively different properties of signal detection, and also leads to the appearance of transient post-stimulus bistability. Our results suggest testable hypothesis with regard to the self-organization and dynamics of local neuronal circuits.
Correlation-based Hebbian plasticity is thought to shape neuronal connectivity during development and learning, whereas homeostatic plasticity would stabilize network activity. Here we investigate another, new aspect of this dichotomy: Can Hebbian associative properties also emerge as a network effect from a plasticity rule based on homeostatic principles on the neuronal level? To address this question, we simulated a recurrent network of leaky integrate-and-fire neurons, in which excitatory connections are subject to a structural plasticity rule based on firing rate homeostasis. We show that …
A recurrent loop consisting of a single neuron is considered which is influenced by a chemical excitatory delayed synaptic feedback. We show the response of the system is dependent to the duration of the activity of the synapse which is determined by the deactivation time constant of the synapse. We show that loops with slow synapses, those which the effect of the synaptic activation remains for time constants comparable to the period of firing, show more predictable results where the effect of the fast synapses is tightly dependent on the loop delay time. The results are compared to those of …
In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly Gaussian -- which they tend to be in large networks -- we obtain deterministic equations for the temporal evolution of the mean firing rates and the noise covariance matrix that can be solved straightforwardly given the network connectivity. We also obtain spike count statistics such as Fano factors and pairwise correlations, assuming doubly-stochastic action po…
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…
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level coexists with regular oscillations at the global level is still unclear. Here we show that a combination of stochastic recurrence-based initiation with deterministic refractoriness in an excitable network can reconcile these two features, leading to maximum collective coherence for an intermediate noise level. We report this behavior in the slow oscillation reg…
INESC-ID（INESC-ID（里斯本高等工程系统与计算机研究所））；IST Tecnico Lisboa（里斯本高等理工学院）；Universidade de Lisboa（里斯本大学）
Given the inner complexity of the human nervous system, insight into the dynamics of brain activity can be gained from understanding smaller and simpler organisms, such as the nematode C. Elegans. The behavioural and structural biology of these organisms is well-known, making them prime candidates for benchmarking modelling and simulation techniques. In these complex neuronal collections, classical, white-box modelling techniques based on intrinsic structural or behavioural information are either unable to capture the profound nonlinearities of the neuronal response to different stimuli or gen…
Although conditional branching between possible behavioural states is a hallmark of intelligent behavior, very little is known about the neuronal mechanisms that support this processing. In a step toward solving this problem we demonstrate by theoretical analysis and simulation how networks of richly inter-connected neurons, such as those observed in the superficial layers of the neocortex, can embed reliable robust finite state machines. We show how a multi-stable neuronal network containing a number of states can be created very simply, by coupling two recurrent networks whose synaptic weigh…
The representation of the natural-density, heterogeneous connectivity of neuronal network models at relevant spatial scales remains a challenge for Computational Neuroscience and Neuromorphic Computing. In particular, the memory demands imposed by the vast number of synapses in brain-scale network simulations constitutes a major obstacle. Limiting the number resolution of synaptic weights appears to be a natural strategy to reduce memory and compute load. In this study, we investigate the effects of a limited synaptic-weight resolution on the dynamics of recurrent spiking neuronal networks res…
We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning dynamics. Previous numerical works have reported that Hebbian learning drives the system from chaos to a steady state through a sequence of bifurcations. Here, we interpret these results mathematically and show that these effects, involving a complex coupling between neuronal dynamics and synaptic graph structure, can be analyzed using Jacobian matrices, which int…
Synchronized bursts (SBs) with complex structures are common in neuronal cultures. Although the origin of SBs is still unclear, they have been studied for their information processing capabilities. Here, we investigate the properties of these SBs in a culture on multi-electrode array system. We find that structures of these SBs are related to the different developmental stages of the cultures. A model based on short term synaptic plasticity, recurrent connections and astrocytic recycling of neurotransmitters has been developed successfully to understand these structures. A phase diagram obtain…
In a manner similar to the molecular chaos that underlies the stable thermodynamics of gases, neuronal system may exhibit microscopic instability in individual neuronal dynamics while a macroscopic order of the entire population possibly remains stable. In this study, we analyze the microscopic stability of a network of neurons whose macroscopic activity obeys stable dynamics, expressing either monostable, bistable, or periodic state. We reveal that the network exhibits a variety of dynamical states for microscopic instability residing in given stable macroscopic dynamics. The presence of a va…
Sequential activation of neurons is a common feature of network activity during a variety of behaviors, including working memory and decision making. Previous network models for sequences and memory emphasized specialized architectures in which a principled mechanism is pre-wired into their connectivity. Here we demonstrate that, starting from random connectivity and modifying a small fraction of connections, a largely disordered recur- rent network can produce sequences and implement working memory efficiently. We use this process, called Partial In-Network Training (PINning), to model and ma…
"More Is Different'' in Neural Circuits: Algebraic Emergence of Effective Theories in Canonical Recurrent Motifs of Biological Neuronal Networks
McGovern Institute for Brain Research, Massachusetts Institute of Technology（麻省理工学院麦戈文脑研究所）；The NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI)（美国国家科学基金会人工智能与基础相互作用AI研究所）
Through evolution, animals have acquired central nervous systems (CNSs), which are extremely efficient information processing devices that improve an animal's adaptability to various environments. It has been proposed that the process of information maximization (infomax), which maximizes the information transmission from the input to the output of a feedforward network, may provide an explanation of the stimulus selectivity of neurons in CNSs. However, CNSs contain not only feedforward but also recurrent synaptic connections, and little is known about information retention over time in such r…
Dynamics and function of neuronal networks are determined by their synaptic connectivity. Current experimental methods to analyze synaptic network structure on the cellular level, however, cover only small fractions of functional neuronal circuits, typically without a simultaneous record of neuronal spiking activity. Here we present a method for the reconstruction of large recurrent neuronal networks from thousands of parallel spike train recordings. We employ maximum likelihood estimation of a generalized linear model of the spiking activity in continuous time. For this model the point proces…
Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a non-monotonic function of stimulus frequency, reveali…
We study the characteristics of weak signal detection by a recurrent neuronal network with plastic synaptic coupling. It is shown that in the presence of an asynchronous component in synaptic transmission, the network acquires selectivity with respect to the frequency of weak periodic stimuli. For non-periodic frequency-modulated stimuli, the response is quantified by the mutual information between input (signal) and output (network's activity), and is optimized by synaptic depression. Introducing correlations in signal structure resulted in the decrease of input-output mutual information. Our…
Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in contrast, are scale-free cascades of neural activity, often considered as evidence of brain tuning to criticality. While models have been developed to account for oscillations or avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically, or intractable to infer from data rigorously. Here we propose a non-equil…
Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static (quenched) disorder of the connectivity in recurrent random networks was so far elusive. We here derive a finite-size mean-field theory that reduces a disordered to a highly symmetric network with fluctuating auxiliary fields. The exposed analytical relation between the statistics of connections and the statistics of pairwise covariances shows that both, aver…
Neural networks are complex algorithms that loosely model the behaviour of the human brain. They play a significant role in computational neuroscience and artificial intelligence. The next generation of neural network models is based on the spike timing activity of neurons: spiking neural networks (SNNs). However, model parameters in SNNs are difficult to search and optimise. Previous studies using genetic algorithm (GA) optimisation of SNNs were focused mainly on simple, feedforward, or oscillatory networks, but not much work has been done on optimising cortex-like recurrent SNNs. In this wor…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad principles underlying collective spiking activity in neural circuits. The first is that local features of network connectivity can be surprisingly effective in predicting global statistics of activity across a network. The second is that, for the important case of large networks with excitatory-inhibitory balance, correlated spiking persists or vanishes depending …
A rigorous understanding of brain dynamics and function requires a conceptual bridge between multiple levels of organization, including neural spiking and network-level population activity. Mounting evidence suggests that neural networks of cerebral cortex operate at criticality. How operating near this network state impacts the variability of neuronal spiking is largely unknown. Here we show in a computational model that two prevalent features of cortical single-neuron activity, irregular spiking and the decline of response variability at stimulus onset, are both emergent properties of a recu…
Harvard University（哈佛大学）；MIT-IBM Watson AI Lab（麻省理工-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
While deep neural networks take loose inspiration from neuroscience, it is an open question how seriously to take the analogies between artificial deep networks and biological neuronal systems. Interestingly, recent work has shown that deep convolutional neural networks (CNNs) trained on large-scale image recognition tasks can serve as strikingly good models for predicting the responses of neurons in visual cortex to visual stimuli, suggesting that analogies between artificial and biological neural networks may be more than superficial. However, while CNNs capture key properties of the average…
Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network model of integrate and fire neurons. For a range of network architectures, we find that the pairwise correlation coefficients, averaged across the network, can be closely approximated using only three statistics of network connectivity. These are the overall network connection probability and the frequencies of two second-order motifs: diverging motifs, in which one cell provides in…
Trial-to-trial variability is an essential feature of neural responses, but its source is a subject of active debate. Response variability (Mast and Victor, 1991; Arieli et al., 1995 & 1996; Anderson et al., 2000 & 2001; Kenet et al., 2003; Petersen et al., 2003a & b; Fiser, Chiu and Weliky, 2004; MacLean et al., 2005; Yuste et al., 2005; Vincent et al., 2007) is often treated as random noise, generated either by other brain areas, or by stochastic processes within the circuitry being studied. We call such sources of variability external to stress the independence of this form of noise from ac…
In dynamical models of cortical networks, the recurrent connectivity can amplify the input given to the network in two distinct ways. One is induced by the presence of near-critical eigenvalues in the connectivity matrix W, producing large but slow activity fluctuations along the corresponding eigenvectors (dynamical slowing). The other relies on W being nonnormal, which allows the network activity to make large but fast excursions along specific directions. Here we investigate the tradeoff between nonnormal amplification and dynamical slowing in the spontaneous activity of large random neuron…
Biological cortical networks are potentially fully recurrent networks without any distinct output layer, where recognition may instead rely on the distribution of activity across its neurons. Because such biological networks can have rich dynamics, they are well-designed to cope with dynamical interactions of the types that occur in nature, while traditional machine learning networks may struggle to make sense of such data. Here we connected a simple model neuronal network (based on the 'linear summation neuron model' featuring biologically realistic dynamics (LSM), consisting of 10 of excitat…
The computational properties of neural systems are often thought to be implemented in terms of their network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit (MSU) recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a state space representation of the dynamics, but would wish to have access to its governing equations for in-depth analysis. Recurrent neural networks (RNNs) are a computationally powerful and dynamically universal formal framework w…
The co-occurrence of action potentials of pairs of neurons within short time intervals is known since long. Such synchronous events can appear time-locked to the behavior of an animal and also theoretical considerations argue for a functional role of synchrony. Early theoretical work tried to explain correlated activity by neurons transmitting common fluctuations due to shared inputs. This, however, overestimates correlations. Recently the recurrent connectivity of cortical networks was shown responsible for the observed low baseline correlations. Two different explanations were given: One arg…
Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect is less understood. This limitation is further magnified by the impossibility of traditional neuronal mean-field models ---also known as firing rate models, or firing rate equations--- to account for electrical synapses. Here we introduce a novel firing rate model that exactly describes the mean field dynamics of heterogeneous populations of quadratic integra…
Stochastic dynamics and synchronization in motif-based neuronal networks
Toronto Metropolitan University（多伦多都会大学）；University of Toronto（多伦多大学）；Florida State University（佛罗里达州立大学）；Institute of Molecular Biophysics, Florida State University（佛罗里达州立大学分子生物物理研究所）；St. Michael’s Hospital, Unity Health Toronto（圣迈克尔医院（联合健康多伦多））
Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies, Peking University（北京大学前沿交叉学科研究院定量生物学中心）；School of Physics, Peking University（北京大学物理学院）；Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences and Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies,Peking University（北京大学生命科学学院、前沿交叉学科研究院定量生物学中心及蛋白质工程与植物基因工程国家重点实验室生物信息中心）；CNRS, LJAD and Institute NeuroMod, Université Côte d’Azur（法国蔚蓝海岸大学神经调节研究所、LJAD及法国国家科学研究中心）
Recurrent neural networks (RNNs) are widely used in computational neuroscience and machine learning applications. In an RNN, each neuron computes its output as a nonlinear function of its integrated input. While the importance of RNNs, especially as models of brain processing, is undisputed, it is also widely acknowledged that the computations in standard RNN models may be an over-simplification of what real neuronal networks compute. Here, we suggest that the RNN approach may be made both neurobiologically more plausible and computationally more powerful by its fusion with Bayesian inference …
Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of t…
Topology-Dependent Emergence of Polychronous Neuronal Groups: A Recurrence-Plot Characterization
Complex Systems Modelling Graduate Program, School of Arts, Sciences and Humanities (EACH), University of São Paulo（圣保罗大学艺术与人文科学学院复杂系统建模研究生项目）；Department of Physics, Faculty of Philosophy, Sciences and Letters of Ribeirão Preto (FFCLRP), University of São Paulo（圣保罗大学里贝朗普雷图哲学、科学与文学院物理系）
Working memory is a cognitive function involving the storage and manipulation of latent information over brief intervals of time, thus making it crucial for context-dependent computation. Here, we use a top-down modeling approach to examine network-level mechanisms of working memory, an enigmatic issue and central topic of study in neuroscience and machine intelligence. We train thousands of recurrent neural networks on a working memory task and then perform dynamical systems analysis on the ensuing optimized networks, wherein we find that four distinct dynamical mechanisms can emerge. In part…
Random matrix theory of sparse neuronal networks with heterogeneous timescales
Complex Systems, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand；High Energy Physics Research Unit, Faculty of Science, Chulalongkorn University, Bangkok, Thailand；International Solvay Institutes, Brussels, Belgium；Mark Kac Center for Complex Systems Research, Jagiellonian University, Krak\'ow, Poland；Department of Mathematics, King's College London, London, UK
Recurrent network dynamics explain the time course of perceptual grouping in natural scenes
Netherlands Institute for Neuroscience（荷兰神经科学研究所）；Brown University（布朗大学）；Carney Institute for Brain Science, Brown University（布朗大学卡尼脑科学研究所）；Centrum Wiskunde & Informatica（数学与计算机科学中心）；University of Amsterdam（阿姆斯特丹大学）；Sorbonne Université（索邦大学）；Institut National de la Santé et de la Recherche Médicale（国家健康与医学研究院）；Centre National de la Recherche Scientifique（法国国家科学研究中心）；Institut de la Vision（视觉研究所）；VU University（自由大学）；Academic University Medical Center（学术医学中心）
Harnessing cortical geometry, wiring, and function as inductive biases for recurrent neural networks
Neuromatch Academy, Neuromatch, Inc., USA（Neuromatch学院，Neuromatch公司，美国）；McGovern Institute for Brain Research, Massachusetts Institute of Technology (MIT)（麦戈文脑科学研究所，麻省理工学院（MIT））
We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or `short-cuts' and the delay in the neuronal interactions. Persistent activity arises for a small fraction of `short-cuts', while a transition to failure occurs at a critical value of the `short-cut' density. The persistent activity consists of multi-stable periodic attractors, the number of which is at least on the order of the number of neurons in the network. F…
