Many networks in the brain are sparsely connected, and the brain eliminates synapses during development and learning. How could the brain decide which synapses to prune? In a recurrent network, determining the importance of a synapse between two neurons is a difficult computational problem, depending on the role that both neurons play and on all possible pathways of information flow between them. Noise is ubiquitous in neural systems, and often considered an irritant to be overcome. Here we suggest that noise could play a functional role in synaptic pruning, allowing the brain to probe network structure and determine which synapses are redundant. We construct a simple, local, unsupervised plasticity rule that either strengthens or prunes synapses using only synaptic weight and the noise-driven covariance of the neighboring neurons. For a subset of linear and rectified-linear networks, we prove that this rule preserves the spectrum of the original matrix and hence preserves network dynamics even when the fraction of pruned synapses asymptotically approaches 1. The plasticity rule is biologically-plausible and may suggest a new role for noise in neural computation.
The impairment of cognitive function in Alzheimer's is clearly correlated to synapse loss. However, the mechanisms underlying this correlation are only poorly understood. Here, we investigate how the loss of excitatory synapses in sparsely connected random networks of spiking excitatory and inhibitory neurons alters their dynamical characteristics. Beyond the effects on the network's activity statistics, we find that the loss of excitatory synapses on excitatory neurons shifts the network dynamic towards the stable regime. The decrease in sensitivity to small perturbations to time varying inpu…
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 …
Synfire chains are thought to underlie precisely-timed sequences of spikes observed in various brain regions and across species. How they are formed is not understood. Here we analyze self-organization of synfire chains through the spike-timing dependent plasticity (STDP) of the synapses, axon remodeling, and potentiation decay of synaptic weights in networks of neurons driven by noisy external inputs and subject to dominant feedback inhibition. Potentiation decay is the gradual, activity-independent reduction of synaptic weights over time. We show that potentiation decay enables a dynamic and…
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…
The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent t…
Recent evidence in rodent cerebral cortex and olfactory bulb suggests that short-term dynamics of excitatory synaptic transmission is correlated to stereotypical connectivity motifs. It was observed that neurons with short-term facilitating synapses form predominantly reciprocal pairwise connections, while neurons with short-term depressing synapses form unidirectional pairwise connections. The cause of these structural differences in synaptic microcircuits is unknown. We propose that these connectivity motifs emerge from the interactions between short-term synaptic dynamics (SD) and long-term…
Excitatory synaptic connections in the adult neocortex consist of multiple synaptic contacts, almost exclusively formed on dendritic spines. Changes of dendritic spine shape and volume, a correlate of synaptic strength, can be tracked in vivo for weeks. Here, we present a combined model of spike-timing dependent dendritic spine plasticity and turnover that explains the steady state multi-contact configuration of synapses in adult neocortical networks. In this model, many presynaptic neurons compete to make strong synaptic connections onto postsynaptic neurons, while the synaptic contacts compr…
National Engineering School of Tunis（突尼斯国立工程学院）；Université Tunis El Manar（突尼斯艾尔马纳尔大学）
Synaptic plasticity seems to be a capital aspect of the dynamics of neural networks. It is about the physiological modifications of the synapse, which have like consequence a variation of the value of the synaptic weight. The information encoding is based on the precise timing of single spike events that is based on the relative timing of the pre- and post-synaptic spikes, local synapse competitions within a single neuron and global competition via lateral connections. In order to classify temporal sequences, we present in this paper how to use a local hebbian learning, spike-timing dependent …
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…
A new learning scheme called time divergence-convergence (TDC) is proposed for two-layer dynamic synapse neural networks (DSNN). DSNN is an artificial neural network model, in which the synaptic transmission is modeled by a dynamic process and the information between neurons are transmitted through spike timing. In TDC, the intra-layer neurons of a DSNN are trained to map input spike trains to a higher dimension of spike trains called a feature-domain, and the output neurons are trained to build the desired spike trains by processing the spike timing of intralayer neurons. The DSNN performance…
Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population dynamics with static synapses to the case of dynamic synapses exhibiting short-term plasticity (STP). Under the assumption that spike arrivals at synapses have Poisson statistics, we derive analytically stochastic mean-field dynamics for the effective synaptic coupling between finite-size populations undergoing Tsodyks-Markram STP. The novel mean-field equations a…
We present a method of estimating the gradient of an objective function with respect to the synaptic weights of a spiking neural network. The method works by measuring the fluctuations in the objective function in response to dynamic perturbation of the membrane conductances of the neurons. It is compatible with recurrent networks of conductance-based model neurons with dynamic synapses. The method can be interpreted as a biologically plausible synaptic learning rule, if the dynamic perturbations are generated by a special class of ``empiric'' synapses driven by random spike trains from an ext…
We investigate from a computational perspective the efficiency of the Willshaw synaptic update rule in the context of familiarity discrimination, a binary-answer, memory-related task that has been linked through psychophysical experiments with modified neural activity patterns in the prefrontal and perirhinal cortex regions. Our motivation for recovering this well-known learning prescription is two-fold: first, the switch-like nature of the induced synaptic bonds, as there is evidence that biological synaptic transitions might occur in a discrete stepwise fashion. Second, the possibility that …
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…
Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network scenario, whose prototype is the Hopfield model. The model has a poor storage capacity, compared with the capacity achieved with perceptron learning algorithms. Here, by transforming the perceptron learning rule, we present an online learning rule for a recurrent neural network that achieves near-maximal storage capacity without an explicit supervisory error s…
There is consensus in the current literature that stable states of asynchronous irregular spiking activity require (i) large networks of 10 000 or more neurons and (ii) external background activity or pacemaker neurons. Yet already in 1963, Griffith showed that networks of simple threshold elements can be persistently active at intermediate rates. Here, we extend Griffith's work and demonstrate that sparse networks of integrate-and-fire neurons assume stable states of self-sustained asynchronous and irregular firing without external input or pacemaker neurons. These states can be robustly indu…
Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but quantitative links between neural network structure and function are complex and subtle. For example, many networks can give rise to similar functional responses, and the same network can function differently depending on context. Whether certain patterns of synaptic connectivity are required to generate specific network-level computations is largely unknown. H…
We introduce a novel, biologically plausible local learning rule that provably increases the robustness of neural dynamics to noise in nonlinear recurrent neural networks with homogeneous nonlinearities. Our learning rule achieves higher noise robustness without sacrificing performance on the task and without requiring any knowledge of the particular task. The plasticity dynamics -- an integrable dynamical system operating on the weights of the network -- maintains a multiplicity of conserved quantities, most notably the network's entire temporal map of input to output trajectories. The outcom…
Cortical networks can maintain memories for decades despite the short lifetime of synaptic strength. Can a neural network store long-lasting memories in unstable synapses? Here, we study the effects of random noise on the stability of memory stored in synapses of an attractor neural network. The model includes ongoing spike timing dependent plasticity (STDP). We show that certain classes of STDP rules can lead to the stabilization of memory patterns stored in the network. The stabilization results from rehearsals induced by noise. We show that unstructured neural noise, after passing through t…
Modelling chronic stress as excitation-inhibition perturbation in recurrent working-memory networks
Leibniz Institute for Resilience Research (LIR)（莱布尼茨韧性研究所）；Institute for Quantitative and Computational Biosciences (IQCB), Johannes Gutenberg University（约翰内斯·古腾堡大学定量与计算生物学研究所）；University Medical Center of the Johannes Gutenberg University（约翰内斯·古腾堡大学医学中心）
Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could presumably be learned by adjusting connection weights in a recurrent biological neural network. However, this is greatly complicated by the credit assignment problem for learning in recurrent network, e.g. the contribution of each connection to the global output error cannot be determined based only on locally accessible quantities to the synapse. Combining …
We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the Hodgkin-Huxley model or by one of its simplified version, the Fitzhugh-Nagumo model. The synapses between neurons are either electrical or chemical. The network is assumed to be fully connected. The maximum conductances vary randomly. Under the condition that all neurons initial conditions are drawn independently from the same law that depends only on the population t…
Spike-timing dependent plasticity (STDP) is an organizing principle of biological neural networks. While synchronous firing of neurons is considered to be an important functional block in the brain, how STDP shapes neural networks possibly toward synchrony is not entirely clear. We examine relations between STDP and synchronous firing in spontaneously firing neural populations. Using coupled heterogeneous phase oscillators placed on initial networks, we show numerically that STDP prunes some synapses and promotes formation of a feedforward network. Eventually a pacemaker, which is the neuron w…
Network models are routinely downscaled compared to nature in terms of numbers of nodes or edges because of a lack of computational resources, often without explicit mention of the limitations this entails. While reliable methods have long existed to adjust parameters such that the first-order statistics of network dynamics are conserved, here we show that limitations already arise if also second-order statistics are to be maintained. The temporal structure of pairwise averaged correlations in the activity of recurrent networks is determined by the effective population-level connectivity. We f…
Understanding how recurrent neural circuits can learn to implement dynamical systems is a fundamental challenge in neuroscience. The credit assignment problem, i.e. determining the local contribution of each synapse to the network's global output error, is a major obstacle in deriving biologically plausible local learning rules. Moreover, spiking recurrent networks implementing such tasks should not be hugely costly in terms of number of neurons and spikes, as they often are when adapted from rate models. Finally, these networks should be robust to noise and neural deaths in order to sustain t…
Recent experiments revealed that a certain class of inhibitory neurons in the cerebral cortex make synapses not onto cell bodies but at distal parts of dendrites of the target neurons, mediating highly nonlinear dendritic inhibition. We propose a novel form of competitive neural network model that realizes such dendritic inhibition. Contrary to the conventional lateral inhibition in neural networks, our dendritic inhibition models don't always show winner-take-all behaviors; instead, they converge to "I don't know" states when unknown input patterns are presented. We derive reduced two-dimensi…
Restricted Boltzmann Machines (RBMs) and Deep Belief Networks have been demonstrated to perform efficiently in a variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on neuromorphic hardware platforms emulating large-scale networks of spiking neurons can have significant advantages from the perspectives of scalability, power dissipation and real-time interfacing with the environment. However the traditional RBM architecture and the commonly used training algorithm known as Contrastive Divergence (CD) are based on discrete updates…
The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro. Based on a propagation of the membrane autocorrelation across spike bursts, we provide an analytical derivation of the neural activation function that holds for a large parameter space, including the high-conductance state. On this basis, we show how an ensemble of leaky integrate-and-fire neurons with conductance-based synapses embedded in a spiking enviro…
High-level brain function such as memory, classification or reasoning can be realized by means of recurrent networks of simplified model neurons. Analog neuromorphic hardware constitutes a fast and energy efficient substrate for the implementation of such neural computing architectures in technical applications and neuroscientific research. The functional performance of neural networks is often critically dependent on the level of correlations in the neural activity. In finite networks, correlations are typically inevitable due to shared presynaptic input. Recent theoretical studies have shown…
Attractor neural network is an important theoretical scenario for modeling memory function in the hippocampus and in the cortex. In these models, memories are stored in the plastic recurrent connections of neural populations in the form of "attractor states". The maximal information capacity for conventional abstract attractor networks with unconstrained connections is 2 bits/synapse. However, an unconstrained synapse has the capacity to store infinite amount of bits in a noiseless theoretical scenario: a capacity that conventional attractor networks cannot achieve. Here, I propose a hierarchi…
An open problem in neuroscience is to explain the functional role of oscillations in neural networks, contributing, for example, to perception, attention, and memory. Cross-frequency coupling (CFC) is associated with information integration across populations of neurons. Impaired CFC is linked to neurological disease. It is unclear what role CFC has in information processing and brain functional connectivity. We construct a model of CFC which predicts a computational role for observed $θ- γ$ oscillatory circuits in the hippocampus and cortex. Our model predicts that the complex dynamics in rec…
Experiments show that spike-triggered stimulation performed with Bidirectional Brain-Computer-Interfaces (BBCI) can artificially strengthen connections between separate neural sites in motor cortex (MC). What are the neuronal mechanisms responsible for these changes and how does targeted stimulation by a BBCI shape population-level synaptic connectivity? The present work describes a recurrent neural network model with probabilistic spiking mechanisms and plastic synapses capable of capturing both neural and synaptic activity statistics relevant to BBCI conditioning protocols. When spikes from …
Recurrent networks of spiking neurons (RSNNs) underlie the astounding computing and learning capabilities of the brain. But computing and learning capabilities of RSNN models have remained poor, at least in comparison with artificial neural networks (ANNs). We address two possible reasons for that. One is that RSNNs in the brain are not randomly connected or designed according to simple rules, and they do not start learning as a tabula rasa network. Rather, RSNNs in the brain were optimized for their tasks through evolution, development, and prior experience. Details of these optimization proc…
The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore consider that the neuron dynamics may occur at a (shorter) time scale than synaptic plasticity and consider the possibility of learning rules with passive forgetting. We show that the application of such Hebbian learning leads to drastic changes in the network dynamics and structure. In particular, the learning rule contracts the norm of the weight matrix a…
We study the learning of an external signal by a neural network and the time to forget it when this network is submitted to noise. The presentation of an external stimulus to the recurrent network of binary neurons may change the state of the synapses. Multiple presentations of a unique signal leads to its learning. Then, during the forgetting time, the presentation of other signals (noise) may also modify the synaptic weights. We construct an estimator of the initial signal thanks to the synaptic currents and define by this way a probability of error. In our model, these synaptic currents evo…
Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings
School of Physics, Sun Yat-sen University（中山大学物理学院）；Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University（中山大学广东省磁电物理与器件重点实验室）
Sequence learning, prediction and replay have been proposed to constitute the universal computations performed by the neocortex. The Hierarchical Temporal Memory (HTM) algorithm realizes these forms of computation. It learns sequences in an unsupervised and continuous manner using local learning rules, permits a context specific prediction of future sequence elements, and generates mismatch signals in case the predictions are not met. While the HTM algorithm accounts for a number of biological features such as topographic receptive fields, nonlinear dendritic processing, and sparse connectivit…
Qiushi Academy for Advanced Studies, Zhejiang University（浙江大学求是高等研究院）；College of Biomedical Engineering and Instrument Science, Zhejiang University（浙江大学生物医学工程与仪器科学学院）；College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；China Nanhu Academy of Electronics and Information Technology (CNAEIT)（中国电子科技南湖研究院）
Despite its better bio-plausibility, goal-driven spiking neural network (SNN) has not achieved applicable performance for classifying biological spike trains, and showed little bio-functional similarities compared to traditional artificial neural networks. In this study, we proposed the motorSRNN, a recurrent SNN topologically inspired by the neural motor circuit of primates. By employing the motorSRNN in decoding spike trains from the primary motor cortex of monkeys, we achieved a good balance between classification accuracy and energy consumption. The motorSRNN communicated with the input by…
Recurrent spiking neural networks (RSNN) in the human brain learn to perform a wide range of perceptual, cognitive and motor tasks very efficiently in terms of energy consumption and requires very few examples. This motivates the search for biologically inspired learning rules for RSNNs to improve our understanding of brain computation and the efficiency of artificial intelligence. Several spiking models and learning rules have been proposed, but it remains a challenge to design RSNNs whose learning relies on biologically plausible mechanisms and are capable of solving complex temporal tasks. …
We study a model of spiking neurons, with recurrent connections that result from learning a set of spatio-temporal patterns with a spike-timing dependent plasticity rule and a global inhibition. We investigate the ability of the network to store and selectively replay multiple patterns of spikes, with a combination of spatial population and phase-of-spike code. Each neuron in a pattern is characterized by a binary variable determining if the neuron is active in the pattern, and a phase-lag variable representing the spike-timing order among the active units. After the learning stage, we study t…
Credit Assignment via Neural Manifold Noise Correlation
Howard Hughes Medical Institute（霍华德·休斯医学研究所）；Department of Neurobiology, Harvard Medical School（哈佛医学院神经生物学系）；Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University（哈佛大学自然与人工智能研究所在）
A complex interplay of single-neuron properties and the recurrent network structure shapes the activity of cortical neurons. The single-neuron activity statistics differ in general from the respective population statistics, including spectra and, correspondingly, autocorrelation times. We develop a theory for self-consistent second-order single-neuron statistics in block-structured sparse random networks of spiking neurons. In particular, the theory predicts the neuron-level autocorrelation times, also known as intrinsic timescales, of the neuronal activity. The theory is based on an extension…
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））
