A discrete time neural network model with spiking neurons

We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in Soula et al. (Neural Comput. 18, 1, 2006). Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns (“raster plots”). Moreover, though the dynamics is generically periodic, it has a weak form of initial conditions sensitivity due to the presence of a sharp threshold in the model definition. As a consequence, the model exhibits a dynamical regime indistinguishable from chaos in numerical experiments.      

Modeling motor cortical operations by an attractor network of stochastic neurons

Understanding the neural computations performed by the motor cortex requires biologically plausible models that account for cell discharge patterns revealed by neurophysiological recordings. In the present study the motor cortical activity underlying movement generation is modeled as the dynamic evolution of a large fully recurrent network of stochastic spiking neurons with noise superimposed on the synaptic transmission. We show that neural representations of the learned movement trajectories can be stored in the connectivity matrix in such a way that, when activated, a particular trajectory evolves in time as a dynamic attractor of the system while individual neurons fire irregularly with large variability in their interspike intervals. Moreover, the encoding of trajectories as attractors ensures high stability of the ensemble dynamics in the presence of synaptic noise. In agreement with neurophysiological findings, the suggested model can provide a wide repertoire of specific motor behaviors, whereas the number of specialized cells and specific connections may be negligibly small if compared with the whole population engaged in trajectory retrieving. To examine the applicability of the model we study quantitatively the relationship between local geometrical and kinematic characteristics of the trajectories generated by the network. The relationship obtained as a result of simulations is close to the 2/3 power law established by psychophysical and neurophysiological studies.     

An STDP training algorithm for a spiking neural network with dynamic threshold neurons

This paper proposes a supervised training algorithm for Spiking Neural Networks (SNNs) which modifies the Spike Timing Dependent Plasticity (STDP)learning rule to support both local and network level training with multiple synaptic connections and axonal delays. The training algorithm applies the rule to two and three layer SNNs, and is benchmarked using the Iris and Wisconsin Breast Cancer (WBC) data sets. The effectiveness of hidden layer dynamic threshold neurons is also investigated and results are presented.     

Modeling fluctuations in default-mode brain network using a spiking neural network

Recently, numerous attempts have been made to understand the dynamic behavior of complex brain systems using neural network models. The fluctuations in blood-oxygen-level-dependent (BOLD) brain signals at less than 0.1 Hz have been observed by functional magnetic resonance imaging (fMRI) for subjects in a resting state. This phenomenon is referred to as a "default-mode brain network." In this study, we model the default-mode brain network by functionally connecting neural communities composed of spiking neurons in a complex network. Through computational simulations of the model, including transmission delays and complex connectivity, the network dynamics of the neural system and its behavior are discussed. The results show that the power spectrum of the modeled fluctuations in the neuron firing patterns is consistent with the default-mode brain network's BOLD signals when transmission delays, a characteristic property of the brain, have finite values in a given range.     

A spiking neural network model of the midbrain superior colliculus that generates saccadic motor commands

Single-unit recordings suggest that the midbrain superior colliculus (SC) acts as an optimal controller for saccadic gaze shifts. The SC is proposed to be the site within the visuomotor system where the nonlinear spatial-to-temporal transformation is carried out: the population encodes the intended saccade vector by its location in the motor map (spatial), and its trajectory and velocity by the distribution of firing rates (temporal). The neurons’ burst profiles vary systematically with their anatomical positions and intended saccade vectors, to account for the nonlinear main-sequence kinematics of saccades. Yet, the underlying collicular mechanisms that could result in these firing patterns are inaccessible to current neurobiological techniques. Here, we propose a simple spiking neural network model that reproduces the spike trains of saccade-related cells in the intermediate and deep SC layers during saccades. The model assumes that SC neurons have distinct biophysical properties for spike generation that depend on their anatomical position in combination with a center–surround lateral connectivity. Both factors are needed to account for the observed firing patterns. Our model offers a basis for neuronal algorithms for spatiotemporal transformations and bio-inspired optimal controllers.     

On the stationary state of a network of inhibitory spiking neurons

The background activity of a cortical neural network is modeled by a homogeneous integrate-and-fire network with unreliable inhibitory synapses. For the case of fast synapses, numerical and analytical calculations show that the network relaxes into a stationary state of high attention. The majority of the neurons has a membrane potential just below the threshold; as a consequence the network can react immediately – on the time scale of synaptic transmission- on external pulses. The neurons fire with a low rate and with a broad distribution of interspike intervals. Firing events of the total network are correlated over short time periods. The firing rate increases linearly with external stimuli. In the limit of infinitely large networks, the synaptic noise decreases to zero. Nevertheless, the distribution of interspike intervals remains broad. Action Editor: Misha Tsodyks     

Testing of information condensation in a model reverberating spiking neural network

Information about external world is delivered to the brain in the form of structured in time spike trains. During further processing in higher areas, information is subjected to a certain condensation process, which results in formation of abstract conceptual images of external world, apparently, represented as certain uniform spiking activity partially independent on the input spike trains details. Possible physical mechanism of condensation at the level of individual neuron was discussed recently. In a reverberating spiking neural network, due to this mechanism the dynamics should settle down to the same uniform/ periodic activity in response to a set of various inputs. Since the same periodic activity may correspond to different input spike trains, we interpret this as possible candidate for information condensation mechanism in a network. Our purpose is to test this possibility in a network model consisting of five fully connected neurons, particularly, the influence of geometric size of the network, on its ability to condense information. Dynamics of 20 spiking neural networks of different geometric sizes are modelled by means of computer simulation. Each network was propelled into reverberating dynamics by applying various initial input spike trains. We run the dynamics until it becomes periodic. The Shannon's formula is used to calculate the amount of information in any input spike train and in any periodic state found. As a result, we obtain explicit estimate of the degree of information condensation in the networks, and conclude that it depends strongly on the net's geometric size.     

A discrete time neural network model with spiking neurons: II: Dynamics with noise

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.     

Case study on a self-organizing spiking neural network for robot navigation

This paper presents a Spiking Neural Network (SNN) architecture for mobile robot navigation. The SNN contains 4 layers where dynamic synapses route information to the appropriate neurons in each layer and the neurons are modeled using the Leaky Integrate and Fire (LIF) model. The SNN learns by self-organizing its connectivity as new environmental conditions are experienced and consequently knowledge about its environment is stored in the connectivity. Also a novel feature of the proposed SNN architecture is that it uses working memory, where present and previous sensor states are stored. Results are presented for a wall following application.     

Generating oscillatory bursts from a network of regular spiking neurons without inhibition

Avian nucleus isthmi pars parvocellularis (Ipc) neurons are reciprocally connected with the layer 10 (L10) neurons in the optic tectum and respond with oscillatory bursts to visual stimulation. Our in vitro experiments show that both neuron types respond with regular spiking to somatic current injection and that the feedforward and feedback synaptic connections are excitatory, but of different strength and time course. To elucidate mechanisms of oscillatory bursting in this network of regularly spiking neurons, we investigated an experimentally constrained model of coupled leaky integrate-and-fire neurons with spike-rate adaptation. The model reproduces the observed Ipc oscillatory bursting in response to simulated visual stimulation. A scan through the model parameter volume reveals that Ipc oscillatory burst generation can be caused by strong and brief feedforward synaptic conductance changes. The mechanism is sensitive to the parameter values of spike-rate adaptation. In conclusion, we show that a network of regular-spiking neurons with feedforward excitation and spike-rate adaptation can generate oscillatory bursting in response to a constant input.     

Electrical characteristics of neurons in the cat motor cortex

Electrical characteristics of motor cortical neurons were studied in acute experiments on immobilized cats. Values of the input resistances varied from units to tens of megohms (mean 11.11±3.93 MΩ). The threshold current is a hyperbolic function of input resistance of the corresponding neurons and negative correlation was found between the axonal conduction velocity and input resistance. The time constant (τ₀) of the membrane was 7.1±3.46 msec. A time constant τ₁, of 1.65±0.36 msec, could also be distinguished in some neurons. Electrotonic lengths of dendrites of the cortical neurons were calculated by the use of Rall's model: mean 3.66±0.94 (in units of length constant).     

Self-organization of spiking neural network that generates autonomous behavior in a real mobile robot

In this paper, we propose self-organization algorithm of spiking neural network (SNN) applicable to autonomous robot for generation of adoptive and goal-directed behavior. First, we formulated a SNN model whose inputs and outputs were analog and the hidden unites are interconnected each other. Next, we implemented it into a miniature mobile robot Khepera. In order to see whether or not a solution(s) for the given task(s) exists with the SNN, the robot was evolved with the genetic algorithm in the environment. The robot acquired the obstacle avoidance and navigation task successfully, exhibiting the presence of the solution. After that, a self-organization algorithm based on a use-dependent synaptic potentiation and depotentiation at synapses of input layer to hidden layer and of hidden layer to output layer was formulated and implemented into the robot. In the environment, the robot incrementally organized the network and the given tasks were successfully performed. The time needed to acquire the desired adoptive and goal-directed behavior using the proposed self-organization method was much less than that with the genetic evolution, approximately one fifth.     

Coincidence detection of place and temporal context in a network model of spiking hippocampal neurons

Recent advances in single-neuron biophysics have enhanced our understanding of information processing on the cellular level, but how the detailed properties of individual neurons give rise to large-scale behavior remains unclear. Here, we present a model of the hippocampal network based on observed biophysical properties of hippocampal and entorhinal cortical neurons. We assembled our model to simulate spatial alternation, a task that requires memory of the previous path through the environment for correct selection of the current path to a reward site. The convergence of inputs from entorhinal cortex and hippocampal region CA3 onto CA1 pyramidal cells make them potentially important for integrating information about place and temporal context on the network level. Our model shows how place and temporal context information might be combined in CA1 pyramidal neurons to give rise to splitter cells, which fire selectively based on a combination of place and temporal context. The model leads to a number of experimentally testable predictions that may lead to a better understanding of the biophysical basis of information processing in the hippocampus.     

Effect of inhibitory feedback on correlated firing of spiking neural network

Understanding the properties and mechanisms that generate different forms of correlation is critical for determining their role in cortical processing. Researches on retina, visual cortex, sensory cortex, and computational model have suggested that fast correlation with high temporal precision appears consistent with common input, and correlation on a slow time scale likely involves feedback. Based on feedback spiking neural network model, we investigate the role of inhibitory feedback in shaping correlations on a time scale of 100 ms. Notably, the relationship between the correlation coefficient and inhibitory feedback strength is non-monotonic. Further, computational simulations show how firing rate and oscillatory activity form the basis of the mechanisms underlying this relationship. When the mean firing rate holds unvaried, the correlation coefficient increases monotonically with inhibitory feedback, but the correlation coefficient keeps decreasing when the network has no oscillatory activity. Our findings reveal that two opposing effects of the inhibitory feedback on the firing activity of the network contribute to the non-monotonic relationship between the correlation coefficient and the strength of the inhibitory feedback. The inhibitory feedback affects the correlated firing activity by modulating the intensity and regularity of the spike trains. Finally, the non-monotonic relationship is replicated with varying transmission delay and different spatial network structure, demonstrating the universality of the results.     

Learning compositional sequences with multiple time scales through a hierarchical network of spiking neurons

Sequential behaviour is often compositional and organised across multiple time scales: a set of individual elements developing on short time scales (motifs) are combined to form longer functional sequences (syntax). Such organisation leads to a natural hierarchy that can be used advantageously for learning, since the motifs and the syntax can be acquired independently. Despite mounting experimental evidence for hierarchical structures in neuroscience, models for temporal learning based on neuronal networks have mostly focused on serial methods. Here, we introduce a network model of spiking neurons with a hierarchical organisation aimed at sequence learning on multiple time scales. Using biophysically motivated neuron dynamics and local plasticity rules, the model can learn motifs and syntax independently. Furthermore, the model can relearn sequences efficiently and store multiple sequences. Compared to serial learning, the hierarchical model displays faster learning, more flexible relearning, increased capacity, and higher robustness to perturbations. The hierarchical model redistributes the variability: it achieves high motif fidelity at the cost of higher variability in the between-motif timings.     

Activation of a wide-spread network of inhibitory neurons in barrel cortex

Abstract The one-to-one correspondence of whiskers to barrels in layer IV of rodent somatosensory cortex can be demonstrated by a precise match between columns of heavy 2-deoxyglucose (2DG) label in layer IV barrels and other layers which correspond to stimulated whiskers. While there is specificity of peripheral-to-central mapping, the extent to which integration and/or modulation are generated by circuitry within or interactions between the barrel-defined whisker columns is not clear. Following stimulation of selected whiskers, large cells at the layer IV-V boundary throughout the barrel field are heavily labeled by 2-deoxyglucose (2DG) at high resolution. Many of these cells are outside the barrel columns of the stimulated whiskers. Further, the number of cells labeled is not directly related to the number of activated barrel columns. These neurons are not labeled in animals anesthetized before 2DG injection and are not as heavily labeled in barrel fields of somnolent animals. Most of the heavily labeled neurons immunolabel for glutamate decarboxylase (GAD) and are presumed to be inhibitory, while a smaller number of labeled neurons, presumed to be excitatory, immunolabel for glutamate (Glu). Similar populations of large, heavily 2DG-labeled neurons are found in other cortical areas. These relatively few neurons are exceptionally active and may modulate integrative functions of cerebral cortex.     

Multisensory convergence on neurons of the motor cortex in unanesthetized cats

Postsynaptic potentials (PSPs) of 83 neurons in the motor cortex of unanesthetized cats in response to electrodermal, photic, and acoustic stimulation were investigated by intra-and quasi-intracellular recording methods. Most cells responded to stimulation of at least one limb. About 60% of neurons of the posterior and over 75% of neurons of the anterior sigmoid gyrus responded to stimulation of two (or more) limbs. In 29 of 39 neurons of the anterior and 12 of 44 of the posterior sigmoid gyrus PSPs with a short (less than 50 msec) and stable latent period were evoked by flashes and clicks. On presentation of two somesthetic stimuli complete blocking (if the interval was less than 30–60 msec) or weakening (interval 30–200 msec) of responses to the second (testing) stimulus was observed. On presentation of paired photic (or acoustic) stimuli or paired stimuli of different modalities at various intervals from 0 to 100 msec, the testing response was often potentiated. The character of the responses and their interaction thus differed from those obtained under chloralose anesthesia [6, 7]. It is postulated that under the action of chloralose a system of neurons with strong excitatory feedback is formed in the motor cortex which may respond to stimuli of different modalities by something resembling the "all or nothing" principle.Brain Institute, Academy of Medical Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 3, No. 6, pp. 563–573, November–December, 1971.