Analog-digital simulations of full conductance-based networks of spiking neurons with spike timing dependent plasticity

We introduce and test a system for simulating networks of conductance-based neuron models using analog circuits. At the single-cell level, we use custom-designed analog circuits (ASICs) that simulate two types of spiking neurons based on Hodgkin-Huxley like dynamics: "regular spiking" excitatory neurons with spike-frequency adaptation, and "fast spiking" inhibitory neurons. Synaptic interactions are mediated by conductance-based synaptic currents described by kinetic models. Connectivity and plasticity rules are implemented digitally through a real time interface between a computer and a PCI board containing the ASICs. We show a prototype system of a few neurons interconnected with synapses undergoing spike-timing dependent plasticity (STDP), and compare this system with numerical simulations. We use this system to evaluate the effect of parameter dispersion on the behavior of small circuits of neurons. It is shown that, although the exact spike timings are not precisely emulated by the ASIC neurons, the behavior of small networks with STDP matches that of numerical simulations. Thus, this mixed analog-digital architecture provides a valuable tool for real-time simulations of networks of neurons with STDP. They should be useful for any real-time application, such as hybrid systems interfacing network models with biological neurons.     

Information recall using relative spike timing in a spiking neural network

We present a neural network that is capable of completing and correcting a spiking pattern given only a partial, noisy version. It operates in continuous time and represents information using the relative timing of individual spikes. The network is capable of correcting and recalling multiple patterns simultaneously. We analyze the network's performance in terms of information recall. We explore two measures of the capacity of the network: one that values the accurate recall of individual spike times and another that values only the presence or absence of complete patterns. Both measures of information are found to scale linearly in both the number of neurons and the period of the patterns, suggesting these are natural measures of network information. We show a smooth transition from encodings that provide precise spike times to flexible encodings that can encode many scenes. This makes it plausible that many diverse tasks could be learned with such an encoding.     

脉冲神经元脉冲序列学习方法综述

脉冲神经元是一种新颖的人工神经元模型,其有监督学习的目的是通过学习使得神经元激发出一串通过精确时间编码来表达特定信息的脉冲序列,故称为脉冲序列学习。针对单神经元的脉冲序列学习应用价值显著、理论基础多样、影响因素众多的特点,对已有脉冲序列学习方法进行了综述对比。首先介绍了脉冲神经元模型与脉冲序列学习的基本概念;然后详细介绍了典型的脉冲序列学习方法,指出了每种方法的理论基础和突触权值调整方式;最后通过实验比较了这些学习方法的性能,系统总结了每种方法的特点,并且讨论了脉冲序列学习的研究现状和进一步的发展方向。该研究结果有助于脉冲序列学习方法的综合应用。     

Simple model of spiking neurons

A model is presented that reproduces spiking and bursting behavior of known types of cortical neurons. The model combines the biologically plausibility of Hodgkin-Huxley-type dynamics and the computational efficiency of integrate-and-fire neurons. Using this model, one can simulate tens of thousands of spiking cortical neurons in real time (1 ms resolution) using a desktop PC.     

基于梯度下降的脉冲神经元精确序列学习算法

基于梯度下降的脉冲神经元有监督学习算法通过计算梯度最小化目标序列和实际输出序列间的误差使得神经元能激发出目标脉冲序列。然而该算法中的误差函数是基于实际输出脉冲序列和相对应的目标输出脉冲序列动态构建而成,导致算法在收敛时可能出现实际输出序列的个数和期望输出个数不相等的情况。针对这一缺陷提出了一种改进的脉冲神经元梯度下降学习算法,算法在学习过程中检测目标序列脉冲个数和实际激发脉冲个数,并引入虚拟实际激发脉冲和期望激发脉冲构建误差函数以分别解决激发个数不足和激发个数多余的问题。实验结果证明该算法能有效地防止学习算法在输出脉冲个数不等的情况下提前结束,使得神经元能够精确地激发出目标脉冲序列。     

The impact of spike timing variability on the signal-encoding performance of neural spiking models.

It remains unclear whether the variability of neuronal spike trains in vivo arises due to biological noise sources or represents highly precise encoding of temporally varying synaptic input signals. Determining the variability of spike timing can provide fundamental insights into the nature of strategies used in the brain to represent and transmit information in the form of discrete spike trains. In this study, we employ a signal estimation paradigm to determine how variability in spike timing affects encoding of random time-varying signals. We assess this for two types of spiking models: an integrate-and-fire model with random threshold and a more biophysically realistic stochastic ion channel model. Using the coding fraction and mutual information as information-theoretic measures, we quantify the efficacy of optimal linear decoding of random inputs from the model outputs and study the relationship between efficacy and variability in the output spike train. Our findings suggest that variability does not necessarily hinder signal decoding for the biophysically plausible encoders examined and that the functional role of spiking variability depends intimately on the nature of the encoder and the signal processing task; variability can either enhance or impede decoding performance.     

Which model to use for cortical spiking neurons?

We discuss the biological plausibility and computational efficiency of some of the most useful models of spiking and bursting neurons. We compare their applicability to large-scale simulations of cortical neural networks.     

Theory of input spike auto- and cross-correlations and their effect on the response of spiking neurons

Spike correlations between neurons are ubiquitous in the cortex, but their role is not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input generated by presynaptic correlated neuronal populations. Input correlations are characterized in terms of the firing rates, Fano factors, correlation coefficients, and correlation timescale of the neurons driving the target neuron. We show that the sum of the presynaptic spike trains cannot be well described by a Poisson process. In fact, the total input current has a nontrivial two-point correlation function described by two main parameters: the correlation timescale (how precise the input correlations are in time) and the correlation magnitude (how strong they are). Therefore, the total current generated by the input spike trains is not well described by a white noise gaussian process. Instead, we model the total current as a colored gaussian process with the same mean and two-point correlation function, leading to the formulation of the problem in terms of a Fokker-Planck equation. Solutions of the output firing rate are found in the limit of short and long correlation timescales. The solutions described here expand and improve on our previous results (Moreno, de la Rocha, Renart, & Parga, 2002) by presenting new analytical expressions for the output firing rate for general IF neurons, extending the validity of the results for arbitrarily large correlation magnitude, and by describing the differential effect of correlations on the mean-driven or noise-dominated firing regimes. Also the details of this novel formalism are given here for the first time. We employ numerical simulations to confirm the analytical solutions and study the firing response to sudden changes in the input correlations. We expect this formalism to be useful for the study of correlations in neuronal networks and their role in neural processing and information transmission.     

Effects of spike timing on winner-take-all competition in model cortical circuits

Synaptic interactions in cortical circuits involve strong recurrent excitation between nearby neurons and lateral inhibition that is more widely spread. This architecture is commonly thought to promote a winner-take-all competition, in which a small fraction of neuronal responses is selected for further processing. Here I report that such a competition is remarkably sensitive to the timing of neuronal action potentials. This is shown using simulations of model neurons and synaptic connections representing a patch of cortical tissue. In the simulations, uncorrelated discharge among neuronal units results in patterns of response dominance and suppression, that is, in a winner-take-all competition. Synchronization of firing, however, prevents such competition. These results demonstrate a novel property of recurrent cortical-like circuits, suggesting that the temporal patterning of cortical activity may play an important part in selection among stimuli competing for the control of attention and motor action.     

Dynamics of strongly-coupled spiking neurons

We present a dynamical theory of integrate-and-fire neurons with strong synaptic coupling. We show how phase-locked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to states characterized by spatiotemporal variations in the interspike intervals (ISIs). The dynamics is compared with that of a corresponding network of analog neurons in which the outputs of the neurons are taken to be mean firing rates. A fundamental result is that for slow interactions, there is good agreement between the two models (on an appropriately defined timescale). Various examples of desynchronization in the strong coupling regime are presented. First, a globally coupled network of identical neurons with strong inhibitory coupling is shown to exhibit oscillator death in which some of the neurons suppress the activity of others. However, the stability of the synchronous state persists for very large networks and fast synapses. Second, an asymmetric network with a mixture of excitation and inhibition is shown to exhibit periodic bursting patterns. Finally, a one-dimensional network of neurons with long-range interactions is shown to desynchronize to a state with a spatially periodic pattern of mean firing rates across the network. This is modulated by deterministic fluctuations of the instantaneous firing rate whose size is an increasing function of the speed of synaptic response.     

Multidimensional encoding strategy of spiking neurons

Neural responses in sensory systems are typically triggered by a multitude of stimulus features. Using information theory, we study the encoding accuracy of a population of stochastically spiking neurons characterized by different tuning widths for the different features. The optimal encoding strategy for representing one feature most accurately consists of narrow tuning in the dimension to be encoded, to increase the single-neuron Fisher information, and broad tuning in all other dimensions, to increase the number of active neurons. Extremely narrow tuning without sufficient receptive field overlap will severely worsen the coding. This implies the existence of an optimal tuning width for the feature to be encoded. Empirically, only a subset of all stimulus features will normally be accessible. In this case, relative encoding errors can be calculated that yield a criterion for the function of a neural population based on the measured tuning curves.     

Image segmentation by networks of spiking neurons

A network of leaky integrate-and-fire (IAF) neurons is proposed to segment gray-scale images. The network architecture with local competition between neurons that encode segment assignments of image blocks is motivated by a histogram clustering approach to image segmentation. Lateral excitatory connections between neighboring image sites yield a local smoothing of segments. The mean firing rate of class membership neurons encodes the image segmentation. A weight modification scheme is proposed that estimates segment-specific prototypical histograms. The robustness properties of the network implementation make it amenable to an analog VLSI realization. Results on synthetic and real-world images demonstrate the effectiveness of the architecture.     

Movement generation with circuits of spiking neurons

How can complex movements that take hundreds of milliseconds be generated by stereotypical neural microcircuits consisting of spiking neurons with a much faster dynamics? We show that linear readouts from generic neural microcircuit models can be trained to generate basic arm movements. Such movement generation is independent of the arm model used and the type of feedback that the circuit receives. We demonstrate this by considering two different models of a two-jointed arm, a standard model from robotics and a standard model from biology, that each generates different kinds of feedback. Feedback that arrives with biologically realistic delays of 50 to 280 ms turns out to give rise to the best performance. If a feedback with such desirable delay is not available, the neural microcircuit model also achieves good performance if it uses internally generated estimates of such feedback. Existing methods for movement generation in robotics that take the particular dynamics of sensors and actuators into account (embodiment of motor systems) are taken one step further with this approach, which provides methods for also using the embodiment of motion generation circuitry, that is, the inherent dynamics and spatial structure of neural circuits, for the generation of movement.     

Dynamics of spiking neurons with electrical coupling

We analyze the existence and stability of phase-locked states of neurons coupled electrically with gap junctions. We show that spike shape and size, along with driving current (which affects network frequency), play a large role in which phase-locked modes exist and are stable. Our theory makes predictions about biophysical models using spikes of different shapes, and we present simulations to confirm the predictions. We also analyze a large system of all-to-all coupled neurons and show that the splay-phase state can exist only for a certain range of frequencies.     

Synchrony in heterogeneous networks of spiking neurons

The emergence of synchrony in the activity of large, heterogeneous networks of spiking neurons is investigated. We define the robustness of synchrony by the critical disorder at which the asynchronous state becomes linearly unstable. We show that at low firing rates, synchrony is more robust in excitatory networks than in inhibitory networks, but excitatory networks cannot display any synchrony when the average firing rate becomes too high. We introduce a new regime where all inputs, external and internal, are strong and have opposite effects that cancel each other when averaged. In this regime, the robustness of synchrony is strongly enhanced, and robust synchrony can be achieved at a high firing rate in inhibitory networks. On the other hand, in excitatory networks, synchrony remains limited in frequency due to the intrinsic instability of strong recurrent excitation.     

Solving graph algorithms with networks of spiking neurons

Spatio-temporal coding that combines spatial constraints with temporal sequencing is of great interest to brain-like circuit modelers. In this paper we present some new ideas of how these types of circuits can self-organize. We introduce a temporal correlation rule based on the time difference between the firing of neurons. With the aid of this rule we show an analogy between a graph and a network of spiking neurons. The shortest path, clustering based on the nearest neighbor, and the minimal spanning tree algorithms are solved using the proposed approach.     

Information geometry of interspike intervals in spiking neurons

An information geometrical method is developed for characterizing or classifying neurons in cortical areas, whose spike rates fluctuate in time. Under the assumption that the interspike intervals of a spike sequence of a neuron obey a gamma process with a time-variant spike rate and a fixed shape parameter, we formulate the problem of characterization as a semiparametric statistical estimation, where the spike rate is a nuisance parameter. We derive optimal criteria from the information geometrical viewpoint when certain assumptions are added to the formulation, and we show that some existing measures, such as the coefficient of variation and the local variation, are expressed as estimators of certain functions under the same assumptions.     

Stationary bumps in networks of spiking neurons.

We examine the existence and stability of spatially localized "bumps" of neuronal activity in a network of spiking neurons. Bumps have been proposed in mechanisms of visual orientation tuning, the rat head direction system, and working memory. We show that a bump solution can exist in a spiking network provided the neurons fire asynchronously within the bump. We consider a parameter regime where the bump solution is bistable with an all-off state and can be initiated with a transient excitatory stimulus. We show that the activity profile matches that of a corresponding population rate model. The bump in a spiking network can lose stability through partial synchronization to either a traveling wave or the all-off state. This can occur if the synaptic timescale is too fast through a dynamical effect or if a transient excitatory pulse is applied to the network. A bump can thus be activated and deactivated with excitatory inputs that may have physiological relevance.