Over the past decade there has been a growing interest in the development of parallel hardware systems for simulating large-scale networks of spiking neurons. Compared to other highly-parallel systems, GPU-accelerated solutions have the advantage of a relatively low cost and a great versatility, thanks also to the possibility of using the CUDA-C/C++ programming languages. NeuronGPU is a GPU library for large-scale simulations of spiking neural network models, written in the C++ and CUDA-C++ programming languages, based on a novel spike-delivery algorithm. This library includes simple LIF (leaky-integrate-and-fire) neuron models as well as several multisynapse AdEx (adaptive-exponential-integrate-and-fire) neuron models with current or conductance based synapses, user definable models and different devices. The numerical solution of the differential equations of the dynamics of the AdEx models is performed through a parallel implementation, written in CUDA-C++, of the fifth-order Runge-Kutta method with adaptive step-size control. In this work we evaluate the performance of this library on the simulation of a cortical microcircuit model, based on LIF neurons and current-based synapses, and on a balanced network of excitatory and inhibitory neurons, using AdEx neurons and conductance-based synapses. On these models, we will show that the proposed library achieves state-of-the-art performance in terms of simulation time per second of biological activity. In particular, using a single NVIDIA GeForce RTX 2080 Ti GPU board, the full-scale cortical-microcircuit model, which includes about 77,000 neurons and $3 \cdot 10^8$ connections, can be simulated at a speed very close to real time, while the simulation time of a balanced network of 1,000,000 AdEx neurons with 1,000 connections per neuron was about 70 s per second of biological activity.
Being permanently confronted with an uncertain world, brains have faced evolutionary pressure to represent this uncertainty in order to respond appropriately. Often, this requires visiting multiple interpretations of the available information or multiple solutions to an encountered problem. This gives rise to the so-called mixing problem: since all of these "valid" states represent powerful attractors, but between themselves can be very dissimilar, switching between such states can be difficult. We propose that cortical oscillations can be effectively used to overcome this challenge. By acting…
The brain exhibits capabilities of fast incremental learning from few noisy examples, as well as the ability to associate similar memories in autonomously-created categories and to combine contextual hints with sensory perceptions. Together with sleep, these mechanisms are thought to be key components of many high-level cognitive functions. Yet, little is known about the underlying processes and the specific roles of different brain states. In this work, we exploited the combination of context and perception in a thalamo-cortical model based on a soft winner-take-all circuit of excitatory and …
Top-down feedback in cortex is critical for guiding sensory processing, which has prominently been formalized in the theory of hierarchical predictive coding (hPC). However, experimental evidence for error units, which are central to the theory, is inconclusive, and it remains unclear how hPC can be implemented with spiking neurons. To address this, we connect hPC to existing work on efficient coding in balanced networks with lateral inhibition, and predictive computation at apical dendrites. Together, this work points to an efficient implementation of hPC with spiking neurons, where predictio…
Spiking neural networks (SNNs) communicate through the all-or-none spiking activity of neurons. However, fitting the large number of SNN model parameters to observed neural activity patterns, for example, in biological experiments, remains a challenge. Previous work using genetic algorithm (GA) optimisation on a specific efficient SNN model, using the Izhikevich neuronal model, was limited to a single parameter and objective. This work applied a version of GA, called non-dominated sorting GA (NSGA-III), to demonstrate the feasibility of performing multi-objective optimisation on the same SNN, …
Sleep is essential for learning and cognition, but the mechanisms by which it stabilizes learning, supports creativity, and manages the energy consumption of networks engaged in post-sleep task have not been yet modelled. During sleep, the brain cycles between non-rapid eye movement (NREM), a mainly unconscious state characterized by collective oscillations, and rapid eye movement (REM), associated with the integrated experience of dreaming. We propose a biologically grounded two-area thalamo-cortical plastic spiking neural network model and investigate the role of NREM - REM cycles on its awa…
Complex systems are typically characterized as an intermediate situation between a complete regular structure and a random system. Brain signals can be studied as a striking example of such systems: cortical states can range from highly synchronous and ordered neuronal activity (with higher spiking variability) to desynchronized and disordered regimes (with lower spiking variability). It has been recently shown, by testing independent signatures of criticality, that a phase transition occurs in a cortical state of intermediate spiking variability. Here, we use a symbolic information approach t…
Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50 -- 2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history eff…
Decoding finger velocity from cortical spike trains with recurrent spiking neural networks
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）；Friedrich Miescher Institute for Biomedical Research（弗里德里希·米歇尔生物医学研究所）；Faculty of Science, University of Basel（巴塞尔大学理学院）；China Nanhu Academy of Electronics and Information Technology (CNAEIT)（中国南湖电子信息技术研究院）
Scalable Construction of Spiking Neural Networks using up to thousands of GPUs
University of Cagliari（卡利亚里大学）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Jülich Research Centre（于利希研究中心）；RWTH Aachen University（亚琛工业大学）
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…
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…
Hybrid Spiking Neural Networks for Low-Power Intra-Cortical Brain-Machine Interfaces
Karlsruhe Institute of Technology, Karlsruhe, Germany（卡尔斯鲁厄理工大学）；FZI Research Center for Information Technology, Karlsruhe, Germany（弗劳恩霍夫信息与通信技术研究中心）；Infineon Technologies, Dresden, Germany（英飞凌科技）
Network algorithmics and the emergence of synchronization in cortical models
当大脑信号被记录在脑电图或一些类似的大规模大脑活动记录中时，通常会观察到振荡模式，这些模式被认为反映了底层神经元集合的总电活动。虽然现在看来，这种模式在时间上与神经元的尖峰和空间上与其他大脑区域都参与了反馈回路，但可能解释这种回路存在的机制基本上仍然未知。在这里，我们提出了一个理论研究，这些问题的皮质模型，我们介绍了较早[内森A，巴博萨VC（2010年）网络算法和皮质突触重量分布的出现。Phys Rev E 81：021916]。我们开始与两个同步措施，旨在捕捉同步的可能性模型提供的整体尖峰活动的神经元和尖峰活动，导致突触后神经元的立即发射的定义。我们目前的计算结果，我们的皮质模型，在Erdens-Rényi意义上的模型是随机的，并在结构上确定性模型。我们已经发现，我们的皮层模型的算法组件最终提供了，通过两个同步措施，在所有情况下，这两种类型的同步出现一个强大的定量基础。反过来，这可以解释神经元组合电活动中的时间反馈回路和空间反馈回路的增加，因为空间上分离的大脑区域参与节奏行为。
There are indications that for optimizing neural computation, neural networks - including the brain - operate at criticality. Previous approaches have, however, used diverse fingerprints of criticality, leaving open the question whether they refer to a unique critical point or whether there could be several. Using a recurrent spiking neural network as the model, we demonstrate that avalanche criticality does not necessarily lie at the dynamical edge-of-chaos and that therefore, the different fingerprints indicate distinct phenomena with an as yet unclarified relationship.
The dominant modeling framework for understanding cortical computations are heuristic firing rate models. Despite their success, these models fall short to capture spike synchronization effects, to link to biophysical parameters and to describe finite-size fluctuations. In this opinion article, we propose that the refractory density method (RDM), also known as age-structured population dynamics or quasi-renewal theory, yields a powerful theoretical framework to build rate-based models for mesoscopic neural populations from realistic neuron dynamics at the microscopic level. We review recent ad…
Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) b…
We measured the impact of long-range exponentially decaying intra-areal lateral connectivity on the scaling and memory occupation of a distributed spiking neural network simulator compared to that of short-range Gaussian decays. While previous studies adopted short-range connectivity, recent experimental neurosciences studies are pointing out the role of longer-range intra-areal connectivity with implications on neural simulation platforms. Two-dimensional grids of cortical columns composed by up to 11 M point-like spiking neurons with spike frequency adaption were connected by up to 30 G syna…
Laboratory of Biological Modeling, NIDDK/NIH（美国国立糖尿病、消化系统疾病和肾病研究所（NIDDK）/美国国立卫生研究院（NIH）生物建模实验室）
Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that emerge after learning remains unknown. Here we show that modifying the recurrent connectivity with a recursive least squares algorithm provides sufficient flexibility for synaptic and spiking rate dynamics of spiking networks to produce a wide range of spatiotemporal activity. We apply the training method to learn arbitrary firing patterns, stabilize irregular sp…
Real-time simulation of a large-scale biologically representative spiking neural network is presented, through the use of a heterogeneous parallelisation scheme and SpiNNaker neuromorphic hardware. A published cortical microcircuit model is used as a benchmark test case, representing approx. 1 square mm of early sensory cortex, containing 77k neurons and 0.3 billion synapses. This is the first true real-time simulation of this model, with 10 s of biological simulation time executed in 10 s wall-clock time. This surpasses best published efforts on HPC neural simulators (3x slowdown) and GPUs ru…
In the study of biological networks, one of the major challenges is to understand the relationships between network structure and dynamics. In this paper, we model in vitro cortical neuronal cultures as stochastic dynamical systems and apply a method that reconstructs directed networks from dynamics [Ching and Tam, Phys. Rev. E 95, 010301(R), 2017] to reveal directed effective connectivity, namely the directed links and synaptic weights, of the neuronal cultures from voltage measurements recorded by a multielectrode array. The effective connectivity so obtained reproduces several features of c…
Self-sustained asynchronous irregular states and Up/Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons
To understand the collective spiking activity in neuronal populations, it is essential to reveal basic circuit variables responsible for these emergent functional states. Here, I develop a mean field theory for the population coupling recently proposed in the studies of visual cortex of mouse and monkey, relating the individual neuron activity to the population activity, and extend the original form to the second order, relating neuron-pair's activity to the population activity, to explain the high order correlations observed in the neural data. I test the computational framework on the salama…
Several studies with brain signals suggested that bottom-up and top-down influences are exerted through distinct frequency bands among visual cortical areas. It has been recently shown that theta and gamma rhythms subserve feedforward, whereas the feedback influence is dominated by the alpha-beta rhythm in primates. A few theoretical models for reproducing these effects have been proposed so far. Here we show that a simple but biophysically plausible two-network motif composed of spiking-neuron models and chemical synapses can exhibit feedforward and feedback influences through distinct freque…
Spiking networks that perform probabilistic inference have been proposed both as models of cortical computation and as candidates for solving problems in machine learning. However, the evidence for spike-based computation being in any way superior to non-spiking alternatives remains scarce. We propose that short-term plasticity can provide spiking networks with distinct computational advantages compared to their classical counterparts. In this work, we use networks of leaky integrate-and-fire neurons that are trained to perform both discriminative and generative tasks in their forward and back…
A Bayes-Markov Neuromorphic Model of Cortical Orientation Selectivity: A Computational Re-implementation and Quantitative Simulation Study
Sharif University of Technology（谢里夫理工大学）；University of Tehran（德黑兰大学）；Islamic Azad University（伊斯兰阿扎德大学）；Pasargad Institute for Advanced Innovative Solutions (PIAIS)（帕萨加德高级创新解决方案研究所）
Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory and decision-making. Yet, very little is known about the network mechanisms responsible for its genesis. It is often assumed that the onset of state sequences is triggered by an external stimulus. Here we show that state sequences can be observed also in the absence of overt sensory stimulation. Analysis of multielectrode recordings from the gustatory cortex…
Spike synchrony, which occurs in various cortical areas in response to specific perception, action and memory tasks, has sparked a long-standing debate on the nature of temporal organization in cortex. One prominent view is that this type of synchrony facilitates the binding or grouping of separate stimulus components. We argue instead for a more general function: A measure of the prior probability of incoming stimuli, implemented by long-range, horizontal, intra-cortical connections. We show that networks of this kind -- pulse-coupled excitatory spiking networks in a noisy environment -- can …
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…
Dynamical Mechanisms for Coordinating Long-term Working Memory Based on the Precision of Spike-timing in Cortical Neurons
Computational Neurobiology Laboratory, Salk Institute for Biological Sciences（计算神经生物学实验室，萨尔克生物科学研究所）；Department of Neurobiology, University of California, San Diego（神经生物学系，加州大学圣地亚哥分校）
During wakefulness and deep sleep brain states, cortical neural networks show a different behavior, with the second characterized by transients of high network activity. To investigate their impact on neuronal behavior, we apply a pairwise Ising model analysis by inferring the maximum entropy model that reproduces single and pairwise moments of the neuron's spiking activity. In this work we first review the inference algorithm introduced in Ferrari,Phys. Rev. E (2016). We then succeed in applying the algorithm to infer the model from a large ensemble of neurons recorded by multi-electrode arra…
Application of deep convolutional spiking neural networks (SNNs) to artificial intelligence (AI) tasks has recently gained a lot of interest since SNNs are hardware-friendly and energy-efficient. Unlike the non-spiking counterparts, most of the existing SNN simulation frameworks are not practically efficient enough for large-scale AI tasks. In this paper, we introduce SpykeTorch, an open-source high-speed simulation framework based on PyTorch. This framework simulates convolutional SNNs with at most one spike per neuron and the rank-order encoding scheme. In terms of learning rules, both spike…
Cortical synapse organization supports a range of dynamic states on multiple spatial and temporal scales, from synchronous slow wave activity (SWA), characteristic of deep sleep or anesthesia, to fluctuating, asynchronous activity during wakefulness (AW). Such dynamic diversity poses a challenge for producing efficient large-scale simulations that embody realistic metaphors of short- and long-range synaptic connectivity. In fact, during SWA and AW different spatial extents of the cortical tissue are active in a given timespan and at different firing rates, which implies a wide variety of loads…
A pressing scientific challenge is to understand how brains work. Of particular interest is the neocortex,the part of the brain that is especially large in humans, capable of handling a wide variety of tasks including visual, auditory, language, motor, and abstract processing. These functionalities are processed in different self-organized regions of the neocortical sheet, and yet the anatomical structure carrying out the processing is relatively uniform across the sheet. We are at a loss to explain, simulate, or understand such a multi-functional homogeneous sheet-like computational structure…
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…
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…
To understand the behavior of a neural circuit it is a presupposition that we have a model of the dynamical system describing this circuit. This model is determined by several parameters, including not only the synaptic weights, but also the parameters of each neuron. Existing works mainly concentrate on either the synaptic weights or the neural parameters. In this paper we present an algorithm to reconstruct all parameters including the synaptic weights of a spiking neuron model. The model based on works of Eugene M. Izhikevich (Izhikevich 2007) consists of two differential equations and cove…
We investigate a recently proposed model for cortical computation which performs relational inference. It consists of several interconnected, structurally equivalent populations of leaky integrate-and-fire (LIF) neurons, which are trained in a self-organized fashion with spike-timing dependent plasticity (STDP). Despite its robust learning dynamics, the model is susceptible to a problem typical for recurrent networks which use a correlation based (Hebbian) learning rule: if trained with high learning rates, the recurrent connections can cause strong feedback loops in the network dynamics, whic…
