Sequential Desynchronization in Networks of Spiking Neurons with Partial Reset

Biologically plausible solutions for spiking networks with efficient coding

Understanding how the dynamics of neural networks is shaped by the computations they perform is a fundamental question in neuroscience. Recently, the framework of efficient coding proposed a theory of how spiking neural networks can compute low-dimensional stimulus signals with high efficiency. Efficient spiking networks are based on time-dependent minimization of a loss function related to information coding with spikes. To inform the understanding of the function and dynamics of biological networks in the brain, however, the mathematical models have to be informed by biology and obey the sam…

A Numerical Study of the Time of Extinction in a Class of Systems of Spiking Neurons

In this paper we present a numerical study of a mathematical model of spiking neurons introduced by Ferrari et al. in an article entitled Phase transition forinfinite systems of spiking neurons. In this model we have a countable number of neurons linked together in a network, each of them having a membrane potential taking value in the integers, and each of them spiking over time at a rate which depends on the membrane potential through some rate function $ϕ$. Beside being affected by a spike each neuron can also be affected by leaking. At each of these leak times, which occurs for a given neu…

High-parallelism Inception-like Spiking Neural Networks for Unsupervised Feature Learning

Spiking Neural Networks (SNNs) are brain-inspired, event-driven machine learning algorithms that have been widely recognized in producing ultra-high-energy-efficient hardware. Among existing SNNs, unsupervised SNNs based on synaptic plasticity, especially Spike-Timing-Dependent Plasticity (STDP), are considered to have great potential in imitating the learning process of the biological brain. Nevertheless, the existing STDP-based SNNs have limitations in constrained learning capability and/or slow learning speed. Most STDP-based SNNs adopted a slow-learning Fully-Connected (FC) architecture an…

模块化架构促进神经元网络中由噪声驱动的同步性控制

Modular architecture facilitates noise-driven control of synchrony in neuronal networks

本研究针对神经科学中网络架构与外部扰动如何调控同步性的难题，结合神经工程实验与模型，揭示模块化架构下外部噪声通过降低突触资源、增加模块间作用随机性促进去同步的机制，并构建介观模型阐明异步输入调控结构化网络动力学的原理。

具有同步突触输入的电导型神经元模型阈下变异性的精确分析

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

本文提出一种基于可交换性和跳跃过程的分析框架，精确计算电导型神经元在同步突触输入下的阈下膜电位变异性，发现异步状态需大突触驱动，而皮层输入需弱同步性。

突触延迟调节振荡兴奋-抑制网络中的群体相位与振幅响应

Synaptic delays modulate population phase and amplitude responses in oscillatory excitatory-inhibitory networks

该研究探究突触延迟对PING regime下兴奋-抑制脉冲网络振荡相位与振幅响应的影响，发现其调节振荡频率与相干性的权衡，为理解振荡脑网络的延迟依赖性调控提供计算框架。

非线性随机积分发放神经元网络中的亚稳态

Metastability in networks of nonlinear stochastic integrate-and-fire neurons

本研究针对单神经元非线性与神经群体集体活动的关联问题，采用随机漏性积分发放模型的场论公式，揭示了非线性尖峰强度与膜电位重置的相互作用可诱发循环网络亚稳态，并对发放率和膜电位产生同向或反向调控效应。

网络中单突触神经元和多突触神经元近似的等价性

Equivalence of approximation by networks of single- and multi-spike neurons

研究探讨了单突触和多突触神经元在近似能力上的等价性，证明两者在机器学习任务中具有相同的能力，从而扩展了单突触神经网络的近似结果。

Synchrony-induced modes of oscillation of a neural field model

We investigate the modes of oscillation of heterogeneous ring-networks of quadratic integrate-and-fire neurons with non-local, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient standing waves with a specific frequency, analogous to those in a tense string. In the neuronal network, the equilibrium corresponds to a spatially homogeneous, asynchronous state. Perturbations of this state excite the network's oscillatory modes, which reflect the interplay of episodes of synchronous spiking with the excitatory-inhibitory spatial interacti…

Entrainment and chaos in a pulse-driven Hodgkin-Huxley oscillator

The Hodgkin-Huxley model describes action potential generation in certain types of neurons and is a standard model for conductance-based, excitable cells. Following the early work of Winfree and Best, this paper explores the response of a spontaneously spiking Hodgkin-Huxley neuron model to a periodic pulsatile drive. The response as a function of drive period and amplitude is systematically characterized. A wide range of qualitatively distinct responses are found, including entrainment to the input pulse train and persistent chaos. These observations are consistent with a theory of kicked osc…

Global solutions with infinitely many blowups in a mean-field neural network

We recently introduced idealized mean-field models for networks of integrate-and-fire neurons with impulse-like interactions -- the so-called delayed Poissonian mean-field models. Such models are prone to blowups: for a strong enough interaction coupling, the mean-field rate of interaction diverges in finite time with a finite fraction of neurons spiking simultaneously. Due to the reset mechanism of integrate-and-fire neurons, these blowups can happen repeatedly, at least in principle. A benefit of considering Poissonian mean-field models is that one can resolve blowups analytically by mapping…