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A Principled Dimension-Reduction Method for the Population Density Approach to Modeling Networks of Neurons with Synaptic Dynamics

机译:带有神经元网络的突触动力学建模的人口密度方法的原理降维方法

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摘要

The population density approach to neural network modeling has been utilized in a variety of contexts. The idea is to group many similar noisy neurons into populations and track the probability density function for each population that encompasses the proportion of neurons with a particular state rather than simulating individual neurons (i.e., Monte Carlo). It is commonly used for both analytic insight and as a time-saving computational tool. The main shortcoming of this method is that when realistic attributes are incorporated in the underlying neuron model, the dimension of the probability density function increases, leading to intractable equations or, at best, computationally intensive simulations. Thus, developing principled dimension-reduction methods is essential for the robustness of these powerful methods. As a more pragmatic tool, it would be of great value for the larger theoretical neuroscience community. For exposition of this method, we consider a single uncoupled population of leaky integrate-and-fire neurons receiving external excitatory synaptic input only. We present a dimension-reduction method that reduces a two-dimensional partial differential-integral equation to a computationally efficient one-dimensional system and gives qualitatively accurate results in both the steady-state and nonequilibrium regimes. The method, termed modified mean-field method, is based entirely on the governing equations and not on any auxiliary variables or parameters, and it does not require fine-tuning. The principles of the modified mean-field method have potential applicability to more realistic (i.e., higher-dimensional) neural networks.
机译:用于神经网络建模的人口密度方法已在多种情况下使用。想法是将许多类似的嘈杂神经元分组为种群,并跟踪每个种群的概率密度函数,该函数包括具有特定状态的神经元的比例,而不是模拟单个神经元(即,蒙特卡洛)。它通常用于分析洞察力和节省时间的计算工具。该方法的主要缺点是,当将现实属性合并到基本神经元模型中时,概率密度函数的维数会增加,从而导致难以求解的方程式或至多只能产生计算密集型的模拟。因此,开发有原则的降维方法对于这些强大方法的鲁棒性至关重要。作为更实用的工具,它对于更大的理论神经科学界将具有巨大的价值。为了说明这种方法,我们考虑了一个仅接收外部兴奋性突触输入的泄漏的整合与发射神经元的单个未耦合种群。我们提出了一种降维方法,该方法将二维偏微分积分方程简化为计算有效的一维系统,并在稳态和非平衡状态下都给出了定性准确的结果。该方法称为修正均值场方法,完全基于控制方程,而不基于任何辅助变量或参数,并且不需要微调。改进的均值场方法的原理具有潜在的适用性,可应用于更现实的(即高维)神经网络。

著录项

  • 来源
    《Neural computation》 |2013年第10期|2682-2708|共27页
  • 作者

    Cheng Ly;

  • 作者单位

    Department of Statistical Sciences and Operations Research, Virginia Commonwealth University Richmond, VA 23284-3083, U.S.A.;

  • 收录信息 美国《科学引文索引》(SCI);美国《化学文摘》(CA);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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