Stochastic neural fields as gradient dynamical systems
Stochastic neural fields as gradient dynamical systems
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作为梯度动力系统的随机神经场
DOI：
10.1103/physreve.100.012402
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发表时间：
2019
影响因子：
2.4
通讯作者：
Carroll, Samuel R.
中科院分区：
文献类型：
--
作者：
Bressloff, Paul C.;Carroll, Samuel R.
连续吸引子神经网络被广泛用于模拟各种实验观察到的相干大脑状态，从皮层活动波到静止活动颠簸。后者被认为在各种形式的神经信息处理中发挥重要作用，包括初级视觉皮层（V1）的群体编码和前额叶皮层的工作记忆。然而，连续吸引子网络的一个局限性是，由于固有的网络噪声，活动碰撞（或波）的峰值位置可能会扩散。这反映了凸点解相对于底层连续对称群的作用的边际稳定性。先前的研究已经使用微扰理论推导出一个近似的随机微分方程的峰值（相位）的凸块的位置。虽然该方法捕获了凸块解决方案的扩散漂移，但它忽略了凸块幅度的波动。在本文中，我们展示了如何振幅波动可以通过减少潜在的随机神经场方程到一个有限维的随机梯度动力系统，跟踪随机运动的幅度和相位的凸点解决方案进行分析。这使我们能够推导出稳态概率密度及其矩的精确表达式，然后将其用于研究两个主要问题：（i）神经变异性的输入依赖性抑制和（ii）噪声诱导的过渡到碰撞灭绝。我们通过考虑具有对称性的环形吸引子网络的特定例子来发展理论，这是V1中工作记忆和人口调整的吸引子模型中最常见的体系结构。然而，我们也扩展到一个高维的球形吸引子网络的对称性，这是以前提出的方向和空间频率调谐在V1的模型的分析。因此，我们建立了如何结合随机分析和群论方法提供了一个强大的工具，调查连续吸引子网络中的噪声的影响。
Continuous attractor neural networks are used extensively to model a variety of experimentally observed coherent brain states, ranging from cortical waves of activity to stationary activity bumps. The latter are thought to play an important role in various forms of neural information processing, including population coding in primary visual cortex (V1) and working memory in prefrontal cortex. However, one limitation of continuous attractor networks is that the location of the peak of an activity bump (or wave) can diffuse due to intrinsic network noise. This reflects marginal stability of bump solutions with respect to the action of an underlying continuous symmetry group. Previous studies have used perturbation theory to derive an approximate stochastic differential equation for the location of the peak (phase) of the bump. Although this method captures the diffusive wandering of a bump solution, it ignores fluctuations in the amplitude of the bump. In this paper, we show how amplitude fluctuations can be analyzed by reducing the underlying stochastic neural field equation to a finite-dimensional stochastic gradient dynamical system that tracks the stochastic motion of both the amplitude and phase of bump solutions. This allows us to derive exact expressions for the steady-state probability density and its moments, which are then used to investigate two major issues: (i) the input-dependent suppression of neural variability and (ii) noise-induced transitions to bump extinction. We develop the theory by considering the particular example of a ring attractor network withsymmetry, which is the most common architecture used in attractor models of working memory and population tuning in V1. However, we also extend the analysis to a higher-dimensional spherical attractor network withsymmetry which has previously been proposed as a model of orientation and spatial frequency tuning in V1. We thus establish how a combination of stochastic analysis and group theoretic methods provides a powerful tool for investigating the effects of noise in continuous attractor networks.