陶乐天课题组

发布日期:2018-01-03 来源:本站

北京大学生命科学学院陶乐天课题组近期在Physical Review E上发表了题为“Cusps Enable Line Attractors for Neural Computation”的论文。该工作在脉冲门控同步放电链(pulse-gated synfire chain)的基础上,采取Fokker-Planck方程对前馈神经网络(feed-forward network)的随机放电行为进行解析,揭示了该动力系统中线性吸引子(line attractors)存在的条件,也即信息在前馈神经网络中准确传递的前提条件。

线性吸引子在大脑神经网络中被视作许多大脑功能的动力学基础,比如工作记忆、眼动控制、感觉信号传递等。由于在线性吸引子附近的稳定性,该动力系统的轨线会快速收敛到线性吸引子附近,而后在吸引子上缓慢的移动。这样的行为在神经网络的神经元放电过程中,就对应于前馈神经网络每一层的神经元都可以小误差的保持此前针对不同的外界输入所给出的不同程度的响应。此前,由于其自身动力学性质的限制,synfire chain只能传递“有或无”的二值化信息,不能传递具有多幅值的分层信息来实现更加复杂的计算功能。陶乐天课题组针对此提出了pulse-gated synfire chain模型,并经过大量随机过程模拟验证说明该模型可传递多幅值的信息

本文采取Fokker-Planck方程来描述synfire chain中每一层神经元膜电压的分布函数演化,以此来计算该层实时的放电率,以模拟原本随机的放电过程。在前馈网络里,这是在时间上的函数迭代系统。通过对该系统的降维和分析我们发现线性吸引子由经典的鞍-结分岔所造成。最后结果显示线性吸引子存在且在一定参数范围内稳定,而并不需要准确的参数调节。这也同时揭示了在整个三维的参数空间内该鞍结分岔的结构。

生科院12级本科生肖卓成(现美国亚利桑那大学应用数学系研究生)为本文第一作者,北京计算科学所张继伟教授为第二作者,加州大学戴维斯分校数学系教授Andrew T. Sornborger与陶乐天研究员为共同通讯作者。此项工作得到了国家自然科学基金委、认知神经科学与学习国家重点实验室开放课题基金、北京市科学技术委员会、以及美国国立卫生研究院CRCNS项目的支持。北京大学生科院本科生强化挑战班亦对本文第一作者给予了科研训练与基金支持。


Cusps Enable Line Attractors for Neural Computation

Abstract. Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. Because of their neutral stability along a linear manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. In this paper, we make the connection between line attractors and pulse-gating in feedforward neuronal networks. To understand how pulse-gating manifests itself in a high dimensional, non-linear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze the dynamics of the system. After making a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, we identify an approximate line attractor in state space as the essential structure underlying graded information propagation in our solutions. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the linear manifold defined by the fixed points, the dynamics are slow giving rise to ghost dynamics. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and thus, dynamically control the processing of graded information.

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