神经网络动力学的势能地貌与环流理论

发布时间：2018-04-25 01:31

本文选题：能量地貌与环流 + 神经网络　；参考：《吉林大学》2016年博士论文

【摘要】：理解人类大脑的功能一直都是当今科学界的一大重要目标。最近几年,人们在理论和实验神经科学领域都取得了巨大的成绩。尽管人们已经做了很多有意义的工作,关于大脑行为与功能的全局和物理角度的理解对于我们仍是巨大的挑战。在本文中,为了面对这一挑战,我们构建了普适的非平衡态神经网络地貌与环流理论进一步建立起理论预测结果与实验观测结果之间的联系。在之前的研究工作中,大脑的记忆与学习过程通过对称连接神经网络中所构建的平衡态能量来定量描述。各个能量的吸引子存储着不同的记忆,记忆检索的动力学过程是由能量的梯度力决定的。然而在真实的神经网络中,神经元之间通常都是非对称连接的,而且与生理韵律调控相关的振荡行为在对称的神经网络中也并不会出现。这里我们首先为普通的神经网络系统发展了一套普适的非平衡态地貌与环流理论。为量化网络系统的全局稳定性和功能,我们定量求解出了与系统稳态概率分布相关的势能地貌和相应的Lyapunov函数。我们发现大脑中的神经元振荡活动不仅由地貌的梯度力决定同时也由环流所决定。我们发现回旋环流源自于网络的非对称连接部分。神经振荡的地貌展现出了一个闭合环状吸引子的拓扑形状。在被势能地貌的梯度力吸引到环上后,环流作为主要的驱动力驱使系统做周期振荡运动。我们发现环流力可能为不同记忆间的联系提供了驱动力。接下来,我们利用地貌理论探讨了一个与做决定相关的神经网络。与关联记忆的网络相似,如做决定等大脑认知功能可以通过吸引子动力学所描述。然而相应量化的吸引子地貌却仍然没有给出过。这里我们量化了做决定过程的势能地貌并在地貌中量化了从未决定态到决定态这一做决定过程的最优路径。我们定量讨论了做决定时速度,准确性与能量消耗三者间的权衡问题。此外,我们也讨论了做决定过程中改变主意的机制。我们还将势能地貌与环流理论应用到了基底节神经环路这一运动调控网络来探索其相应机制,特别是帕金森症里出现的异常同步振荡活动的相应机制。我们发现因多巴胺耗竭而出现异常振荡活动时,网络的势能地貌是一个墨西哥草帽状的闭合环形山谷。量化的地貌和环流可以直接反映出网络中突触连接和外部输入变化是如何影响系统的动力学行为的。我们定量研究了脑深部刺激术(DBS)对帕金森症的治疗机制,即其可以有效减小环路中的同步振荡活动。我们的方法为定量研究神经网络提供了一个普适的方法,其也可能有助于发现更有效的治疗运动障碍的疗法。
[Abstract]:Understanding the functioning of the human brain has always been a major goal of today's scientific community. In recent years, great achievements have been made in the field of theoretical and experimental neuroscience. Although a lot of meaningful work has been done, understanding the global and physical aspects of brain behavior and function remains a huge challenge. In this paper, in order to face this challenge, we construct a universal nonequilibrium neural network geomorphology and circulation theory to further establish the relationship between theoretical prediction results and experimental observation results. In previous studies, the brain's memory and learning processes were quantitatively described by the energy of the equilibrium state constructed in the symmetrically connected neural network. Different energy attractors store different memories. The dynamic process of memory retrieval is determined by the gradient force of energy. However, in real neural networks, the connections between neurons are usually asymmetric, and oscillatory behaviors associated with physiological prosody regulation do not occur in symmetric neural networks. Here we first develop a set of universal nonequilibrium geomorphology and circulation theory for ordinary neural network systems. In order to quantify the global stability and function of the network system, we quantitatively solve the potential energy geomorphology and the corresponding Lyapunov function related to the steady probability distribution of the system. We find that the oscillatory activity of neurons in the brain is determined not only by the gradient force of the geomorphology but also by the circulation. We find that the circumferential circulation originates from the asymmetric connection of the network. The physiognomy of neural oscillations shows the topological shape of a closed ring attractor. After being attracted to the ring by the gradient force of the potential geomorphology, the circulation drives the system to oscillate periodically as the main driving force. We find that the circulation force may provide a driving force for the relationship between different memories. Next, we discuss a decision-making neural network using geomorphological theory. Similar to the network of associated memory, cognitive functions such as decision making can be described by attractor dynamics. However, the corresponding quantized attractor geomorphology has not been given. Here we quantify the potential energy geomorphology of the decision making process and quantify the optimal path of the decision making process from the never determined state to the decision state in the geomorphology. We quantitatively discuss the tradeoff between speed, accuracy and energy consumption in making decisions. In addition, we discussed the mechanism of change of mind in the process of making a decision. We also apply the theory of potential energy geomorphology and circulation to the basal ganglion loop to explore the corresponding mechanism, especially the mechanism of abnormal synchronous oscillation in Parkinson's disease. We found that the potential energy landform of the network is a closed circular valley in the shape of a Mexican straw cap when abnormal oscillations occur due to the depletion of dopamine. The quantitative geomorphology and circulation can directly reflect how the changes of synaptic connections and external inputs in the network affect the dynamic behavior of the system. We quantitatively studied the therapeutic mechanism of deep brain stimulation (DBS) for Parkinson's disease, that is, it can effectively reduce the synchronous oscillation activity in the loop. Our method provides a general method for quantitative study of neural networks, which may also contribute to the discovery of more effective treatments for dyskinesia.
【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O175;TP183

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