循环神经网络的微观不稳定性
Microscopic instability in recurrent neural networks
摘要：
以类似于气体稳定热力学的分子混沌的方式，神经元系统可能在单个神经元动力学中表现出微观不稳定性，而整个群体的宏观秩序可能保持稳定。在这项研究中，我们分析的微观稳定性的神经元网络的宏观活动服从稳定的动力学，表达单稳态，双稳态，或周期性状态。我们发现，该网络表现出各种动力学状态的微观不稳定性驻留在给定的稳定的宏观动力学。在这样一个简单的随机网络中存在着各种各样的动力学状态，这意味着在真实的神经网络中存在着更丰富的微观波动，而真实的神经网络由更复杂和层次结构化的相互作用组成。
英文摘要：
In a manner similar to the molecular chaos that underlies the stable thermodynamics of gases, neuronal system may exhibit microscopic instability in individual neuronal dynamics while a macroscopic order of the entire population possibly remains stable. In this study, we analyze the microscopic stability of a network of neurons whose macroscopic activity obeys stable dynamics, expressing either monostable, bistable, or periodic state. We reveal that the network exhibits a variety of dynamical states for microscopic instability residing in given stable macroscopic dynamics. The presence of a variety of dynamical states in such a simple random network implies more abundant microscopic fluctuations in real neural networks, which consist of more complex and hierarchically structured interactions.
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