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arXiv · 1502.01513

Microscopic instability in recurrent neural networks

Yuzuru Yamanaka·Shun-ichi Amari·Shigeru Shinomoto
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Abstract

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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Yuzuru Yamanaka, Shun-ichi Amari, Shigeru Shinomoto. 2015-02-05. Microscopic instability in recurrent neural networks. https://doi.org/10.1103/physreve.91.032921

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