Microscopic instability in recurrent neural networks

TL;DR

This paper investigates how individual neuron dynamics can be unstable while the overall neural network remains stable, revealing diverse microscopic states that suggest complex fluctuations in real neural systems.

Contribution

It demonstrates the coexistence of microscopic instability with stable macroscopic dynamics in recurrent neural networks, highlighting the richness of neural fluctuations.

Findings

Microscopic instability can occur in stable macroscopic neural states.

Neural networks exhibit various microscopic dynamical states.

Implications for understanding fluctuations in biological neural systems.

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.