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Title:
Nonequilibrium neural network dynamics and thermodynamics revealed by the global landscape and flux quantifications
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Abstract:
The brain map project aims to map out the neuron connections of the human brain. Even with all the wirings mapped out, the global and physical understandings of the function and behavior are still challenging. Hopfield quantified the learning and memory process of symmetrically connected neural networks globally through equilibrium energy. The energy basins of attractions represent memories and the memory retrieval dynamics is determined by the energy gradient. However, the realistic neural networks are asymmetrically connected and oscillations cannot emerge from symmetric neural networks. Here, we developed a non-equilibrium landscape-flux theory for realistic asymmetrically connected neural networks [1]. We uncovered the underlying potential landscape and the associated Lyapunov function for quantifying the global stability and function. We found the dynamics and oscillations responsible for cognitive processes and physiological rhythm regulations are determined not only by the landscape gradient but also by the flux. We found that the flux is closely related to the degrees of the asymmetrical connections in neural networks and is the origin of the neural oscillations. The neural oscillation landscape shows a closed ring attractor topology. The landscape gradient attracts the network down to the ring. The flux is responsible for coherent oscillations on the ring. We suggest the flux may provide the driving force for associations among memories. We applied our theory to rapid eye movement (REM) sleep cycle. We identified the key regulation factors for function through global sensitivity analysis of landscape topography against wirings. Our predictions are consistent with experimental observations.
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