Noisy Adaptation Generates Lévy Flights in Attractor Neural Networks
Authors: Xingsi Dong, Tianhao Chu, Tiejun Huang, Zilong Ji, Si Wu

Lévy flights describe a special class of random walks whose step sizes satisfy a power-law tailed distribution. As being an efficientsearching strategy in unknown environments, Lévy flights are widely observed in animal foraging behaviors. Recent studies further showed that human cognitive functions also exhibit the characteristics of Lévy flights.  Despite being a general phenomenon, the neural mechanism at the circuit level for generating Lévy flights remains unresolved. Here, we investigate how Lévy flights can be achieved in attractor neural networks. To elucidate the underlying mechanism clearly, we first study continuous attractor neural networks (CANNs), and find that noisy neural adaptation, exemplified by spike frequency adaptation (SFA) in this work,  can generate Lévy flights representing transitions of the network state in the attractor space. Specifically, the strength of SFA defines a travelling wave boundary, below which the network state displays local Brownian motion, and above which the network state displays long-jump motion. Noises in neural adaptation causes the network state to intermittently switch between these two motion modes, manifesting the characteristics of Lévy flights. We further extend the study to a general attractor neural network, and demonstrate that our model can explain the Lévy-flight phenomenon observed during free memory retrieval of humans. We hope that this study will give us insight into understanding the neural mechanism for optimal information processing in the brain.