Feedback Coupling Induced Synchronization of Neural Networks.

Synchronization emerges ubiquitously in natural and engineering systems and at different scales. For real-world systems with invisible governing equations, recurrent neural networks provide effective approach to embed their dynamics from observations and facilitate intensive study, including the synchronization and its mechanisms. Synchronization at a scale of neural networks’ dynamics instead of the component neurons’ has seldom been studied. Here, we define the synchronization of reservoir computers at a macroscopic level, named by hyper-synchronization, from a viewpoint of dynamical systems theory. HyperSync is realized, with a merged attractor emerging, in reservoir computers trained by different chaotic systems through a proposed feedback coupling mechanism. Numerical experiments demonstrate its effectiveness, and we further provide guidance for realizing synchronization among multiple reservoir computers coupled with different topologies. This work articulates an appealing framework to realize synchronization of neural networks and anticipates potential applications in fields such as communications and biological systems.