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DY: Fachverband Dynamik und Statistische Physik

DY 42: Focus Session: Computing with Dynamical Systems: New Perspectives on Reservoirs and Applications I – Fundamentals

DY 42.3: Talk

Thursday, March 21, 2024, 10:15–10:30, BH-N 243

Generation of persistent memory using stable chaos in random neural networks — •Hiromichi Suetani — Faculty of Science and Technology, Oita University, Oita, Japan — International Research Center for Neurointelligence, The University of Tokyo, Tokyo, Japan

In high-dimensional nonlinear dynamical systems, it is well established that even when fixed points or (quasi) periodic orbits serve as stable attractors, the system often undergoes prolonged irregular transient states before settling into the attractor. This phenomenon is known as super transient chaos. Particularly within coupled dynamical systems comprising elements characterized by strong nonlinearities such as discontinuous changes, they may display unstable transient states concerning finite perturbations, despite their linear stability to infinitely small perturbations. This phenomenon is termed stable chaos.

In this study, we explore a version of random neural networks. We begin by quantifying trajectory instability using the finite-size Lyapunov exponent (FSLE) and presenting the corresponding phase diagram. Our findings confirm the presence of stable chaos in the critical region between periodic attractors and super-transient chaos. Additionally, introducing external input shows that stable chaos achieves generalized synchronization at a lower amplitude than super-transient chaos. Employing the reservoir computing framework, we reveal the utility of stable chaos in information processing tasks such as the delayed classification of nonlinear signals.

Keywords: stable chaos; random neural networks; memory; reservoir computing