Reservoir computing with state-dependent time delay

Area of Science:

• Nonlinear dynamics
• Computational neuroscience
• Reservoir computing

Background:

• Reservoir computing (RC) leverages the dynamics of complex systems for computation.
• Traditional RC often relies on fixed or randomly connected recurrent neural networks.
• Exploring novel system designs for enhanced computational capabilities is crucial.

Purpose of the Study:

• To introduce and analyze a new reservoir computing design based on a linear dynamical system with state-dependent feedback delay.
• To investigate the computational potential arising from the emergent nonlinearity in this system.
• To demonstrate the tunability of the system's nonlinearity and memory capacity.

Main Methods:

• Design of a dynamical system with a state-dependent time delay.
• Analysis of system dynamics, including Hopf bifurcations.
• Benchmarking computational performance on tasks like delayed XOR, Iris classification, and time-series prediction.

Main Results:

• The system exhibits emergent nonlinearity despite its apparent linearity, suitable for time-delay reservoir computing.
• Close multiple Hopf bifurcation points result in a sawtooth-shaped transient response beneficial for computation.
• The system's memory capacity and nonlinearity can be effectively tuned by adjusting the time-delay dependence.

Conclusions:

• The proposed state-dependent time-delay reservoir computing system offers a novel approach to harnessing nonlinear dynamics for computation.
• The system's tunable nonlinearity and memory capacity present opportunities for advanced information processing.
• This design provides a flexible platform for exploring the interplay between dynamics and computation.