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Reservoir computing with state-dependent time delay.

G O Danilenko1, A V Kovalev1, D S Citrin2,3

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This study introduces a novel reservoir computing system with state-dependent time delays, enabling nonlinear computation. The system

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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.