Consistency in echo-state networks.

Consistency is an extension to generalized synchronization which quantifies the degree of functional dependency of a driven nonlinear system to its input. We apply this concept to echo-state networks, which are an artificial-neural network version of reservoir computing. Through a replica test, we measure the consistency levels of the high-dimensional response, yielding a comprehensive portrait of the echo-state property.

[1]  Henry Markram,et al.  Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations , 2002, Neural Computation.

[2]  Harald Haas,et al.  Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication , 2004, Science.

[3]  Atsushi Uchida,et al.  Local conditional Lyapunov exponent characterization of consistency of dynamical response of the driven Lorenz system. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[5]  Antonio Politi,et al.  Characterizing the response of chaotic systems. , 2010, Physical review letters.

[6]  Arkady Pikovsky,et al.  Synchronization and desynchronization of self-sustained oscillators by common noise. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Stefano Boccaletti,et al.  Generalized synchronization in mutually coupled oscillators and complex networks. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  J. Teramae,et al.  Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators. , 2004, Physical review letters.

[9]  T. Sejnowski,et al.  Reliability of spike timing in neocortical neurons. , 1995, Science.

[10]  Herbert Jaeger,et al.  Reservoir computing approaches to recurrent neural network training , 2009, Comput. Sci. Rev..

[11]  Arkady Pikovsky,et al.  Interplay of coupling and common noise at the transition to synchrony in oscillator populations , 2016, Scientific Reports.

[12]  H. Abarbanel,et al.  Generalized synchronization of chaos: The auxiliary system approach. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  R. Brockett,et al.  Reservoir observers: Model-free inference of unmeasured variables in chaotic systems. , 2017, Chaos.

[14]  Herbert Jaeger,et al.  Echo State Property Linked to an Input: Exploring a Fundamental Characteristic of Recurrent Neural Networks , 2013, Neural Computation.

[15]  S. Massar,et al.  Mean Field Theory of Dynamical Systems Driven by External Signals , 2012, ArXiv.

[16]  M. C. Soriano,et al.  Consistency properties of chaotic systems driven by time-delayed feedback. , 2018, Physical review. E.

[17]  Stefan J. Kiebel,et al.  Re-visiting the echo state property , 2012, Neural Networks.

[18]  Daniel Brunner,et al.  Conditions for reservoir computing performance using semiconductor lasers with delayed optical feedback. , 2017, Optics express.

[19]  Laurent Larger,et al.  Optimal nonlinear information processing capacity in delay-based reservoir computers , 2014, Scientific Reports.

[20]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[21]  Arkady Pikovsky,et al.  Antireliability of noise-driven neurons. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[23]  Jaideep Pathak,et al.  Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data. , 2017, Chaos.

[24]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[25]  T. Sanger,et al.  Probability density estimation for the interpretation of neural population codes. , 1996, Journal of neurophysiology.

[26]  Kestutis Pyragas Conditional Lyapunov exponents from time series , 1997 .

[27]  Atsushi Uchida,et al.  Consistency and complexity in coupled semiconductor lasers with time-delayed optical feedback. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Debra Rose Wilson,et al.  A Bradford Book , 2011 .

[29]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[30]  L. Appeltant,et al.  Information processing using a single dynamical node as complex system , 2011, Nature communications.

[31]  J. Yorke,et al.  The liapunov dimension of strange attractors , 1983 .

[32]  W. Kinzel,et al.  Strong and weak chaos in nonlinear networks with time-delayed couplings. , 2011, Physical review letters.

[33]  Laurent Larger,et al.  Dynamical complexity and computation in recurrent neural networks beyond their fixed point , 2018, Scientific Reports.

[34]  Ingo Fischer,et al.  Consistency properties of a chaotic semiconductor laser driven by optical feedback. , 2015, Physical review letters.

[35]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[36]  Atsushi Uchida,et al.  Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal. , 2016, Optics express.

[37]  Ulrich Parlitz,et al.  Observing spatio-temporal dynamics of excitable media using reservoir computing. , 2018, Chaos.

[38]  Atsushi Uchida,et al.  Consistency of nonlinear system response to complex drive signals. , 2004 .