Information Processing Capacity of Dynamical Systems
By Joni Dambre, David Verstraeten, Benjamin Schrauwen, Serge Massar. Scientific Reports, 2012
482 citations recorded by the source corpus.
Many dynamical systems, both natural and artificial, are stimulated by time dependent external signals, somehow processing the information contained therein. We demonstrate how to quantify the different modes in which information can be processed by such systems and combine them to define the computational capacity of a dynamical system. This is bounded by the number of linearly independent state variables of the dynamical system, equaling it if the system obeys the fading memory condition. It can be interpreted as the total number of linearly independent functions of its stimuli the system can compute. Our theory combines concepts from machine learning (reservoir computing), system modeling, stochastic processes and functional analysis. We illustrate our theory by numerical simulations for the logistic map, a recurrent neural network and a two-dimensional reaction diffusion system, uncovering universal trade-offs between the non-linearity of the computation and the system's short-term memory.
Subfields: Artificial Intelligence, Cognitive Neuroscience
View Paper: https://www.semanticscholar.org/paper/c577dbe113809adfdce7fdc3b57f74956e0cde31
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Citations in the corpus
- Physical reservoir computing—an introductory perspective (2020, background): “…is further generalized and extended to be able to evaluate the nonlinear memory capacities by decomposing the function φ into the combinations of multiple orthogonal polynomials [55], and the trade-off between the expressiveness of φ for linear and nonlinear functions is investigated [55, 56].”
- Parallel photonic information processing at gigabyte per second data rates using transient states (2013, background): “Theoretical 8,9 and experimental 7,10–12 investigations show that our scheme can indeed be interpreted as RC.”