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Information processing capacity of dynamical systems

Joni Dambre UGent, David Verstraeten UGent, Benjamin Schrauwen UGent and Serge Massar (2012) SCIENTIFIC REPORTS. 2. p.1-7
abstract
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
MEMORY, NETWORKS, PATTERNS, COMPUTATION
journal title
SCIENTIFIC REPORTS
Sci Rep
volume
2
article_number
514
pages
1 - 7
Web of Science type
Article
Web of Science id
000306708000001
JCR category
MULTIDISCIPLINARY SCIENCES
JCR impact factor
2.927 (2012)
JCR rank
8/56 (2012)
JCR quartile
1 (2012)
ISSN
2045-2322
DOI
10.1038/srep00514
project
IAP, P7-35 photonics@be: Towards smart photonics in 2020
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2972574
handle
http://hdl.handle.net/1854/LU-2972574
date created
2012-08-16 16:18:30
date last changed
2012-10-26 14:16:47
@article{2972574,
  abstract     = {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{\textquoteright}s short-term memory.},
  articleno    = {514},
  author       = {Dambre, Joni and Verstraeten, David and Schrauwen, Benjamin and Massar, Serge},
  issn         = {2045-2322},
  journal      = {SCIENTIFIC REPORTS},
  keyword      = {MEMORY,NETWORKS,PATTERNS,COMPUTATION},
  language     = {eng},
  pages        = {514:1--514:7},
  title        = {Information processing capacity of dynamical systems},
  url          = {http://dx.doi.org/10.1038/srep00514},
  volume       = {2},
  year         = {2012},
}

Chicago
Dambre, Joni, David Verstraeten, Benjamin Schrauwen, and Serge Massar. 2012. “Information Processing Capacity of Dynamical Systems.” Scientific Reports 2: 1–7.
APA
Dambre, J., Verstraeten, D., Schrauwen, B., & Massar, S. (2012). Information processing capacity of dynamical systems. SCIENTIFIC REPORTS, 2, 1–7.
Vancouver
1.
Dambre J, Verstraeten D, Schrauwen B, Massar S. Information processing capacity of dynamical systems. SCIENTIFIC REPORTS. 2012;2:1–7.
MLA
Dambre, Joni, David Verstraeten, Benjamin Schrauwen, et al. “Information Processing Capacity of Dynamical Systems.” SCIENTIFIC REPORTS 2 (2012): 1–7. Print.