An experimental unification of reservoir computing methods
Abstract
Three different uses of a recurrent neural network (RNN) as a reservoir that is not trained but instead read out by a simple external classification layer have been described in the literature: Liquid State Machines (LSMs), Echo State Networks (ESNs) and the Backpropagation Decorrelation (BPDC) learning rule. Individual descriptions of these techniques exist, but a overview is still lacking. Here, we present a series of experimental results that compares all three implementations, and draw conclusions about the relation between a broad range of reservoir parameters and network dynamics, memory, node complexity and performance on a variety of benchmark tests with different characteristics. Next, we introduce a new measure for the reservoir dynamics based on Lyapunov exponents. Unlike previous measures in the literature, this measure is dependent on the dynamics of the reservoir in response to the inputs, and in the cases we tried, it indicates an optimal value for the global scaling of the weight matrix, irrespective of the standard measures. We also describe the Reservoir Computing Toolbox that was used for these experiments, which implements all the types of Reservoir Computing and allows the easy simulation of a wide range of reservoir topologies for a number of benchmarks.
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A randomly connected circuit model, akin to a 'reservoir' network, can reproduce the observed distribution of timescales, provided that the network operates at the critical point (or 'edge of chaos').
“Finally, we show that a randomly connected circuit model, akin to a “reservoir” network13-15, can reproduce the observed distribution of timescales, provided that the network operates at the critical point (or “edge of chaos”)16-18.”
From A reservoir of time constants for memory traces in cortical neurons (2011) · cites this paper as [15]
Reservoir models predict that the memory of input signals is stored in a large, recurrent and heterogeneous network in a distributed manner, and that a desired output is obtained by a trainable combination of the response signals in the reservoir.
“Those models predict that the memory of input signals is stored in a large, recurrent and heterogeneous network (reservoir), in a distributed manner, and that a desired output is obtained by a trainable combination of the response signals in the reservoir.”
From A reservoir of time constants for memory traces in cortical neurons (2011) · cites this paper as [15]
Reservoir-type networks have been the subject of active research in computational neuroscience and machine learning, but experimental support that such networks are adopted by the brain has been lacking.
“Reservoir-type networks have been the subject of active research in computational neuroscience and machine learning13-15, but so far experimental support that such networks are adopted by the brain has been lacking.”
From A reservoir of time constants for memory traces in cortical neurons (2011) · cites this paper as [15]
Cites
Collective dynamics of ‘small-world’ networks
Watts, D. J., & Strogatz, S. H. (1998) · Nature · doi:10.1038/30918 · Cited by 43,060 · see citing works
The Nature of Statistical Learning Theory
Vapnik, V. N. (1995) · doi:10.1007/978-1-4757-2440-0 · Cited by 39,138 · see citing works
Neural Networks: A Comprehensive Foundation
Haykin, S. (1998) · Cited by 30,070 · see citing works
Seel, N. M. (2012) · Springer eBooks · doi:10.1007/978-1-4419-1428-6_5195 · Cited by 19,525 · see citing works
Advances in Neural Information Processing Systems 14
(2002) · The MIT Press eBooks · doi:10.7551/mitpress/1120.001.0001 · Cited by 9,184 · see citing works
Russell, E. L., Chiang, L. H., & Braatz, R. D. (2000) · Advances in industrial control · doi:10.1007/978-1-4471-0409-4_3 · Cited by 7,938 · see citing works
The Nature of Statistical Learning Theory
Sain, S. R., & Vapnik, V. N. (1996) · Technometrics · doi:10.2307/1271324 · Cited by 4,097 · see citing works
Maass, W., Natschläger, T., & Markram, H. (2002) · Neural Computation · doi:10.1162/089976602760407955 · Cited by 4,025 · see citing works
Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs
Markram, H., Lübke, J., Frotscher, M., & Sakmann, B. (1997) · Science · doi:10.1126/science.275.5297.213 · Cited by 3,832 · see citing works
Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication
Jaeger, H., & Haas, H. (2004) · Science · doi:10.1126/science.1091277 · Cited by 3,811 · see citing works
Perceptrons: An Introduction to Computational Geometry
Minsky, M., & Papert, S. A. (1969) · Cited by 3,273 · see citing works
Nazuno, J. F. (2000) · Computación y Sistemas · Cited by 3,185 · see citing works
Pattern Classification (2nd ed.)
Duda, R. O., Hart, P. E., & Stork, D. G. (1999) · Cited by 2,509 · see citing works
Small worlds: the dynamics of networks between order and randomness
(2000) · Choice Reviews Online · doi:10.5860/choice.37-5722 · Cited by 2,384 · see citing works
<i>Chaos: An Introduction to Dynamical Systems</i>
Alligood, K. T., Sauer, T. D., Yorke, J. A., & Crawford, J. D. (1997) · Physics Today · doi:10.1063/1.882006 · Cited by 1,469 · see citing works
Getting to Know You: Reputation and Trust in a Two-Person Economic Exchange
King-Casas, B., Tomlin, D., Anen, C., Camerer, C. F., Quartz, S. R., & Montague, P. R. (2005) · Science · doi:10.1126/science.1108062 · Cited by 1,345 · see citing works
Gerstner, W. (2009) · Elsevier eBooks · doi:10.1016/b978-008045046-9.01405-4 · Cited by 1,218 · see citing works
(1998) · The MIT Press eBooks · doi:10.7551/mitpress/5704.001.0001 · Cited by 1,129 · see citing works
IEEE 1988 International Conference on Neural Networks
(1988) · doi:10.1109/icnn.1988 · Cited by 890 · see citing works
1995 IEEE International Symposium on Circuits and Systems
(1995) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.1995.523901 · Cited by 725 · see citing works
LSTM recurrent networks learn simple context-free and context-sensitive languages
Gers, F. A., & Schmidhuber, E. (2001) · IEEE Transactions on Neural Networks · doi:10.1109/72.963769 · Cited by 724 · see citing works
Chaos: an introduction to dynamical systems
(1997) · Choice Reviews Online · doi:10.5860/choice.35-0336 · Cited by 715 · see citing works
IEEE International Conference on Neural Networks
(1993) · doi:10.1109/icnn.1993 · Cited by 550 · see citing works
New results on recurrent network training: unifying the algorithms and accelerating convergence
Atiya, A. F., & Parlos, A. G. (2000) · IEEE Transactions on Neural Networks · doi:10.1109/72.846741 · Cited by 522 · see citing works
Small Worlds: The Dynamics of Networks between Order and Randomness.
Grossman, J. W., & Watts, D. J. (2000) · American Mathematical Monthly · doi:10.2307/2589138 · Cited by 475 · see citing works
Jaeger, H. (2007) · Scholarpedia · doi:10.4249/scholarpedia.2330 · Cited by 459 · see citing works
An application of recurrent nets to phone probability estimation
Robinson, A. J. (1994) · IEEE Transactions on Neural Networks · doi:10.1109/72.279192 · Cited by 441 · see citing works
A computational model of filtering, detection, and compression in the cochlea
Lyon, R. F. (2005) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.1982.1171644 · Cited by 420 · see citing works
Proceedings of the International Conference on Artificial Neural Networks
Dorffner, G., Bischof, H., & Hornik, K. (2001) · Cited by 377 · see citing works
Moore, K. L. (1992) · IEEE Potentials · doi:10.1109/45.127697 · Cited by 319 · see citing works
Isolated word recognition with the Liquid State Machine: a case study
Verstraeten, D., Schrauwen, B., Stroobandt, D., & Campenhout, J. V. (2005) · Information Processing Letters · doi:10.1016/j.ipl.2005.05.019 · Cited by 263 · see citing works
Self-citationBackpropagation-decorrelation: online recurrent learning with O(N) complexity
Steil, J. J. (2005) · IEEE International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2004.1380039 · Cited by 206 · see citing works
Short term memory in echo state networks
Jaeger, H. (2022) · Fraunhofer-Publica (Fraunhofer-Gesellschaft) · doi:10.24406/publica-fhg-291107 · Cited by 197 · see citing works
A tighter bound for the echo state property
Buehner, M. R., & Young, P. M. (2006) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2006.872357 · Cited by 154 · see citing works
BSA, a fast and accurate spike train encoding scheme
Schrauwen, B., & Campenhout, J. V. (2004) · doi:10.1109/ijcnn.2003.1224019 · Cited by 147 · see citing works
Self-citationNoisy Spiking Neurons with Temporal Coding have more Computational Power than Sigmoidal Neurons
Maass, W. (1996) · neural information processing systems · Cited by 146 · see citing works
Artificial Neural Networks for Modeling and Control of Non-Linear Systems
Suykens, J. A. K., Vandewalle, J. P. L., & Moor, B. D. (1995) · Cited by 146 · see citing works
Nonlinear modeling : advanced black-box techniques
Suykens, J. A. K., & Vandewalle, J. P. L. (1998) · Medical Entomology and Zoology · Cited by 137 · see citing works
Markram, H., Pikus, D., Gupta, A., & Tsodyks, M. V. (1998) · Neuropharmacology · doi:10.1016/s0028-3908(98)00049-5 · Cited by 122 · see citing works
The Dynamic Universality of Sigmoidal Neural Networks
Kilian, J., & Siegelmann, H. T. (1996) · Information and Computation · doi:10.1006/inco.1996.0062 · Cited by 119 · see citing works
Biologically Plausible Speech Recognition with LSTM Neural Nets
Graves, A., Eck, D., Beringer, N., et al. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-27835-1_10 · Cited by 108 · see citing works
What Makes a Dynamical System Computationally Powerful?
Legenstein, R. A., & Maass, W. (2006) · The MIT Press eBooks · doi:10.7551/mitpress/4977.003.0008 · Cited by 106 · see citing works
Reservoir riddles: suggestions for echo state network research (extended abstract)
Jaeger, H. (2006) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2005.1556090 · Cited by 95 · see citing works
Fading memory and kernel properties of generic cortical microcircuit models
Maass, W., Natschläger, T., & Markram, H. (2004) · Journal of Physiology-Paris · doi:10.1016/j.jphysparis.2005.09.020 · Cited by 90 · see citing works
Simple Recurrent Networks Learn Context-Free and Context-Sensitive Languages by Counting
Rodriguez, P. F. (2001) · Neural Computation · doi:10.1162/089976601750399326 · Cited by 84 · see citing works
A Model for Real-Time Computation in Generic Neural Microcircuits
Maass, W., Natschläger, T., & Markram, H. (2002) · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · Cited by 81 · see citing works
New Directions In Statistical Signal Processing: From Systems To Brains
Haykin, S., Príncipe, J. C., B, T. J. S. A., & McWhirter, J. G. (2009) · Medical Entomology and Zoology · Cited by 73 · see citing works
Computer Models and Analysis Tools for Neural Microcircuits
Natschläger, T., Markram, H., & Maass, W. (2003) · Springer eBooks · doi:10.1007/978-1-4615-1079-6_9 · Cited by 63 · see citing works
Minimum mean squared error time series classification using an echo state network prediction model
Skowronski, M. D., & Harris, J. G. (2006) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2006.1693294 · Cited by 62 · see citing works
Bertschinger, N., Natschläger, T., & Legenstein, R. A. (2004) · neural information processing systems · Cited by 60 · see citing works
Synergies between Intrinsic and Synaptic Plasticity in Individual Model NeuronsPreprint
Triesch, J. (2004) · Cited by 55 · see citing works
Online stability of backpropagation–decorrelation recurrent learning
Steil, J. J. (2006) · Neurocomputing · doi:10.1016/j.neucom.2005.12.012 · Cited by 50 · see citing works
Slaney, M. (1997) · Cited by 47 · see citing works
Modeling reward functions for incomplete state representations via echo state networks
Bush, K., & Anderson, C. W. (2005) · IEEE International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2005.1556402 · Cited by 44 · see citing works
Movement Generation and Control with Generic Neural Microcircuits
Joshi, P., & Maass, W. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-27835-1_20 · Cited by 43 · see citing works
A New Approach towards Vision Suggested by Biologically Realistic Neural Microcircuit Models
Maass, W., Legenstein, R. A., & Markram, H. (2002) · Lecture notes in computer science · doi:10.1007/3-540-36181-2_28 · Cited by 42 · see citing works
Reservoir Computing with Stochastic Bitstream Neurons
Verstraeten, D., Schrauwen, B., & Stroobandt, D. (2005) · Cited by 37 · see citing works
Self-citationMemory in Backpropagation-Decorrelation O(N) Efficient Online Recurrent Learning
Steil, J. J. (2005) · Lecture notes in computer science · doi:10.1007/11550907_103 · Cited by 22 · see citing works
Constructing deterministic finite-state automata in sparse recurrent neural networks
Omlin, C. W. P., & Giles, C. L. (2002) · doi:10.1109/icnn.1994.374417 · Cited by 19 · see citing works
Accelerating Event Based Simulation for Multi-synapse Spiking Neural Networks
D’Haene, M., Schrauwen, B., & Stroobandt, D. (2006) · Lecture notes in computer science · doi:10.1007/11840817_79 · Cited by 6 · see citing works
Self-citation
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Reservoir computing approaches to recurrent neural network training
Lukoševičius, M., & Jaeger, H. (2009) · Computer Science Review · doi:10.1016/j.cosrev.2009.03.005 · Cited by 2,956 · see citing works
The Functional Benefits of Criticality in the Cortex
Shew, W. L., & Plenz, D. (2013) · The Neuroscientist · doi:10.1177/1073858412445487 · Cited by 607 · see citing works
Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning
Fujii, K., & Nakajima, K. (2017) · Physical Review Applied · doi:10.1103/physrevapplied.8.024030 · Cited by 337 · see citing works
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Nakajima, K., Hauser, H., Li, T., & Pfeifer, R. (2015) · Scientific Reports · doi:10.1038/srep10487 · Cited by 324 · see citing works
A reservoir of time constants for memory traces in cortical neurons
Bernacchia, A., Seo, H., Lee, D., & Wang, X.-J. (2011) · Nature Neuroscience · doi:10.1038/nn.2752 · Cited by 292 · see citing works
A soft body as a reservoir: case studies in a dynamic model of octopus-inspired soft robotic arm
Nakajima, K., Hauser, H., Kang, R., Guglielmino, E., Caldwell, D. G., & Pfeifer, R. (2013) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2013.00091 · Cited by 180 · see citing works
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Nakajima, K., Li, T., Hauser, H., & Pfeifer, R. (2014) · Journal of The Royal Society Interface · doi:10.1098/rsif.2014.0437 · Cited by 128 · see citing works
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Alomar, M. L., Canals, V., Martinez-Moll, V., & Rossello, J. L. (2014) · 2014 24th International Workshop on Power and Timing Modeling, Optimization and Simulation (PATMOS) · doi:10.1109/patmos.2014.6951899 · Cited by 20 · see citing works
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Pau, D., Khiari, A., & Denaro, D. (2021) · 2021 IEEE 11th International Conference on Consumer Electronics (ICCE-Berlin) · doi:10.1109/icce-berlin53567.2021.9720009 · Cited by 21 · see citing works
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- Authors
- Verstraeten, D., Schrauwen, B., D’Haene, M., & Stroobandt, D.
- Affiliations
- Ghent University (BE)
- Corresponding author
- Verstraeten, D.
- ORCID
- Stroobandt, D.
- Venue
- Neural Networks
- Publisher
- Elsevier BV
- Published
- 2007-04
- Volume
- 20
- Issue
- 3
- Pages
- 391-403
- ISSN
- 0893-6080 (ISSN-L)
- OpenAlex
- W2036451492
- Cited by
- 1,135
- References
- 60
- Citations by year
- 2026: 66 · 2025: 113 · 2024: 118 · 2023: 90 · 2022: 86 · 2021: 85 · 2020: 71 · 2019: 86 · 2018: 62 · 2017: 45 · 2016: 36 · 2015: 47 · 2014: 40 · 2013: 41 · 2012: 48
- FWCI
- 28.77
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Networks (publishedVersion)
- PubMed (publishedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion)
- Funders
- Fonds Wetenschappelijk Onderzoek
- Vlaamse regering
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Reservoir Computing
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Memory and Neural Computing
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- reservoir computing, recurrent neural networks, liquid state machines, echo state networks, reservoir dynamics, Lyapunov exponents, memory, benchmark comparison
- MeSH terms
- Humans, Memory, Pattern Recognition, Automated, Information Storage and Retrieval, Neural Networks, Computer, Nonlinear Dynamics
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