Echo State Network
An Echo State Network (ESN) is a Reservoir Computing Neural Network with a randomly connected hidden layer.
- Context:
- It can be trained by a Echo State Network Training System that applies Echo State Network Training Algorithms.
- Example(s)
- Counter-Example(s)
- a Backpropagation-Decorrelation Network,
- a Bidirectional Associative Memory (BAM) Network,
- a Context Reverberation Network,
- a DAG Recurrent Neural Network,
- an Elman Network,
- a Fractal Prediction Machine,
- a Gated Recurrent Unit (GRU) Network,
- a Hopfield Recurrent Neural Network,
- a Jordan Network,
- a Liquid State Machine,
- a Long Short-Term Memory (LSTM) Network,
- a Nonlinear Transient Computation System,
- a Recurrent Multilayer Perceptron Network,
- a Recursive Neural Network.
- See: Artificial Neural Network, Fully Connected Neural Network Layer, Machine Learning System, Neural Network Training System.
References
2018a
- (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Echo_state_network Retrieved:2018-3-4.
- The echo state network (ESN), [1] [2] is a recurrent neural network with a sparsely connected hidden layer (with typically 1% connectivity). The connectivity and weights of hidden neurons are fixed and randomly assigned. The weights of output neurons can be learned so that the network can (re)produce specific temporal patterns. The main interest of this network is that although its behaviour is non-linear, the only weights that are modified during training are for the synapses that connect the hidden neurons to output neurons. Thus, the error function is quadratic with respect to the parameter vector and can be differentiated easily to a linear system. Alternatively, one may consider a nonparametric Bayesian formulation of the output layer, under which: (i) a prior distribution is imposed over the output weights; and (ii) the output weights are marginalized out in the context of prediction generation, given the training data. This idea has been demonstrated in [3] by using Gaussian priors, whereby a Gaussian process model with ESN-driven kernel function is obtained. Such a solution was shown to outperform ESNs with trainable (finite) sets of weights in several benchmarks.
Some publicly available implementations of ESNs are: (i) aureservoir: an efficient C++ library for various kinds of echo state networks with python/numpy bindings; and (ii) Matlab code: an efficient matlab for an echo state network.
- The echo state network (ESN), [1] [2] is a recurrent neural network with a sparsely connected hidden layer (with typically 1% connectivity). The connectivity and weights of hidden neurons are fixed and randomly assigned. The weights of output neurons can be learned so that the network can (re)produce specific temporal patterns. The main interest of this network is that although its behaviour is non-linear, the only weights that are modified during training are for the synapses that connect the hidden neurons to output neurons. Thus, the error function is quadratic with respect to the parameter vector and can be differentiated easily to a linear system. Alternatively, one may consider a nonparametric Bayesian formulation of the output layer, under which: (i) a prior distribution is imposed over the output weights; and (ii) the output weights are marginalized out in the context of prediction generation, given the training data. This idea has been demonstrated in [3] by using Gaussian priors, whereby a Gaussian process model with ESN-driven kernel function is obtained. Such a solution was shown to outperform ESNs with trainable (finite) sets of weights in several benchmarks.
- ↑ Herbert Jaeger and Harald Haas. Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication. Science 2 April 2004: Vol. 304. no. 5667, pp. 78 – 80 PDF (preprint)
- ↑ Herbert Jaeger (2007) Echo State Network. Scholarpedia.
- ↑ Sotirios P. Chatzis, Yiannis Demiris, “Echo State Gaussian Process,” IEEE Transactions on Neural Networks, vol. 22, no. 9, pp. 1435-1445, Sep. 2011. [1]
2018b
- (Gallicchio et al., 2018) ⇒ Claudio Gallicchio, Alessio Micheli, and Luca Pedrelli. (2018). “Design of Deep Echo State Networks.” In: Neural Networks - Elsevier Journal, 108. doi:10.1016/j.neunet.2018.08.002
2017
- (Miikkulainen, 2017) ⇒ Risto Miikkulainen. (2017). "Reservoir Computing". In: (Sammut & Webb, 2017) DOI:10.1007/978-1-4899-7687-1_731
- QUOTE: Reservoir computing is an approach to sequential processing where recurrency is separated from the output mapping (Jaeger 2003; Maass et al. 2002). The input sequence activates neurons in a recurrent neural network (a reservoir, where activity propagates as in a liquid). The recurrent network is large, nonlinear, randomly connected, and fixed. A linear output network receives activation from the recurrent network and generates the output of the entire machine. The idea is that if the recurrent network is large and complex enough, the desired outputs can likely be learned as linear transformations of its activation. Moreover, because the output transformation is linear, it is fast to train. Reservoir computing has been successful in particular in speech and language processing and vision and cognitive neuroscience.
2013
- (Gallicchio & Micheli, 2013) ⇒ Claudio Gallicchio, and Alessio Micheli. (2013). “Tree Echo State Networks.” In: Neurocomputing Journal, 101. doi:10.1016/j.neucom.2012.08.017
2012
- (Rodan, 2012) ⇒ Ali Rodan. (2012). “Architectural Designs of Echo State Network .” In: Doctoral dissertation, University of Birmingham.
- QUOTE: Reservoir computing (RC) refers to a new class of state-space models with a fixed state transition structure (the “reservoir”) and an adaptable readout from the state space. The reservoir is supposed to be sufficiently complex so as to capture a large number of features of the input stream that can be exploited by the reservoir-to-output readout mapping. The field of RC has been growing rapidly with many successful applications. However, RC has been criticised for not being principled enough. Reservoir construction is largely driven by a series of randomised model building stages, with both researchers and practitioners having to rely on a series of trials and errors. Echo State Networks (ESNs), Liquid State Machines (LSMs) and the back-propagation decorrelation neural network (BPDC) are examples of popular RC methods. In this thesis we concentrate on Echo State Networks, one of the simplest, yet effective forms of reservoir computing.
Echo State Network (ESN) is a recurrent neural network with a non-trainable sparse recurrent part (reservoir) and an adaptable (usually linear) readout from the reservoir. Typically, the reservoir connection weights, as well as the input weights are randomly generated. ESN has been successfully applied in time-series prediction tasks, speech recognition, noise modelling, dynamic pattern classification, reinforcement learning, and in language modelling, and according to the authors, they performed exceptionally well. .
- QUOTE: Reservoir computing (RC) refers to a new class of state-space models with a fixed state transition structure (the “reservoir”) and an adaptable readout from the state space. The reservoir is supposed to be sufficiently complex so as to capture a large number of features of the input stream that can be exploited by the reservoir-to-output readout mapping. The field of RC has been growing rapidly with many successful applications. However, RC has been criticised for not being principled enough. Reservoir construction is largely driven by a series of randomised model building stages, with both researchers and practitioners having to rely on a series of trials and errors. Echo State Networks (ESNs), Liquid State Machines (LSMs) and the back-propagation decorrelation neural network (BPDC) are examples of popular RC methods. In this thesis we concentrate on Echo State Networks, one of the simplest, yet effective forms of reservoir computing.
2008
- (Holzmann, 2008) ⇒ Georg Holzmann (2007, 2008). aureservoir - Efficient C++ library for analog reservoir computing neural networks (Echo State Networks).
- QUOTE: Reservoir computing is a recent kind of recurrent neural network computation, where only the output weights are trained. This has the big advantage that training is a simple linear regression task and one cannot get into a local minimum. Such a network consists of a randomly created, fixed, sparse recurrent reservoir and a trainable output layer connected to this reservoir. Most known types are the “Echo State Network” and the “Liquid State Machine", which achieved very promising results on various machine learning benchmarks.
2007
- (Jaeger, 2007) ⇒ Herbert Jaeger (2007),"Echo state network" Scholarpedia, 2(9):2330. doi:10.4249/scholarpedia.2330
- QUOTE: Echo state networks (ESN) provide an architecture and supervised learning principle for recurrent neural networks (RNNs). The main idea is (i) to drive a random, large, fixed recurrent neural network with the input signal, thereby inducing in each neuron within this "reservoir" network a nonlinear response signal, and (ii) combine a desired output signal by a trainable linear combination of all of these response signals.
The basic idea of ESNs is shared with Liquid State Machines (LSM), which were developed independently from and simultaneously with ESNs by Wolfgang Maass (Maass W., Natschlaeger T., Markram H. 2002). Increasingly often, LSMs, ESNs and the more recently explored Backpropagation Decorrelation learning rule for RNNs (Schiller and Steil 2005) are subsumed under the name of Reservoir Computing. Schiller and Steil (2005) also showed that in traditional training methods for RNNs, where all weights (not only the output weights) are adapted, the dominant changes are in the output weights. In cognitive neuroscience, a related mechanism has been investigated by Peter F. Dominey in the context of modelling sequence processing in mammalian brains, especially speech recognition in humans (e.g., Dominey 1995, Dominey, Hoen and Inui 2006). Dominey was the first to explicitly state the principle of reading out target information from a randomly connected RNN. The basic idea also informed a model of temporal input discrimination in biological neural networks (Buonomano and Merzenich 1995). The earliest known clear formulation of the reservoir computing idea, however, is due to K. Kirby who exposed this concept in a largely forgotten (1 Google cite, as of 2017) conference contribution (Kirby 1991)(...)
- QUOTE: Echo state networks (ESN) provide an architecture and supervised learning principle for recurrent neural networks (RNNs). The main idea is (i) to drive a random, large, fixed recurrent neural network with the input signal, thereby inducing in each neuron within this "reservoir" network a nonlinear response signal, and (ii) combine a desired output signal by a trainable linear combination of all of these response signals.
2003
- (Jaeger, 2003) ⇒ Herbert Jaeger (2003). "Adaptive nonlinear system identification with echo state networks". In: Becker S, Thrun S, Obermayer K (eds) Advances in Neural Information Processing Systems, vol 15. MIT, Cambridge, pp 593–600
2002
- (Maass et al., 2002) ⇒ Wolfgang Maass, Thomas Natschlager, and Henry Markram. (2002) "Real-time computing without stable states: a new framework for neural computation based on perturbations". Neural Comput 14:2531–2560