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Echo State Networks

What are Echo State Networks?

Echo State Networks (ESNs) are a kind of Recurrent Neural Network with a sparsely hidden layer (it usually has less than 10% connectivity). They essentially give an architecture and a supervised learning principle for RNNs and are part of the reservoir computing framework. 

The connectivity and weights of the hidden layer’s (reservoir) neurons are fixed (not trainable) and they are randomly assigned. The output neurons have weights that are trainable and can be learned so that the network is capable to produce or reproduce particular temporal patterns.

The reservoir architecture creates a nonlinear embedding of the input. This is connected to the output that is needed and then the final weights are capable of being trained.

So, the aim of Echo State Networks is to drive a big, random, fixed RNN with the input signal, thus inducing a nonlinear response signal in every neuron in the reservoir and connect it to a desired output signal using a trainable linear combination of all of the response signals.

What is the Echo State Property?

For the Echo State Network to work, the reservoir needs to have the Echo State Property (ESP). This property relates asymptotic properties of the excited reservoir dynamics to the driving signal.

The property states that the reservoir asymptotically washes out any information from initial conditions. 

This property is guaranteed for additive-sigmoid neuron reservoirs, when the reservoir weight matrix and the leaking rates fulfill specific algebraic conditions in terms of singular values.

In reservoirs that have a tanh sigmoid, the Echo State Property gets violated for zero input if the spectral radius of the reservoir weight matrix is more than unity. The converse also holds true. If for any input if this spectral radius is less than unity, the ESP is granted.

Why should you use Echo State Networks?

Echo State Networks do not suffer from the vanishing/exploding gradient problem which causes the parameters in the hidden layers either to not change much or lead to numeric instability and chaotic behavior.

While traditional neural networks are computationally expensive, ESNs tend to be fast due to the lack of a backpropagation phase on the reservoir.

Echo State Networks are effective at handling chaotic time series and are not disrupted by bifurcations, unlike traditional neural networks.



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Echo State Networks

October 14, 2020

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Key takeawaysCollaboration platforms are essential to the new way of workingEmployees prefer engati over emailEmployees play a growing part in software purchasing decisionsThe future of work is collaborativeMethodology

What are Echo State Networks?

Echo State Networks (ESNs) are a kind of Recurrent Neural Network with a sparsely hidden layer (it usually has less than 10% connectivity). They essentially give an architecture and a supervised learning principle for RNNs and are part of the reservoir computing framework. 

The connectivity and weights of the hidden layer’s (reservoir) neurons are fixed (not trainable) and they are randomly assigned. The output neurons have weights that are trainable and can be learned so that the network is capable to produce or reproduce particular temporal patterns.

The reservoir architecture creates a nonlinear embedding of the input. This is connected to the output that is needed and then the final weights are capable of being trained.

So, the aim of Echo State Networks is to drive a big, random, fixed RNN with the input signal, thus inducing a nonlinear response signal in every neuron in the reservoir and connect it to a desired output signal using a trainable linear combination of all of the response signals.

What is the Echo State Property?

For the Echo State Network to work, the reservoir needs to have the Echo State Property (ESP). This property relates asymptotic properties of the excited reservoir dynamics to the driving signal.

The property states that the reservoir asymptotically washes out any information from initial conditions. 

This property is guaranteed for additive-sigmoid neuron reservoirs, when the reservoir weight matrix and the leaking rates fulfill specific algebraic conditions in terms of singular values.

In reservoirs that have a tanh sigmoid, the Echo State Property gets violated for zero input if the spectral radius of the reservoir weight matrix is more than unity. The converse also holds true. If for any input if this spectral radius is less than unity, the ESP is granted.

Why should you use Echo State Networks?

Echo State Networks do not suffer from the vanishing/exploding gradient problem which causes the parameters in the hidden layers either to not change much or lead to numeric instability and chaotic behavior.

While traditional neural networks are computationally expensive, ESNs tend to be fast due to the lack of a backpropagation phase on the reservoir.

Echo State Networks are effective at handling chaotic time series and are not disrupted by bifurcations, unlike traditional neural networks.



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