Echo state network

The echo state network (ESN) is a recurrent neural network with a sparsely connected hidden layer (with typically 1% connectivity). The connectivity and weights of hidden neurons are randomly assigned and are fixed. 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 parameters are the weights of the output layer. The error function is thus quadratic with respect to the parameter vector and can be differentiated easily to a linear system.

See also

• Liquid-state machine: a similar concept with generalized signal and network.
• Reservoir computing
• aureservoir: an efficient C++ library for various kinds of echo state networks with python/numpy bindings.
• Matlab code: an efficient matlab for an echo state network
• Extreme Learning Machines

References

• 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 doi:10.1126/science.1091277PDF (preprint)
• Herbert Jaeger (2007) Echo State Network. Scholarpedia.