A Novel Method for Training an Echo State Network with Feedback-Error Learning

Echo state networks are a relatively new type of recurrent neural networks that have shown great potentials for solving non-linear, temporal problems. The basic idea is to transform the low dimensional temporal input into a higher dimensional state, and then train the output connection weights to make the system output the target information. Because only the output weights are altered, training is typically quick and computationally efficient compared to training of other recurrent neural networks. This paper investigates using an echo state network to learn the inverse kinematics model of a robot simulator with feedback-error-learning. In this scheme teacher forcing is not perfect, and joint constraints on the simulator makes the feedback error inaccurate. A novel training method which is less influenced by the noise in the training data is proposed and compared to the traditional ESN training method. 1. Introduction A recurrent neural network (RNN) is a neural network with feedback connections. Mathematically RNNs implement dynamical systems, and in theory they can approximate arbitrary dynamical systems with arbitrary precision [1]. This makes them “in principle promising” as solutions for difficult temporal tasks, but in practice, supervised training of RNNs is difficult and computationally expensive. Echo state networks (ESNs) were proposed as a cheap and fast architectural and supervised learning scheme and are therefore suggested to be useful in solving real problems [2]. The basic idea is to transform the low dimensional temporal input into a higher dimensional echo state, and then train the output connection weights to make the system output the desired information. The idea was independently developed by Maass [3] and Jaeger [4] as liquid state machine (LSM) and echo state machine (ESM), respectively. LSMs and ESMs, together with the more recently explored Backpropagation Decorrelation learning rule for RNNs [5], are given the generic term reservoir computing [6]. Typically large, complex RNNs are used as reservoirs, and their function resembles a tank of liquid. One can think of the input as stones thrown into the liquid, creating unique ripples that propagate, interact, and eventually fade away. After learning how to read the water’s surface, one can extract a lot of information about recent events, without having to do the complex input integration. Real water has successfully been used as a reservoir [7]. Because only the output weights are altered, training is typically quick and computationally efficient compared to training of other