Research Article FPGA-Based Stochastic Echo State Networks for Time-Series Forecasting Miquel L. Alomar, Vincent Canals, Nicolas Perez-Mora, Víctor Martínez-Moll, and Josep L. Rosselló Physics Department, University of the Balearic Islands, 07122 Palma de Mallorca, Spain Correspondence should be addressed to Josep L. Rossell´ o; j.rossello@uib.es Received 2 August 2015; Revised 8 October 2015; Accepted 15 October 2015 Academic Editor: Mikhail A. Lebedev Copyright © 2016 Miquel L. Alomar et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Hardware implementation of artifcial neural networks (ANNs) allows exploiting the inherent parallelism of these systems. Nevertheless, they require a large amount of resources in terms of area and power dissipation. Recently, Reservoir Computing (RC) has arisen as a strategic technique to design recurrent neural networks (RNNs) with simple learning capabilities. In this work, we show a new approach to implement RC systems with digital gates. Te proposed method is based on the use of probabilistic computing concepts to reduce the hardware required to implement diferent arithmetic operations. Te result is the development of a highly functional system with low hardware resources. Te presented methodology is applied to chaotic time-series forecasting. 1. Introduction Introduction to Reservoir Computing. Recurrent neural net- works (RNNs) [1] are a class of artifcial neural networks (ANNs) characterized by the existence of closed loops. RNNs are inspired by the way the brain processes information generating dynamic patterns of neuronal activity excited by input sensory signals [2]. Reservoir Computing (RC) [3–10] is a recently introduced efcient technique for implementing and confguring recurrent neural networks (RNNs). It is well suited for applications that require processing time dependent signals such as temporal pattern classifcation and time-series prediction [5]. In an RC system, all the interconnection weights of the RNN are kept fxed and only an output layer is confgurable as illustrated in Figure 1. In recent years, RNNs have been extensively used to successfully solve computationally hard problems [11–15]. Nevertheless, the complex training procedure of RNNs is very time- consuming. On the other hand, RC presents an easy training procedure, which can be performed, in practice, via a simple linear regression. Te RC architecture is composed of three parts: an input layer, the reservoir, and an output layer (see Figure 1). Te input layer feeds the input signals u() = ( 1 (), . . . ,   ()) to the reservoir with fxed random weight connections W in . Te reservoir consists of a relatively large num- ber of randomly interconnected neurons () with states x() = ( 1 (), . . . ,   ()) and internal weights W. Under the infuence of input signals, the network exhibits transient responses which are read out at the output layer y() = ( 1 (), . . . ,   ()) by means of a linear weighted sum of the individual node states. As the only part of the system which is trained (assessment of the output weights W out ) is the output layer, the training does not afect the dynamics of the reservoir itself unless a recurrence exists between the reservoir and the readout (recurrence weights given by W back ). Te general expression to estimate the neuron states is given by x ( + 1) = f (W in u ( + 1) + Wx () + W back y ()), (1) where f = ( 1 ,...,  ) are the neuron transfer functions (typically sigmoidal). In the simplest case of avoiding direct connections between the input and the output layer as well as Hindawi Publishing Corporation Computational Intelligence and Neuroscience Volume 2016, Article ID 3917892, 14 pages http://dx.doi.org/10.1155/2016/3917892