1 A tutorial on training recurrent neural networks, covering BPPT, RTRL, EKF and the "echo state network" approach Herbert Jaeger Fraunhofer Institute for Autonomous Intelligent Systems (AIS) since 2003: International University Bremen First published: Oct. 2002 First revision: Feb. 2004 Second revision: March 2005 Third revision: April 2008 Forth revision: July 2013 Fifth revision: Dec 2013 Abstract: This tutorial is a worked-out version of a 5-hour course originally held at AIS in September/October 2002. It has two distinct components. First, it contains a mathematically-oriented crash course on traditional training methods for recurrent neural networks, covering back-propagation through time (BPTT), real-time recurrent learning (RTRL), and extended Kalman filtering approaches (EKF). This material is covered in Sections 2 – 5. The remaining sections 1 and 6 – 9 are much more gentle, more detailed, and illustrated with simple e
