Gradient calculations for dynamic recurrent neural networks: A survey

We survey learning algorithms for recurrent neural networks with hidden units, and put the various techniques into a common framework. We discuss fixed point learning algorithms, namel recurrent back propagation and deterministic Boltzmann Machines, and non-fixed point algorithms, namely back propagation through time, Elman's history cut off, and Jordan's output feedback architecture. Forward propagation, an outline technique that uses adjoint equations, and variations thereof, are also discussed. In many cases, the unified presentation leads to generalizations of carious sorts. We discuss advantages and disadvantages of temporally continuous neural networks in contrast to clocked ones, continue with some "tricks of the trade" for training, using, and simulating continuous time and recurrent neural networks. We present some simulations, and at the end, address issues of computational complexity and learning speed