Pii: S0893-6080(98)00018-5

Learning long-term temporal dependencies with recurrent neural networks can be a difficult problem. It has recently been shown that a class of recurrent neural networks called NARX networks perform much better than conventional recurrent neural networks for learning certain simple long-term dependency problems. The intuitive explanation for this behavior is that the output memories of a NARX network can be manifested as jump-ahead connections in the time-unfolded network. These jump-ahead connections can propagate gradient information more efficiently, thus reducing the sensitivity of the network to long-term dependencies. This work gives empirical justification to our hypothesis that similar improvements in learning long-term dependencies can be achieved with other classes of recurrent neural network axchitectures simply by increasing the order of the embedded memory. In particular we explore the impact of learning simple long-term dependency problems on three classes of recurrent neural network architectures: globally recurrent networks, locally recurrent networks, and NARX (output feedback) networks. Comparing the performance of these architectures with different orders of embedded memory on two simple long-term dependencies problems shows that all of these classes of network architectures demonstrate significant improvement on learning long-term dependencies when the orders of embedded memory are increased. These results can be important to a user comfortable with a specific recurrent neural network architecture because simply increasing the embedding memory order of that architecture will make it more robust to the problem of long-term dependency learning. q 1998 Elsevier Science Ltd. All rights reserved.