The Power of Linear Recurrent Neural Networks

Recurrent neural networks are a powerful means to cope with time series. We show how linear, i.e., linearly activated recurrent neural networks (LRNNs) can approximate any time-dependent function f(t) given by a number of function values. The approximation can effectively be learned by simply solving a linear equation system; no backpropagation or similar methods are needed. Furthermore, the size of an LRNN can be reduced significantly in one step, after inspecting the eigenvalues of the network transition matrix, by taking only the most relevant components. Therefore, in contrast to others, we do not only learn network weights but also the network architecture. LRNNs have interesting properties: They end up in ellipse trajectories in the long run and allow the prediction of further values and compact representations of functions. We demonstrate this by several experiments, among them multiple superimposed oscillators (MSO), robotic soccer, and predicting stock prices. LRNNs outperform the previous state-of-the-art for the MSO task with a minimal number of units.